**3. Toward optimum design of industrial steam and power systems**

The concept of simultaneous process and utility design optimization was developed by Saudi Aramco protected by 2-granted patents. **Figure 3** provides an overview of the steps used for the optimization. In Refs [3, 4], the techniques used in optimizing new CHP systems are being derived from unit commitment and economic dispatch power generation concepts. Our optimization problem includes integer (binary), linear, and nonlinear relations between the objective function, variables, and constraints.

**Figure 3.** *Key elements of a steam system optimization tool.*

The problem formulation for a typical steam system can be summarized as follows: *Objective function* is the Net Present Value (NPV) for the new design, and it is a function of capital cost of equipment as well as the expected operating cost of the system configuration.

$$\text{Objective function} = \sum\_{i=1}^{n} \text{NPV} \left( \text{Capex}\_i + \text{Opex}\_i \ast \frac{Hrs}{yr} \ast LC \right) \tag{1}$$

Where,

NPV: Net Present Value for the project.

LC: Life Cycle of the new facility, normally used 25 years.

The total capital cost includes major equipment used in the optimization analysis as decision variables

$$\begin{aligned} \mathbf{x} &= \sum\_{i=1}^{n} \left( \mathbf{Capex}\_{\text{Blr}\_{i}} + \mathbf{Capex}\_{\text{Cogen}\_{i}} + \mathbf{Capex}\_{\text{STG}\_{i}} + \mathbf{Capex}\_{\text{STi}} + \mathbf{Capex}\_{\text{Motor}\_{i}} \right) \\ &+ \mathbf{Capex}\_{\text{RO}} + \mathbf{Capex}\_{\text{MED}}) \end{aligned} \tag{2}$$

Capital cost would be function of number and sizes of major equipment (i.e., decision variables for the optimization algorithm):


*Industrial Design Energy Efficiency and GHG Emission Reduction via Steam and Power… DOI: http://dx.doi.org/10.5772/intechopen.102544*

The total operating cost is function of the equipment performance and the impact on the energy consumption of the facility. The operating cost includes the following key elements:


In the optimization analysis, there are key constraints that have to be met by the optimizer to confirm the validity of the results. Some of these constraints are related to equipment limitations and others related to systems limitations. Below are some examples of the key constraints used in the optimization analysis:


Below is a generic mathematical representation for the steam system: Steam balance representation includes:

$$\text{Steam balance for a steam header (a)} = \sum\_{i=1}^{n} \text{Stm}\_{in} - \text{Stm}\_{out} \tag{3}$$

Where i and n are representing the equipment connected to this steam header. Boiler Feed Water (BFW) Balance is calculated as per the formula below

$$\zeta = \sum\_{i=1}^{n} Blr\_{BFW} + \sum\_{i=1}^{n} \text{Cogen}n\_{BFW} - \sum\_{i=1}^{n} DSH\_{BFW} \tag{4}$$

Makeup water compensates for all loses from steam system, thus makeup water is equal to all loses in the steam system.

BFW makeup balance is calculated as follows:

$$\mathbf{x} = \sum\_{i=1}^{n} \text{Proc}\_{\text{stm}} \ast (\mathbf{1} - \text{RC\%}) + \sum\_{i=1}^{n} \text{Blr}\_{\text{BD}} + \sum\_{i=1}^{n} \text{Cogen}\_{\text{BD}} + \sum\_{i=1}^{n} \text{Vent}\_{\text{stm}} \tag{5}$$

Whereas, BFW: Boiler feed water. B\_BFW: Boiler feed water to boilers. COG\_BFW: Boiler feed water to Cogen units. DSH\_BFW: De-super heater water into steam network. BD: Blow down flow. Bstm: steam generation from boilers. COG\_stm: steam generation from Cogen units. Steam users.

#### **Case study: grassroot facility.**

This section covers the (CHP) optimization assessment to identify the optimum configurations and equipment sizing for the supply side of a new petrochemical complex. References [5–7] include other examples, which can help explaining the concept further.

The assessment for the optimum configuration started with reflecting the utility's initial design data into a newly developed (CHP) for design. The CHP model key input is shown in **Table 1** summary.

For new facilities, 70% (HHV basis) is considered as the minimum efficiency of a site's overall CHP systems thermal efficiency. CHP systems' thermal efficiency for the site can be defined as the ratio between all useful energies generated by the system and total energy input as fuel:

$$\text{CHP system Thermal Effect} \cdot \%= \frac{\text{Useful Energy Out}}{\text{Energy Input}} \tag{6}$$

Where:

**Useful Energy Out =** Total net power generated by Cogen and STGs + total mechanical power recovered in the steam system by STs + total mechanical power driven by GTs + total heat consumed by process at different headers in (MMBtu/hr);

**Energy Input =** Total fuel consumed by the facility including boilers, Cogeneration units, simple cycle gas turbines, process heaters generating steam, other process heaters, and SEC equivalent fuel for imported power in (MMBtu/hr).

The CHP optimization study evaluated four design scenarios. The CHP analysis and its related economics considered the optimum configuration meeting operational and design requirement. The design requirement accounts for one steam supply unit under T&I and a trip of another unit. The CHP analysis covered the following cases:


*Note: Five different cogeneration frames from different GT manufacturers have been used for the CHP optimization analysis. This is just to give a better understanding and more accurate outcomes from energy efficiency point of view. It is worth highlighting that the analysis for each case is based on the average result of the different frames and not for any specific one.*

#### **Table 1.** *Process steam headers.*

*Industrial Design Energy Efficiency and GHG Emission Reduction via Steam and Power… DOI: http://dx.doi.org/10.5772/intechopen.102544*

1.Base Case: (5 Cogen Units – 1 standby boiler).

2.Case-1: (4 Cogen Units – 2 boiler Units).

3.Case-2: (3 Cogen Units – 3 boiler Units).

4.Case-3: (2 Cogen Units – 4 boiler Units).

Base Case: The base case composed of five gas turbines each with its heat recovery steam generator and two STGs and with one spare boiler, as shown in **Table 2**.

**Table 3** shows that the average CHP model's output from overall supply-side thermal efficiency is in the range of 69%, which is slightly lower than the minimum efficiency requirement of (70%).

Case-1: In this case, the CHP configuration includes four Cogen units, two boiler, and two STGs. The result showed that the average steam system efficiency for the different frames is around 70–73% (**Tables 4** and **5**).

Case-2: In this case, the configuration is composed of three Cogen units, three boilers, and two STGs, where the average steam system efficiency is around (74%) (**Tables 6** and **7**).


**Table 2.**

*Base-case scenario.*


#### **Table 3.**

*Base-case CHP model output.*


**Table 4.** *Case-1 design basis.*


#### **Table 5.**

*Case-1 CHP model output.*


#### **Table 6.**

*Case-2 design basis.*


#### **Table 7.**

*Case-2 CHP model output.*

Case-3: in this case, the CHP configuration composed of two Cogen units, four boilers, and two STGs resulted in steam system supply-side efficiency around 69%. The reason for having a larger STG in this case is to reduce the power import as much as possible (**Tables 8** and **9**).

To identify the optimum steam and power systems configurations for petrochemical complex, all options have been simulated via CHP optimization model as shown in the previous section.


**Table 8.** *Case 3 design basis.*


*Industrial Design Energy Efficiency and GHG Emission Reduction via Steam and Power… DOI: http://dx.doi.org/10.5772/intechopen.102544*

#### **Table 9.**

*Case-3 CHP model output.*

#### **Figure 4.**

*System efficiency summary of the different design configurations.*

**Figure 5.** *Base case: Petrochemical complex steam system CHP.*

**Figure 6.** *Case 3: Petrochemical complex steam system CHP.*

The study evaluated (4) different cases and compares the outcomes with the base case to identify the best configuration. In summary, in all cases there exist at least two GT frames that can meet the 70% minimum steam system efficiency requirement (**Figures 4**–**6**).
