Thermal response test numerical modeling using a dynamic simulator
 Sara Focaccia^{1, 2}Email author
Received: 12 June 2013
Accepted: 26 August 2013
Published: 11 September 2013
Abstract
Background
Borehole heat exchangers are a growing technology in the area of house/building air conditioning, most of all in northern Europe.
Methods
In order to have a good project, we need to have a reliable value of ground thermal conductivity, which is normally obtained by interpreting the data retrieved by running a thermal response test. Different are the ways of interpreting the data provided by the test (e.g., infinite line source theory, finite line source theory, etc.), and in this paper.
Results
We will first simulate a thermal response test using finite element subsurface flow system, a heat and flow dynamic simulator.
Conclusions
Then, a sensitivity analysis of the effect of the different grout properties on the results of a thermal response test is shown.
Keywords
Background
Borehole heat exchanger technology is growing in Europe, and its applications are present as well in the southern part of Europe, namely in Spain and Italy. In contrast to the northern part of Europe (for example, the Scandinavian regions), the typical shallow ground in the southern part of Europe is not made of rocks (granite, basalt), but it is composed mainly of loose materials (sand, clay, marl, etc.). This fact complicates the application because of drilling issues, the reduced homogeneity of the soil, and lower thermal conductivity.
Spatial variability of the geological properties and spacetime variability of hydrogeological conditions, specific to each installation, affect the real power rate of heat exchangers and consequently the amount of energy extracted from/injected into the ground. For this reason, it is not an easy task to identify the underground thermal properties to be considered when designing (Witte and van Gelder 2006).
If the test is run for around 3 days, it is impossible to have a full characterization of the involved area, simply because TRT characterizes only the neighborhood of the heat exchanger at hand and just for the test duration. In fact, the 3D/2D variability of the thermal properties through the whole reservoir cannot be studied if just one test is available, which is the standard practice. Such variability can be an important concern if a multiborehole geothermal field has to be implemented. Moreover, the temporal variability of groundwater level could change the equivalent thermal properties of each heat exchanger (Lee and Lam 2012). Nevertheless, TRT is the most adequate, popular, and efficient tool for identifying the parameters to be considered when designing the BTES system.
As a matter of fact, TRT data can be considered as a thermal production test on the studied area. As there is a wellknown parallelism between the oil and gas case and groundwater production wells (Raymond et al. 2011) and as it is clear the parallelism between the geothermal heat exchanger and groundwater production wells, we can therefore find a similarity between the oil and gas tests and the thermal response test. In fact, in both cases, we have a sort of production test, which is, for the former, a well test, while for the latter, the TRT. Through these tests, we want to obtain the most important parameters for our cases: hydraulic conductivity, porosity, and saturations for the oil and gas case; and ground thermal conductivity, ground volumetric heat capacity, borehole thermal resistance, and undisturbed ground temperature for the geothermal problem.
Starting from these assumptions, it is correct to apply to the shallow geothermal reservoirs the same tools and techniques used for fluid reservoirs, tailored on the heat exchange issue. That is why we adopted the approach of inverse modeling (MataLima 2006) for reservoir characterization, typical of oil and gas field analysis, given the existing similarities. The software used to develop the dynamic simulation is FEFLOW 6.1 (finite element subsurface flow system) (AlKhoury et al. 2010). In this study, a geostatistical reservoir model has been set up based on the studies on thermal properties and spatial variability hypotheses, and a real TRT has been tested.
Methods
Modelization of an oil reservoir requires the characterization of both the formation field (lithology, permeability, porosity, saturation distribution, etc.) and fluid mobility properties (MataLima 2008). Moreover it requires the knowledge of production data for modeling the internal properties of the reservoir. Normally, in a simple problem of porous flow, a progressive mathematical modeling (forward modeling) is used, in which it is assumed that the underground properties and the initial and boundary conditions are known.
In reality, the information characterizing the entire spatial domain in the considered case does not exist; on the other hand, indirect methods used to obtain data give us secondary information (soft data) that needs a joint validation with primary information (hard data). This information furnishes the spatial distribution of the reservoir properties.
 (1)
Probabilistic or stochastic (with static data)
 (2)
Deterministic (with dynamic data)
 (3)
Emergent (combining previous methods).
If in reservoir engineering, the system is physically inaccessible, emergent methods are used, coupled with inverse modeling to characterize its petrophysical properties. In its general form, an inverse problem refers therefore to the determination of the plausible physical properties of the system, or information about these properties, given the observed response of the system to some stimulus (Oliver et al. 2008).
In a geostatistical approach to the inverse problem, a set fine grid values of permeability and porosity is perturbed in order to match the synthetic response of the model with real production data (MataLima 2008). The biggest advantage of this method is that by perturbing the images (previously created through a geostatistical process as different realizations of the same variable), we preserve the spatial distribution of the data as revealed by variograms and distributions of the original variables (Hu 2002; Hu et al. 2001).
By applying this technique to the geothermal case, we will create different realizations of thermal conductivity (through a direct sequential simulation; Soares 2001), and we will find which one is the best to fit the real production data (temperature evolution along time). The software used to develop this procedure is FEFLOW 6.1.
The whole process of the inverse problem applied to the shallow geothermal exploitation suffers the problem of lack of thermal conductivity measurements. In fact, up to now, there are no well developed and inexpensive technologies for direct measuring, in laboratory and on site, of ground thermal properties. For rocks, the technology is much further developed. Moreover, the thermal conductivity maps are being developed in few regions.
 (1)
To give heterogeneity to our reservoir (accurate grids)
 (2)
To quantify uncertainty through different models with the same heterogeneity
 (3)
To integrate different types of data at different scale and precisions (hard and soft data) through cokriging and cosimulations.
The resolution method proposed for this kind of problem is an algorithm of inverse modeling whose objective is reservoir characterization by the integration of dynamic data in stochastic modeling using direct sequential simulation (DSS) and cosimulation as a convergent process of global and regional perturbation of the permeability images. This algorithm allows obtaining a spatial distribution of the reservoir permeability which respects both static data (variogram and histogram of permeability distribution in the stochastic model) and dynamic data (flux in the observations boreholes).
 (1)
Stochastic modeling of the reservoir properties is made by the facies geometry simulation and by the petrophysical properties distribution in the facies exploiting geostatistics
 (2)
Dynamic modeling of the reservoir fluids, based on energy and mass conservation laws, Darcy law, dynamic models equation (state equation), and relationship between relative permeability and capillary pressure. This simulation model is composed by:
 (a)
Equation regulating the fluid dynamics
 (b)
Maps to define the study area
 (c)
Data describing the area and the parameters
 (d)
Initial and boundary conditions.
Creation of the stochastic model of thermal properties
In order to represent the variability of the natural medium, we need to perform geostatistical simulation of the parameters characterizing the soil (Bruno et al. 2011). We decide to neglect the simulation of thermal capacity because its variability is very low, and it does not influence much the dynamic simulation of the reservoir. On the other hand, the thermal conductivity is the most important parameter controlling the dynamic simulation, and that is the reason why we will proceed in its geostatistical simulation.
Different are the types of simulation that could be used for the purpose: the chosen one is the direct sequential simulation (Soares 2001). In this simulation, no transformation of the original variable into a Gaussian one is needed (in contrast to the sequential Gaussian simulation), which lets us deal with different types of initial distributions of the properties. The simulation has the objective of using local averages and variance for resampling the global distribution law.
VDI information about thermal conductivity of different type of soils
Sandstone  Saturated clay  Dry clay  Limestone  Marl  Saturated sand  Dry sand  Clay scists  

Average  2.3  1.7  0.5  2.8  2.1  2.4  0.4  2.1 
Minimum  1.3  0.9  0.4  2.5  1.5  1.7  0.3  1.5 
Maximum  5.1  2.3  1  4  3.5  5  0.8  2.1 
Variance  1.267  0.467  0.2  0.5  0.67  1.1  0.17  0.2 
The simulations of thermal conductivity were run on a domain of 60 × 60 × 125 meters, using some fictitious data obtained from a borehole (these data were created randomly by knowing the average, maximum, and minimum per soil). The software used for running the geostatistical simulation was GeoMS, a geostatistical tool developed by the Centre for Natural Resources and Environment of Instituto Superior Técnico of Lisbon.
After that, the data from the six boreholes were analyzed geostatistically (average, variance, and variogram), and by using them as input, other geostatistical simulations were run (DSS) in order to obtain different realizations from the same thermal conductivity data and for the same study area.
Dynamic modeling of thermal response test using FEFLOW
FEFLOW is a dynamic flow simulator that includes also a module for BHE modeling and simulation. In the new version, 6.1, the boundary conditions of BHE were improved, and they now allow defining directly the inlet temperature (as constant or transient value) and differentials of power or temperature to represent the operation of heat pumps. Moreover, it is possible to create arbitrary connections between the inlet and outlet pipes of the BHEs, both parallel and serial.
Fluid, grout and borehole properties
BHE  Value  Fluid  Value  Grout (bentonitic mortar)  Value 

Type  Double Utube  Mass density  1000 kg/m^{3}  Thermal conductivity  0.347 to 0.386 W/mK 
Borehole diameter  0.127 m  Thermal conductivity  0.52 W/m·K  Volumetric thermal capacity  1.704 M J/m^{3}∙K 
Length  100 m  Specific heat capacity  4186 J/kg·K  Density  1420 kg/m^{3} 
Outer pipe diameter  0.032 m  Dynamic viscosity  0.001 kg/m·s  Thermal resistance  0.018 to 0.02 m^{2}∙K/W 
Wall thickness  0.0029 m  
Pipe thermal conductivity  0.4 W/m·K  
Volume flow rate/pipe  36 m^{3}/day 
From the stratigraphic point of view, in this case, we have a very simple one:

0 to 1.5m dry clay with a thermal capacity of 1.6 MJ/m^{3}K

1.5 to 100m marl with a thermal capacity of 2.25 MJ/m^{3}K (there are some small infiltrations of water between 60 and 65m depths).
The average inlet temperature of the test was 30.82°C, while that of the average outlet was 27.2°C. As an input for the simulator, we have to enter a reference temperature for the test, which is 30°C, an average flow rate which corresponds to 36 m^{3}/day (1,500 l/h of circulating water with Re = 20.248, turbulent flow), and a variable heat input rate (that will be the one used in the real thermal response test).
The FEFLOW model comprises an area of 60 m × 60 m and a depth of 125 m, divided into 21 layers, the first 20 of 5m thickness, while the last one of 25m thickness (creating the bottom boundary condition for the borehole heat exchanger). The first layer of 1.5 m of clay was neglected in the model, and all the volume was set as marl.
The thermal conductivity values for all the different layers were used, the ones obtained by running direct sequential simulations on GeoMS and whose calculations were described in the previous paragraph. There is no groundwater. The BHEs are disposed in a circular line inside the domain area; each of them has the same inlet temperature which is the same as that of the thermal response test run. In this way, we will try to reproduce the TRT in different parts of the domain, showing if FEFLOW manages to reproduce a thermal response test and if there are differences in the response due to the local variability of ground thermal conductivity.
Results and discussion
The shape of the curve is exactly like what we have in the real TRT, but the temperature shows a systematic difference of almost 1°C between the two curves. The difference between the real curve and the simulated ones oscillates within 4% and 8%; the simulated curve is always higher than the real one. The results obtained with the infinite line source analysis are that the borehole thermal resistance is 0.08 K·m/W, while the ground thermal conductivity is 1.65 W/m·K.
When comparing the results obtained with different images of thermal conductivity, the difference is very low (less than 1%), and it does not affect the thermal response test curve. As we are considering a homogeneous geology, in this case, it is more interesting to focus on the variation of the curve due to the changes in terms of the borehole characteristics.
Input parameters for the different simulations
Simulation 1  Simulation 2  Simulation 3  Simulation 4  Simulation 5  Simulation 6  

Grout thermal conductivity (W/m·K)  0.4  2  1  2  2  1 
Reference temperature (°C)  30  30  32  30  28.5  32 
Underground temperature  Variable  Variable  Variable  Constant (14.6°C)  Constant (14.6°C)  Constant (14.6°C) 
Concluding the remarks about this sensitivity analysis, we can conclude that whether or not we change the reference temperature, the results will remain the same; on the contrary, if we play with the grout thermal conductivity, we will for sure experience a variation in the borehole thermal resistance and in the ground thermal conductivity.
Thermal characteristics of a house case study
Characteristics  Values 

Peak winter energy load (kW)  60 
Peak summer energy load (kW)  −80 
Heating equivalent hours per year (h/y)  1.600 
Cooling equivalent hours per year (h/y)  950 
Average COP  4.7 
Peak COP  3.8 
Heat pump input/output water temperature in winter (°C)  6 to 2 
Heat pump input/output water temperature in summer (°C)  27 to 32 
Average EER  4.05 
Peak EER  3.3 
Results for the house case study
Borehole length (summer)  Borehole length (winter)  

Case a  1,418  933 
Case b  1,488  975 
Difference (%)  5%  4.5% 
As we can see from this example, the bigger the project, the greater the difference; of course, if we are dealing with a singlehouse application, there will be a less than 5m difference for the single borehole needed.
It is, therefore, possible to conclude that the grouting (and then the borehole thermal resistance) plays a very important role in the calculation of ground thermal conductivity, and it has to be taken into account while evaluating the TRT results (BorinagaTrevino et al. 2013).
Conclusions
This paper has shown that the problem of defining the thermal properties of a shallow geothermal reservoir is a complex one. The traditional methodology for reservoir characterization is simplified because it ignores the space time variability and the linked uncertainties; therefore, for a robust analysis, new probabilistic approaches are needed.
Particularly, in this paper, a geostatistical approach was proposed to get the best image of a ground thermal conductivity for shallow geothermal applications. In practice, an inverse approach is applied on the case of a thermal response test (which can be seen as a production test in the oil field) in order to get the image of thermal conductivity of the area involved in the test. As the case considered was a very simple one, with homogeneous ground geology, we were only able to verify that there is a good reconstruction of the shape of the thermal response test curve, with all the geostatistical models. Knowing that, a sensitivity study was developed in order to understand which parameter is the one that most influenced the test and how it changes the results. It was seen that one of the most influential parameters is the grout thermal conductivity of the borehole, which can change the results up to a 10% of the ground thermal conductivity from one simulation to another. This leads to a 5% difference in the borehole length.
Declarations
Authors’ Affiliations
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