PROCEEDINGS, 45th Workshop on Geothermal Reservoir Engineering

Stanford University, Stanford, California, February 10-12, 2020

SGP-TR-216

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Site-Scale and Regional-Scale Modeling for Geothermal Resource Analysis and Exploration

M. K. Mudunuru, B. Ahmmed, S. Karra, V. V. Vesselinov, D. R. Livingston, and R. S. Middleton

Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Correspondence: maruti@lanl.gov, ahmmedb@lanl.gov

Keywords: Geothermal energy, 3D site-scale and regional-scale models, coupled thermal-hydrologic-chemical (THC) modeling.

ABSTRACT

Detailed knowledge of site and regional permeability is critical for geothermal resource analysis and exploration. However, the

knowledge of reservoir rock permeability is very limited and needs to be inferred from various types of data streams that can be applied

to inform indirectly fluid flow in the reservoir. Generally, the permeability values of rock formations within prospective geothermal

reservoirs are low. To develop an economically viable enhanced geothermal systems, the reservoir permeability needs to be enhanced

(e.g., using hydraulic fracturing). However, identification of areas suitable for enhanced thermal energy production is challenging.

These prospective geothermal reservoirs would need to satisfy various requirements. But most importantly they would need to be

associated with elevated heat flux and formation suitable for permeability enhancement and reservoir stimulation. Furthermore, the

evaluation of the risk associated with geothermal exploration requires sensitivity and uncertainty analyses based on reservoir models

that can account for governing physical processes (e.g., fluid flow, heat flux, chemical transport) and plausible range of reservoir

properties. To achieve this, in this work we present a preliminary coupled thermal-hydrologic-chemical (THC) model that is applied to

analyze coupled fluid flow, chemical transport (e.g., lithium, boron), and heat transfer within Truth and Consequences region in

southwest New Mexico. We perform high-fidelity numerical simulations for different types of geological settings. The materials

properties and associated geology applied in the multi-physics model are obtained from the previous works by New Mexico Geological

Society (New Mexico highway geologic map from 1982) and recent Geothermal Play Fairways Analysis project. We developed a

reservoir model based on realistic permeabilities of the Truth and Consequences site. The modeling work demonstrates that rock

permeability plays a major role in the evolving temperature profile in the site-scale reservoir. We also show that enhanced permeability

in the geological layers provides a means for improved energy transfer from the rock to fluid. Due to high permeability, the fluid flows

upward from the deep subsurface toward the ground surface, and accumulates energy due to prolonged contact with reservoir rock. This

resulted in increased temperature at the upper portion of the reservoir. For the case where permeability is low in the middle layers, the

temperature increase at the surface is limited. This is because there is minimal fluid movement to the surface due to low permeable

layers. To conclude, this preliminary modeling work showed that manipulating permeability to reasonable values is key to improving

energy extraction from a site-scale reservoir. The developed models will be applied to assimilate existing observational data to infer

reservoir flow properties and their uncertainties; these models will be also applied to estimate the risk associated with geothermal

exploration.

1. INTRODUCTION

Enhanced Geothermal Systems (EGS) present a significant and long-term opportunity for widespread renewable power production

(Brown et al., 2012). The EGS approach makes it possible to utilize otherwise inaccessible geothermal resources (Kelkar et al., 2015). It

is estimated that within the U.S. alone the electricity production potential of EGS is in excess of 100 GWe. Hence, the efforts to

accurately model and predict the performance of EGS reservoirs under various reservoir conditions (e.g., formation permeability,

reservoir temperature, existing fracture/fault connectivity, geothermal tracers, and the in-situ stress distribution) are vital (McClure and

Horne, 2014, Mudunuru et al. 2017). Herein, we present a preliminary site-scale and regional-scale modeling study based on field data

(e.g., realistic model domain with field-relevant material properties) from New Mexico (e.g., Bielicki et al. (2015), Pepin et al. (2015)).

The developed model represents the coupled fluid flow, energy transport, and chemical transport occurring in the geothermal reservoir

by using PFLOTRAN, a massively parallel multi-physics subsurface simulator. The subsurface material properties are varied to

generate three different realizations of permeabilities that are potentially representative of the actual site settings. Based on the

simulations, we investigate the evolution of temperature in the reservoir domain. The modeling analysis presented in this paper is a part

of a project exploring the use of machine learning tools for geothermal energy production; the project is being supported by the US

Department of Energy – Geothermal Technologies Office.

2. GOVERNING EQUATIONS AND NUMERICAL METHODOLOGY

In this section, we briefly describe the governing equations for modeling thermal-hydrologic-chemical physical processes involved in

heat conduction and energy transfer due to fluid flow and chemical transport in a site-scale reservoir. Here, we shall restrict to solving

the governing equations resulting for fluid flow, chemical transport, and heat transfer processes.

2.1 Governing equations: Fluid flow, chemical transport, and heat transfer

The governing mass conservation equation for single phase saturated flow is given by:

𝜕(𝜑𝜌)

𝜕𝑡 + div[𝜌𝒒] = 0 (1)

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where 𝜑 is the porosity, 𝜌 is the fluid density [Kg m-3], and 𝒒 is the volumetric flux [m s-1]. The Darcy’s flux is given as follows:

𝑞 = −𝑘

𝜇grad[𝑃 − 𝜌𝑔𝑧] (2)

where 𝑘 is the intrinsic permeability [m2], 𝜇 is the dynamic viscosity [Pa s], 𝑃 is the pressure [Pa], 𝑔 is the gravity [m s-2], and 𝑧 is the

vertical component of the position vector [m]. The governing equations for chemical transport (e.g., Lithium, Boron) is given by

𝜕(𝜑𝑐)

𝜕𝑡 + div[𝑐𝒒 − 𝜑𝜏𝐷grad[𝑐]] = 0 (3)

where 𝑐 [molality] is the solute concentration, 𝐷 [m2 s-1] is the diffusion/dispersion coefficient, and 𝜏 [–] is the tortuosity (related to the

path length of the fluid flow).

The governing equation for energy conservation is given as follows:

𝜕(𝜑𝜌𝑈+ (1−𝜑 )𝜌𝑟𝑜𝑐𝑘 𝑐𝑝,𝑟𝑜𝑐𝑘𝑇)

𝜕𝑡 + div[𝜌𝐻𝒒 − 𝜅effgrad[𝑇]] = 0 (4)

where 𝑈 is the internal energy of the fluid, 𝜌𝑟𝑜𝑐𝑘 is the density of the porous rock, 𝑐𝑝,𝑟𝑜𝑐𝑘 is the heat capacity of the porous rock filled

with fluid, 𝑇 is the temperature of the fluid, 𝐻 is the enthalpy of the fluid, and 𝜅eff is the effective thermal conductivity of porous rock

filled with fluid. The effective thermal conductivity is given by the full saturated rock thermal conductivity.

2.2 Numerical methodology

The subsurface simulator PFLOTRAN (Lichtner et al., 2015) solves a system of nonlinear partial differential equations describing

multiphase, multicomponent, and multiscale reactive flow and transport in porous materials. The governing equations for the THC

model described in Sec.2.1 are solved using a fully implicit backward Euler for discretizing time and a two-point flux finite volume

method for spatial discretization. The resulting non-linear algebraic equations are solved using a Newton-Krylov solver.

3. NUMERICAL MODEL AND RESULTS

In this section, we present a numerical thermal-hydrological-chemical (THC) model to simulate the evolution of temperature for three

different scenarios/cases of geological properties. Figure 1 shows the study area for site-scale and regional-scale numerical simulations.

In this figure, we show a map and projected coordinates of southwest New Mexico for numerical model development. The blue triangles

represent known-geothermal resources, where temperatures are sampled and recorded. We focus on the Truth or Consequences site-

scale study area (represented by red color rectangle) in the southwest NM region.

Figure 2 shows a site-scale model domain, whose dimensions are 6000×6000×6000 m3. The numerical model consists of nine geologic

layers as shown in Figure 2. The depth of each layer is listed in Table 1 based on geologic time spans from Precambrian Era–Quaternary

Period (NM Geological Society Report,1982 and Bielicki et al., 2015). The numerical model has a total of 30000 finite-volume mesh

cells. Each mesh cell has dimension of 600×600×20 m3. The number of grid cells are 10×10×300, respectively. Figure 3 shows the

details of the generalized stratigraphy of southwest New Mexico (modified from New Mexico Geological Society, 1982 and Bielicki et

al., 2015). The material properties (e.g., Table 1, Table 2, and Fig.2) assumed in the numerical model are based on this Fig.3. The

hydro-stratigraphy and corresponding geologic units are shown on left and right columns of Fig.3, respectively. Black, white, and gray

color on left column represent aquitard, aquifer, and fair aquifer, respectively. The corresponding material properties (e.g., different

types of permeability, porosity, diffusivity, thermal conductivity of rock and fluid) of the geological layers are shown in Table 1 and 2

for three different realizations. These three different case studies represent different realistic reservoir settings.

The boundary conditions (BC) used in PFLOTRAN numerical simulations are shown in Fig.2. Pressure BCs are set as 1 MPa at top

surface and 7 MPa at bottom surface so that fluid and tracer tend to flow and transport upward, from bottom to top. Heat conduction and

energy transfer also occur in a similar fashion. Zero gradient in temperature is enforced at the top surface and an energy flux of 0.08

Wm⁻ 2 is prescribed at the bottom surface. Zero concentration and zero gradient in concentration flux are prescribed at the bottom and

top surfaces of the domain. On the north, south, east, and west sides of the boundary, we prescribe Neumann BCs. These are zero

energy flux, no fluid/water flow condition, and zero concentration flux. These boundary conditions allow the heat to conduct due to

thermal conduction and fluid to transfer energy due to flow from bottom to top surface. Initial pressure in the domain is assumed to be 1

MPa and initial temperature at top surface is assumed to be 25°C. In the entire domain, initial temperature was set to be proportional of

depth assuming a uniform geothermal gradient of 23°C/km (e.g., see Pepin et al., 2015, Bielicki et al., 2015). This results in a bottom

surface temperature to be equal to 163°C. Figure 4 shows a vertical contour of initial temperature along a section of the model domain.

PFLOTRAN simulations are performed for a total time of 500 years (in the consequent modeling analyses, we will increase the spatial

resolution of the model domain and expand simulation time to reach steady-state flow conditions). Table 3 shows the simulation time of

a single realization, which takes approximately an hour to run on a two-core processor. Figure 5 shows the contours of fluid pressure

and tracer (Lithium and Boron) concentrations at a cross section y = 0 at the end of the simulation period for these three different

realizations.

The explored permeability profiles in our preliminary modeling analyses are also shown in Figure 5. For Case 1, the permeability in the

bottom geological layers (e.g., layer 6 to 9) are lower compared to Case 2 and Case 3. Hence, the pressure changes in the layers 1 to 6

are small compared to Case 2. For Case 2, the pressure varies considerably in the bottom set of layers due to enhanced permeability.

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However, as the middle layers (e.g., layer 3 and 4) have a very low permeability, the pressure decreases and equilibrates to 1 MPa. For

Case 3, the permeability profile increases slowly from the bottom surface to top. There are no rapid changes in the permeability across

the layers. As a result, the heated fluid flow at the bottom surface (e.g., see Fig.7) slowly moves to the top.

Figures 6 and 7 show the evolution of the temperature at the top and bottom of the reservoir. The temperature dynamics reflect both heat

conduction due to rock and energy transfer due to fluid movement. The main inference from these figures is that permeability plays an

important role in the evolution of temperature at the bottom and top surfaces. From Fig.7, it is evident that the temperature at the bottom

surface for Case 3 is higher compared to Case 1 and Case 2. This is because due to gradual change in the permeability values across the

layers, the bottom layer fluid is able flow into the upper layers. This results in increased fluid temperature in the upper layers due to

prolong contact with hot rock. As a result, the upper layers temperature increases and eventually the top surface temperature increases

from 25oC to 29oC (see Fig.6) over a span of 500 years. For Case 2, even though the permeability values are high in the bottom layers,

the middle set of layers (e.g., layer 3 to 5) have a very low value. These set of layers act like a barrier/cap to fluid flow due to reduced

permeability. As a result, energy transfer from the heated rock to fluid is less compared to Case 3. Similar inference can be drawn on

Case 1 due to low permeability. Hence, the temperature increase at the surface is also low for Case 2 and Case 1, when compared to

Case 3. Moreover, due to low permeability and low diffusivity, the tracer concentrations of Lithium and Boron (Fig.5) diffuses slowly

and is confined to the bottom most layers. Clearly, longer simulation times are needed to capture migration of tracers through the model

domains. To conclude, permeability plays a major role in enhancing the heat flow and increasing reservoir temperature.

Table 1: Hydrologic parameters assigned to different geological layers (Pepin et al., (2015) and Bielicki et al., (2015)) for three

different realizations for PFLOTRAN simulations. For more details on the information given in the table, please refer to Pepin

et al., (2015).

Layer Major rock type (geologic

time)

Total

depth

of layer

[m]

Log(kx) [m2] Anisotropy

[kx/kz]

Effective

Porosity Case 1 Case 2 Case 3

Layer 1 Fluvial sediments (Upper

Tertiary – Quaternary)

950 -12 -12 -12 100 0.3

Layer 2 Lava flow and ash flow

(Lower Tertiary)

880 -13 -15 -12.5 1 0.15

Layer 3 Sandstone, shale, and

conglomerate (Cretaceous)

2000 -14.5 -16 -13 1 0.25

Layer 4 Sandstone, shale, and

conglomerate (Triassic–

Jurassic)

270 -15 -17 -13.5 1 0.25

Layer 5 Mudstone, sandstone, and

siltstone (Permian)

240 -15.5 -15 -14 1 0.25

Layer 6 Limestone, shale and

dolomite (Pennsylvanian)

700 -16 -11 -14.5 1 0.2

Layer 7 Limestone and shale

(Devonian–Mississippian)

260 -16.5 -12 -15 1 0.2

Layer 8 Limestone and dolomite

(Cambrian–Silurian)

400 -17 -13 -15.5 1 0.2

Layer 9 Granite and metamorphic

rocks (Precambrian).

300 -18 -15 -16 1 0.05

Table 2: Thermal transport, tracer transport (e.g., Lithium, Boron), and physical parameters that are held constant for all three

different case studies. Note that these values are assumed to be constant for all hydrostratigraphic units. In our future work, we

will be varying these parameters from the ArcGIS data (e.g., from Bielicki et al., 2015)

Symbol Variable Value

𝜆f Fluid thermal conductivity 0.58

Wm−1⁰ C−1

𝜆r Solid thermal conductivity 2.5 Wm−1⁰ C−1

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𝜌s Rock density 2600 kgm−3

D Diffusivity 10-9 m2s-1

Figure 1: Site-scale (Truth or Consequence) and regional-scale study areas in New Mexico; the blue triangles indicate existing

known-geothermal resources, where temperatures are sampled and recorded.

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Figure 2: 3D model domain of the Truth or Consequences site-scale study area as shown in Fig.1. The domain consists of 9

different geological layers with permeabilities ranging from 10-18 to 10-12 m2.

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Figure 3: Generalized stratigraphy of southwest New

Mexico (Courtesy from New Mexico Geological Society,

1982 and Bielicki et al., 2015).

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Figure 4: Initial temperature profile in the domain. Temperature is computed assuming a uniform geothermal gradient of 23

C/km. Temperature contour is shown along a cross-section at y = 0.

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Figure 5: Demonstrative model outputs of the pressure and tracer (Lithium and Boron) concentrations distribution in the model

domain after 500 years. Results are plotted along a cross-section at y = 0 for three different model settings (Cases 1, 2 and 3).

The Lithium and Boron tracers are released in the left and right portions of the model cross-section.

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Figure 6: Model predicted temperature evolution over a span of

500 years at the top surface of the reservoir.

Figure 7: Model predicted temperature evolution over

a span of 500 years at the bottom surface of the

reservoir.

Figure 5: Subcrop map of the geology of the southwest New Mexico.

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4. CONCLUSIONS

We have developed a thermal-hydrologic-chemical numerical model to simulate coupled fluid flow, chemical transport, and heat

transfer in the southwest New Mexico region. The material properties in the model are based on Truth or Consequences site-scale study

area. High-fidelity numerical simulations are performed using PFLOTRAN for three different scenarios of geological settings. The three

different realizations represent realistic permeabilities of the site. We demonstrated that permeability plays a major role in the evolving

temperature profile at the top and bottom surface of the site-scale reservoir. A gradual change in the permeability values across the

layers provided a means for the high-temperature fluid at the bottom to flow into the upper geological layers. This fluid movement to

the upper layers resulted in an enhanced transfer of thermal energy from the rock to fluid, resulting in increased temperature at the top

surface. For the case where permeability is low in the middle layers, the temperature increase at the surface is limited. This is because

there is a minimal fluid movement to the surface due to low permeable layers. Hence, the heat transfer from the reservoir rock to fluid is

less predominant. We note that our case studies did not account for fractured rock properties, which may improve the fluid flow

movement resulting in enhanced energy transfer to the rock.

5. FUTURE WORK

Our next step is to account for site- and regional-scale heterogeity in the material properties (e.g., upscaled permeability, thermal

conductivity, diffusivity) as represented in our numerical model. We will perform these analyses accounting for existing site- and

regional-scale data. For example, Figure 8 shows a regional-scale subcrop map of the geology of the southwest New Mexico. This is a

chronostratigraphic (geologic age) map at the surface of the study area. The map was developed by incorporating domain expertise with

geophysical data such as field observation, rock dating, etc. (Barroll, 1990; Witcher, 2002). We will use this geology map along with

other spatial data (Bielicki et al., 2015) to generate spatial permeability distribution to improve our PFLOTRAN 3D regional-scale

model. In addition, existing fault density maps will be used to account for fracture paths in the permeability profile. In summary, we will

implement data analytics and machine learning tools to combine and mine various existing datasets to estimate the material properties

and reservoir attributes that will be applied into extensive THC modeling site- and regional-scale analyses.

ACKNOWLEDGEMENTS

This material is based upon work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy

(EERE) under the Geothermal Technology Office (GTO) Machine Learning (ML) for Geothermal Energy funding opportunity, Award

Number DE-EE-3.1.8.1. PFLOTRAN source code can be downloaded at https://bitbucket.org/pflotran/pflotran. Additional information

regarding the simulation datasets and input files can be obtained from Bulbul Ahmmed (Email: ahmmedb@lanl.gov) and Maruti Kumar

Mudunuru (Email: maruti@lanl.gov).

Disclaimer: This paper was prepared as an account of work sponsored by an agency of the United States Government. Neither the

United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any

legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process

disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product,

process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement,

recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed

herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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