Discrete Element Modeling of Thermo-Hydro-Mechanical Coupling in Enhanced Geothermal Reservoirs

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1 PROCEEDINGS, Thirty-Eighth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California Discrete Element Modeling of Thermo-Hydro-Mechanical Coupling in Enhanced Geothermal Reservoirs Azadeh Riahi Itasca Consulting Group, Inc. Berkeley, California Branko Damjanac & Jason Furtney Itasca Consulting Group, Inc. Minneapolis, Minnesota 55401, United States ABSTRACT This study focuses on evaluating the correlation between heat production and field and operational parameters in Enhanced Geothermal Systems (EGS) using a thermo-hydro-mechanically coupled numerical modeling approach. A series of sensitivity studies are performed, and the correlation between heat production metrics and different field and operational parameters are investigated. The results of this study provide insights into the complex mechanisms that control the response of EGS reservoirs to injection, and further emphasize the role that numerical modeling can play in better addressing the issue of data uncertainty. INTRODUCTION The objective of this study is to evaluate how field characteristics and operational parameters affect the response of Enhanced Geothermal Reservoirs (EGS). A series of sensitivity studies with respect to various reservoir characteristics, such as fracture size distribution, fracture dilation angle and operational parameters (i.e., injection rate) are carried out. The sensitivity of stimulation phase to these parameters is investigated in a series of previous publications [1, 2]. In this paper, the effect of these parameters on the production indices is studied. The studies are performed in a two-dimensional framework, and both stimulation and production phases are modeled. The purpose of the stimulation phase is to enhance the overall permeability of the reservoir by inducing hydro-shearing, i.e., the irreversible aperture increase due to slip. In the numerical modeling studies, the duration of stimulation typically varies between hours to a few days. Subsequent to the stimulation phase, the production phase for a typical period of five to ten years is modeled. The numerical modeling approach is based on the discrete element technique in which the pre-existing discrete fracture network is generated stochastically and explicitly represented. In the adopted technique, the transient response of laminar flow through the pre-existing fracture network is modeled. The advective heat transfer by fluid flow, the convection at the boundary between moving fluid and rock, and the conduction of heat through surrounding rock are taken into account. The mechanical solution is fully coupled with thermal and hydraulic responses. In order to compare different cases, a series of metrics that quantify the response of the reservoir during stimulation and production phases are monitored through time. The stimulation indices include total area of pressurized fractures and area of stimulated (sheared) fractures. The production indices include temperature draw down at the production wells, rate of production, rate of generated power and total energy produced. The result of these sensitivity studies are presented in the subsequent sections. REPRESENTATION OF THE DISCRETE FRACTURE NETWORK It is believed that the characteristics of the Discrete Fracture Network (DFN) are key to the way injection interacts with the EGS formation during both stimulation and production phases. To evaluate the importance of DFN characteristics, the reservoir fracture network is represented explicitly in this study.

2 Numerous realizations of different DFNs have been generated stochastically. The statistical parameters associated with a DFN typically characterize the fracture size distribution, orientation distribution and density of each fracture set. The DFN used in this study consists of two fracture sets, each with a given fixed orientation. The fracture length distribution follows a power law distribution, which relates the probability of occurrence of a fracture with a length of l to the negative exponent of the length, i.e., n ( l ) l. The value of is site specific, but often ranges between 2 and 4. In this two-dimensional study, P21 is used as the measure of the fracture density. P21 is defined as the sum of the lengths of all of the fracture or traces divided by the area of the sampling or mapping domain i.e., 2 P 2 1 l / L, where L is the linear dimension of i the DFN domain. The flow characteristics of the DFN are determined by identifying the fracture clusters and evaluating the overall DFN connectivity. A cluster is a group of fractures that are connected to each other; no fracture inside a cluster intersects a fracture belonging to a different cluster. A fully connected DFN is defined as a DFN in which one cluster extends to a part of the boundary of the domain. The fully connected DFN was created through a trial-and-error process, at the critical density that would lead to formation of one cluster. The partially and sparsely connected DFNs were created by decreasing the fracture density and visually inspecting the size of formed clusters relative to the size of the model. It is intended that the DFNs used in this study closely represent the real conditions; however, to meet computational requirements, the DFNs are further simplified. A brief description of the simplification process is discussed in [2]. NUMERICAL APPROACH The numerical analyses of this study simulated the hydro-thermo-mechanical response of the discrete fracture network in rock mass at elevated temperatures to cold fluid injection. In each analysis, both the stimulation and production phase are modeled. In order to be able to compare different models, similar production scenarios were considered in all analyses. In each case, two productions wells located approximately 250 m to 500 m from the injection well are installed. Considering the change of apertures in the stimulated reservoir, the location of the wells is chosen such that they are favorably 2 positioned for production. Quantitative evaluation of the response of the reservoir to injection is conducted by looking at the time history of generated power and energy, as well as injectivity. The numerical analyses of this study are carried out using a discrete-element modeling approach. Simulations were completed using distinct element code UDEC [3]. In this approach, the rock formation is represented by an assembly of rock blocks separated by a pre-existing fracture network. Fluid flow can only occur within the fractures. The blocks are considered to be impermeable and elastic. The pre-existing fractures are represented explicitly. They are discontinuities which deform elastically, but also can open and slip (as governed by the Coulomb slip law) as a function of pressure and total stress. UDEC can model fracture propagation along the predefined planes only; it is noted that in this study propagation of pre-existing fractures is disregarded. In order to model propagation of a hydraulic fracture (HF), the trajectory of the fracture should be defined explicitly in the model before starting the analysis. In this model, the HF is assumed to be planar, aligned with the direction of the major principal stress. The two incipient surfaces of the HF plane are bonded initially with a strength that is equivalent to a specified fracture-toughness. Propagation of the HF corresponds to breaking of these bonds. Clearly, the assumption of propagation of the HF as a single planar surface is a simplification. In practice, the massive hydraulic fracturing, used in shale stimulation for example, results in a large number of fractures propagating simultaneously or sequentially. Under certain conditions, the mechanical interaction between these fractures can lead to non-planar and complex trajectories as demonstrated by the results of numerical modeling [4, 5] and by experimental observations [6]. Also, non-planar fracture geometry may develop as a result of the interaction with preexisting fractures and frictional interfaces [7, 8, 9]. It is assumed that the pre-existing fractures are already open and conductive, with a uniform aperture for each fracture set. The initial apertures of each fracture set are calculated based on their orientation relative to the in-situ principal stresses. The primary and secondary fracture sets are assigned initial apertures of m and m, respectively. The failure criterion of the pre-existing fractures is defined by the Coulomb slip law, with zero cohesion, friction angle of 30 and dilation angle of 7.5. Figure 1 shows the geometry and set-up of the UDEC model. The model represents a 2D horizontal section through a reservoir with a thickness of 350 m. It is

3 assumed that the injection is through a vertical well located at the center of the model. The core part of the model containing the DFN is embedded into a larger domain with a regular network of pipes with a permeability equivalent to that of the core region. The linear dimensions of the full model are twice as large as those of the core part. In all studies, except the study of the effect of injection rate, the model core measures 1000 m 1000 m. The state of stress in the plane of the model is assumed to be anisotropic, with the maximum principal-horizontal stress equal to the vertical stress and the minimum principal-horizontal stress equal to half of the vertical stress. RESULTS Effect of Fracture Size Distribution The objective of this study is to evaluate the effect of fracture size distribution on the response of the DFN to fluid injection and heat production. The DFNs used in this study have identical connectivity characteristics; all three realizations (shown in Figure 2) are fully connected. However, the realizations belong to three different DFNs with different length exponent, α. Also, in Realization I the maximum fracture length, l max is limited to 250 m, while in Realization II and III the fracture length is unbounded. Both the primary and secondary fracture sets are oriented favorably (at 160 and 45 with respect to maximum principal stress) for slip. In these analyses, injection pressure remains below the HF pressure. Figure 1: Geometry and model set-up. During the stimulation phase, fluid was injected into the reservoir at a rate higher than that of the production phase. For all studies, except the study of the sensitivity to injection rate, the rate used during stimulation is m 3 /s/m, which for the assumed height of 350 m is equal to 0.07 m 3 /s or 70 kg/s. The injection rate used during production was m 3 /s/m. The stimulation phase calculation uses the UDEC compressible transient flow model to represent the strong hydromechanical interaction; thermal effects are not included in the stimulation phase model. Results of the stimulation phase, after excess pressures are dissipated, are used as initial conditions for the production phase model. During the production phase, thermal effects are more important so a different solution method is used, mainly because of the time scale of the production phase. A thermal-flow model is coupled with models of the rock temperature and rock mechanical deformation. Thermo-hydro-mechanical interactions are represented: the flow is a strong function of the fracture aperture, the fracture aperture is a function of temperature and mechanical stress, mechanical stresses are influenced by temperature change, changes in fluid flow affects how heat is distributed in the rock. Figure 33 shows contours of permanent aperture increase due to stimulation, after the excess pore pressure has dissipated. The stimulation period for these models was 14 hours. The blue circles on this pictures show the location of injection (middle circle) and two production wells. Location of the production wells are chosen at 250 m from the injection well and within the stimulated fracture volume. Realization I 2 and l m ax m Realization II 2.5 and l m a x n o lim it (c) Realization III 3 and l m a x n o lim it Figure 2: The effect of the fracture size distribution: DFN geometry. 3

4 Realization I Realization II Realization I Realization II Apertures (m) (c) Realization III Figure 3: The effect of the fracture size distribution: apertures after 14 hours of injection. Figure 4 shows the history of shear stimulated area versus time for these three realizations. Figure 5 shows the contour of rock temperature for three realizations after 34 months of production. Graphs of temperature draw-down and power for each well in all three realizations are shown in Figure 6. There are three observations from Figure 6. (1) For the first 60 months of production, in all three realizations, only one of the two production wells is producing. (2) The temperature draw-down in realization II, where flow is localized through one large fracture only, is the quickest. (3) Graphs of temperature draw-down for realization III-Well II suggest that after 8 months of production, the second well becomes producing. (c) Realization III Figure 5: The effect of fracture size distribution: contours of rock temperature after 34 months of production. Finally, Figure 6(c) shows the total generated energy (summed over both wells) for the three realizations. This graph shows that Realization I, in which a large portion of the rock mass is stimulated, shows the best result for energy production. This observation is consistent with the graphs and contours of shearstimulated area, which show large stimulated volume for this realization. Overall, these results indicate that the heat production indices, as well as shear-stimulated area, can be correlated to the uniformity of the fracture size and also to the probability of having large fractures relative to the domain size. In this case, in Realization I, the maximum fracture length is capped to a value which is approximately one quarter of the DFN domain region. Thus, the DFN has a relatively uniform fracture size distribution with a mean length that is much smaller than the reservoir size. This condition seems to be optimum for shear stimulation. Figure 4: The effect of fracture size distribution: history of shear-stimulated area and DFN affected area. 4

5 Dilation: 3º Dilation:7.5º Apertures(m) (c) Dilation :15º Figure 7: Effects of dilation angle: contours of aperture increase after 20 hours of stimulation. (c) Figure 6: The effect of fracture size distribution: history of heat production metrics. EFFECT OF DILATION ANGLE Understanding the effect of fracture dilation angle is important, because dilation determines how much irreversible opening and permeability increase can occur during stimulation. The DFN realization for all cases studied in this case is the same, the difference between these models is the dilation angle of fractures. Figure 7 shows contours of aperture after 20 hours of stimulation. Figure 8 shows history of shearstimulated area for models with different dilation angle. It is seen from these graphs that higher dilation angle results in a lower shear-stimulated area. However, comparing graphs of average DFN aperture suggest that, as expected, higher dilation angle results in higher average DFN aperture. Figure 8: Effects of dilation angle: history of shear stimulated area and DFN affected area, and average DFN aperture. Figure 9 shows history of production-phase indices for models with different dilation angles. There does not seem to be a monotonic trend in the production indices. However, based on Figure 9 and also based on contours of rock temperature shown in Figure 14, it can be concluded that the model with a dilation angle of zero has the lowest recovery. For the rest of the three models, the rates are relatively close; again, indicating that for angles above 3º sensitivity the dilation angle reduces. Figure 9(d), which shows history of injectivity, indicates that dilation angle

6 affects injectivity in a more consistent manner. Higher dilation angle results in better injectivity, which is contributed to higher apertures for stimulated fractures, and thus higher permeability. Dilation: 0º Dilation: 3º (c) (c) Dilation: 7.5º (d) Dilation: 15º Figure 10. Effect of dilation angle: contours of rock temperature after 26 months of production. EFFECT OF STIMULATION RATE DURING INJECTION This study focuses on how different injection rate during the stimulation phase affect the production. The effect of using different rates during stimulation on the stimulation indices has been shown in previous studies [2]. It is shown in [2] that for a similar injected volume a lower injection rate results in a larger area of affected fractures, while higher injection rates result in a better shear-stimulated area. However, a higher injection rate results in a quicker pressure built-up, and thus increases the potential of reaching the critical hydraulic fracturing pressure and flow localization at an earlier stimulation time. Figure 11 shows the model used in the study of the effect of injection rate. The DFN core region has a dimension of 2 by 2 km, the exponent of fracture size distribution curve is 2, and the maximum fracture size is capped at 500 m. (d) Figure 9: Effect of dilation angle: history of production indices. Figure 11. Core region of model (with explicit representation of DFN) used in the study for effect of injection rate. 6

7 Figure 12 shows the shear-stimulated area for the three stimulation rates. Again, the graph shows that higher injection rates have resulted in a greater shearstimulated volume. Figure 13 shows the location of the production wells and plots of the shear-stimulated area (permanent aperture increase) for 84 m 3 /m of injected volume. Figure 14 shows the production indices for the models with different injection rates. The produced water temperatures at the production wells are shown in Figure 14, and indicate that in the model with the stimulation rate of m 3 /s/m, both wells are producing, while in the model with m 3 /s/m and m 3 /s/m, only one of the two wells are producing. This is also observed in the contours of the rock temperature shown in Figure 15. The recovery rate for all three models is close to 100% (Figure 14 ), and the total energy produced is relatively close for all three models; however, a major difference is observed in the injectivity. As expected, the model with higher stimulation rate has resulted in better injectivity (Figure 14 (c)). Figure 12: Effect of stimulation injection rate: history graph of shear stimulated surface area. (c) 2e-4 m 3 /s/m 4e-4 m 3 /s/m Aperture (m) (c) 8e-4 m 3 /s/m Figure 13: Effect of stimulation injection rate: plots of shear stimulated area for 84 m 3 /m of injected volume (d) Figure 14: Effect of stimulation injection rate: production indices 7

8 angle, injectivity is affected noticeably by the variation of this parameter m 3 /s/m m 3 /s/m (c) m 3 /s/m Figure 15: Effect of stimulation injection rate: contours of rock temperature. CONCLUSIONS This paper presents some initial results of a study on thermo-hydro-mechanical response of EGS reservoirs. In a series of 2D numerical sensitivity studies, the hydro-mechanical response of the reservoir during stimulation and thermo-hydromechanical response of reservoirs during the production were modeled. The numerical approach was based on a discrete element technique, in which the pre-existing fracture network was explicitly represented in the model. For each sensitivity study, a series of quantitative metrics, such as shear-stimulated area of fractures, injectivity, generated thermal power, and produced temperature were evaluated and results were compared to a base case scenario. It was observed that the potential for shear stimulation, measured by the surface area of fractures that experience slip, increases as the probability of having large fractures in the model increases. This condition affects the stimulated area and also generated heat indices, such as rate of temperature draw-down and power. Dilation angle of fractures is also an important parameter for stimulation. The results of this study show that for similar injected volume, a higher dilation angle results in a smaller shear-stimulated area, but better connectivity and greater permanent aperture increases within the stimulated region. It is shown that while generated power and temperature draw-down are less sensitive to variation of dilation The effect of the stimulated injection rate, one of the operational parameters, on the stimulation and production is also evaluated. It is shown that for a similar injected volume, higher injection rates result in a better stimulated area and a higher average aperture of stimulated fractures. These conclusions are valid only when the injection pressure remains below the hydraulic fracturing pressure. It was also observed that the application of a different stimulation rate affects the injectivity index; while indices, such as generated power and temperature draw-down, remained less sensitive to variation of the injection rate during stimulation. Overall, these numerical studies show the complex responses of reservoirs to stimulation and production. It is observed that, compared to shear-stimulated indices, some of the heat production indices, such as generated power and temperature draw-down, showed a more non-monotonic response to variation of a particular parameter. Nevertheless, it seemed that the overall stimulation can lead to better recovery and consistently better injectivity indices. Multiple studies with various DFN realizations and well locations are required to be able to draw general conclusions on the sensitivity of indices, such as generated power, which are more affected by fracture geometry and flow localization. ACKNOWLEDGMENTS The authors acknowledge the financial support of Sandia National Laboratories for this project. REFERENCES [1] Riahi A, Damjanac, B. Numerical Study of Interaction between Hydraulic Fracture and Discrete Fracture Network, submitted for publication in the Proceedings, International Conference for Effective and Sustainable Hydraulic Fracturing, Brisbane, Australia, May [2] Riahi A, Damjanac, B. Numerical Study of the Interaction between Injection and the Discrete Fracture network in Enhanced Geothermal Reservoirs, in Proceedings, 47th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, June 2013 [3] Itasca UDEC (Universal Distinct Element Code), Version 5.0, Itasca Consulting Group, Inc., Minneapolis,

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