**Financial Feasibility Analysis of Natura Rab Business: Case Study Provisional chapterFinancial Feasibility Analysis of Natura Rab Business: Case Study**

Karmen Pažek, Matija Kaštelan, Martina Bavec, Črtomir Rozman and Jernej Prišenk Karmen Pažek, Matija Kaštelan, Martina Bavec, Črtomir Rozman and Jernej Prišenk

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65307

#### **Abstract**

[23] Rekecki R., Kuzmann E., Homonnay Z., Ranogajec J. Mossbauer and X‐ray study of the firing process for production of improved roofing tiles. Hyperfine Interact.

[24] Rekecki R., Ranogajec J. Design of ceramic microstructures based on waste materials.

[25] Lalić Ž., Aresenović M., Janaćković Đ., Vasić M., Radojević Z. Influence of increased temperature on clay fast drying process. Romanian Journal of Materials. 2009;39(3):

Processing and Application of Ceramics. 2008;2(2):89–95.

2013;217(35):27–35.

86 Operations Research - the Art of Making Good Decisions

175–179.

In 2015 Natura Rab decided to provide three very important investments that will greatly change and facilitate its future business activities, especially the first project. The first and largest financial investment is the construction of the new organic shop with products at the central farm called Natura Rab. The second investment project is the new 2500 m2 olive plantation. The third investment in the analyzed family company is related to the beekeeping sector, and it involves several activities like buying new beekeeping equipment and new work vehicle. Before implementing the three invest‐ ment projects, some financial parameters for the further assessment of investments were used, such as the net present value (NPV) and the internal rate of return (IRR). The investment value of the new shop is 38315.88 €, and the annual cash flow is 13,288 €. The net present value at the discount rate of 5.5% in the fourth year is 8260.55 €. The internal rate of return is 14.51%. The investment value for the second project, the new olive plantation, is 6620 €, and the annual cash flow is 2664.02 €. The net present value at the discount rate of 5.5% in the third year is 567.35 €. The internal rate of return is 10.04%. The investment value of the beekeeping sector for this year is 18428.50 €, and the annual cash flow is 41537.20 €. The net present value at the discount rate of 5.5% after the first year is 20943.25 €.

**Keywords:** Business project, Financial feasibility, Organic farming, Investments, CBA

#### **1. Introduction**

The aim of a successful agriculture business in the twenty‐first century is to achieve high profit in the shortest time possible, regardless of the type of agriculture production. This kind of

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

business activity requires constant care and concentration but also the monitoring of compe‐ tition. The success or failure of agricultural production is directly connected with the compe‐ tence of a farmer, or, in other words, the one with a higher profit in agricultural production has managed to optimize investment costs in agricultural production [1].

In the field of agricultural economics, there are two main types of costs. The permanent (fixed) costs that are substantially independent of the production volume and variable costs that are significantly altered in changes in production output. It is the basic classification of costs. However, the dilemma lies in something else. Functionality of brought investment will be revealed with more precise data than just fixed and variable costs, which have direct or indirect impact on the investment [1]. So in financial analysis, there is a wide variety of different costs. In [2] author explains six most important management views in agricultural projects (cited in [3]):

—*Technical aspects* (analysis of the availability of production means, determining the quantity of inputs and associated production levels, identification of the existing relations between different business entities of agricultural production, etc.).

—*Institutional-organizational aspects* (the study of the institutional environment, within which the performance of a given investment project is predicted, especially in light of the evaluation of its organizational tidiness).

—*Commercial aspects* (dynamic evaluation of different production options while checking the abilities in marketing of agricultural products).

—*Financial aspects* (financial evaluation of the meaningfulness of investment in agriculture by identifying the resulting income or loss).

—*Economic aspects* (evaluation of the real contribution of specific agricultural project to positive growth of the entire economy).

—*Socio*‐*social aspects* (specific socioeconomic analysis of the effects that can go in national economic system by individual investment project in agriculture).

The organic farm that was analyzed wanted to invest in three different projects in 2015 in order to improve sales and production conditions on the farm. All this progress goes for increasing productivity of the family company. Our own considerations and head calculations for projects were not enough and not correct. Economic parameters were used for the assessment of investments. A dynamic method of investment evaluation (CBA analysis) was applied to all three projects. The main goal was to develop a model for the assessment of the investment. It was examined by net present value (NPV) and internal rate of return (IRR). Planned annual cash flow and calculations for products were also developed with all additional costs in order to rate the investment more precisely, which gave us a realistic picture of the exact return of each investment. Economically efficient agricultural media system is the fundamental goal of the guidelines of every agricultural policy. Assessment of investment projects in agriculture is a multifaceted process [3]. The evaluation of specific agricultural projects is planned like evaluation of certain investments and has to be based on a variety of input costs and bring some types of benefits. In agricultural economics, in this case we are talking about the Cost‐ benefit analysis (CBA). That is a comparative analysis of the total cost and total revenue of the agricultural project.

#### **2. Materials and methods**

business activity requires constant care and concentration but also the monitoring of compe‐ tition. The success or failure of agricultural production is directly connected with the compe‐ tence of a farmer, or, in other words, the one with a higher profit in agricultural production

In the field of agricultural economics, there are two main types of costs. The permanent (fixed) costs that are substantially independent of the production volume and variable costs that are significantly altered in changes in production output. It is the basic classification of costs. However, the dilemma lies in something else. Functionality of brought investment will be revealed with more precise data than just fixed and variable costs, which have direct or indirect impact on the investment [1]. So in financial analysis, there is a wide variety of different costs. In [2] author explains six most important management views in agricultural projects (cited in

—*Technical aspects* (analysis of the availability of production means, determining the quantity of inputs and associated production levels, identification of the existing relations between

—*Institutional-organizational aspects* (the study of the institutional environment, within which the performance of a given investment project is predicted, especially in light of the evaluation

—*Commercial aspects* (dynamic evaluation of different production options while checking the

—*Financial aspects* (financial evaluation of the meaningfulness of investment in agriculture by

—*Economic aspects* (evaluation of the real contribution of specific agricultural project to positive

—*Socio*‐*social aspects* (specific socioeconomic analysis of the effects that can go in national

The organic farm that was analyzed wanted to invest in three different projects in 2015 in order to improve sales and production conditions on the farm. All this progress goes for increasing productivity of the family company. Our own considerations and head calculations for projects were not enough and not correct. Economic parameters were used for the assessment of investments. A dynamic method of investment evaluation (CBA analysis) was applied to all three projects. The main goal was to develop a model for the assessment of the investment. It was examined by net present value (NPV) and internal rate of return (IRR). Planned annual cash flow and calculations for products were also developed with all additional costs in order to rate the investment more precisely, which gave us a realistic picture of the exact return of each investment. Economically efficient agricultural media system is the fundamental goal of the guidelines of every agricultural policy. Assessment of investment projects in agriculture is a multifaceted process [3]. The evaluation of specific agricultural projects is planned like evaluation of certain investments and has to be based on a variety of input costs and bring some types of benefits. In agricultural economics, in this case we are talking about the Cost‐

has managed to optimize investment costs in agricultural production [1].

different business entities of agricultural production, etc.).

economic system by individual investment project in agriculture).

abilities in marketing of agricultural products).

identifying the resulting income or loss).

88 Operations Research - the Art of Making Good Decisions

of its organizational tidiness).

growth of the entire economy).

[3]):

On 4000 m2 of land in the Barbat village at the south end of the island of Rab, a unique organic farm Natura Rab is developed. It is a family‐run business comprising of both production and sale, growing typical medicinal and cultivated herbs, beekeeping, and sale of our own products right at our front door.

**•** In the research we will present three different projects we invested in this year. Project 1 is the new organic shop, project 2 is the new olive plantation, and project 3 is investment in beekeeping facilities. Further in text each project is presented separately, the reasons for their implementation are given as well as our ultimate goals. For each project identical tables in Microsoft Word and Microsoft Excel were made. All the necessary parameters are provided in order to have precise results and correct economic assessment of investment. Fixed and variable costs were separated in the CBA analysis. Costs of annual production of certain final products are also considered which serve as the production output. For each project there is a product table with explanations. It was necessary to be as realistic as possible to avoid imaginary situations, because then we lie to ourselves and the return of investment is not authentic. Technical specifications are made in detail especially in the first two projects that were technically demanding and the work dynamics was longer. Using the program developed in Microsoft Excel, it is easier to calculate the net present value and internal rate of return for each project using input data like amount of investment, annual cash flow, and discount rate with fixed value of 5.5% in all three projects.

#### **3. Methodology of total cost calculation**

#### **3.1. Costs**

Before we start describing complex economic parameters in this context, it is necessary to explain the theory of production costs. Costs are an integral part of each production process, and they appear as a result of different activities in the production chain [1]. We distinguish between fixed and variable costs, due to the fact that there are some costs that change during longer time period.

Fixed costs, which are independent of the production volume, reflect the use of fixed produc‐ tion assets. For example, fixed costs are land rent, interest related to the acquisition of agri‐ cultural land, various mortgage, and insurance premiums. However, various types of amortizations in agriculture production (buildings, machinery) are defined also like fixed costs which relate to noncash payments in agriculture [1].

Variable costs are dependent on the volume of production. This group of costs represents a wide range of various agricultural inputs and costs related to their use (pesticides, fertilizers, seeds, animal feed) [1].

The total cost of production as the sum of all production costs

$$\text{TC} = \text{FC} + \text{VC} \tag{1}$$

FC, fixed costs (€); VC, variable costs (€); and TC, total costs (€).

#### **3.2. Investment costs**

Investment costs are present in all three business projects. Consequently, they indicate the amount of each investment. In particular, they are separated in the first two projects, like investment construction costs and investment material costs.

#### **3.3. CBA analysis in agricultural projects**

The CBA analysis is the main methodological tool in the process of evaluation of specific agricultural projects or investments made in farming industry or some other agriculture types [3]. Comparative analysis of total revenues and total costs provides an answer to the question of selection of some investment projects in agriculture. All potential costs and revenues must be identified. As we look at all costs and revenues, we have to decide which investment projects will be selected and which will be denied [3]. The most important are the net present value (NPV) and the internal rate of return (IRR).

#### **3.4. Annual cash flow (FR)**

The annual cash flow is calculated as the difference between the total revenues and total costs:

$$\text{FR} = \text{TR} - \text{TC} \tag{2}$$

FR, annual cash flow (€); TR, total revenues (€); and TC, total costs (€).

#### **3.5. Method of net present value (NPV)**

In financial terms, the net present value (NPV) is defined as the sum of the present values (PVs) of incoming and outgoing cash flows over a period of time. Incoming and outgoing cash flows can also be described as benefit and cost cash flows, respectively [4]. It is a basic norm for financial decision‐making. NPV encompasses the concept of the time value of money taking into account the present and future value of money such as in times of inflation [5]. Net present value (NPV) is determined by calculating the costs for each period of an investment, and after the cash flow is calculated, the present value (PV) of each period is achieved by discounting its future value at a periodic rate of return [6]. NPV is the sum of all the discounted future cash flows. NPV is a useful tool to determine whether a project or investment will result in a net profit or a loss. A positive NPV results in profit, while a negative NPV results in loss (**Table 1**) [4]:


**Table 1.** NPV use in decision‐making process.

Variable costs are dependent on the volume of production. This group of costs represents a wide range of various agricultural inputs and costs related to their use (pesticides, fertilizers,

Investment costs are present in all three business projects. Consequently, they indicate the amount of each investment. In particular, they are separated in the first two projects, like

The CBA analysis is the main methodological tool in the process of evaluation of specific agricultural projects or investments made in farming industry or some other agriculture types [3]. Comparative analysis of total revenues and total costs provides an answer to the question of selection of some investment projects in agriculture. All potential costs and revenues must be identified. As we look at all costs and revenues, we have to decide which investment projects will be selected and which will be denied [3]. The most important are the net present value

The annual cash flow is calculated as the difference between the total revenues and total costs:

In financial terms, the net present value (NPV) is defined as the sum of the present values (PVs) of incoming and outgoing cash flows over a period of time. Incoming and outgoing cash flows can also be described as benefit and cost cash flows, respectively [4]. It is a basic norm for financial decision‐making. NPV encompasses the concept of the time value of money taking into account the present and future value of money such as in times of inflation [5]. Net present value (NPV) is determined by calculating the costs for each period of an investment, and after the cash flow is calculated, the present value (PV) of each period is achieved by discounting its future value at a periodic rate of return [6]. NPV is the sum of all the discounted future cash

FR, annual cash flow (€); TR, total revenues (€); and TC, total costs (€).

TC FC VC = + (1)

FR TR TC = - (2)

The total cost of production as the sum of all production costs

FC, fixed costs (€); VC, variable costs (€); and TC, total costs (€).

investment construction costs and investment material costs.

**3.3. CBA analysis in agricultural projects**

(NPV) and the internal rate of return (IRR).

**3.5. Method of net present value (NPV)**

**3.4. Annual cash flow (FR)**

seeds, animal feed) [1].

90 Operations Research - the Art of Making Good Decisions

**3.2. Investment costs**

$$\text{NPV} = -I + \sum\_{i=1}^{n} \frac{\text{TR} - \text{TC}}{\left(1 + r\right)^{i}} \tag{3}$$

NPV, net present value (€); *I*, amount of each agricultural investment (€); TR, total revenue (€); TC, total costs (€); *r*, average annual discount rate (%); and *t*, time period (number of years).

#### **3.6. Method of internal rate of return (IRR)**

Internal rate of return is the second important decision‐making tool. Associated concept of net present value is internal rate of return, which is not served by a nominal value but the percent (interest) on the basis, and it still financially justifies the implementation of a certain investment in agriculture [3]. Simply put, the internal rate of return is a rate where NPV of the project is equal to zero that can be seen in the formula below:

$$\text{IRRR} = -I + \sum\_{i=1}^{n} \frac{\text{TR} - \text{TC}}{\left(1 + r\right)^{i}} = 0 \tag{4}$$

IRR, internal rate of return (%); *I*, amount of each agricultural investment (€); TR, total revenue (€); TC, total costs (€); *r*, average annual discount rate (%); and *t*, time period (number of years).

#### **4. Results and discussion**

#### **4.1. Project 1: investment in the new organic shop**

In 2015, we decided to expand our existing organic shop. We want to have a unique space which is larger and more comfortable than the previous one, to obtain space for tasting and sale of our organic products. The new organic shop becomes our only direct sales channel on the island, because we closed the second shop in the old town of Rab. Through the years we became a must‐see station of our island of Rab. With good organization, development, and quality, we became a well‐established company, and our old customers always keep coming back to buy and enjoy our products, and there always new ones as well. We create long‐term relationships with customers based on high development of trust, as one of our main business goals.

In our new organic shop, we want to show all the riches of our hundred‐year‐old family tradition by representing old agricultural tools and beekeeping equipment of our ancestors; things that were hidden for years in cellars and were full of dust, just show them to people, and show how people used to live before. So it will be a diverse space with more facilities all our visitors can enjoy. The shop was finished in record time of just two months, including preliminary work in obtaining the necessary documentation to the last screw at the store. The shop is open all year, so we are always available to our customers.

The investment costs for the new organic shop are:

[T1] Investment construction costs for bio shop = 22,458 €

[T2] Costs of material during the construction of bio shop = 5544.88 €

[T3] Costs of interior design including installation = 10,313 €

starting from project documentation and geodetic study to the creation of all the necessary work finalization of the new shop.

Total investment costs (TIC)

$$\begin{aligned} \text{TIC} &= \text{Tl} + \text{T2} + \text{T3} \\ \sum \text{(TIC)} &= \text{38315.88 } \text{€} \end{aligned} \tag{5}$$

#### *4.1.1. Production plan for sales in the new organic shop*

Production plan is as realistic as possible with the planned annual quantities in order to treat them as further planned business activities and investment for our new shop, the place where we are going to sell our organic products. This kind of business philosophy is more known as direct sales. Our organic farm lives by a system of family‐run business, and according to this statement, we have human and natural limits of the production on the island. Nature is generous but it has limitations. It is an unwritten rule that depending on how much we give the nature, this much she gives back to us. Organic production is divided into six groups: honey, immunity products, olive oil, natural cosmetics, noble drinks, and island delicacies. Our farm, with its space and technology, integrates the process of gathering, enriching, and packing honey and other agricultural produces. Our production standards are realized through the hazard analysis and critical control point (HACCP) program, and the production object is the export object of the final product in the European Union countries.

#### *4.1.2. Honey*

sale of our organic products. The new organic shop becomes our only direct sales channel on the island, because we closed the second shop in the old town of Rab. Through the years we became a must‐see station of our island of Rab. With good organization, development, and quality, we became a well‐established company, and our old customers always keep coming back to buy and enjoy our products, and there always new ones as well. We create long‐term relationships with customers based on high development of trust, as one of our main business

In our new organic shop, we want to show all the riches of our hundred‐year‐old family tradition by representing old agricultural tools and beekeeping equipment of our ancestors; things that were hidden for years in cellars and were full of dust, just show them to people, and show how people used to live before. So it will be a diverse space with more facilities all our visitors can enjoy. The shop was finished in record time of just two months, including preliminary work in obtaining the necessary documentation to the last screw at the store. The

starting from project documentation and geodetic study to the creation of all the necessary

Production plan is as realistic as possible with the planned annual quantities in order to treat them as further planned business activities and investment for our new shop, the place where we are going to sell our organic products. This kind of business philosophy is more known as direct sales. Our organic farm lives by a system of family‐run business, and according to this statement, we have human and natural limits of the production on the island. Nature is generous but it has limitations. It is an unwritten rule that depending on how much we give the nature, this much she gives back to us. Organic production is divided into six groups: honey, immunity products, olive oil, natural cosmetics, noble drinks, and island delicacies. Our farm, with its space and technology, integrates the process of gathering, enriching, and packing honey and other agricultural produces. Our production standards are realized through the hazard analysis and critical control point (HACCP) program, and the production

å <sup>=</sup> (5)

TIC T1 T2 T3 TIC 38315.88 € = ++

shop is open all year, so we are always available to our customers.

[T2] Costs of material during the construction of bio shop = 5544.88 €

( )

object is the export object of the final product in the European Union countries.

The investment costs for the new organic shop are:

92 Operations Research - the Art of Making Good Decisions

*4.1.1. Production plan for sales in the new organic shop*

work finalization of the new shop.

Total investment costs (TIC)

[T1] Investment construction costs for bio shop = 22,458 €

[T3] Costs of interior design including installation = 10,313 €

goals.

Beekeeping in our farm is based on mobile ecological beekeeping on the south part of the island of Rab, the Barbat village and the Gorski kotar region. From the beginning of our activities, we have an average of one hundred beehives. As part of our business philosophy, we produce rare highly aromatic honeys that with their direct bactericidal and medicinal effect take up the lead position in everyday alimentation. After the bee pastures of sage (*Salvia officinalis* L.) and other medicinal honey plants on the island of Rab, we transport our bees (late June) into the mountains, in the region of Gorski kotar where we have bee pasture in mountain meadows and spruce and fir, the forest honey. Taking the two different locations of our apiaries into account, we estimated the production quantities in 2015 to be sold in our organic shop on the island of Rab. The plan for sage honey is 280 kg. The plan for multifloral honey "Bilje Kvarnera" is 480 kg. The plan for the forest honey "Šuma Kvarnera" is about 600 kg. The quantities will be divided and distributed in jars of various sizes, ranging from 212 to 580 ml. Production costs with quantities for honeys are:

Honey Salvia (150 g) = 666 € Honey Salvia (260 g) = 576 € Honey Bilje Kvarnera (400 g) = 2800 € Honey Bilje Kvarnera (780 g) = 1300 € Honey Šuma Kvarnera (400 g) = 2800 € Honey Šuma Kvarnera (780 g) = 1300 € Total costs (Σ) = 9442 €

#### *4.1.3. Immune system products*

This group represents four products. It is a synthesis of multiple products from the beehives. When they are blended together, they achieve much better effect on the human body. There is a strong emphasis on sage as a natural antiseptic as well as other products such as propolis, which has a great antibacterial effect. These are the planned production quantities for 2015 and sale through our organic shop: "Salvia Immunity" 260 g, 700 pieces; "Salvia Protect" 30 ml, 800 pieces; "Abies Immunity" 260 g, 400 pieces; and "Propolis" 30 ml, 200 pieces. Production costs with quantities for this group of products are:

Abies Immunity (260 g) = 2000 € Salvia Immunity (260 g) = 4900 € Salvia Protect (30 ml) = 800 € Propolis (30 ml) = 800 € Total costs (Σ) = 8500 €

#### *4.1.4. Olive oil*

Olive oil has always been known for its medicinal characteristics. Regular and long‐term usage of olive oil in our diets reduces the risk of many diseases [7]. For better understanding, here is the classification with description of olive oil.

The top quality olive oil is labeled like extra‐virgin comes from virgin oil production only. The spiciness and bitterness sometimes seem too aggressive, but it is only a proof that the oil is rich in all those ingredients that have a beneficial effect on health and which are a waste to lose through cooking or frying [8].

Virgin olive oil comes from virgin oil production only but is of slightly lower quality with free acidity of up to 1.5% and is judged to have a good taste but may include some sensory defects [9]. Olive pomace oil is refined pomace olive oil often blended with some virgin oil. It is fit for consumption, but may not be described simply as olive oil. It has a neutral flavor and also a high smoke point [9].

Natura Rab has only premium quality extra‐virgin olive oil, usually with oleic acids below 0.5%. In our plantations you can find different olive varieties, like "Oblica," "Levantinka," "Leccino," and "Pendolino." Olives are harvested on a daily basis by a handpicking system and immediately transported into the mill for processing into the finest olive oil. Almost all annual quantity of olive oil is sold through direct sale on our farm. In 2015, we plan to have 250 l of extra‐virgin olive oil. This quantity we want to divide in 150 0.75 l bottles and 50 2 l bottles of. Production costs with quantities for olive oil are:

Olive oil (2 l) = 850 € Olive oil (0.75 l) = 1400 € Total costs (Σ) = 2250 €

#### *4.1.5. Natural cosmetics*

The richness of the Rab archipelago in over 800 herb species is a source of the island's aroma‐ therapy. Some of them we use in production of our natural cosmetic line. We produce creams, oils, and soaps. The result of the continuous development in this sector is reflected by the entry in the register of the open cosmetic manufacturers. It is our duty but also a further confidence for end consumers of our products. For production, we use natural resources that grow on our organic farm, such as organic beeswax and extra‐virgin olive oil. There are three main plants we use for the production of our cosmetic products. These are St. John's wort, immortelle, and lavender. These are the planned production quantities for 2015 for further sale in our organic shop: "St. John's wort" cream 50 ml, 300 pieces; "St. John's wort" oil 100 ml, 300 pieces; "Imortelle" cream 50 ml, 500 pieces; "Imortelle" oil 100 ml, 400 pieces; "Lavender" cream 50 ml, 200 pieces; and "Lavander" oil 100 ml, 200 pieces. In 2015, we produced 600 pieces of natural soaps, random kinds. Production costs with quantities for natural cosmetics are:

Imm. cream (50 ml) = 3000 €

St. John's wort cream (50 ml) = 1500 €

Lav. cream (50 ml) = 900 € Imm. oil (100 ml) = 2200 € St. John's wort oil (100 ml) = 1500 € Lav. oil (100 ml) = 800 € Gentle soaps (100 g) = 1200 € Total costs (Σ) = 11,100 € *4.1.6. Brandies and liqueurs*

*4.1.4. Olive oil*

the classification with description of olive oil.

94 Operations Research - the Art of Making Good Decisions

bottles of. Production costs with quantities for olive oil are:

through cooking or frying [8].

high smoke point [9].

Olive oil (2 l) = 850 €

Olive oil (0.75 l) = 1400 € Total costs (Σ) = 2250 €

*4.1.5. Natural cosmetics*

Imm. cream (50 ml) = 3000 €

St. John's wort cream (50 ml) = 1500 €

Olive oil has always been known for its medicinal characteristics. Regular and long‐term usage of olive oil in our diets reduces the risk of many diseases [7]. For better understanding, here is

The top quality olive oil is labeled like extra‐virgin comes from virgin oil production only. The spiciness and bitterness sometimes seem too aggressive, but it is only a proof that the oil is rich in all those ingredients that have a beneficial effect on health and which are a waste to lose

Virgin olive oil comes from virgin oil production only but is of slightly lower quality with free acidity of up to 1.5% and is judged to have a good taste but may include some sensory defects [9]. Olive pomace oil is refined pomace olive oil often blended with some virgin oil. It is fit for consumption, but may not be described simply as olive oil. It has a neutral flavor and also a

Natura Rab has only premium quality extra‐virgin olive oil, usually with oleic acids below 0.5%. In our plantations you can find different olive varieties, like "Oblica," "Levantinka," "Leccino," and "Pendolino." Olives are harvested on a daily basis by a handpicking system and immediately transported into the mill for processing into the finest olive oil. Almost all annual quantity of olive oil is sold through direct sale on our farm. In 2015, we plan to have 250 l of extra‐virgin olive oil. This quantity we want to divide in 150 0.75 l bottles and 50 2 l

The richness of the Rab archipelago in over 800 herb species is a source of the island's aroma‐ therapy. Some of them we use in production of our natural cosmetic line. We produce creams, oils, and soaps. The result of the continuous development in this sector is reflected by the entry in the register of the open cosmetic manufacturers. It is our duty but also a further confidence for end consumers of our products. For production, we use natural resources that grow on our organic farm, such as organic beeswax and extra‐virgin olive oil. There are three main plants we use for the production of our cosmetic products. These are St. John's wort, immortelle, and lavender. These are the planned production quantities for 2015 for further sale in our organic shop: "St. John's wort" cream 50 ml, 300 pieces; "St. John's wort" oil 100 ml, 300 pieces; "Imortelle" cream 50 ml, 500 pieces; "Imortelle" oil 100 ml, 400 pieces; "Lavender" cream 50 ml, 200 pieces; and "Lavander" oil 100 ml, 200 pieces. In 2015, we produced 600 pieces of natural

soaps, random kinds. Production costs with quantities for natural cosmetics are:

According to the rich family tradition, we produce three types of our local brandies made with grape brandy as basis. The first one is the popular medica, homemade herb-flavored brandy. The second one is the fig liqueur, pure nature and phenomenal taste for someone who likes sweeter drinks. It is macerated organic dried fig in grape brandy. The third one, honestly, requires the least work in the production, but it does not mean that it is less valuable. It's called "Ruta" (*Ruta graveolens* L.); it got its name from the medicinal herb that is the main ingredient of this brandy. For all three brandies, we have one rule. It is a great experience to drink it out of a clay bićerin (small brandy glass) as an aperitif but also as a digestive. The special taste remains if it is drunk well chilled. These are the planned production quantities for 2015: "Travarica i eko med" 0.5 l, 400 pieces; "Smokovača" 0.5 l, 500 pieces; and "Ruta" 0.5 l, 250 pieces. Production costs with quantities are:

Medica (500 ml) = 2400 € Smokovača (500 ml) = 3500 € Ruta (500 ml) = 1000 € Total costs (Σ) = 6900 €

#### *4.1.7. Island delicacies*

Island delicacies represent products like fig jam, lemon jam, organic honey vinegar, and organic olives in brine. These are the products that are created by a long-based family tradition of preparing natural food. Some of them are made only on demand (special orders or business gifts), while most of them are constantly available in our shop. These are the planned production quantities for 2015: organic honey vinegar 0.5 l, 400 pieces; olives 370 g, 200 pieces; fig jam 630 g, 300 pieces; lemon jam 630 g, 200 pieces; and honey biscuits 200 g, 300 pieces. Production costs with quantities are:

Honey vinegar (500 ml) = 1000 € Olives in brine (380 g) = 500 € Fig jam (630 g) = 900 €

Lemon jam (630 g) = 400 €

Honey biscuits (220 g) = 600 €

Total costs (Σ) = 3400 €

*4.1.8. Variable costs and fixed costs on an annual basis in organic shop*

Variable costs:

—Tasting the products on an annual basis = 800 €

—Cardboard packaging (bags and other supplies) = 1200 €

—Maintenance and cleaning = 500 €

—Energy (electricity, water) = 420 €

Total = 2720 €

Fixed costs:

—Promotional material = 300 €

—Costs of salesperson in the shop = 4500 €

—Insurance of shop (fire, earthquake, theft) = 100 €

Total = 4900€

*4.1.9. Planned income cash in the new organic shop on an annual basis*

Total investment costs = 38315.88 € Total production and sale costs = 49,212 €

TR = 62,500 €

FR = TR – TC

FR = 13,288 €

#### **4.2. Project 2: investment in olive plantation**

If we look from the perspective of agriculture on the Croatian islands, specifically on the island of Rab, there is a problem with the available land for cultivation. There are many reasons for that: smaller areas, difficult access to fields (sometimes just on foot), unsorted fields with undivided ownership, etc. In our case, it requires constant investments of new plantations with typical plants for our area. Maybe it is weird but it is certainly true; the ratio between islands and mainland is as follows: a thousand square meters land on the is‐ land is like one hectare of land on the mainland. Generally, the Mediterranean plant species such as olives, figs, lemons, and vine are grown. Agricultural land in which we would like to invest is located on the island a few kilometers away from our organic farm, and the sur‐ face is 2500 m2 . The land is a family legacy, and on it are already five adult olive trees. There is a place for more trees, and we decided to plant new 18 olive trees of our typical varieties. For better understanding, planting of olive trees is the easy part of the project. Before that, the land has to be prepared and protected against external factors, so we decided to make a 40‐meter stone wall and 150‐meter long fence. We also have to ensure an agricultural water connection for the irrigation system. Later, when the whole project is completed, crops should be maintained. According to our estimates, this location should give in their full fer‐ tility about 1200 kg of olives per year in ideal conditions. With the implementation of this project (calculated total costs of investment is 6620 €), we increase the annual production of olive oil, but also the work volume increases. Under "construction costs of the new planta‐ tion, surface 2500 m2 ," the types of costs stated below have been taken into account:

—Excavation and cleaning channel

Lemon jam (630 g) = 400 €

Total costs (Σ) = 3400 €

Variable costs:

Total = 2720 € Fixed costs:

Total = 4900€

TR = 62,500 € FR = TR – TC FR = 13,288 €

Honey biscuits (220 g) = 600 €

96 Operations Research - the Art of Making Good Decisions

*4.1.8. Variable costs and fixed costs on an annual basis in organic shop*

—Tasting the products on an annual basis = 800 €

—Maintenance and cleaning = 500 € —Energy (electricity, water) = 420 €

—Promotional material = 300 €

Total investment costs = 38315.88 €

Total production and sale costs = 49,212 €

**4.2. Project 2: investment in olive plantation**

—Costs of salesperson in the shop = 4500 €

—Insurance of shop (fire, earthquake, theft) = 100 €

*4.1.9. Planned income cash in the new organic shop on an annual basis*

If we look from the perspective of agriculture on the Croatian islands, specifically on the island of Rab, there is a problem with the available land for cultivation. There are many reasons for that: smaller areas, difficult access to fields (sometimes just on foot), unsorted fields with undivided ownership, etc. In our case, it requires constant investments of new plantations with typical plants for our area. Maybe it is weird but it is certainly true; the ratio between islands and mainland is as follows: a thousand square meters land on the is‐ land is like one hectare of land on the mainland. Generally, the Mediterranean plant species such as olives, figs, lemons, and vine are grown. Agricultural land in which we would like to invest is located on the island a few kilometers away from our organic farm, and the sur‐

—Cardboard packaging (bags and other supplies) = 1200 €


The cost of the new investment plan we want to restore with picking up the new olives and transforming them into our product, the extra‐virgin olive oil (production and total revenue based on 18 olive trees). From experience and knowledge in agriculture, in the first 4 years, we cannot count on the return of the investment because there is no cash flow from selling the products. Trees are too young, and the first crops will be available in the fifth year of growth.

Calculation scheme:

Total costs (variable + fixed costs) = 558 €

*N* = 10 years TC = 58.8 €/year TC = 976.65 + 58.8 € TC(y) = 1035.45 € CP = total costs/yield CP = 1035.45 €/1260 kg CP = 0.82 €/kg olives 100 kg olives = 16 l olive oil 6.25 kg = 1 l olive oil CP = 0.82 € × 6.25 kg CP = 5.14 €/L

Price of 5.14 € is the breakeven for 1 l of olive oil based on the price of 0.82 €/1 kg olives. This input data is used in the next calculation for olive oil production (see **Table 2**).


**Table 2.** Production and total revenue based on 18 olive trees (reproduction 16%).

In intensive plantations, the life of olive trees spans to about 50 years and can be divided into several periods. The nonproductive period is until the end of the fourth year. From sixth to seventh year is the period of initial cropping. From 8 to 30 years (the most important period) is a period of full fertility and economic standpoint. Variable costs for olive oil production from the eighth year onward including costs such as extra‐virgin olive oil, chemical and sensory analysis, charge costs of oil bottle "Dorica" 750 ml, labels, PVC caps, plastic screw cap, and dispenser 31 × 24 mm is 1355.98 €.

Planned annual cash flow from sales of olive oil 0.75 l is calculated as:

CP = TC/Y CP = 1355.98 €/201.6 l CP = 6.73 €/L FR = TR – TC FR = 4020 € – 1355.98 € FR = 2664.02 €

#### **4.3. Project 3: beekeeping investment**

In 2015 we decided to invest in the field of beekeeping. Optimization of transport resources is solved with purchase of a new work vehicle, which is also the largest investment this year in beekeeping (total investment costs = 18428.50 €). Of course, a multipurpose vehicle has more functions, so it will be used for other agricultural works as well. Also, we made a decision to widen the existing apiary. Therefore, we bought new wooden beehives which will be applied when necessary. There is also other necessary professional equipment and tools which have to be changed, some of it at short‐time intervals, some of them not so often. The maintenance in beekeeping has to be mentioned, because it represents a large item in annual costs, like the maintenance of trailer, truck, and others. It should be noted that beekeeping demands the greatest amount of work and time on our farm, and consequently, the whole family is involved in beekeeping activities. In recent years, we have invested significantly in the field of beekeep‐ ing, but nature is very unpredictable. It is normal to always hope for the best, but the human factor is not the most relevant here. So, we cannot be sure about the quantities of honey products on an annual basis. This year's investments are analyzed through the planned revenue from the sales of bee products through our three sales channel, such as export through distributers, Web shop, and fairs which presents total income cash = 66,124 €, considering all cost parameters (variable outdoor production costs = 8562 € and variable costs of indoor production and sale = 16024.80 €). Particularities of our micro‐region are always represented through the sales of our organic products, and we always emphasize the relationship between possibilities and realities in nature.

Estimated annual cash flow through three sales channels is calculated as:

Total revenue = 66,124 € Total costs = 24586.80 € FR = TR − TC FR = 66,124 € – 24586.80 € FR = 41537.20 €

6.25 kg = 1 l olive oil CP = 0.82 € × 6.25 kg

98 Operations Research - the Art of Making Good Decisions

Price of 5.14 € is the breakeven for 1 l of olive oil based on the price of 0.82 €/1 kg olives. This

1260 20.6 4032

In intensive plantations, the life of olive trees spans to about 50 years and can be divided into several periods. The nonproductive period is until the end of the fourth year. From sixth to seventh year is the period of initial cropping. From 8 to 30 years (the most important period) is a period of full fertility and economic standpoint. Variable costs for olive oil production from the eighth year onward including costs such as extra‐virgin olive oil, chemical and sensory analysis, charge costs of oil bottle "Dorica" 750 ml, labels, PVC caps, plastic screw cap, and

In 2015 we decided to invest in the field of beekeeping. Optimization of transport resources is solved with purchase of a new work vehicle, which is also the largest investment this year in beekeeping (total investment costs = 18428.50 €). Of course, a multipurpose vehicle has more functions, so it will be used for other agricultural works as well. Also, we made a decision to

**Cash flow through years €20/l**

input data is used in the next calculation for olive oil production (see **Table 2**).

**6.25 kg/1 l**

**Years Yield (kg) Olive oil production**

1–4 0 0 0 180 28.8 576 360 57.6 1152 720 115.2 2304

**Table 2.** Production and total revenue based on 18 olive trees (reproduction 16%).

Planned annual cash flow from sales of olive oil 0.75 l is calculated as:

CP = 5.14 €/L

8th and further years (a 70‐kg tree)

CP = TC/Y

CP = 6.73 €/L FR = TR – TC

FR = 2664.02 €

CP = 1355.98 €/201.6 l

FR = 4020 € – 1355.98 €

dispenser 31 × 24 mm is 1355.98 €.

**4.3. Project 3: beekeeping investment**

#### **4.4. Financial (CBA) analysis of individual investment projects**

#### *4.4.1. New organic shop*


#### *4.4.2. New olive plantation*


—Repayment period of investment is in year 3, where Investment flow is 0.36 € (**Table 4**).


**Table 3.** NPV assessment for project 1.


**Table 4.** NPV assessment for project 2.

#### *4.4.3. Beekeeping investment*



**Table 5.** NPV assessment for project 3.

#### **5. Conclusion**

—Annual income cash is 4020 €.

100 Operations Research - the Art of Making Good Decisions

**Table 3.** NPV assessment for project 1.

**Table 4.** NPV assessment for project 2.

—Investment value for project 3 is 18428.50 €.

—Financial result for project 3 is 41537.20 €.

*4.4.3. Beekeeping investment*

—Financial result for this project is 2664.02 €.

—Net present value is 567.35 € at the discount rate of 5.5%.

 11604.23 −26711.65 10133.81 −16577.84 8849.72 −7728.13 7728.34 **0.21€** 6749.05 6749.26 5893.85 12643.11 5147.02 17790.13 4494.82 22284.95 3925.26 26210.21 3427.88 29638.09

**Year Discount rate 14.51% NPV-investment flow**

**Year Discount rate 10.04% NPV-investment flow**

—Total production and sale costs through three channels are 24586.80 €.

—Repayment period of investment is in year 1, where Investment flow is 0.53 € (**Table 5**).

—Planned annual base income cash for project 3 is 66,124 €.

—Net present value is 20943.25 € at the discount rate of 5.5%.

 2420.96 −4199.04 2200.07 −1998.97 1999.34 **0.36€** 1816.92 1817.28 1651.14 3468.42 1500.49 4968.91 1363.59 6332.50 1239.18 7571.68 1126.11 8697.79 1023.37 9721.16

—Repayment period of investment is in year 3, where Investment flow is 0.36 € (**Table 4**).

The aim of this research was to study the economic validity of the three projects, considering economic parameters for the return of the investment (the net present value and the internal rate of return) and my input information. A model was developed in Microsoft Excel for the net present value assessment, which serves as a support for decision‐making, should we go into the investment or not, or better said does the investment make sense, and when we expect the return in the terms of time.

Using the NPV and IRR methods showed, the return of the investment into new organic shop will be in 4 years. The return of the investment into new olive plantation will be in 3 years. The last investment into new beekeeping facilities will be by 5.5% discount rate in the first year (NPV = 20943.25 €).

With the implementation of these projects, we wanted to optimize our business resources, and in terms of productivity, we are much better than before. The projects have enabled easier performance in our obligations, but consequently, they increased the workload in both parts, first in the sales (project 1) and in terms of production (projects 2 and 3).

#### **Author details**

Karmen Pažek, Matija Kaštelan, Martina Bavec, Črtomir Rozman and Jernej Prišenk\*

\*Address all correspondence to: jernej.prisenk@um.si

Faculty of Agriculture and Life Sciences, University of Maribor, Hoče, Slovenia

#### **References**


#### **Influence of Phosphorus Precipitation on Wastewater Treatment Processes Influence of Phosphorus Precipitation on Wastewater Treatment Processes**

Ján Derco, Rastislav Kuffa, Barbora Urminská, Jozef Dudáš and Jana Kušnierová Ján Derco, Rastislav Kuffa, Barbora Urminská, Jozef Dudáš and Jana Kušnierová

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65492

#### **Abstract**

**References**

2015-09-28]

and Life Sciences; 1998. 176 p.

102 Operations Research - the Art of Making Good Decisions

Pearson, Canada; 2015. 64 p.

of Agriculture and Life Sciences; 2001. 225 p.

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wiki/Net\_present\_value [Accessed: 2016-07-26]

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[1] Turk, J. Agricultural economics: theory and aplication. Maribor: Faculty of Agriculture

[2] Gittinger, J.P. Economic analysis of Agricultural Projects [Internet]. 1985. Available from: http://www-wds.worldbank.org/external/default/WDSContentServer/WDSP/IB/ 2000/04/19/000178830\_98101903531847/Rendered/PDF/multi0page.pdf [Accessed:

[3] Turk, J. Theoretical and empirical analysis in agricultural economics. Maribor: Faculty

[4] Berk, J., De Marzo, P., Stangeland, D. Corporate Finance (3rd Canadian ed.). Toronto

[5] Law, A.M. Using net present value as a decision-making tool. Air Medical Journal .

[6] Wikipedia. Net present value [Internet]. 2016. Available from: https://en.wikipedia.org/

[7] Covas, M. Olive oil and the cardiovascular system. Pharmacological Research.

[8] Eko centar Natura Rab. Natura Rab [Internet]. 2016. Available from: http://

[9] International Olive Council. Designations and definitions of olive oils [Internet]. 2015. Available from: http://www.internationaloliveoil.org/estaticos/view/83-designationsPhosphorus stimulates aquatic plant growth and contributes to eutrophication process in rivers, lakes and the ocean. A large part of phosphorus is discharged into the receiving waters by wastewater. One of the solutions of this problem is represented by chemical precipitation. Simultaneous precipitation of phosphorus from wastewater with metal salts is commonly applied. Metal salts are dosed directly into aeration tank, and produced precipitates are wasted as a part of the secondary sludge. Thus, not only aerobic and anoxic processes of wastewater treatment plant are carried out in the presence of precipitant metals and precipitates but also the precipitates are, in many cases, accumulated in anaerobic sludge digesters. Operational research of phosphorus precipitation in lab‐scale encompasses the impact of Fe2+, Fe3+ and Al3+ salts on biological nitrification and denitrification processes, sedimentation and thickening characteristics of sludge as well as anaerobic sludge stabilisation processes. The measurements of specific oxygen uptake rate, nitrification and denitrification tests and monitoring of effluent values of quality standards were applied to evaluate the processes performance. Other objective of our research is to contribute to methodology for examination of thickening and dewatering characteristics of sludge with tested precipitation agents. Mathematically processed experimental results are used to compare sedimentation, precipitation and dewatering characteristics of activated sludge cultivated in the presence of selected precipitation agents. Better description of the experimental results was obtained with three parameters model of particles mass flow density curve. Comparison of minimum sedimentation tank size necessary for gravitational separation of individual sludge was used to examine sedimentation characteristics of activated sludge. Thickening characteristics of sludge were evaluated based upon thickening area needed to maintain the required sludge concentration in activated sludge model, which corresponds to maximum surface load in undissolved substances. Chemical precipita‐ tion of phosphorus produces metal precipitates. These are transported with the waste sludge to the digestion tanks. Impact of the precipitates on the anaerobic sludge

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

stabilisation process as well as on the sludge water quality was tested in the work. The main aim of the research and proposed chapter submission is a pursuit of decision making regarding selection of type of precipitating agent and strategy of chemical phosphorus precipitation.

**Keywords:** aerobic, aluminium salts, anaerobic digestion, anoxic, activated sludge, denitrification, dewatering, excess sludge, ferric and ferrous precipitants, inhibition, heterotrophic microorganisms, nitrification, operating research, plug flow, respiromet‐ ric measurements, simultaneous phosphorus precipitation, sludge water, solids flux flow, specific oxygen uptake rate, stimulation, thickening

#### **1. Introduction**

The requirement for removal of phosphorus from wastewater (WW) is rising due to increasing problem of eutrophication all over the world. Biologically enhanced phosphorus removal represents the most convenient way. The main disadvantage of this approach is the require‐ ment for an anaerobic bioreactor, that is, an increase of capital costs. As a result, chemical precipitation with ferric, ferrous, aluminium or calcium salts is usually applied. There are various technological strategies (**Figure 1**), which depend on the place of precipitants dosing with regard to the position of biological stage of the wastewater treatment plant (WWTP). Other reason for chemical phosphorus removal can be temporary solution during upgrading of a WWTP for enhanced biological phosphorus removal. There are also circumstances in WW treatment practice (e.g. lower organics content in WW for sufficient biological phosphorus removal, lower winter temperatures or more stringent effluent phosphorus standards) for application of chemical phosphorus precipitation as a complementary solution. Combined chemical and biological phosphorus removal is more effective and chemical saving.

**Figure 1.** Phosphate removal processes (PD—precipitant dosing, AGCH—aerated grid chamber, PST—primary sedi‐ mentation tank, AT—aeration tank, SST—secondary sedimentation tank, D—dosing, F—flocculation, S—sedimenta‐ tion, RCHS—returned chemical sludge).

The addition of chemicals to raw wastewater for precipitation of phosphorus in primary sedimentation facilities is termed "*pre‐precipitation"* [1]. Precipitates of phosphorus are withdrawn from the system as a part of primary sludge with low effect on activated sludge microorganisms. Increase in the amount of primary sludge is typical for this treatment technology. Precipitants are helpful to eliminate fluctuations of organic mass loading to biological stage of WWTP. However, simultaneous coagulation of organic matter occurs, leading to a decrease in BOD5 and possible negative impact on efficiency of denitrification process.

stabilisation process as well as on the sludge water quality was tested in the work. The main aim of the research and proposed chapter submission is a pursuit of decision making regarding selection of type of precipitating agent and strategy of chemical

**Keywords:** aerobic, aluminium salts, anaerobic digestion, anoxic, activated sludge, denitrification, dewatering, excess sludge, ferric and ferrous precipitants, inhibition, heterotrophic microorganisms, nitrification, operating research, plug flow, respiromet‐ ric measurements, simultaneous phosphorus precipitation, sludge water, solids flux

The requirement for removal of phosphorus from wastewater (WW) is rising due to increasing problem of eutrophication all over the world. Biologically enhanced phosphorus removal represents the most convenient way. The main disadvantage of this approach is the require‐ ment for an anaerobic bioreactor, that is, an increase of capital costs. As a result, chemical precipitation with ferric, ferrous, aluminium or calcium salts is usually applied. There are various technological strategies (**Figure 1**), which depend on the place of precipitants dosing with regard to the position of biological stage of the wastewater treatment plant (WWTP). Other reason for chemical phosphorus removal can be temporary solution during upgrading of a WWTP for enhanced biological phosphorus removal. There are also circumstances in WW treatment practice (e.g. lower organics content in WW for sufficient biological phosphorus removal, lower winter temperatures or more stringent effluent phosphorus standards) for application of chemical phosphorus precipitation as a complementary solution. Combined

chemical and biological phosphorus removal is more effective and chemical saving.

**Figure 1.** Phosphate removal processes (PD—precipitant dosing, AGCH—aerated grid chamber, PST—primary sedi‐ mentation tank, AT—aeration tank, SST—secondary sedimentation tank, D—dosing, F—flocculation, S—sedimenta‐

flow, specific oxygen uptake rate, stimulation, thickening

phosphorus precipitation.

104 Operations Research - the Art of Making Good Decisions

**1. Introduction**

tion, RCHS—returned chemical sludge).

Simple implementation of precipitating reagent dosing but no recovery of phosphorus from primary sludge is characteristic for this strategy.

The addition of chemicals to form precipitates that are removed along with wasted biological sludge is defined as "*coprecipitation"* [1]. Chemicals can be added to the effluent from primary sedimentation tank—the mixed liquor, that is, directly to the biological stage, or to the effluent from biological treatment process before secondary sedimentation.

Enhanced sedimentation of activated sludge is the advantage of phosphorus *coprecipitation* or *simulated precipitation*. Very simple dosing of precipitating chemicals and sufficient mixing and flocculation in biological treatment facilities are typical for this strategy. Concentration of mixed liquor in biological treatment tank increases, and solid retention time (SRT) decreases as a consequence of phosphorus precipitation. Phosphorus precipitates are removed from the treatment system as a part of excess sludge from which the phosphorus is not recoverable. Decrease in acid neutralisation capacity and pH in biological treatment tank and direct impact of precipitant agents on activated sludge microorganisms are also typical features of this phosphorus removal strategy.

*"Post‐precipitation"* involves the addition of chemicals to the effluent from secondary sedimen‐ tation facilities and the subsequent removal of chemical precipitates. In this process, the chemical precipitates are usually removed in a separate sedimentation facilities or in effluent filters [1]. For this strategy, the elimination of effect of reagents on activated sludge microor‐ ganisms is characteristic. Main advantage is the achievement of minimal concentration values of total phosphorus in effluent (1 mg L‐1). Phosphorus is recoverable from chemical sludge. Main disadvantage of this technology is high investments related to separate flocculation and sedimentation tanks.

Simultaneous precipitation of phosphorus from wastewater with iron and aluminium salts is commonly used. Precipitation agents are dosed directly into the aeration tank, and produced precipitates are wasted as a part of the secondary sludge. Thus, not only aerobic and anoxic processes at WWTP are carried out in the presence of heavy metals, but precipitates are in many cases accumulated also in anaerobic sludge digester.

The most important operating parameter of simultaneous phosphorus removal is precipitating agent dosage. A lot of information about the dosing of precipitants can be found in the literature. Dosage of aluminium and iron salts usually falls into the range of 1–3 metal ion/ phosphorus on a molar ratio basis [Eq. (1)] if the residual phosphorus in the secondary effluent is >0.5 mg L‐1. To achieve phosphorus levels below 0.5 mg L‐1, significantly higher metal salt doses and filtration will be required [1]:

$$
\beta = \frac{\mathbf{n}\_{\text{Mc}}}{\mathbf{n}\_{\text{p}}} \tag{1}
$$

where nMe is the molar concentration of precipitating agent required for precipitation [mol L‐1], nP the molar concentration of phosphorus to be precipitated [mol L‐1].

Recommended values of β ratio to achieve effluent concentration of phosphorus below 1.9  mg L‐1 are 2–4 in simultaneous precipitation of phosphorus [2]. Under optimal function of separation stage, the concentrations of Al3+, Fe2+ and Fe3+ in the effluent discharge for B = 1.5 are lower than 1 mg L‐1 [3], that is, often lower than in the raw water. The separation by filtration enables to achieve metal concentrations below 0.5 mg L‐1. For urban wastewater with an average concentration of chloride 100 mg L‐1, sulphates 200 mg L‐1 and the total phosphorus 10 mg L‐1 , an increase in chloride concentration by about 50%, respectively 25% for the sulphate, will be the consequence of chemical precipitation process. It is also apparent that precipitation of phosphate contributes to the reduction in the total concentration of dissolved inorganic salts [4].

The required dose of coagulant/precipitant depends on the phosphate concentration, the pH and composition of the water. Due to the varying flow and phosphorus concentrations in raw water, it is advantageous to optimise the dosing of coagulants experimentally.

Significantly less data for the influence of precipitants on activated sludge activity and process efficiency appear in the literature. Mowat [5] published the data related to metal toxicity on microorganisms during biochemical oxygen demand test. At 20 mg L‐1, aluminium corre‐ sponded approximately to trivalent chromium and cyanide, and ferric iron showed similar toxicity. According to Bever and Teichman [3], ferric iron has a stimulation effect on nitrification process but ferrous iron causes an inhibition of this process. but inhibition of this process by ferrous iron was published by Bever and Teichman [3]. Because iron is usually introduced as not very toxic metal, there is a scarcity of literature about its toxicological and inhibitory effects on freshwater organisms. Aluminium and iron are commonly bioaccumulating in their salt form. Aluminium is a non‐essential element, and it is mainly discussed in the context of its suspected detrimental role on the uptake of essential elements [6].

Extending spectrum of applied wastewater treatment processes and technologies follows the ever stricter requirements for discharged wastewater quality. Chemical precipitation of phosphorus is applicable in municipal wastewater treatment, and although being less envi‐ ronmentally favourable compared to enhanced biological phosphorus removal, the amount of investment funds is often decisive at this stage. Furthermore, enhanced biological phosphorus removal process frequently requires the application of chemical precipitation/post‐precipita‐ tion as well, taking the increasingly stringent requirements for phosphorus removal from wastewater into account.

Simultaneous chemical phosphorus precipitation in biological stage of WWTP represents one of the most commonly used technologies when Fe2+, Fe3+ and Al3+ salts are dosed into biological treatment facilities to precipitate the excess phosphorus in wastewater. These salts and their precipitates then become a part of the excess sludge and are thus transported also into anaerobic stabilisation tank.

Similarly to most treatment processes, chemical phosphorus precipitation is accompanied with generation of side products, interactions and impact on other simultaneously running processes. The aim of our research was to compare the impact of Fe2+, Fe3+ and Al3+ salts on sedimentation and thickening characteristics of sludge, biological transformation processes and ammonia nitrogen removal, that is, nitrification and denitrification processes, as well as anaerobic sludge stabilisation processes. The objective of our research is to contribute to methodology for examination of thickening and dewatering characteristics of sludge with investigated precipitation agents. Mathematically processed experimental results of lab‐scale‐ operated activated sludge models are used to compare sedimentation, precipitation and dewatering characteristics of activated sludge cultivated in the presence of selected precipita‐ tion agents, that is, Fe2+, Fe3+ and Al3+ salts. Other purpose of this study is to find methods for quantification of precipitants influence on activated sludge activity.

#### **2. Experimental and data processing methods**

is >0.5 mg L‐1. To achieve phosphorus levels below 0.5 mg L‐1, significantly higher metal salt

Me P n n b

where nMe is the molar concentration of precipitating agent required for precipitation [mol L‐1],

Recommended values of β ratio to achieve effluent concentration of phosphorus below 1.9  mg L‐1 are 2–4 in simultaneous precipitation of phosphorus [2]. Under optimal function of separation stage, the concentrations of Al3+, Fe2+ and Fe3+ in the effluent discharge for B = 1.5 are lower than 1 mg L‐1 [3], that is, often lower than in the raw water. The separation by filtration enables to achieve metal concentrations below 0.5 mg L‐1. For urban wastewater with an average concentration of chloride 100 mg L‐1, sulphates 200 mg L‐1 and the total phosphorus

sulphate, will be the consequence of chemical precipitation process. It is also apparent that precipitation of phosphate contributes to the reduction in the total concentration of dissolved

The required dose of coagulant/precipitant depends on the phosphate concentration, the pH and composition of the water. Due to the varying flow and phosphorus concentrations in raw

Significantly less data for the influence of precipitants on activated sludge activity and process efficiency appear in the literature. Mowat [5] published the data related to metal toxicity on microorganisms during biochemical oxygen demand test. At 20 mg L‐1, aluminium corre‐ sponded approximately to trivalent chromium and cyanide, and ferric iron showed similar toxicity. According to Bever and Teichman [3], ferric iron has a stimulation effect on nitrification process but ferrous iron causes an inhibition of this process. but inhibition of this process by ferrous iron was published by Bever and Teichman [3]. Because iron is usually introduced as not very toxic metal, there is a scarcity of literature about its toxicological and inhibitory effects on freshwater organisms. Aluminium and iron are commonly bioaccumulating in their salt form. Aluminium is a non‐essential element, and it is mainly discussed in the context of its

Extending spectrum of applied wastewater treatment processes and technologies follows the ever stricter requirements for discharged wastewater quality. Chemical precipitation of phosphorus is applicable in municipal wastewater treatment, and although being less envi‐ ronmentally favourable compared to enhanced biological phosphorus removal, the amount of investment funds is often decisive at this stage. Furthermore, enhanced biological phosphorus removal process frequently requires the application of chemical precipitation/post‐precipita‐ tion as well, taking the increasingly stringent requirements for phosphorus removal from

water, it is advantageous to optimise the dosing of coagulants experimentally.

suspected detrimental role on the uptake of essential elements [6].

, an increase in chloride concentration by about 50%, respectively 25% for the

nP the molar concentration of phosphorus to be precipitated [mol L‐1].

= (1)

doses and filtration will be required [1]:

106 Operations Research - the Art of Making Good Decisions

10 mg L‐1

inorganic salts [4].

wastewater into account.

#### **2.1. Influence of aerobic and anoxic biological processes**

The process of simultaneous precipitation of phosphorus in aerobic biological WWTP was simulated in lab‐scale. The activated sludge was cultivated in semicontinuous reactors in order to simulate plug‐flow hydraulic regime at real aerated tanks of municipal WWTPs. The volume of one unit was equal to 1.5 L. The cultivation was carried out by applying different synthetic wastewater composition, that is, an individual substrate (methanol) or mixed substrates (methanol, glucose, natrium acetate and peptone or the mixture of natrium acetate and glucose) and ammonium nitrate in accordance with the ratio BOD5:N = 100:5.

Operational conditions were changed during the experiments in order to investigate also the influence of these variables on activated sludge activity. The volumetric load related to COD varied between 1.0 and 2.0 kg m‐3 d‐1. The bioreactors were operated over the solid retention time (SRT) of 8 or 10 days. The hydraulic retention time (HRT) of 46 h was maintained in the bioreactor. The amount of phosphorus added into the systems corresponded to its effluent concentration approximately 9.0 mg L‐1. Ferrous, ferric and aluminium salts were dosed as phosphorus precipitants and were applied after 50 days of cultivation (activated sludge acclimation). The amounts of precipitants required for dosing were obtained in accordance with metal/phosphorus molar ratios ranging from 1.5 to 3.0. The alkalinity was adjusted with sodium hydrocarbonate solution.

The analysis of chemical oxygen demand (COD), total suspended solids (TSS), volatile suspended solids (VSS) and soluble phosphorus content was performed in accordance with procedures described in the standard methods [7]. The content of total organic carbon (TOC) was obtained by TOC 2000 P analyser produced by IPU.

Respirometric measurements of oxygen uptake rate (OUR) which were performed by an oxygen Syland probe evaluated the influence of the above given precipitants on the activated sludge activity. These measurements were performed according to [8–10] and were carried out before the new aeration cycle started, that is, with endogenous biomass. With the resulting values, the maximum total oxygen uptake rates (the sum of exogenous and endogenous rates) were obtained. The effect of precipitants on activated sludge was evaluated from the total specific oxygen uptake rate (SOUR) values of metal‐laden system related to the total SOUR values of the control system (without metals exposition). Thus, stimulation effect of metal to the activated sludge is calculated as follows:

$$\text{SSE} = \left( \frac{\mathbf{r}\_{\text{x},\text{t}}}{\mathbf{r}\_{\text{x},\text{t},\text{con}}} \cdot 1 \right) . 100 \ \left[ \% \right] \tag{2}$$

where SE is the stimulation effect [%]; rx,t,con the total specific oxygen uptake rate of control sludge [mg g‐1 h‐1]; rx,t is the total specific oxygen uptake rate of heavy metal‐laden sludge [mg g‐1 h‐1].

The measurements of specific substrate removal rate RX at various substrate concentrations were performed by respirometric method [8, 9], and the values of maximum respiration rate Rx,max and half saturation constant Ks of the Monod equation:

$$\mathbf{R}\_{\mathbf{x}} = \mathbf{R}\_{\mathbf{x}, \max} \frac{\mathbf{S}}{\mathbf{K}\_{\mathbf{S}} + \mathbf{S}} \tag{3}$$

where KS is the half saturation constant [mg L‐1], RX is the specific rate of substrate removal [mg g‐1 h‐1], RX,max is the maximum specific rate of substrate removal [mg g‐1 h‐1], S is the substrate concentration [mg L−1],

were also evaluated in order to compare the influence of precipitants on activated sludge activity. Grid search method [11–13] was applied to evaluate respirometric measurements carried out at different substrate concentrations.

#### **2.2. Impact on sedimentation, thickening and dewatering properties**

Monitoring the impact of phosphorus precipitation agents to sedimentation, thickening and filtration characteristics of activated sludge formed another part in our research of the impact of precipitation agents to biological wastewater treatment processes and sludge treatment. Real activated sludge process performed in systems with concentration gradient was simulated in the lab in semi‐continuous models operated with default sludge age of 10 days. Retention time of synthetic wastewater was 2 days, and organic load rate expressed as COD was 1.5 kg  m‐3 d‐1. Salts of Fe2+, Fe3+ and Al3+ were dosed to the systems together with the substrate. Fe was added as FeSO4·7H2O. Trivalent Fe was added only after FeSO4·7H2O oxidation. Al3+ salts were added in form of AlCl3·6H2O. Metals doses to precipitate excess phosphates were calculated for β = 1.5. A control model was operated in parallel, that is, without precipitation agents. Synthetic wastewater contained glucose and sodium acetate (COD = 3000 mg L‐1).

procedures described in the standard methods [7]. The content of total organic carbon (TOC)

Respirometric measurements of oxygen uptake rate (OUR) which were performed by an oxygen Syland probe evaluated the influence of the above given precipitants on the activated sludge activity. These measurements were performed according to [8–10] and were carried out before the new aeration cycle started, that is, with endogenous biomass. With the resulting values, the maximum total oxygen uptake rates (the sum of exogenous and endogenous rates) were obtained. The effect of precipitants on activated sludge was evaluated from the total specific oxygen uptake rate (SOUR) values of metal‐laden system related to the total SOUR values of the control system (without metals exposition). Thus, stimulation effect of metal to

[ ] x, t

where SE is the stimulation effect [%]; rx,t,con the total specific oxygen uptake rate of control sludge [mg g‐1 h‐1]; rx,t is the total specific oxygen uptake rate of heavy metal‐laden sludge

The measurements of specific substrate removal rate RX at various substrate concentrations were performed by respirometric method [8, 9], and the values of maximum respiration rate

where KS is the half saturation constant [mg L‐1], RX is the specific rate of substrate removal [mg g‐1 h‐1], RX,max is the maximum specific rate of substrate removal [mg g‐1 h‐1], S is the

were also evaluated in order to compare the influence of precipitants on activated sludge activity. Grid search method [11–13] was applied to evaluate respirometric measurements

Monitoring the impact of phosphorus precipitation agents to sedimentation, thickening and filtration characteristics of activated sludge formed another part in our research of the impact of precipitation agents to biological wastewater treatment processes and sludge treatment.

K S <sup>=</sup> <sup>+</sup> (3)

x x,max <sup>S</sup> <sup>S</sup> R R (2)

x, t,con

SE - 1 . 100 % <sup>r</sup> æ ö ç ÷ <sup>=</sup> ç ÷ è ø

r

Rx,max and half saturation constant Ks of the Monod equation:

was obtained by TOC 2000 P analyser produced by IPU.

the activated sludge is calculated as follows:

108 Operations Research - the Art of Making Good Decisions

[mg g‐1 h‐1].

substrate concentration [mg L−1],

carried out at different substrate concentrations.

**2.2. Impact on sedimentation, thickening and dewatering properties**

Solid flux method [1, 14–16] for the analysis of settling/thickening data and filtration equation [17–19] for processing of dewatering data were applied. Respiration measurements of SOUR were performed in order to evaluate the influence of precipitating agents on activated sludge microorganism activity.

In the case of non‐standard sludge/suspension, it is possible to define the thickening area from experimental curve of particles mass flow density [18] that defines the relation of particles mass flow density q [kg m‐2 h‐1] and sludge concentration [Eq. (4)]:

$$q = X \, . \,\mu\_0 \left( \text{l} \, \text{l} \, \frac{X}{\text{c}\_k} \right)^\* \tag{4}$$

Particles mass flow density values may be gained as a product of sludge concentration values and respective measured precipitation rate or free sedimentation [15]. Analogically, the below formula applies for thickening rate *uz* at specific solids concentration X:

$$u\_z = u\_0 \cdot \left( \left( 1 - \frac{X}{c\_k} \right)^u \right) \tag{5}$$

where X means sludge concentration [kg m‐3]; *u0*, *ck* and *n* are empirical parameters; *ck* parameter value characterises the given suspension; it represents the maximal solids concen‐ tration (compression region). The constant *u0* represents thickening rate at unit suspension porosity. Simplified two parameters formula below may be used to describe the dependence of thickening rate and sludge concentration [18]:

$$
\mu\_z = k \, . \, e^{\cdot \beta \, . \, X} \tag{6}
$$

The values of *k* [m h‐1] and *ß* [m3  kg‐1] parameters describe the sludge thickening characteristics. Required thickening area may then be calculated from the equation:

$$A\_{\mathcal{Z}} = \frac{\mathcal{Q}\_0 \cdot (\mathbf{l} + R) \cdot X\_{\mathcal{A}}}{q\_{\min}} \tag{7}$$

where Az means the required thickening area of thickening tank [m2 ]; Q0 is wastewater flow [m3  h‐1]; Xa means concentration of solids [kg m‐3]; and R means return sludge recirculation ratio. Minimum particles flow density qmin may be defined graphically pursuant to Yoshioka et al. [20] or calculated for example from the equation:

$$q\_{\min} = \frac{\mu\_0 \cdot X\_k \cdot X\_r}{X\_r \cdot X\_k} \left(1 - \frac{X\_k}{c\_k}\right)^{\gamma} \tag{8}$$

If simplified two parameters thickening rate model is used [Eq. (6)], the below will apply for minimum flux of solids qmin (kg m‐2 min‐1) moving downward:

$$q\_{\rm min} = k \, . \,\beta \, . \, X\_k^2 \, . \, e^{\beta \, . X\_k} \tag{9}$$

Tuček and Koníček [18] describe how the Eqs. (8) and (9) are derived, as well as the formulae to calculate critical concentration value Xk and returned sludge concentration Xr.

Thickening rate corresponding to the sludge concentration [Eq. (5)] needs to be higher than solid flux of tank, that is, the below applies for minimum thickening area AZ,min:

$$A\_{Z, \text{min}} \ge \frac{\underline{Q}}{\mu\_{\varepsilon}(X\_a)} = \frac{\underline{Q}}{\mu\_0} \left( 1 - \frac{X\_a}{c\_k} \right)^{\kappa} \tag{10}$$

where Q means sludge flow rate [m3  h‐1]

Assuming that flow rate is laminar when the filtrate flows through the porous material, filtration process may be described by the equation [16, 17]:

$$\frac{dV}{dS \cdot d\tau} = \frac{\Delta p \cdot S}{a \cdot \eta \cdot C \cdot (V + V\_e)}\tag{11}$$

where Δp means overall pressure difference [Pa] prior and after the filter that needs to be developed in order the required filtrate flow rate is reached; S means the filter size [m2 ]; dV means filtrate volume increment [m3 ] in time dτ [s]; *u* means filtration rate [m s‐1]; α means specific cake resistance [m kg‐1]; η means dynamic filtrate viscosity [Pa s]; C means solids concentration in suspension [kg m‐3]; V means filtrate volume [m3 ] in time τ [s]; and Ve means fictive filtrate volume [m3 ] that would be developed by a cake with the same resistance as the filtrate material resistance.

0

*Q RX <sup>A</sup> q*

*Z*

where Az means the required thickening area of thickening tank [m2

0

. . 1 - æ ö <sup>=</sup> ç ÷

min .. . *Xk <sup>k</sup> q k Xe*

to calculate critical concentration value Xk and returned sludge concentration Xr.

solid flux of tank, that is, the below applies for minimum thickening area AZ,min:

( )

 h‐1]

t ah

*QQX <sup>A</sup> uX u c*

 = b

*kr k rk k uXX X <sup>q</sup> XX c*

If simplified two parameters thickening rate model is used [Eq. (6)], the below will apply for

2 - .

Tuček and Koníček [18] describe how the Eqs. (8) and (9) are derived, as well as the formulae

Thickening rate corresponding to the sludge concentration [Eq. (5)] needs to be higher than

0 1 -

*z a k*

Assuming that flow rate is laminar when the filtrate flows through the porous material,

.

where Δp means overall pressure difference [Pa] prior and after the filter that needs to be developed in order the required filtrate flow rate is reached; S means the filter size [m2

. . . .( )*<sup>e</sup> dV p S Sd C V V*

³ = ç ÷

æ ö

*n a*

è ø

b

min

minimum flux of solids qmin (kg m‐2 min‐1) moving downward:

,min

*Z*

filtration process may be described by the equation [16, 17]:

where Q means sludge flow rate [m3

means filtrate volume increment [m3

et al. [20] or calculated for example from the equation:

110 Operations Research - the Art of Making Good Decisions

[m3

min . (1 ) . *<sup>A</sup>*

 h‐1]; Xa means concentration of solids [kg m‐3]; and R means return sludge recirculation ratio. Minimum particles flow density qmin may be defined graphically pursuant to Yoshioka


*n*

è ø

<sup>+</sup> <sup>=</sup> (7)

(9)

<sup>D</sup> <sup>=</sup> <sup>+</sup> (11)

] in time dτ [s]; *u* means filtration rate [m s‐1]; α means

]; Q0 is wastewater flow

(8)

(10)

]; dV

Integrating Eq. (11) and other adjustments lead into Eq. (12) for filtration at constant pressure [18]:

$$
\left(\frac{V\_2 \cdot V\_1}{2}\right)\frac{2}{k} + \frac{2V\_e}{k} = \frac{\Delta \tau}{\Delta V} \tag{12}
$$

Characteristic filtration constants, that is, Ve and *k* quantities may be determined based upon measured values Vi , Vi+1 and τi a τi+1. Then, the filtration cake‐specific resistance may be calculated from Eq. (13):

$$k = \frac{2\text{ }\Delta p \text{ }.S^2}{\alpha \text{ }.\eta \text{ }.C} \tag{13}$$

Another approach to determine filtration cake‐specific resistance value is based on the assumption of negligible filtration material resistance with regard to filtration cake resistance [15]:

$$\alpha = \frac{\Delta p \, .S^2}{\eta \, .C \, .V\_1 \dot{V}\_1} \tag{14}$$

Neglecting filtration support material resistance results in a relative error *n* defined as below:

$$n = \frac{\Delta\alpha}{\alpha} \, 100 = \frac{\dot{V}\_1}{\dot{V}\_0 \cdot \dot{V}\_1} \, 100 \, \text{ [\%]} \tag{15}$$

where 1 means the volume of filtrate used to create the cake; ˙ <sup>0</sup> means filtrate volumetric flow rate through the filtration material; and ˙ <sup>1</sup> means volumetric filtrate flow rate through the cake and filtration material.

The dependence of specific resistance of compressible cake from pressure difference may be expressed as [15]:

$$
\alpha = \alpha\_0 + a \, . \,\Delta p^\times \tag{16}
$$

For certain suspensions α0 = 0 and Eq. (16) shall thus be transformed to Eq. (17):

$$
\alpha = a \, . \, \Delta p^{\times} \tag{17}
$$

where *a* is constant.

Mathematically, the constant *a* equals to specific cake resistance at unit pressure difference for Eq. (16). Parameter *x* represents the filtration cake compressibility rate; x = 0 for non‐ compressible cake. Mathematically, α0 represents specific cake resistance at Δp = 0.

Sedimentation characteristics of sludge from individual systems were evaluated based upon the minimum thickening area AZ,min values [Eq. (10)] that correspond to those of maximum hydraulic surface load of sedimentation tank in order to ensure for sludge separation condi‐ tions.

Thickening characteristics of sludge were examined by comparing the thickening area values calculated for measured solids concentration and the same flow rates of wastewater and return sludge. Three parameters model of particles flow curve [Eq. (4)] was applied onto the results of thickening curves measurements, or the dependence of thickening rate from sludge concentration [Eq. (5)], and two parameters dependence of thickening curve from sludge concentration [Eq. (6)] was applied.

Experimental values of filtration characteristics (specific filtration cake resistance α and fictive filtrate volume Ve) determined in filtrate rate measurement at constant pressure difference were used to assess dewatering sludge characteristics. At the same time, α dependence from pressure difference was also measured.

Grid search optimisation method [10, 12] was used to determine parameters in Eqs (4), (6), (16) and (17). Residual sum square S2 R between experimental and calculated *q*, *u* and α values was applied as objective functions [12]:

$$\left(S\right)^{2}\_{\;R} = \frac{\sum \left(\mathcal{y}\_{i}^{\text{exp}} - \mathcal{y}\_{i}^{cal}\right)^{2}}{n \cdot m} \tag{18}$$

where *n* represents the number of measurements and *a* means the number of model parame‐ ters.

#### **2.3. Impact on anaerobic sludge stabilisation**

Experimental models to simulate the processes occurring in the anaerobic digesters of stabilising raw sludge (**Figure 2**) consisted of three parts:


<sup>0</sup> . *<sup>x</sup>*

. *<sup>x</sup>*

Mathematically, the constant *a* equals to specific cake resistance at unit pressure difference for Eq. (16). Parameter *x* represents the filtration cake compressibility rate; x = 0 for non‐

Sedimentation characteristics of sludge from individual systems were evaluated based upon the minimum thickening area AZ,min values [Eq. (10)] that correspond to those of maximum hydraulic surface load of sedimentation tank in order to ensure for sludge separation condi‐

Thickening characteristics of sludge were examined by comparing the thickening area values calculated for measured solids concentration and the same flow rates of wastewater and return sludge. Three parameters model of particles flow curve [Eq. (4)] was applied onto the results of thickening curves measurements, or the dependence of thickening rate from sludge concentration [Eq. (5)], and two parameters dependence of thickening curve from sludge

Experimental values of filtration characteristics (specific filtration cake resistance α and fictive filtrate volume Ve) determined in filtrate rate measurement at constant pressure difference were used to assess dewatering sludge characteristics. At the same time, α dependence from

Grid search optimisation method [10, 12] was used to determine parameters in Eqs (4), (6), (16)

exp 2

where *n* represents the number of measurements and *a* means the number of model parame‐

Experimental models to simulate the processes occurring in the anaerobic digesters of

*cal i i*

<sup>2</sup> ( -) -

*R*

R between experimental and calculated *q*, *u* and α values was

*y y <sup>S</sup> n m* <sup>=</sup> <sup>å</sup> (18)

=+D *a p* (16)

= D *a p* (17)

a a

For certain suspensions α0 = 0 and Eq. (16) shall thus be transformed to Eq. (17):

a

compressible cake. Mathematically, α0 represents specific cake resistance at Δp = 0.

where *a* is constant.

112 Operations Research - the Art of Making Good Decisions

concentration [Eq. (6)] was applied.

pressure difference was also measured.

**2.3. Impact on anaerobic sludge stabilisation**

stabilising raw sludge (**Figure 2**) consisted of three parts:

and (17). Residual sum square S2

applied as objective functions [12]:

tions.

ters.

Reference model was also operated in parallel.

Anaerobically stabilised sludge sampled from the digester at WWTP Bratislava (applied as inoculum) was loaded with primary and excess sludge taken from the abovementioned WWTP. Anaerobic digesters were operated in batch mode at a residence time of 5 days. In both systems, during the tests carried out with the raw sludge the processes of the hydrolysis were investigated by measuring changes in the concentration of ammonia, and the methanogenesis process was investigated by measuring the production of biogas. Effect of iron on the processes of anaerobic digestion was evaluated by comparing the output values of the experimental (addition of Fe) and reference model. The pH was adjusted dosing systems NaHCO3 and NaOH to the same value (about 7.8) to increase buffering capacity of both systems. The models were run at 37°C.

**Figure 2.** Schematic representation of lab‐scale anaerobic stabilisation equipment (1‐thermostat, 2—reactors, 3—safety vessels, 4—bubbler with KOH, 4—measurement of produced gas volume, 6—storage reservoirs for water).

#### **3. Results and discussion**

#### **3.1. Impact on aerobic and anoxic biological treatment processes**

The process of simultaneous precipitation of phosphorus in aerobic biological wastewater treatment system has been studied in semi‐continuous lab‐scale bioreactors. Operational conditions, type and dose of precipitants (ferric, ferrous and aluminium salts) were changed during experiments in order to investigate the influence of these variables on activated sludge activity. Short‐term and long‐term effects of precipitants on activated sludge activity have been studied. Respirometric measurements were performed in order to evaluate the influence of precipitant metals on activated sludge activity. The effect of precipitants was evaluated with regard to specific oxygen uptake rate (SOUR) of the control activated sludge system operated at the same conditions excluding the precipitants dosing.

**Figure 3** shows the effect of ferrous (FeSO4·7H2O) and aluminium (Al2(SO4)3·18H2O) precipi‐ tants on activated sludge respiration activity. Model wastewater containing glucose, methanol, sodium acetate and peptone was used as a substrate. Bioreactors including control system were operating at SRT of 8 days and the volumetric load of 1.0 kg m‐3 d‐1, related to COD. The precipitants during this set of experiments were dosed at metal to phosphorus molar ratios equal to 3.

**Figure 3.** Stimulation effect of Fe2+ and Al3+ precipitating agents on activated sludge respiration activity.

The inhibition effect of about 30% for both precipitants few days after the beginning of the experiments follows from **Figure 3**. In the next period, after approximately 15 days from the beginning of the precipitants dosing, the stimulation effect of ferrous iron on activated sludge activity of about 30–40% [Eq. (2)] can be estimated from **Figure 3**. On the other hand, only small inhibition or insignificant stimulation influence of aluminium precipitant resulted from the measurements as can be seen in **Figure 3**.

The results on stimulation or inhibition effects of the precipitants on the activated sludge respiration activity can be influenced by the procedure applied in the evaluation.

From Eq. (2) follows that the values of relative SOUR can be considered to be a measure of these effects. The values of total suspended solids (TSS) are usually applied as a basis of specific rate expressions in wastewater engineering. It is obvious that the values of TSS concentration in the systems with precipitant dosing increase due to the precipitates formation and accu‐ mulation in activated sludge and will be higher in comparison with the control system.

Significant differences between the values of VSS versus the duration of experiments duration were observed in all three bioreactors maintained the same values of operational parameters (HRT, SRT, volumetric load) and used equal substrate composition [21]. These differences can be related for example to possible influence of heavy metals on biomass yield or to thermal decomposition of precipitates with hardly defined composition during performing the VSS content determination procedure. For example, the value of VSS for Fe precipitate based on our experiment is about 13% and for Al precipitate about 27% (both precipitates were prepared by coagulation, precipitation and filtration) [21]. It is also assumed that the differences between the VSS content in the studied systems can be partially ascribed to absorption of both dispersed form of biomass and slowly biodegradable products of microorganisms. This assumption follows from higher treatment efficiency of organic pollution removal in the systems with phosphorus precipitation with regard to dissolved as well as dispersed organic substances observed in our previous work [21]. Thus, adsorbed organics on activated sludge flocs practically decrease the observed values of activated sludge SOUR. This is due to the higher values of biomass concentration approximated by VSS content to which the values of SOUR are related.

during experiments in order to investigate the influence of these variables on activated sludge activity. Short‐term and long‐term effects of precipitants on activated sludge activity have been studied. Respirometric measurements were performed in order to evaluate the influence of precipitant metals on activated sludge activity. The effect of precipitants was evaluated with regard to specific oxygen uptake rate (SOUR) of the control activated sludge system operated

**Figure 3** shows the effect of ferrous (FeSO4·7H2O) and aluminium (Al2(SO4)3·18H2O) precipi‐ tants on activated sludge respiration activity. Model wastewater containing glucose, methanol, sodium acetate and peptone was used as a substrate. Bioreactors including control system were operating at SRT of 8 days and the volumetric load of 1.0 kg m‐3 d‐1, related to COD. The precipitants during this set of experiments were dosed at metal to phosphorus molar ratios

0 10 20 30 40 50

The inhibition effect of about 30% for both precipitants few days after the beginning of the experiments follows from **Figure 3**. In the next period, after approximately 15 days from the beginning of the precipitants dosing, the stimulation effect of ferrous iron on activated sludge activity of about 30–40% [Eq. (2)] can be estimated from **Figure 3**. On the other hand, only small inhibition or insignificant stimulation influence of aluminium precipitant resulted from the

The results on stimulation or inhibition effects of the precipitants on the activated sludge

From Eq. (2) follows that the values of relative SOUR can be considered to be a measure of these effects. The values of total suspended solids (TSS) are usually applied as a basis of specific rate expressions in wastewater engineering. It is obvious that the values of TSS concentration in the systems with precipitant dosing increase due to the precipitates formation and accu‐ mulation in activated sludge and will be higher in comparison with the control system.

**Figure 3.** Stimulation effect of Fe2+ and Al3+ precipitating agents on activated sludge respiration activity.

respiration activity can be influenced by the procedure applied in the evaluation.

Fe3+ Al3+

**time (d)** 

at the same conditions excluding the precipitants dosing.


measurements as can be seen in **Figure 3**.

**stimulation (%)** 

114 Operations Research - the Art of Making Good Decisions

equal to 3.

The TOC content in biomass was also analysed in order to evaluate SOUR and compare the influence of the studied heavy metals on activated sludge activity. The values of TOC content in activated sludge from operated lab‐scale bioreactors are given in **Table 1** [22].


**Table 1.** TOC content in activated sludge cultivated in observed lab‐scale aerated system.

**Figure 4.** Dependence of SOUR (related to TOC mass unit) on substrate concentration.

**Figure 5.** Dependence of SOUR (related to VSS mass unit) on substrate concentration.

The courses of the experimental and calculated values of SOUR (related to TOC concentration values) at different values of substrate concentration are presented in **Figure 4**. The highest values of SOUR can be concluded for the activated sludge cultivated in the presence of ferrous precipitant. On the other hand, this figure indicates only small differences between the SOUR courses obtained for activated sludge, which was cultivated in the control system and in the presence of ferric iron or aluminium precipitate. In **Figure 5**, similar concentration depend‐ encies are plotted, but the values of SOUR for the same measurements are related to VSS content in individual bioreactors. Similarly to **Figure 4**, the highest values of SOUR have been achieved with activated sludge cultivated in the bioreactor with ferrous precipitant dosing. The values of Monod equation parameters obtained by the evaluation of SOUR values shown in **Figure 4** are given in **Table 2**.


**Table 2.** The values of biokinetic parameter values [Eq. (3)] related to different forms of activated sludge in aerated systems.

The courses of calculated values of SOUR with the same parameter values are also presented in **Figure 4**. A very good agreement between the experimental values (points) and the calcu‐ lated ones (lines) follows from this figure. The values of maximum specific substrate removal

rates confirm the stimulation effect of ferrous ion on activated sludge respiration activity. As it was mentioned earlier, only small differences between the values of maximum SOUR obtained for ferric iron, aluminium precipitant and control systems resulted from the work. The values of maximum SOUR given in **Table 2** also confirm the stimulation effect of iron salts on activated sludge respiration activity.

From **Table 2** is obvious that Rx,max value for the sludge cultivated in presence of Fe2+ is significantly higher than the value for the sludge cultivated in presence of Al3+ indicating a stimulatory effect of ferric salts to the respiration rate. However, sludge cultivated in the presence of ferrous salts showed the lowest measured respiration activity. From this knowl‐ edge, it leads to the conclusion that the ferrous and ferric forms of iron have different effects on the activity of the sludge. Stimulation effect of ferric salts is highly dependent on the pH in aeration tank.

Higher stimulation of heterotrophic microorganisms activity by ferrous salts in comparison with ferric precipitant is also of technological importance, for example, with regard to the place of ferrous precipitant dosing. This form of iron salts should be preferable dosed directly into the aeration tank. In other words, ferrous sludge should not be metered prior to aerated sand traps because the presence of oxygen would oxidize ferrous iron to ferric. Ferric iron has significantly less stimulation effect on the activity of the sludge in the aeration tank as ferrous salts dispensed directly to this aeration tank. In addition, ferrous salts dosing will save operating costs for the simultaneous precipitation of phosphorus in comparison with ferric salts. However, one should keep in mind when designing activated sludge process with simultaneous phosphorus removal that dosing of the ferrous salts will increase oxygen consumption in this part of aeration tank.

The courses of the experimental and calculated values of SOUR (related to TOC content in activated sludge) at different values of substrate concentration are presented in **Figure 4**. The highest values of SOUR can be concluded for the activated sludge cultivated in the presence of ferrous precipitant. On the other hand, this figure indicates only small differences between the SOUR courses obtained for activated sludge, which was cultivated in the control system and in the presence of ferric iron or aluminium precipitate. In **Figure 5**, the similar concentra‐ tion dependencies are plotted, but the values of SOUR for the same measurements are related to volatile suspended solids (VSS) concentration in each bioreactor. Similarly to **Figure 4**, the highest values of SOUR have been achieved with activated sludge cultivated in the bioreactor with ferrous precipitant dosing.

Effluent phosphorus concentration varied between 1.0 and 2.0 mg L‐1.

#### *3.1.1. Nitrification tests*

in **Figure 4** are given in **Table 2**.

RX,max [mg g‐

systems.

**Figure 5.** Dependence of SOUR (related to VSS mass unit) on substrate concentration.

**SOUR (mg·g–1·h–1)** 

116 Operations Research - the Art of Making Good Decisions

0 4 8 12 16 20

The courses of the experimental and calculated values of SOUR (related to TOC concentration values) at different values of substrate concentration are presented in **Figure 4**. The highest values of SOUR can be concluded for the activated sludge cultivated in the presence of ferrous precipitant. On the other hand, this figure indicates only small differences between the SOUR courses obtained for activated sludge, which was cultivated in the control system and in the presence of ferric iron or aluminium precipitate. In **Figure 5**, similar concentration depend‐ encies are plotted, but the values of SOUR for the same measurements are related to VSS content in individual bioreactors. Similarly to **Figure 4**, the highest values of SOUR have been achieved with activated sludge cultivated in the bioreactor with ferrous precipitant dosing. The values of Monod equation parameters obtained by the evaluation of SOUR values shown

RX,max [mg g‐1MLSS h‐1] 457.3 476.3 644.8 417.9 RX,max [mg g‐1 TC h‐1] 1176.4 1326.6 2031.4 1252.1 KS [mg L‐1] 10.0 10.0 15.0 10.0

1TOC h‐1] 2553.0 2533.3 4091.3 2659.1

**Table 2.** The values of biokinetic parameter values [Eq. (3)] related to different forms of activated sludge in aerated

The courses of calculated values of SOUR with the same parameter values are also presented in **Figure 4**. A very good agreement between the experimental values (points) and the calcu‐ lated ones (lines) follows from this figure. The values of maximum specific substrate removal

**S (mg·L–1** control Fe2+ Al3+ Fe3+ **)** 

**Control Al3+ Fe2+ Fe3+**

The aim of preliminary short‐term nitrification tests was to evaluate the effect of precipitating salts on nitrification activities of individual sludge after approximately one month of sludge acclimation in presence of individual precipitating agents. Kinetic assays were performed after feeding semi‐continuous models by the model substrate composed of peptone, glucose, ethanol, sodium acetate, ammonium chloride, sodium dihydrogen phosphate and of the

precipitating agent. During the test, the pH was maintained at about 7.5. Measured values of different forms of nitrogen compounds during one cycle of each model are listed in **Tables 3**–**5**. Evaluation and comparison of nitrification rates of each activated sludge are shown in **Table 5**.


**Table 3.** Time variation in nitrogen compounds in control activated sludge model.

Comparing the rate of nitrification of second stage given in **Table 5**, one can conclude stimu‐ latory effect of ferrous salts to the second stage of nitrification. The nitrification rates are based on the value of the total organic carbon (TOC) in individual models that best represent the active part of the biomass of activated sludge. The values of biomass concentrations in systems with the addition of the precipitants contain sufficient portions of the chemical sludge, and therefore, they are not suitable for expressing concentration of active biomass.


**Table 4.** Time variation in nitrogen compounds in activated sludge models with precipitating agents dosing.


**Table 5.** Nitrification rate values.

precipitating agent. During the test, the pH was maintained at about 7.5. Measured values of different forms of nitrogen compounds during one cycle of each model are listed in **Tables 3**–**5**. Evaluation and comparison of nitrification rates of each activated sludge are

Comparing the rate of nitrification of second stage given in **Table 5**, one can conclude stimu‐ latory effect of ferrous salts to the second stage of nitrification. The nitrification rates are based on the value of the total organic carbon (TOC) in individual models that best represent the active part of the biomass of activated sludge. The values of biomass concentrations in systems with the addition of the precipitants contain sufficient portions of the chemical sludge, and

therefore, they are not suitable for expressing concentration of active biomass.

**Al3+ Fe2+ Fe3+**

0 26.1 – 24.4 14.0 23.0 16.9 1 20.9 13.3 21.2 13.9 23.6 16.5

2 17.0 14.9 14.6 14.9 16.8 –

5 7.2 24.1 3.0 24.5 4.6 –

6 – 26.7 1.4 29.7 1.9 26.8 7 1.2 29.7 0.2 29.4 0.6 32.6

**Table 4.** Time variation in nitrogen compounds in activated sludge models with precipitating agents dosing.

3 14,3 – 9.9 19.1 11.2 20.7 4 9.1 21.3 7.7 – 8.3 23.5

 ‐ 4 +  ‐ 3 ‐

 ‐ 4 +  ‐ 3 ‐

**[mg l−1]** 

**[mg l−1]** 

**[mg L−1]**

**[mg L−1]** 

‐ **[mg L−1]** ‐ 3

‐ **[mg L−1]**

<sup>+</sup> **[mg L−1]** ‐ 2

**Table 3.** Time variation in nitrogen compounds in control activated sludge model.

 ‐ 3 ‐

**[mg L−1]** 

0 22.7 6.4 23.8 0.5 23.7 3.3 24.5 1.0 – 2.6 25.0 2.0 21.4 0.9 27.5 3.0 18.3 0.4 32.0 4.0 15.1 0.4 –

shown in **Table 5**.

118 Operations Research - the Art of Making Good Decisions

**Time [h]** ‐ 4

**Time [h]**  ‐ 4

+

**[mg L−1]** 

**Figure 6.** Time dependencies of various forms of nitrogen compounds during 24‐hour cycle in the reference model and in the model with ferrous salts.

**Figure 7.** Time dependencies of various forms of nitrogen compounds during 24‐hour cycle in the model with ferric and aluminium salts.

The rate of transformation of N‐NH4 to nitrite (1st nitrification step) cannot be taken as a benchmark to determine the impact of metal on oxidation of ammonia nitrogen since this value covers not only the rate of oxidation of N‐NO3, but also the consumption of N‐NH4 for the synthesis of biomass. Moreover, it is also influenced by the formation as a result of hydrolysis and ammonification of organically bound nitrogen.

The next kinetic tests were aimed at the investigation of nitrification during the whole reaction cycle in individual laboratory semi‐continuous models. The results of the measurements are shown in **Figures 6** and **7**.

In order to compare individual models, the rates of ammonium nitrogen removal in the first hours of the test (rate includes the process of assimilation and nitrification) were calculated from the experimental data. The measured rates are shown in **Table 6**. In order to thoroughly verify coagulants influence on the process of nitrogen removal, the process of ammonium nitrogen adsorption on biomass was performed. The results of sorption of ammonia nitrogen are shown in **Figures 6** and **7**. From the results follows approximately equal and constant sorption of ammonium nitrogen during the whole cycle in all models. The value of adsorbed ammonia nitrogen is actually the difference between value of nitrogen extraction and the value of ammonia nitrogen measured without extraction. The concentration of ammonium nitrogen adsorbed on the biomass flakes reached 15–40% of the concentration of dissolved ammonium nitrogen, which is in good agreement with published values which ranged from 18 to 30% [23]. These values of sorption of ammonia nitrogen are characteristic for the semi‐continuous system operation laboratory models.


**Table 6.** The measured rate of assimilation and simultaneous nitrification during the daily cycle.

#### *3.1.2. Denitrification test*

The aim of the denitrification test was to monitor the degradation rate of nitrate nitrogen in individual models. For the better approximation of the active biomass, the denitrification rates were based on the concentrations of total organic carbon (TOC) in the individual sludge. The measured concentrations of nitrate and nitrite nitrogen during the denitrification tests are shown in **Table 7**. Experimental values of total suspended solids (TSS) and TOC are shown in **Table 8**.

Experimental and calculated dentrification rates based on TSS and TOC unit values in individual operated lab‐scale models are shown in **Table 9**. From these results follow the stimulatory effects of both forms of iron salts, that is, ferrous and ferric salts on denitrification rate. However, about two times higher denitrification rate follows for ferric salts in comparison with ferrous salts when comparing specific denitrification rates based on TOC values. The


experimental values of denitrification rates are comparable with those published in the literature, that is, 5–20 mg g‐1 h‐1 (based on unit mass of TSS).

**Table 7.** Concentration values of N‐NO2 ‐ and N‐NO3 ‐ in individual models.


**Table 8.** Concentration values of TSS and TOC in individual models.


**Table 9.** Denitrification rates in individual models.

The rate of transformation of N‐NH4 to nitrite (1st nitrification step) cannot be taken as a benchmark to determine the impact of metal on oxidation of ammonia nitrogen since this value covers not only the rate of oxidation of N‐NO3, but also the consumption of N‐NH4 for the synthesis of biomass. Moreover, it is also influenced by the formation as a result of hydrolysis

The next kinetic tests were aimed at the investigation of nitrification during the whole reaction cycle in individual laboratory semi‐continuous models. The results of the measurements are

In order to compare individual models, the rates of ammonium nitrogen removal in the first hours of the test (rate includes the process of assimilation and nitrification) were calculated from the experimental data. The measured rates are shown in **Table 6**. In order to thoroughly verify coagulants influence on the process of nitrogen removal, the process of ammonium nitrogen adsorption on biomass was performed. The results of sorption of ammonia nitrogen are shown in **Figures 6** and **7**. From the results follows approximately equal and constant sorption of ammonium nitrogen during the whole cycle in all models. The value of adsorbed ammonia nitrogen is actually the difference between value of nitrogen extraction and the value of ammonia nitrogen measured without extraction. The concentration of ammonium nitrogen adsorbed on the biomass flakes reached 15–40% of the concentration of dissolved ammonium nitrogen, which is in good agreement with published values which ranged from 18 to 30% [23]. These values of sorption of ammonia nitrogen are characteristic for the semi‐continuous

Maximal rate of assimilation and nitrification Rx,N,m [mg g‐1 h‐1] 0.92 0.78 1.69 1.77 Rate of simultaneous nitrification Rx,N,m [mg g‐1 h‐1] 0.05 0.23 0.99 0.89

The aim of the denitrification test was to monitor the degradation rate of nitrate nitrogen in individual models. For the better approximation of the active biomass, the denitrification rates were based on the concentrations of total organic carbon (TOC) in the individual sludge. The measured concentrations of nitrate and nitrite nitrogen during the denitrification tests are shown in **Table 7**. Experimental values of total suspended solids (TSS) and TOC are shown in

Experimental and calculated dentrification rates based on TSS and TOC unit values in individual operated lab‐scale models are shown in **Table 9**. From these results follow the stimulatory effects of both forms of iron salts, that is, ferrous and ferric salts on denitrification rate. However, about two times higher denitrification rate follows for ferric salts in comparison with ferrous salts when comparing specific denitrification rates based on TOC values. The

**Table 6.** The measured rate of assimilation and simultaneous nitrification during the daily cycle.

**Control Al3+ Fe2+ Fe3+**

and ammonification of organically bound nitrogen.

120 Operations Research - the Art of Making Good Decisions

shown in **Figures 6** and **7**.

system operation laboratory models.

*3.1.2. Denitrification test*

**Table 8**.

#### **3.2. Impact on sedimentation, thickening and dewatering characteristic**

**Table 10** shows experimental values of dry mass concentration for each lab model and calculated values of *u0*, *ck* and *n* parameters in the particles mass flow density Eq. (4). The minimum thickening area values are also given for individual sludge determined from point of view of maximum hydraulic surface load or establishment of conditions for sludge sepa‐ ration in sedimentation tank [Eq. (10)]. Eq. (5) was applied to calculate thickening rate values corresponding to experimental values of sludge concentration in each model (**Table 10**). The same value of activated sludge flow rate (Q0 = 250 m3  h‐1) was applied to calculate minimum thickening area for each operational activated sludge.

The smallest value of minimum thickening area results from **Table 1** for aerated tank with Fe3+ doses; the same area is larger by approximately 16% for reference activated model sludge (without precipitation agents). Minimum thickening area for Fe2+ is larger by app. 19% than in the reference model. The least thickening rate or the largest minimum thickening area are characteristic for sludge with Al3+ doses; this area is almost doubled in size compared to the sludge with Fe2+ dosing. It results from the above that this sludge shows the best sedimentation characteristics despite the highest solids concentration in the system with Fe3+ dosing (thick‐ ening rate decreases with growing sludge concentration).


**Table 10.** Values of dry mass concentration, parameters of particles mass flow density equation [Eq. (1)] and minimum thickening area for each sludge [Eq. (7)].

**Table 11** shows experimental values of volatile suspended solids (VSS) in each lab model sludge, calculated values of *k* and ß parameters in thickening rate equations [Eq. (6)] and relevant values of minimum thickening area [Eq. (10)]. The same above specified activation mixture flow rate was used to calculate minimum thickening area for individual sludge.


**Table 11.** VSS concentrations, thickening rate equations [Eq. (3)] parameters and minimum thickening area [Eq. (7)].

Minimum thickening area values calculated with the simpler two parameters model [Eq. (6), **Table 11**] also prove the above evaluation of sedimentation characteristics of each sludge. **Table 12** shows minimum particles mass flow density values and the necessary thickening area (sedimentation tank) calculated with both above presented mathematical models for individ‐ ual sludge with dosed precipitation agent. Values of qmin,5 [Eq. (8)] and AZ1 [Eq. (10)] correspond to the three parameters model and qmin,6 [Eq. (9)] and AZ3 [Eq. (10)] correspond to the two parameters model. Calculations were made for dry matter concentrations in each activation model presented in **Table 10**, and the above specified wastewater flow rate and the same value of return sludge recirculation ration.

It results from comparison of values presented in **Table 12** that the largest necessary thickening area is required for sludge with aluminium salts dosing in order to reach the required return sludge thickening to maintain the above specified activated sludge concentrations in each system (**Table 10**) at the same flow rate condition (wastewater flow rate and return sludge recirculation ratio), while five to ten times smaller thickening area corresponds to sludge with iron salts dosing. The values of required thickening area for sludge with Fe2+ and Fe3+ dosing calculated with individual mathematical thickening models [Eqs. (4) and (6)] are contradicting. Values higher by app. 23 up to 70% result for simplified, two parameters model from com‐ parison of the measured and calculated residual variation values of particles mass flow density figures. Thus, three parameters model was better in describing experimental values [Eq. (4)].


**Table 12.** Values of qmin a AZ for sludge with dosed precipitation agents.

in the reference model. The least thickening rate or the largest minimum thickening area are characteristic for sludge with Al3+ doses; this area is almost doubled in size compared to the sludge with Fe2+ dosing. It results from the above that this sludge shows the best sedimentation characteristics despite the highest solids concentration in the system with Fe3+ dosing (thick‐

**Model XA [kg m−3] u0 [m h−1] ck [kg m−3] n [–] uz [m h−1] Amin [m2**

**Table 10.** Values of dry mass concentration, parameters of particles mass flow density equation [Eq. (1)] and minimum

**Table 11** shows experimental values of volatile suspended solids (VSS) in each lab model sludge, calculated values of *k* and ß parameters in thickening rate equations [Eq. (6)] and relevant values of minimum thickening area [Eq. (10)]. The same above specified activation mixture flow rate was used to calculate minimum thickening area for individual sludge.

References 2.20 27.6 2.50 14.6 17.1 Fe2+ 2.24 21.1 0.16 12.9 19.4 Fe3+ 2.49 24.8 1.41 15.3 16.3 Al3+ 2.61 9.9 0.18 5.6 44.8

**Table 11.** VSS concentrations, thickening rate equations [Eq. (3)] parameters and minimum thickening area [Eq. (7)].

Minimum thickening area values calculated with the simpler two parameters model [Eq. (6), **Table 11**] also prove the above evaluation of sedimentation characteristics of each sludge. **Table 12** shows minimum particles mass flow density values and the necessary thickening area (sedimentation tank) calculated with both above presented mathematical models for individ‐ ual sludge with dosed precipitation agent. Values of qmin,5 [Eq. (8)] and AZ1 [Eq. (10)] correspond to the three parameters model and qmin,6 [Eq. (9)] and AZ3 [Eq. (10)] correspond to the two parameters model. Calculations were made for dry matter concentrations in each activation model presented in **Table 10**, and the above specified wastewater flow rate and the same value

It results from comparison of values presented in **Table 12** that the largest necessary thickening area is required for sludge with aluminium salts dosing in order to reach the required return sludge thickening to maintain the above specified activated sludge concentrations in each system (**Table 10**) at the same flow rate condition (wastewater flow rate and return sludge

**kg−1] uz [m h−1] Amin [m2**

References 2.5 19.2 12.2 1.58 13.3 18.8 Fe2+ 3.0 16.9 82.6 11.14 11.2 22.3 Fe3+ 3.4 24.8 88.1 12.00 15.5 16.2 Al3+ 3.3 10.0 77.3 13.15 5.7 44.0 **]**

**]**

ening rate decreases with growing sludge concentration).

122 Operations Research - the Art of Making Good Decisions

**Model XSŽ [kg m−3] k [m h−1] β [m3**

thickening area for each sludge [Eq. (7)].

of return sludge recirculation ration.

The relations among thickening rate of sludge from models with precipitation agents dosing are also obvious from **Figure 8** that shows the particles mass (MLSS/TSS) flow density curves. The highest particles mass flow density value corresponds to the selected sludge concentration and thus, also the largest thickening sludge rate with Fe3+ dosing. The least values of these parameters are characteristic for sludge with Al3+ dosing. Alongside the parameters of the applied mathematical model, the value of particles mass flow density depends also on the requested sludge thickening, which relates to sludge concentration maintained in the activa‐ tion tank and also to the return sludge recirculation ratio. This may also explain the seemingly contradicting calculated values of required thickening area for sludge with Fe3+ and Fe3+ (compared to the course of particles mass flow density curves depicted in **Figure 8**). Higher sludge concentration with Fe3+ dosing compared to Fe3+, at the same recirculation ratio, results also in higher required thickening, which was also reflected in smaller minimum particles mass flow density value or higher value of the required thickening area.

**Figure 8.** Particles solids flux flow curve for sludge in models with precipitation agents dosing.


**Table 13.** Values of AZ corresponding to maximum surface load in undissolved substances pursuant to.

**Table 13** presents return sludge concentration XR for each sludge required to maintain the above specified sludge concentrations in the system (**Table 10**), critical concentration XK and the necessary minimum thickening area corresponding to the requirements of maximum surface load in undissolved substances (mass surface load) in compliance with the standard STN 75 6401 [24], that is, 6 kg m‐3h‐1. Respective values of sedimentation rates are given in **Table 13**.

It is obvious that activated sludge process intensification with the purpose of chemical phosphorus precipitation is accompanied with its increased concentration in the system, when unchanged sludge age is maintained. Thus, mass surface load may occur with insufficient sedimentation tanks dimension. It is obvious from **Tables 1** and **3** that the higher sludge concentration in the system, the higher the required thickness of returned sludge, and thus, also higher thickening area.

**Figure 9** shows particles mass flow density curve for reference sludge (no agents dosed). The below sludge volume index (SVI) values were measured in individual bioreactors:

**Figure 9.** Particles mass flow density curve for reference sludge.

Fe2+: 29.8 mL g‐1, Fe3+: 36.3 mL g‐1, Al3+: 42.5 mL g‐1and Ref: 69.9 mL g‐1.

These figures show high sedimentation characteristic of each sludge. SVI, however, is not a good parameter to compare sedimentation and thickening characteristics of these different sludge due to the different dry mass concentrations in each sludge, mineral portion and morphology of floccules.

**Model XR [kg m−3] XK [kg m−3] AZ [m2**

References 12.2 12.2 139.0 Fe2+ 32.0 27.6 135.0 Fe3+ 45.2 40.8 154.0 Al3+ 42.8 38.3 151.0

**Table 13.** Values of AZ corresponding to maximum surface load in undissolved substances pursuant to.

**Table 13**.

also higher thickening area.

124 Operations Research - the Art of Making Good Decisions

**Figure 9.** Particles mass flow density curve for reference sludge.

Fe2+: 29.8 mL g‐1, Fe3+: 36.3 mL g‐1, Al3+: 42.5 mL g‐1and Ref: 69.9 mL g‐1.

**Table 13** presents return sludge concentration XR for each sludge required to maintain the above specified sludge concentrations in the system (**Table 10**), critical concentration XK and the necessary minimum thickening area corresponding to the requirements of maximum surface load in undissolved substances (mass surface load) in compliance with the standard STN 75 6401 [24], that is, 6 kg m‐3h‐1. Respective values of sedimentation rates are given in

It is obvious that activated sludge process intensification with the purpose of chemical phosphorus precipitation is accompanied with its increased concentration in the system, when unchanged sludge age is maintained. Thus, mass surface load may occur with insufficient sedimentation tanks dimension. It is obvious from **Tables 1** and **3** that the higher sludge concentration in the system, the higher the required thickness of returned sludge, and thus,

**Figure 9** shows particles mass flow density curve for reference sludge (no agents dosed). The

below sludge volume index (SVI) values were measured in individual bioreactors:

**]**

**Table 14** presents filtration characteristics for each sludge gained by processing filtrate volume increment measurements in individual time intervals, that is, applying Eqs. (12) and (13). The highest specific filtration resistance value for sludge cultivated with additional iron salts is obvious from **Table 14**. The lease values of fictive volume Ve correspond to this value, which also proves the least transitivity of the sludge cake. Relatively higher specific filtration resistance value and lower throughput are characteristic also for sludge with Al3+ dosing. The highest throughput results for reference sludge and the least specific filtration value are characteristic for sludge with addition of iron salts.


**Table 14.** Filtration characteristics for individual excess sludge measurements at Δp = 19.6 kPa—Eq. (12).

**Table 15** presents specific filtration resistance values corresponding to measurement of filtrate volumetric flow rate through filtration material, filtration material and cake and filtrate volume corresponding to the developed filtration cake. Measurements were made at the same pressure difference as in the previous case, that is, Δp = 19.6 kPa. Measured data were evaluated with Eq. (17). Relative errors [Eq. (15)] did not exceed 4%. The lowest specific filtration resistance values result for sludge with dosed iron salts also from these results. When the same method is applied to define the specific filtration resistance values for other sludge used in our research, the results are very much the same while exceeding the sludge with Fe3+ dosing by approxi‐ mately one order.


**Table 15.** Filtration characteristics of sludge measured at Δp = 19.6 kPa—Eq. (14).


**Table 16.** Parameters of specific filtration resistance dependence from pressure difference Eqs. (16) and (17).

**Table 16** presents the values of specific filtration resistance dependence from pressure difference, that is, the parameters of Eqs. (16) and (17). The data for calculation of specific filtration resistance values at different pressure differences were obtained by measuring volumetric flow rates through filtration material, filtration material and cake and also the filtrate volume when filtration cake was developed. Relative errors calculated with Eq. (15) did not exceed 4% for these measurements. The above mentioned equation describes the experi‐ mental data also for reference sludge and sludge containing aluminium precipitates, with approximately the same quality. The value of α0 equals zero for sludge from model where iron salts was dosed. Better agreement of experimental and calculated α0 values was gained with equation using zero value of α0 also when iron salts were dosed, that is, Eq. (17).

The highest α0 value corresponds to sludge from reference model (lower by app. two orders compared to sludge with Fe3+ or Al3+ dosing). Very low values of *x* parameter result for activated sludge from reference model or low specific filtrate resistance dependence on pressure difference.

#### **4. Influence on anaerobic sludge digestion**

Chemical precipitation of phosphorus produces metals' precipitates (Fe, Al). These are transported with the waste sludge to the digestion tanks where they occur at relatively high concentrations. The Fe precipitation's influence on the sludge anaerobic stabilisation process as well as on the sludge water quality was tested in this part of the work.

The Fe concentration increased in the digestion tank to app. 1000 mg L‐1. This, as a result of the simultaneous P precipitation in the activation, partially inhibited the CH4 generation. When the load in the digestion tank reached 1.9 kg m‐3 d‐1 (kg sludge TS), the inhibition was 15–50%, depending on the number of the sludge inputs during the day. When the load decreased to 1.6 kg m‐3 d‐1, the inhibition decreased to 5–20% depending on the number of sludge additions. The concentration of NH4 and volatile fatty acids (VFA) in the digestion tank with Fe increased probably because the hydrolysis was stimulated and methanogenesis inhibited. Fe and P concentrations in the supernatant (sludge water) were minimal. On the other hand, the stimulation effect on the process of anaerobic stabilisation was measured when applying lower concentration (below 400 mg L‐1) of the metal salts. These phenomena can be the consequence of the stimulation of hydrolysis as a first step of organic matter degradation or the elimination of sulphides by Fe precipitation.

**α0 A x S2**

Control, (16) 2.552 × 1012 0.426 × 1012 0.0005 2.457 × 1025 Control, (17) – 2.958 × 1012 0.0005 2.457 × 1025 Al3+, (16) 0.051 × 1012 0.310 × 1012 0.2048 0.099 × 1025 Al3+, (17) – 0.554 × 1012 0.1941 0.103 × 1025 Fe2+, (16) 0 0.005 × 1012 0.6878 0.192 × 1025 Fe2+, (17) – 0.005 × 1012 0.6878 0.192 × 1025 Fe3+, (16) 0.008 × 1012 0.106 × 1012 0.2500 0.034 × 1025 Fe3+, (17) – 0.001 × 1012 0.7603 0.009 × 1025

**Table 16.** Parameters of specific filtration resistance dependence from pressure difference Eqs. (16) and (17).

equation using zero value of α0 also when iron salts were dosed, that is, Eq. (17).

as well as on the sludge water quality was tested in this part of the work.

**Table 16** presents the values of specific filtration resistance dependence from pressure difference, that is, the parameters of Eqs. (16) and (17). The data for calculation of specific filtration resistance values at different pressure differences were obtained by measuring volumetric flow rates through filtration material, filtration material and cake and also the filtrate volume when filtration cake was developed. Relative errors calculated with Eq. (15) did not exceed 4% for these measurements. The above mentioned equation describes the experi‐ mental data also for reference sludge and sludge containing aluminium precipitates, with approximately the same quality. The value of α0 equals zero for sludge from model where iron salts was dosed. Better agreement of experimental and calculated α0 values was gained with

The highest α0 value corresponds to sludge from reference model (lower by app. two orders compared to sludge with Fe3+ or Al3+ dosing). Very low values of *x* parameter result for activated sludge from reference model or low specific filtrate resistance dependence on pressure

Chemical precipitation of phosphorus produces metals' precipitates (Fe, Al). These are transported with the waste sludge to the digestion tanks where they occur at relatively high concentrations. The Fe precipitation's influence on the sludge anaerobic stabilisation process

The Fe concentration increased in the digestion tank to app. 1000 mg L‐1. This, as a result of the simultaneous P precipitation in the activation, partially inhibited the CH4 generation. When the load in the digestion tank reached 1.9 kg m‐3 d‐1 (kg sludge TS), the inhibition was 15–50%, depending on the number of the sludge inputs during the day. When the load decreased to 1.6 kg m‐3 d‐1, the inhibition decreased to 5–20% depending on the number of sludge additions. The concentration of NH4 and volatile fatty acids (VFA) in the digestion tank with Fe increased probably because the hydrolysis was stimulated and methanogenesis inhibited. Fe and P concentrations in the supernatant (sludge water) were minimal. On the other hand, the

Note: numbers 16, and 17 mean that Eq. (16), or Eq. (17) were applied.

126 Operations Research - the Art of Making Good Decisions

**4. Influence on anaerobic sludge digestion**

difference.

**R**

The most important characterisation of situation in operated reactors with the anaerobic sludge stabilisation in relation to added Fe precipitates (FePO4) wasted from lab‐scale aerobic models with simultaneous phosphorus removal. Anaerobic digestion reactor under current conditions contains only trace Fe concentrations from the wastewater. However, anaerobic stabilisation reactor is subsequently filled with Fe precipitates due to the application of precipitation. Lower part of **Figure 10** shows the course of Fe concentration increase in the reactor during the experiments. Calculated courses predict the experimental Fe concentrations (calculation was done based on the Fe mass balance). Two breaks on the curve represent periods when the reactor was turned off, and no sludge was added to the reactor**.** The ratio of produced CH4 volume in reactors with and without Fe feeding clearly shows that during the first phase of the experiment the biogas production was stimulated by added Fe. Since Fe concentration reached app. 400 mg L‐1 (related to reactor volume) inhibition of the process was observed. During the interruption of the reactor's feeding, both long‐term (18th–33rd day) or short‐term (57th–60st day) biomass regeneration occurred. When the sludge was fed again, very signifi‐ cant stimulation of methanogenesis was observed. Within several days, the process was inhibited again. The inhibition is shown in details in **Figure 10** where are set daily produced amount of CH4.

Relatively high differences in daily biogas volume production can be explained by the fact that digestion reactors were operated with small amounts of a real raw sludge for which the differences in organic content occur. For characterisation of Fe influence on methanogenesis, the most important is the top part of **Figure 10** showing the ratios of biogas volumes produced. After 50 days of experiment at Fe concentration over 800 mg L‐1, (reactor volume) the inhibition reached almost level of 50% compared with control model. During this period, that is, from the beginning of experiment to its 75th day, the digestion reactors were fed once a day. During following days, the feeding procedure was changed in order to eliminate significant level of inhibition. The sludge was added in the same way as at real WWTP, that is, more times a day (3 times a day). It is recommended to add raw sludge more than 2 times a day [25].

From **Figure 11** follows that the decrease in methanogenesis rate was related also to COD accumulation in the sludge supernatant, while the analysis shown preferable presence of acetate. The facts that the decrease in methanogenesis rate increased the COD of the sludge water and that the sludge regeneration stimulated the process indicate that not only the Fe but probably also the presence of volatile fatty acids (VFA) caused the inhibition**.** The accumulation of VFA could result not only due to the fact that slower methanogenesis did not remove all VFA, but also due to the fact that the Fe presence probably significantly increased the rate of hydrolysis and acidogenesis, which caused COD accumulation. Increased concentration of NH4–N concentration can be also considered the factor of methanogenesis inhibition. From **Figure 11**, it can be seen that inhibition of methanogenesis rate, that is, the amount of removed COD/sludge is higher in the system without Fe.

**Figure 10.** Time dependencies of concentration of iron precipitates and their influence on methane production during anaerobic sludge digestion.

**Figure 11.** Time dependencies of concentration of ammonium nitrogen, phosphorus, iron and COD in sludge water during anaerobic sludge digestion.

### **5. Conclusions**

**Figure 10.** Time dependencies of concentration of iron precipitates and their influence on methane production during

**Figure 11.** Time dependencies of concentration of ammonium nitrogen, phosphorus, iron and COD in sludge water

anaerobic sludge digestion.

128 Operations Research - the Art of Making Good Decisions

during anaerobic sludge digestion.

Commonly used approaches to evaluate activated sludge activity through SOUR or specific substrate removal rate related to TSS are not fully satisfactory due to the presence of precipi‐ tates in activated sludge.

The content of VSS is a more representative quantity to relate the values of the specific rates performed by activated sludge from biological reactors operated with simultaneous chemical precipitation of phosphorus. The evaluation of respirometric measurements related to TOC content in activated sludge has proven to be the most convenient method of quantification of the effect of precipitant metals on activated sludge activity.

The decrease in SOUR of activated sludge microorganisms was observed at the initial stage of ferrous salts application. The maximum inhibition impact ranged from 2 to 6 h after the metal dosing. After the operation period of about 10 days, the values of SOUR increased. Stimulation of SOUR was observed at ferrous salts dosing. Only a small differences between the SOUR values with ferric or aluminium precipitants dosing and with sludge from control system were observed.

The highest efficiency of phosphorus removal was achieved in the bioreactor with aluminium precipitant. However, application of ferrous iron precipitant seems to be a more convenient technology of simultaneous precipitation of phosphorus due to the stimulation effect on activated sludge microorganisms activity.

Stimulation effects of ferric/ferrous salts on nitrification processes are evident. Stimulation of denitrification rates was observed for all systems with the higher stimulation in the ferric system.

The influence of dosed Fe2+, Fe3+ and Al3+ salts on the sedimentation, thickening and dewatering characteristics of activated sludge was monitored with simultaneous precipitation of excess phosphorus. In addition to phosphorus elimination and activated sludge activity increase, also the improvement of sludge thickening and dewatering properties was observed.

Better description of experimental results was obtained with three parameters model of particles mass flow density curve. Comparison of minimum sedimentation tank size necessary for gravitational separation of each sludge was used to examine sedimentation characteristics of activated sludge.

Sedimentation and thickening rates increase when appropriate structure of activated sludge floccules is reached due to the higher mineral portion. Metals precipitates act as enhancement thickening agents when compared with control activated sludge thickening. The best sedi‐ mentation/thickening characteristics were reached for sludge from bioreactor where Fe3+ salts were dosed, while the worst sedimentation characteristics were observed in sludge with Al3+ dosing.

Maintaining the required sludge age with simultaneous chemical precipitation of phosphorus and unchanged volume of activation tank is accompanied with higher sludge concentration in activation, which results in higher values of particles mass flow to sedimentation tank.

Application of iron salts seems to be the best option for intensification of biological stage in existing WWTP with chemical phosphorus precipitation. Problems with creating conditions for gravitational sludge separation may occur when aluminium salts are dosed as this sludge is characterised with small and slowly settling floccules.

Thickening characteristics of sludge were evaluated based upon thickening area needed to maintain the required sludge concentration in activation or that corresponding to maximum surface load in non‐dissolved substances.

The highest specific filtration resistance value was measured for activated sludge cultivated with iron salts doses, which is characterised also with the least throughput. The least value of specific filtration resistance was measured for sludge with iron salts dosing. Reference sludge was characterised by high throughput and low dependence of specific filtration resistance.

Precipitates in anaerobic digestion reactor resulted in partial inhibition of the methane generation. The concentrations of ammonium and volatile fatty acids increased, hydrolysis was stimulated, and methanogenic process was inhibited. The stimulation effect was measured for iron salts concentration lower than 400 mg L‐1. The feeding procedure of raw sludge into digestion reactors three times a day resulted from performed lab‐scale operation research on chemical precipitation of phosphorus impact on wastewater and sludge treatment processes as the most convenient one to eliminate significant level of sludge digestion process inhibition.

#### **Acknowledgements**

This work was supported by the Slovak Research and Development Agency under the contract no. APVV‐0656‐12. The authors would like to thank also for the support from the VEGA Grant 1/0859/14.

### **Author details**

Ján Derco\* , Rastislav Kuffa, Barbora Urminská, Jozef Dudáš and Jana Kušnierová

\*Address all correspondence to: jan.derco@stuba.sk

Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovak Republic

#### **References**

[1] Metcalf & Eddy Inc, Tchobanoglous G, Burton LF, Stensel HD. Wastewater engineering: treatment and reuse. 4th edition. Singapore: McGraw‐Hill; 2004. p. 1408

[2] Kayser R. Wastewater treatment with nitrogen and phosphorus removal. Water distribution and wastewater engineering manual. 3rd edition. Essen: Vulkan Verlag; 1989 (in German)

Application of iron salts seems to be the best option for intensification of biological stage in existing WWTP with chemical phosphorus precipitation. Problems with creating conditions for gravitational sludge separation may occur when aluminium salts are dosed as this sludge

Thickening characteristics of sludge were evaluated based upon thickening area needed to maintain the required sludge concentration in activation or that corresponding to maximum

The highest specific filtration resistance value was measured for activated sludge cultivated with iron salts doses, which is characterised also with the least throughput. The least value of specific filtration resistance was measured for sludge with iron salts dosing. Reference sludge was characterised by high throughput and low dependence of specific filtration resistance.

Precipitates in anaerobic digestion reactor resulted in partial inhibition of the methane generation. The concentrations of ammonium and volatile fatty acids increased, hydrolysis was stimulated, and methanogenic process was inhibited. The stimulation effect was measured for iron salts concentration lower than 400 mg L‐1. The feeding procedure of raw sludge into digestion reactors three times a day resulted from performed lab‐scale operation research on chemical precipitation of phosphorus impact on wastewater and sludge treatment processes as the most convenient one to eliminate significant level of sludge digestion process inhibition.

This work was supported by the Slovak Research and Development Agency under the contract no. APVV‐0656‐12. The authors would like to thank also for the support from the VEGA Grant

, Rastislav Kuffa, Barbora Urminská, Jozef Dudáš and Jana Kušnierová

[1] Metcalf & Eddy Inc, Tchobanoglous G, Burton LF, Stensel HD. Wastewater engineering:

treatment and reuse. 4th edition. Singapore: McGraw‐Hill; 2004. p. 1408

Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food

Technology, Slovak University of Technology, Bratislava, Slovak Republic

is characterised with small and slowly settling floccules.

surface load in non‐dissolved substances.

130 Operations Research - the Art of Making Good Decisions

**Acknowledgements**

1/0859/14.

Ján Derco\*

**References**

**Author details**

\*Address all correspondence to: jan.derco@stuba.sk


[16] Tuček F, Koníček Z. Calculation of secondary settling tank area and degree of thickening in the system activation tank – secondary settling tank. Vodní hospodářství. 1989; 6:152–

[17] Tuček F, Rešetka D. Determination of specific filtration resistance. Vodní hospodářství.

[18] Kossaczký E, Surový J. Chemical engineering I. Bratislava: Slovak University of

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[20] Yoshioka N, Hotta Y, Tanaka S, Naito S, Tsugami S. Continuous thickening of homo‐

[21] Derco J, Zarnovský L, Kuffa R, Liptáková E. Influence of iron and aluminium salts on activated sludge process during simultaneous precipitation of phosphorus. Pol. J.

[22] Derco J, Kuffa R, Kušnierová J, Fargašová A, Influence of phosphorus precipitants on

[23] Nielsen P. H., Adsorption of ammonium to activated sludge. Water Res. 1996; 30:762–

[24] STN 75 6401. Sewage treatment plants for more than 500 population equivalents. Slovak Standards Institute, Office of Standards, Metrology and Testing of the Slovak Republic;

[25] Spinoza L, Techniques and experiences in sewage sludge management. Proceedings Conference Water Protection and Waste Water Treatment, No.11, Portoroz; 1993.

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## *Edited by Kuodi Jian*

This book is dedicated to operations research of broad applications, such as improving informational bases of performance measurement with grey relational analysis, application of lean methodologies in a neurosurgery high dependency unit, iteration algorithms in Markov decision processes with state-action-dependent discount factors and unbounded costs, financial feasibility analysis of Natura Rab business case study, and mathematical modeling of isothermal drying and its potential application in the design of the industrial drying regimes of clay products.Operations research is an important topic. In addition to its obvious benefits of winning a war, making most profit in a business endeavor, and constructing a correct mathematical model, it also provides a tool for efficient use of natural resources. Furthermore, both theory and practice of operations research and its related concepts are covered in the book, and a reader can benefit from this balanced coverage.

Operations Research - the Art of Making Good Decisions

Operations Research

the Art of Making Good Decisions

*Edited by Kuodi Jian*

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