**1.1 Previous works**

In a previous work [1], we have already developed a dynamical thermal modeling of solar collectors linked to a seasonal thermal storage (STES) system. The major

#### *Holistic and Affordable Approach to Supporting the Sustainability of Family Houses… DOI: http://dx.doi.org/10.5772/intechopen.103110*

advantage of this model is its simplicity. This model uses one-step time and explicit numerical scheme so that it can be programmed easily on any standard spreadsheet, instead of other complex three-dimensional codes (like TRANSYS). Besides, in this work was deeply discussed that a complex code is completely unnecessary for modeling STES systems based on well-insulated water tanks. On the contrary, it was demonstrated by using physical simplifications that such systems can be modeled as a zero-dimensional system, and so, this simplest (the so-called lumped-capacity model) spatial modeling can be used, in which all the water tanks can be considered at the same homogeneous temperature. Furthermore, this work has also demonstrated that a very refined time simulation neither is necessary, since a large (seasonal) storage system would have only slow variations of temperature (cooled during winter and heated during summer) and so, the STES yearly evolution can be perfectly modeled by using one-day time step. Beyond these useful simplifications, the major strength of this simple model is to provide a useful framework for modeling the solar system (a set of solar collectors) together with the STES system, which in turn allows us to takein-hand all the system parameters. These parameters comprise the solar collectors' parameters (their number, title angle, and their efficiency's equation), as well as the STES parameters (the water storage capacity, the insulation quality, and maximum/ minimum working temperatures). Hence, the analysis performed has surprisingly shown that the behaviors of the STES and solar systems are actually coupled. This way, we have found that a small short-term STES working with many vacuum-tube solar collectors can provide the same overall performance (that is, to fulfill the space heating demand during winter) that a huge seasonal STES working with many flat solar collectors, meanwhile the first design reaches a noticeably lower cost.

In this work will be summarized the major findings obtained in this previous work [1] as the starting point for the present analysis. On this, it will be studying a novel proposal that could enhance the performance of this novel design. It uses an overheated water tank (up to 120°C) instead of the 85°C level previously used, which creates a slight overpressure (2 bar) that can be withstood by using commercial stainless steel tanks. Besides, this proposal follows a holistic approach in order to include all the secondary heat demands related to a family living in a very cold climate location, besides the space heating demand that is concentrated during winter. These demands comprise the sanitary hot water demand, warming a greenhouse (from spring to autumn), and swimming pool (during summer). Therefore, a sustained demand throughout the whole year is created. This is a key to maximizing the production of energy from solar collectors since the small STES only can provide a shortterm (less than one month) storage capacity. This constraint was a serious drawback shown in the previous study, in which the surplus of solar energy produced by solar collectors must be avoided for ten months each year. Hence, we have realized that such kind of solar + STES system could be better utilized since it uses a very large number of solar collectors to fulfill the heating demand concentrated during winter, but its large potential for generating heat during the whole year is not exploited. Here was the starting point for the holistic approach (by including all the secondary demands of heat) studied here.

#### **1.2 Present development of the (solar plus thermal storage) technology**

During the last twenty-five years have been developed several testing projects of Seasonal Thermal Energy Store (STES) associated with a solar system based on many collectors for providing space heating to many houses (or department buildings) in

cold locations, mostly in Canada and Germany [2, 3]. These projects have shown this technology is feasible, although very costly.

The first and most important project that will be considered here is the well-known Okotoks' project, developed by the Drake Lake Solar Community in this place (51°N) within the Alberta State of Canada. This project intends to create a sustainable solar community, and their performances are available online by internet, as well as by several technical reports. For example, Sibbitt et al. [4] has recorded their (solar and thermal) performances. This project works since 2007 up today, and it provides annually 97% of the space heating demand to 52 well-insulated houses (117 kWh/m2 /y and 135 m<sup>2</sup> ea., in this very cold climate (average 5.2°C and 5,020 heating degree days defined according to [5]). This project uses 798 flat solar collectors (2,290 m<sup>2</sup> ) and a long-term storage system that heats the underground rock by means of 144 very deep (40 m depth) wells drilled covering over a 700 m<sup>2</sup> field (that is, covering a 28.000 m<sup>3</sup> volume of rock). This huge STES system is designed to provide seasonal storage (that is, the solar collectors accumulate heat during summer, and houses demand heat during winter), but this design (using the rocky underground) only achieves an overall efficiency of 60%, since there are remarkable heat losses from the reservoir (heated up to 90°C) to the surrounding ground. This huge long-term STES system works together with another short-term system based on 240 m<sup>3</sup> water tanks, which provides the household space heating by using under-floor water systems. This is the right choice in order to maximize the thermal capacity of the reservoir (working within the usable 85–35°C range, instead of working within the usable 85–60°C range when hot-water radiators are selected as the heating system). The solar radiation received on the 45°-inclined collectors (13,902 GJ/y) is collected with an overall 31% efficiency, and can effectively store solar energy only during the warm season [6]. The heating demand in Okotoks is very concentrated during four months (94%), which is a typical characteristic of cold continental climates. These figures present an exigent scenario for a STES system that explains the superlative cost (U\$173,000 per each house) of this project [7], mostly due to the extremely high cost of constructing the rock reservoir.

In previous work, we have already analyzed our novel approach for solving the heating demand of a single house on the Okotoks´ project. However, since this project uses a different kind of STES system, we need to state another two starting points for performing our study. For our purpose, just let us keep in mind the major parameters for every single house of the Okotoks' project: the cost (U\$173,000 ea.), the solar collector area (44m2 ), the rocky reservoir (538 m<sup>3</sup> ), and finally, the annual heating demand (15,795 kWh/y). These parameters will be useful for comparing after with other designs.

The second reference point considered here is the Friedrichshafen (48°N) project, working since 1996 in Germany for heating a department building. This project considered a STES system based on a huge (12,000 m3 and 20 meters height) underground water tank. This tank is also very heavy since it is built by using 60 cm-thickness reinforced-concrete walls that include a 1.2 mm stainless steel liner. Although this STES system is huge, it can satisfy, only partially (just 25%), the space heating demand of a multifamily building (23,000 m2 , 100 kWh/m2 /y) by using hot-water radiators. The solar system comprises 4,050 m2 flat solar collectors installed onto 38° inclined roofs [8, 9]. This project has preferred to use a huge water tank in order to reduce its area/ volume ratio and so their specific heat losses and cost. This goal was achieved when it is compared against other similar (but smaller) German projects. So, this (12,000 m3 ) tank achieves a lower specific cost (112 €/m3 ) than the Hamburg project (4,500 m3 ,

## *Holistic and Affordable Approach to Supporting the Sustainability of Family Houses… DOI: http://dx.doi.org/10.5772/intechopen.103110*

220 €/m3 ) and the Hannover (2,750 m3 , 250 €/m3 ) project [2]. However, due to its heavy mass and large depth, it is also very difficult to wrap this tank with standard isolative materials, which can withstand pressure up to 2 bars. So, the Friedrichshafen project has recognized heat losses of about 40% on this huge tank related to the lack of thermal insulation on its lower third (bottom and walls). Also by considering its heat losses of about 8% in the heat distribution system. This project shows the drawbacks of building a huge communal system, regarding our approach that designs a small system for each house. Besides, regarding the use of flat collectors working up to 90°C in cold climates, this project demonstrated that these collectors can achieve a poor average efficiency (30%). The total investment of this project (4 M€) is recognized by Bauer et al. [8] as a not cost-effective solution, regarding the low percentage (25%) of fossil fuel substituted. Let us note that by comparing the heat productions of the Friedrichshafen and Okotoks projects, the German project achieves an equivalent cost of about 128,000 dollars per Okotoks' house (considering an exchange conversion of 1.2 dollars per euro). So, even recognizing that the German solution is cheaper than Okotoks, it is not enough cheap to become an affordable solution by far. However, there are some interesting learned lessons obtained from these German projects; the feasibility of using water tanks as the main thermal storage system (the cost of this huge tank is about 66,000 dollars per each equivalent Okotoks' house), and the worse performance of using hot-water radiators instead of in-floor water as space heating system, regarding the poor yield obtained from flat solar collectors. The main parameters of this STES system can be calculated in order to compare against the Okotoks one, by taking its equivalent heating demand related to a single Okotoks' house (15,795 kWh/y). Hence, we can obtain: an overall cost of 128,000 dollars, STES water volume of 320 m3 , and solar collector area of 108 m2 . These poor numbers reflect the bad choice using a high-temperature heating system (hot water radiator instead of underfloor hot water) and shows the coupling effects between the three (solar, STES, and heating) systems involved.

The third project that we consider now as a reference point uses a small water tank for heating a single house. The Irish Galway project was initiated in 2006, [10]. It uses a 23 m3 underground water very well insulated (wrapped by an EPS layer of 60 cm thickness) and six vacuum-tube collectors (2 m2 solar area and costing €500 each one) for heating a single house (1,827 kWh/y) within a temperate climate (2,063 heating degree days). This project is important for us because it has demonstrated the economic feasibility of small solar+STES systems, which can reach reasonable investments (€ 28,344). In addition, from the detailed cost breakdown performed by Colclough and Griffiths [10], it is obtained a good starting point for developing now our economic analysis. For example, this project has shown that large fixed costs (€4,300) related to the many auxiliary systems (temperature sensors, valves, piping, controller, pumps, etc.) required, and the same fixed cost will be considered in our project.

Besides, the Galway's project provides some useful lessons:


3.The falling prices of solar collectors and the relatively high cost of the solar installation (€900), has been recognized by Colclough as a reason for installing more collectors since the installation cost is almost a fixed cost. Following this concept, Colclough, Griffiths, and Smyth [11] have estimated by numerical calculation that the solar fraction of the heating demand could be increased by 50% by doubling the number of solar collectors, which implies a modest extra investment of €3,000 when it is compared against the overall cost.

Regarding the last point from Colclough, we can expect significant improvements by performing an economical optimization on the number of collectors. This analysis should be done by considering the performance of both, the solar system and the STES system. However, at present, there is not any modeling tool available for this purpose. Most of the works have performed thermal models of STES by using complex numerical codes, like TRNSYS or ANSYS [11–13]. However, regarding the high complexity of these tools, we have realized that these codes are not suitable for modeling altogether the solar and thermal behaviors and for taking all-in-hand its parameters, as it is provided in this work by developing an explicit numerical model. Otherwise, the TRNSYS and ANSYS codes are suitable for modeling systems having two main characteristics:


The first characteristic is not actually relevant for modeling large-term (as seasonal) STES systems, in which the evolution of the tank temperature is very slow, according to the high ratio between energy stored and energy demanded every day. Therefore, in such kinds of systems is not necessary to consider time steps shorter than a day. The second characteristic is relevant for modeling huge underground STES systems, in which their large weight forbids us to insulate their bottom part as it occurs in the aforementioned Friedrichshafen's project. However, this is not the case with small tanks, as it is proposed here. Those heavy STES systems suffer noticeable heat losses, and high-gradient temperature profiles, in both, radial and axial directions. On the contrary, this behavior can be neglected within small well-insulated tanks, as the Galway project has demonstrated [10].

From these findings, we have developed a simple lumped-capacity thermal model for water tanks, which assumes that both (radial and axial) temperature profiles can be neglected and so, all the water can be considered as having the same (homogeneous) temperature. The axial profile can be minimized by putting the source heat exchange below the sink one (this is the opposite configuration usually used in huge tanks, which is created a stratified temperature profile in order to minimize the heat losses about the not-insulated bottom part of the tank), and so, causing a freeconvection flow that counterbalances the stratification, as the Galway's project has conveniently used [11]. In addition for aboveground tanks, there is a uniform boundary condition (the outdoor temperature) that helps to create a homogeneous axial profile. So, the radial temperature profile could be neglected in small tanks; indeed, this effect not solely depends on the tank size. Regarding the very-well known thermal behavior related to the heat conduction within a body surrounded by a fluid

*Holistic and Affordable Approach to Supporting the Sustainability of Family Houses… DOI: http://dx.doi.org/10.5772/intechopen.103110*

convective cooling [14], the diffusion of heat along the radial axis is complemented by the convective heat losses at the outside surface of the tank: In "large" tanks the heat diffusion is relevant and the convective heat transfer can be neglected. Meanwhile, the opposite behavior occurs in "small" tanks; but, indeed, their relative importance (their quotient) is actually represented by the dimensionless Biot number:

$$\text{Bi} = h \,\, \text{D} / \lambda\_w \tag{1}$$

where *h* is the convective coefficient of heat transfer (at the external surface of tank), *λ<sup>w</sup>* is the thermal conductivity of water, and *D* is the tank diameter. In general, problems involving Biot <1 (in which the heat diffusion within the tank can be neglected) are simple, since they can be considered that the temperature field within the tank is homogeneous [14], and so, the single thermal resistance (and temperature variation) to be considered is the one related to the boundary convective layer. Let us note that for well-insulated aboveground tanks, the convective coefficient (*h*) does not involve solely the thermal resistance of the convective film layer; otherwise, it rather than represents the thermal resistance of the insulation layer (that is, the major thermal resistance involved here), defined by its thermal transmittance (*U*). The reader can check that for the largest tank considered here (*D* = 3 m, *λ<sup>w</sup>* = 660 W/K.m, *U* = *h* = 0.1 W/m<sup>2</sup> K), it is verified that Bi <1. Indeed, even observing some minor temperature difference, as the 2°C difference measured in the Galway's tank [10], it must be considered that the actual temperature of the tank's surface is always lower than the mean temperature of the tank, and so, this homogeneous model is conservative for estimating the heat losses. Besides, by placing the sink heat exchanger on the central axis, the heat is delivered to the house with a temperature higher than the average, and so, this model is again conservative.

## **2. Solar and thermal modeling**

#### **2.1 New system design**

This conceptual design considers many vacuum-tube solar collectors for heating one water tank up to 120°C in order to provide space heating by water in-floor system. Regarding previous works (up to 85°C), this overheating can be achieved with a modest tank overpressure (2 bar) that can be easily withstand by commercial stainless steel tanks (designed with a relief valve at 3 bar), meanwhile, this tank doubles the useful heat capacity (from 120–33°C) of previous tanks (from 85–33°C). So, the water-glycol mixture is heated up to 125°C and the in-floor system is cooled up to 28°C in order to maximize the working range of temperature within the tank, by considering a 5°C temperature jump in both heat exchangers, similarly to the Galway's project. This 5°C difference is enough for using standard tubular-copper exchangers that provide the demanded (�10 kW) heat power while getting affordable costs [15].

On the other hand, our design intends to use a small tank having a storage capacity of between two to four weeks for the winter heating demand. A smaller tank has a lower cost and also, a smaller total area, which in turn implies lower heat losses and insulation cost. This small tank is designed to be heated only around one month previous to the winter demand in order to be ready for this exigent demand, but most part of the year this tank is actually not used, meanwhile the vacuum-tube solar collectors are used for heating the secondary demands. Let us note that, this kind of

collector has a remarkable ability for collecting energy even during cloudy days. For instance, according to measured data of the vacuum-tube collector manufactured by Apricus, its yield during cloudy days is 25% of the yield obtained during clear days [16]. On the other hand, a flat collector would have a negligible yield during cloudy days, and even on sunshine days during cold winters.

#### **2.2 Solar collectors modeling**

The use of vacuum-tube collectors in order to maximize the solar yield during winter is a key within this design, instead of the flat collectors usually used in these tested projects. This point will be discussed now by considering the efficiency curve of commercial vacuum tubes and flat solar collectors (see **Figure 1**), which are provided by the European Solar Industry Federation [17]. The instantaneous efficiency (*η*) of any solar collector can be approximated by its optical efficiency (*a*0) and their linear (*a*1) and quadratic (*a*2) heat-losses coefficients, as is described by Eq. (2). Here,*Tm* is the mean temperature of collector, which receives normal solar flux, *In* (W/m2 ), and *Ta* is the ambient temperature [18].

$$\mathbf{u} = \mathbf{a}\_0 - \mathbf{a}\_1 (\mathbf{T}\_\mathbf{m} - \mathbf{T}\_\mathbf{a}) / \mathbf{I}\_\mathbf{n} - \mathbf{a}\_2 (\mathbf{T}\_\mathbf{m} - \mathbf{T}\_\mathbf{a})^2 / \mathbf{I}\_\mathbf{n} \tag{2}$$

Let us note in Eq. (2) that both heat-losses terms are divided by the normal irradiation (*In*). Hence, regarding that flat collectors have higher heat-losses coefficients than vacuum-tube ones, this effect (penalizing flat collectors) is minimized in **Figure 1** by considering a very high (800 W/m2 ) *In* value, for which both curves intersect at 70°C (by taking the gross area for the vacuum-tube collector, which is another subjective decision that clearly favors flatting collectors). However, this value does not represent by far an actual average condition. Although this flux could be observed as the total solar irradiation (*I*) on clear days, a flat collector would obtain

**Figure 1.** *Efficiency curve for different kinds of solar collectors.*

*Holistic and Affordable Approach to Supporting the Sustainability of Family Houses… DOI: http://dx.doi.org/10.5772/intechopen.103110*

this flux as its normal projection (*In*) only at noon (when its azimuthal angle is null) and twice along the year (when the elevation angle of the sun above the horizons matches normally the collector's tilt angle). Therefore, it is more accurate to consider both efficiency curves for lower *In* values. For instance, **Figure 2** are illustrated the efficiency curve for both collectors working on *In* = 400 W/m<sup>2</sup> and 200 W/m<sup>2</sup> , for which are obtained intersecting points of 34°C and 17°C, respectively. These results show that, in these cases, the flat collector almost never gets higher efficiency than the vacuum-tube collector. In addition, for this last case (*In* = 200 W/m<sup>2</sup> ), the flat collector cannot get energy for temperature differences higher than 37°C, meanwhile, the vacuum-tube collector still gets a remarkable 36% efficiency in this case.

Let us remark that these low values of solar normal flux do not represent necessarily a cloudy-day condition. For example, let us consider now a fully sunny winter day (*I* = 800 W/m<sup>2</sup> ) in the Friedrichshafen project (having 38°-inclined collectors) at 4 pm, that is, when the elevation angle of the sun over the horizon is 2° and thus, the zenithal-angle of the sun with the collector's normal is 50°. For this condition, the sun rays present an azimuthal angle of 60° onto a south-oriented flat collector. So, the product of their cosines (cos60° x cos50° = 0.32) leads to getting a normal irradiation flux over the flat collector *In* = 257 W/m<sup>2</sup> , for which the maximum temperature difference, this flat collector could reach is 47°C. Therefore, it can be inferred that this flat collector always would obtain negligible winter yields working with 55°C hotwater radiators, as was observed in the Friedrichshafen's project. Otherwise, in this case, the vacuum-tube collector gets 34% efficiency, which is calculated by taking *In* = 514 W/m<sup>2</sup> , regarding that for this case, the azimuthal projection (cos60°) must not be considered, due to this cylindrical geometry. This comparison can be extended, for example, to a fully sunny summer day at 4 pm when the elevation angle of the sun is 17° and then, the azimuthal angle over collectors is 35°, leading to *In* = 327 W/m2 for the flat collector and *In* = 654 W/m<sup>2</sup> for the vacuum-tube collector.

Therefore, following the previous discussion, we can conclude that **Figure 2** induces us to make a huge mistake that is to compare both collectors as working on the same *In* value. Another way of saying this is that the crossing-point of both curves cannot be used at all as a criterion for comparing the performance of flat and

**Figure 2.** *Efficiency of flat and vacuum-tube collectors (*In *= 400 and 200 W/m<sup>2</sup> ).*

vacuum-tube collectors. Let us note that a flat collector receives a variable azimuthally-projected solar area along the day, meanwhile, a cylindrical collector always offers the same azimuthally-projected solar area. Although a full discussion of this issue depends on many factors, such as the day of the year and the latitude of the location, etc., maybe we could consider now a useful analogy. Regarding the total solar energy received along the day (*G*, kWh/m<sup>2</sup> ), the flat collector can be represented by a fixed PV panel, and meanwhile, the vacuum-tube collector could be represented by another PV panel mounted onto a one-axis solar-tracking system. Hence, we can compare the yield of both collectors by using the well-known result that the one-axis tracking PV panel produces about 30% more energy than the first fixed PV panel [19]. Therefore, and taking into account that our solar model calculates the *G* received for tube collectors and not for flat collectors (see the solar\_trajectory.xls file in [20]). It will be conservatively estimated the *G* values received by flat collectors by reducing 25% the *G* values calculated for cylindrical collectors. And now, let me be completely clear about this point. In my opinion, it is completely unforgettable that most solar researchers have traditionally neglected this mismatch behavior between flat and vacuum-tube collectors; I guess that this is due to some aversion against vacuum-tube solar collectors, which mostly are manufactured in China. However, and in order to be fair for both kinds of collectors, I have to note also that vacuum-tube solar collectors have a major drawback, regarding their concerns about overheating, which potentially can be very dangerous (especially considering heat-pipe collectors with an integrated water tank above vacuum tubes), but, precisely this kind of solution as is studied here (by using large water tank and controlling system) should be the "silver bullet" for this weakness. In my opinion, from the selection of flat solar collectors within most projects performed up today, we can realize that this aversion exists. As we will discuss here, the huge costs reached for all projects performed up today (by using a huge STES system) are related to this choice, and this is the major cause of the failure of this technology. A failure that may cannot be overpass in the future, since nowadays is been coming to another solar technology with a better perspective for solving the heating household demand. This novel technology is the air/water heat pump (having efficiencies around 400%) that can be linked with photovoltaic panels in order to get a sustainable solution, as well as the proposed (solar + STES) technology, does.
