# 3DHIP-Calculator—A New Tool to Stochastically Assess Deep Geothermal Potential Using the Heat-In-Place Method from Voxel-Based 3D Geological Models

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Background of the HIP Method

^{3}), $\varnothing $ is the rock porosity (parts per unit), $\rho $ is the rock density (kg/m

^{3}), C is the specific heat capacity (kJ/kg·°C), and the F and R sub-indexes account for the fluid and host rock, respectively. Tr is the reservoir temperature (°C) and Ti refers to either the re-injection, reference, or abandonment temperature (°C). Therefore, Ti can refer to the threshold of economic or technological viable temperature, the ambient temperature (i.e., the annual mean surface temperature value), or a temperature value defined according to other criteria [11]. Equation (1) is solved within the 3DHIP-Calculator for each voxel in the model that satisfies the condition that $\left(Tr-Ti\right)\ge 5\xb0\mathrm{C}$. Otherwise, the HIP for that voxel is not evaluated and is set to zero. The HIP is expressed in kJ.

_{e}, in parts per unit) is used to incorporate the effect of the efficiency of the heat exchange from the geothermal fluid to a secondary fluid in a thermal plant. C

_{e}can vary as a function of geothermal exploitation (e.g., heat or electricity production). Finally, since most of the direct heat applications of geothermal energy (such as district heating, greenhouse heating, etc.) do not operate continuously throughout the year, a plant factor (P

_{f}, in parts per unit) is included. This factor considers the fraction of the total time in which the geothermal plant is in operation. Thus, Hrec is expressed in kW.

#### 2.2. Mathematical Background of the Monte Carlo Method

#### 2.3. Program Description

^{®}(v. R2019b) [44] based on the MATLAB App Designer, and then compiled for Windows as a standalone application. The installation files, as well as the user manual and examples, can be freely downloaded from the “Deep geothermal energy” web page of the Institut Cartogràfic i Geològic de Catalunya (ICGC) (under the Creative Commons license Attribution 4.0 International, CC BY 4.0). The source code can also be downloaded from https://github.com/OpenICGC/3DHIP-Calculator (accessed on 15 October 2021).

#### 2.3.1. Pre-Processing: Input Data

_{0}+ ΔT × Dz

_{0}is the mean annual surface temperature, ΔT is the measured thermal regional gradient in C/km, and Dz is the depth z of the target according to the preliminary 3D model. This approach assumes a conductive steady-state regime and is indicated for geothermal plays in passive tectonic settings where no asthenospheric anomalies occur [45].

^{3}) and porosity (parts per unit) that can vary for each voxel. The 3DTM should include the voxel coordinates (X, Y, and Z), the temperature (in °C), and the temperature standard deviation (in °C) for each voxel. The temperature standard deviation is an optional parameter that can be set to zero if it is unknown. Furthermore, the voxel position and resolution (in X, Y, and Z) of the geological and thermal models must be identical and match each other.

^{®}(Paradigm), or GemPy, an open-source 3D geological model based on Python [46], among many other packages able to export 3D models in this format. The files for the testing case presented in this paper were generated using GeoModeller3D (v4.0.8).

#### 2.3.2. Post-Processing: Output Data

- Generate a CDF for each voxel, from which a probability 10% (P10) (very low confidence of the estimation and high values), P50, and P90 (high confidence of the estimation and low values) are extracted. Furthermore, the mean and standard deviation are also calculated.
- Generate a CDF for the entire investigated target (e.g., geological unit, reservoir, etc.) summing the voxel values, and the P10, P50, and P90 are calculated. This approach is only used for the HIP calculation and not for the Hrec one.
- Generate 2D maps using the relationship between the vertical sum of the values calculated in each voxel with respect to the area occupied by the voxel (in km
^{2}). The P10, P50, and P90 of HIP and Hrec are then estimated. - The application allows exporting two ASCII files with all results for further post-processing and generates an automatic report that summarizes the input data and the main results.

#### 2.3.3. Modeling Scenarios Depending on Data Availability

## 3. Example Case Study—The Reus-Valls Basin (NE, Spain)

#### 3.1. Geological Setting

**Figure 4.**Geological map with the delimitation of the Reus-Valls Basin (modified from [50]). Source of EU map: © EuroGeographics for the administrative boundaries, European Commission, Eurostat/GISCO.

#### 3.2. The Potential Hot Deep Sedimentary Aquifers

#### 3.2.1. Example 1: Using a Single-Voxel 1D Geological Model

#### 3.2.2. Example 2: Using a 3DGM but Not a 3DTM

^{2}(see Figure 6 for an example of HIP). In these maps, the voxels with a zero value were left without color. Finally, the results can be exported to GIS software packages for post-processing (e.g., QGIS), as shown in Figure 7, where an isoline map of the HIP_P90 is plotted to highlight the probability results.

^{2}) is concentrated near the Vinyols town (Figure 7). This region coincides with the zone where the RVB is deeper and Triassic attains its higher thickness at the regional scale. This spatial distribution of the results shows not only an estimation of the geothermal potential but also reveals where the prospective zones for geothermal energy production are located within the RVB. This demonstrates the importance of using 3D georeferenced data as inputs, containing the spatial geological information in three dimensions.

#### 3.2.3. Example 3: Using Both a 3DGM and a 3DTM

^{2}) were observed southwest of the basin, concentrated around the town of Vinyols. However, in this scenario, the estimation of HIP values was sensibly lower than those of the previous example. This is because the 3DTM mean gradient is lower than that of the previous scenario.

#### 3.2.4. Example 4: The Use of the Recoverable Heat (Hrec) Values

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**3DHIP-Calculator workflow. It is divided into six main steps: (1) input values, (2) reservoir selection and parameters, (3) HIP and Hrec computation, (4) HIP probability curve, (5) HIP and Hrec probability maps, and (6) export data (modified from Herms et al., 2021 [34]).

**Figure 3.**Internal structure of the data files of the voxel-based geological (

**A**) and thermal (

**B**) models that the 3DHIP-Calculator needs to be imported.

**Figure 5.**(

**a**) Depth–temperature distribution for the Triassic unit using a linear geothermal gradient (example 2). Each blue circle corresponds to a temperature value of each of the voxels that discretize the Triassic unit. The red lines indicate the fixed depth range for the HIP and Hrec calculations. (

**b**) Petrophysical and operational properties, and the corresponding PDFs used for this example. On the right-side: the HIP histogram and its CDF (blue curve) with the P10 (red line), P50 (blue line), and P90 (green line) for the entire targeted reservoir.

**Figure 6.**2D maps of the HIP results of the P10, P50, and P90, and the temperature distribution at the top of the Triassic units below the pre-fixed depth range. For the HIP parameters, the values were calculated as an integration over the depth range and normalized by the voxel area. Units are in PJ/km

^{2}and °C, respectively.

**Figure 7.**The HIP with P90 for the Triassic unit (example 2). The map was plotted with constant contour lines (20 PJ/Km

^{2}) following the described second example (i.e., with a 3DGM but not a 3DTM).

**Figure 8.**Altitude with respect to the temperature distribution for the selected target in example 3 (Triassic unit). Each blue circle corresponds to a voxel temperature value within the target reservoir. The red lines indicate the depth range fixed for performing calculations.

**Figure 9.**2D distribution map of the top, base, and vertical thickness of the Triassic unit. Maximum depth and thickness are observed SW of the basin. The temperature distribution for the Triassic unit is shown in the bottom right diagram.

**Figure 10.**Summary of the petrophysical and operational parameters and PDFs used in example 3. For this example, the 3D geological model includes a rock density value for each voxel, and for this reason, it was not stochastically simulated using a pre-scribed PDF. On the right: the HIP histogram and the HIP CDF’s results for the entire target reservoir (P10, P50, and P90).

**Figure 11.**2D georeferenced map showing the HIP results obtained using example 3. The resulting HIP (P90) values are divided by the voxel area to express the results in PJ/km

^{2}. Only on-shore values are displayed.

**Figure 12.**Two geothermal doublet scenarios comparing the Hrec_P50 (

**A**–

**C**) with the heat demand of the city of Reus (

**B**–

**D**): the red polygon shows the covered area of the Reus total demand. (

**A**,

**B**) The injection and production wells are separated by 2 km and the radius of influence into the reservoir is considered to be 1 km. (

**C**,

**D**) The injection and production wells are separated by 1 km and the well influence radius into the reservoir is 0.5 km.

**Table 1.**Petrophysical and operational parameters used for the HIP and Hrec calculations in example 2 (Low and Upp correspond to the minimum and maximum temperature values assigned to the triangular distribution with lowest frequencies; Max—the value with the highest frequency; PDF—probability distribution function; SD—standard deviation).

Property | Units | PDFs | Values | |
---|---|---|---|---|

Petrophysical | Porosity | - | Triangular | Low: 0.07, Max: 0.12, Upp: 0.18 |

Fluid Density | kg/m^{3} | Normal | Mean: 1020, SD: 5 | |

Fluid specific heat capacity | kJ/kg·°C | Normal | Mean: 4.8, SD: 0.1 | |

Rock density | kg/m^{3} | Triangular | Low: 2450, Max: 2500, Upp: 2600 | |

Rock specific heat capacity | kJ/kg·°C | Normal | Mean: 0.9, SD: 0.01 | |

Operational | Recovery factor | - | Triangular | Min: 0.08, Max: 0.12, Upp: 0.15 |

Reinjection temperature | °C | - | 30 | |

Conversion efficiency | - | - | 0.85 | |

Plant factor | - | - | 0.95 | |

Mean plant lifetime | years | - | 30 |

**Table 2.**Estimated probable heat recovery capacity as a function of the influence radius for a hypothetical geothermal doublet well in the Jurassic reservoir close to the Reus-1 well.

Hrec—Recoverable Heat vs. Estimated R—Radius of Influence | Hrec P10 (kWt) | Hrec P50 (kWt) | Hrec P90 (kWt) |
---|---|---|---|

R = 0.5 km | 1337 | 1140 | 927 |

R = 1 km | 6127 | 5185 | 4211 |

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**MDPI and ACS Style**

Piris, G.; Herms, I.; Griera, A.; Colomer, M.; Arnó, G.; Gomez-Rivas, E.
3DHIP-Calculator—A New Tool to Stochastically Assess Deep Geothermal Potential Using the Heat-In-Place Method from Voxel-Based 3D Geological Models. *Energies* **2021**, *14*, 7338.
https://doi.org/10.3390/en14217338

**AMA Style**

Piris G, Herms I, Griera A, Colomer M, Arnó G, Gomez-Rivas E.
3DHIP-Calculator—A New Tool to Stochastically Assess Deep Geothermal Potential Using the Heat-In-Place Method from Voxel-Based 3D Geological Models. *Energies*. 2021; 14(21):7338.
https://doi.org/10.3390/en14217338

**Chicago/Turabian Style**

Piris, Guillem, Ignasi Herms, Albert Griera, Montse Colomer, Georgina Arnó, and Enrique Gomez-Rivas.
2021. "3DHIP-Calculator—A New Tool to Stochastically Assess Deep Geothermal Potential Using the Heat-In-Place Method from Voxel-Based 3D Geological Models" *Energies* 14, no. 21: 7338.
https://doi.org/10.3390/en14217338