Multiple Interacting Continua Research Articles

Thermal-hydraulic-mechanical analysis of enhanced geothermal reservoirs with hybrid fracture patterns using a combined XFEM and EDFM-MINC model

The long-term fluid circulation of Enhanced Geothermal Systems (EGS) involves complex coupled Thermal-Hydrological-Mechanical (THM) processes dominated by both hydraulic and activated natural fractures. The simulation of such multiphysical processes is known to be a challenging problem. In this work, we have developed an integrated numerical approach to advance the multiphysical simulation of EGS. In our model, the hydraulic fractures of arbitrary shapes in response to pressure changes and thermal strains are handled by the three-dimensional (3D) eXtended Finite Element Method (XFEM). The induced/natural fractures are incorporated into the model and treated as one continuum of the Multiple INteracting Continua (MINC) for the investigation of their impacts. A TOUGH -based program, TOUGH2-EGS, is utilized to simulate the Thermal-Hydrological processes. The 3D Embedded Discrete Fracture Method (EDFM), compatible with the 3D XFEM, is adopted to model the hydraulic fractures. Sensitivity analyses are performed for this model in terms of injection temperature and thermal expansivity. The hybrid EDFM and MINC model is established and analyzed for an EGS with both hydraulic and induced/natural fractures. The convergence performance of the single-fracture model shows that an appropriate stiffness coefficient is essential for this model and different choices of the coefficient values result in distinct behaviors. Our numerical results illustrate that the fracture aperture is opened by the cold fluid injection and the reservoir performance is dominated by the thermal stress/strain, which highlights the necessity of multiphysical simulation. In the hybrid model, the enhancement of the natural fracture permeability notably delays the thermal breakthrough by allowing injected fluid to contact more hot reservoirs. The novelties of this work lie in three aspects. Firstly, the combined 3D XFEM and EDFM is capable of handling arbitrary fracture shapes in a 3D EGS model. Secondly, the hybrid hydraulic and induced/natural fracture model enables us to establish the stimulated reservoir volume of the EGS and investigate the operational and geological parameters. Thirdly, the introduction of fracture stiffness stabilizes the numerical solution.

Modelling the transient effect in naturally fractured reservoirs

Modelling of Naturally Fractured Reservoirs (NFR’s) is a very challenging task. NFR’s are often simulated using the dual-porosity (DP) model, which requires significantly lower computational time and less simulation cost compared with the fine-grid modelling. However, the DP model is unable to capture the transient effect, the saturation front, and its tendency to overestimate the predicted oil recovery, as the invaded fluid is immediately reaching the gridblock centre once its saturation exceeds the critical saturation. The matrix block discretisation and modifying the transfer function are among the widely investigated areas to represent the transient effect and to improve the simulation accuracy. Adjusting the transfer function often results in complicated and unstable solutions, which make this approach limited in use. However, the matrix discretisation technique, such as Multiple Interacting Continua (MINC), is one of the utilised approaches to improve the simulation of NFR’s. The model’s layers provide the required mean to capture the transient effect and to include the matrix heterogeneities. In this work, we present an improvement to the original MINC model to enhance its accuracy and stability using a particular case of two subdomains model. We suggested using an equal volume of the matrix sub-blocks, besides performing an adjustment to the calculation of fluid saturation. The new adjustments have provided a stable solution and improved simulation results compared with the original MINC model. Besides the advantage of the matrix layers to handle various heterogeneities with excellent simulation accuracy and marginal errors, and hence a reliable performance and prediction.

An Improved Multicomponent Diffusion Model for Compositional Simulation of Fractured Unconventional Reservoirs

Summary Most simulators currently use the advection/diffusion model (ADM), where the total flux comprises Darcian advection and Fickian diffusion. However, significant errors can arise, especially for modeling diffusion processes in fractured unconventional reservoirs, if diffusion is modeled by the conventional Fick’s law using molar concentration. Hence, we propose an improved multicomponent diffusion model for fractured reservoirs to better quantify the multiphase multicomponent transport across the fracture/matrix interface. We first give a modified formulation of the Maxwell-Stefan (MS) equation to model the multicomponent diffusion driven by the chemical potential gradients. A physics-based modification is proposed for the ADM in fractured reservoirs, where fracture, matrix, and their interface are represented by three different yet interconnected flow domains to honor the flux continuity at the fracture/matrix interface. The added interface using a more representative fluid saturation and composition of the interface can hence better capture the transient mass fluxes between fracture and matrix. The proposed approach is also implemented in an in-house compositional simulator. The multicomponent diffusion model is validated with both intraphase and interphase diffusion experiments. Then, the improved model for fracture/matrix interaction is compared with a fine-grid model. The proposed multiple interacting continua (MINC) model with three continua (MINC3) can better match the fine-grid model’s result than the double-porosity (DP) model, which only obtains a fair match at an early time. Then, we simulate a gas huff ‘n’ puff (HnP) well in the Permian Basin to investigate the effect of diffusion within the fractured tight oil reservoir. The simulation reveals that diffusion has a minor effect on the performance of depletion when oil is the dominant phase. For gas HnP, the simulation neglecting diffusion will underestimate the oil recovery factor (RF) but overestimate the gas rate. The DP approach tends to overestimate the RF of heavy components but leads to a similar cumulative oil RF compared with MINC3. With the diffusion included in the simulation, gas HnP performance becomes more sensitive to the soaking time than the model without diffusion. Although increasing the soaking time will lead to a higher RF after considering diffusion, the incremental oil is not sufficiently large to justify a prolonged soaking time.

Automatic fracture optimization for shale gas reservoirs based on gradient descent method and reservoir simulation

In shale gas reservoir development, determination of hydraulic fracture geometry for horizontal wells is a demanding yet challenging task. One type of approach for hydraulic fracture optimization is based on reservoir simulation. To improve optimization efficiency and accuracy, an automatic and robust procedure integrating the gradient descent method with gas reservoir simulation has been developed. Fractured reservoir models were constructed using the “Multiple INteracting Continua” method, whereby an in-house shale gas reservoir simulator was implemented to model multiple gas transport mechanisms including non-Darcy flow, gas desorption, Klinkenberg effect, and geomechanical effect. The optimization procedure was first validated against two ideal cases and then applied to two realistic cases to optimize fracture spacing, half-length, and dimensionless fracture conductivity. It showed that the optimization results depend on optimization objective, reservoir property, natural fractures, economics and termination criteria. This gradient descent assisted fracture optimization procedure can achieve significant computational reduction and high prediction accuracy for various shale gas reservoir cases. Cited as : Chen, J., Wang, L., Wang, C., Yao, B., Tian, Y., Wu, Y.-S. Automatic fracture optimization for shale gas reservoirs based on gradient descent method and reservoir simulation. Advances in Geo-Energy Research, 2021, 5(2): 191-201, doi: 10.46690/ager.2021.02.08

Numerical simulation of the feasibility of supercritical CO2 storage and enhanced shale gas recovery considering complex fracture networks

In recent years, the greenhouse gas control has been a hot issue. A solution of injecting supercritical CO 2 (scCO 2 ) in Longmaxi shale gas formation (in Southwest China) is proposed in this study. To evaluate the feasibility of this method that storing CO 2 and enhanced gas recovery (EGR) simultaneously, we first carried out isothermal adsorption experiments on samples from Longmaxi formation to describe the adsorption behavior of CH 4 and CO 2 , and a generalized Ono-Kondo Lattice (OK) model was applied to predict adsorption amount of pure CH 4 /CO 2 and their binary mixtures under supercritical, high-pressure conditions. In addition, discrete fracture network (DFN) model was adopted to characterize the complex hydraulic fracture networks constructed from micro-seismic monitoring (MSM) data and engineering analysis. The porous flow in shale matrix was modeled with the multiple interacting continua (MINC) and fractal theories. A multiscale compositional numerical model based on unstructured tri-prism grids was finally developed and solved by control volume finite element (CVFE) method. The simulation results of base and CO 2 injection cases presented that scCO 2 huff ‘n’ puff in Longmaxi formation might be an effective method for CO 2 storage and EGR, and the orthogonal experiments were designed to optimize scenarios in the field application and obtain a maximum balanced result of EUR and CO 2 storage capacity (CSC) for multistage fractured horizontal well (MFHW) with complex fracture networks in shale. • The OK model was applied to predict pure CH 4 /CO 2 and their mixtures adsorption amount under supercritical conditions. • The hybrid DFN and MINC model was established to describe the flow in fractal porous media and complex fracture system. • The CVFE simulator was successfully conducted for comprehensive analysis of mechanisms of scCO 2 storage and EGR in shale.

Numerical Investigation of Wellbore Methane Leakage From a Dual‐Porosity Reservoir and Subsequent Transport in Groundwater

AbstractThree‐dimensional, multiphase simulations are used to analyze migration of methane leakage from a hydrocarbon wellbore. The objective is to evaluate the relevance and importance of coupling fast, advective transport of methane through fractures with slower, diffusive transport in the shale matrix below a freshwater aquifer on water quality assuming dual‐domain mass transfer (DDMT) in the reservoir by using the multiple interacting continua (MINC) as implemented in TOUGH2. The conceptual model includes a methane gas‐phase leak from a wellbore 20–30 m below an aquifer; multiphase, buoyant transport through shale partially saturated with brine; and, after methane leakage reaches groundwater, multiphase transport under varying lateral groundwater flow gradients. Results suggest that DDMT affects the rate of methane reaching groundwater by (i) providing long‐time secondary storage in less‐mobile pore space and (ii) creating larger methane‐plume diameters than those predicted by a single‐domain advection‐diffusion equation. Compared to models without DDMT, these factors combine to increase methane flow rates by an order of magnitude across the base of the aquifer 100 years after leakage begins. In the simulated aquifer, dissolution of gas‐phase plumes leads to bimodal aqueous‐phase methane breakthrough curves in a simulated water well 100 m downstream from leakage, with peak concentrations appearing decades after a 1‐year pulse of leakage. The major implication is that DDMT in the reservoir can explain newly discovered methane concentrations in water wells attributable to older leakage events. Therefore, remediation of abandoned or legacy wells with wellbore integrity loss may be necessary to prevent future incidents of groundwater contamination.

The MINC proximity function for fractured reservoirs flow modeling with non-uniform block distribution

Reservoir simulation is a powerful technique to predict the amount of produced hydrocarbon. After a solid representation of the natural fracture geometry, an accurate simulation model and a physical reservoir model that account for different flow regimes should be developed. Many models based on dual-continuum approaches presented in the literature rely on the Pseudo-Steady-State (PSS) assumption to model the inter-porosity flow. Due to the low permeability in such reservoirs, the transient period could reach several years. Thus, the PSS assumption becomes unjustified. The numerical solution adopted by the Multiple INteracting Continua (MINC) method was able to simulate the transient effects previously overlooked by dual-continuum approaches. However, its accuracy drops with increasing fracture network complexity. A special treatment of the MINC method, i.e., the MINC Proximity Function (MINC–PF) was introduced to address the latter problem. And yet, the MINC–PF suffers a limitation that arises from the existence of several grid-blocks within a studied cell. In this work, this limitation is discussed and two possible solutions (transmissibility recalculation/adjusting the Proximity Function by accounting for nearby fractures) are put forward. Both proposed methods have demonstrated their applicability and effectiveness once compared to a reference solution.

Impact of equilibration time lag between matrix and fractures on the evolution of coal permeability

In conventional dual porosity models, the interactions between matrix and fractures are normally characterized through two equilibrium systems within the same REV (representative elementary volume). This pseudo-steady approach cannot capture the true impact of the non-equilibrium period within each system since it ignores the true transient nature of the fracture-matrix interaction. In this study, a conventional dual porosity model is extended to include the impact of equilibration time lag between matrix and fractures caused by their contrasting properties. To incorporate this important mechanism, the matrix REV is divided into two sub-REVs by using the MINC concept (Multiple Interacting Continua). The time lag effect is defined as a function of the difference between the strain in the matrix REV and that in the sub-matrix REV, and incorporated into a coal permeability model. Consequently, the coal permeability evolves also from initial to final equilibrium. Conventional dual porosity/permeability models represent two end points (initial and final equilibrium) while this new permeability model represents the evolution of coal permeability between these two end points. The model is verified against experimental observations of the evolution of coal permeability under a constant effective stress that extend for more than 80 days. If effective stress remains unchanged, conventional permeability models predict no permeability changes while our new model predicts that coal permeability evolves as a function of time from initial to ultimate equilibrium. Our results suggest that the impact of matrix strain variations on the evolution of coal permeability is significant and should not be ignored.

A Multi-Scale Modeling of Confined Fluid: from Nanopore to Unconventional Reservoir Simulation

Tight oil and shale gas reservoirs have a significant part of their pore volume occupied by micro (below 2 nm) and mesopores (between 2 and 50 nm). This kind of environment creates strong interaction forces in the confined fluid with pore walls and then changes dramatically the fluid phase behavior. An important work has therefore to be done on thermodynamic modeling of the confined fluid and on developing upscaling methodology of the pore size distribution for large scale reservoir simulations. Firstly, the comparison between molecular simulation results and commonly used modified equation of state (EOS) in the literature highlighted the model of flash with capillary pressure and critical temperature and pressure shift as the best one to model confined fluid behavior. Then, fine grid matrix/fracture simulations have been built and performed for different pore size distributions. The study has shown that the pore size distribution has an important impact on reservoir production and this impact is highly dependent on the volume fraction of nanopores inside the matrix. Afterwards, coarse grid upscaling models have then been performed on the same synthetic case and compared to the reference fine grid results. The commonly used upscaling methodology of dual porosity model with average pore radius for the pore size distribution is unable to match the fine grid results. A new triple porosity model considering fracture, small pores and large pores with their own capillary pressure and EOS, together with MINC (Multiple Interacting Continua) approach, has shown very good agreement with the reference fine grid results. Finally a large scale stimulated reservoir volume with different pore size distribution inside the matrix has been built using the upscaling method developed here.

Comparison of Chemical-Component Transport in Naturally Fractured Reservoirs Using Dual-Porosity and Multiple-Interacting-Continua Models

SummaryWe propose a workflow to optimize the configuration of multiple-interacting-continua (MINC) models and overcome the limitations of the classical dual-porosity (DP) model when simulating chemical-component-transport processes during two-phase flow. Our new approach captures the evolution of the saturation and concentration fronts inside the matrix, which is key to design more effective chemical enhanced-oil-recovery (CEOR) projects in naturally fractured reservoirs. Our workflow is intuitive and derived from the simple concept that fine-scale single-porosity (SP) models capture fracture/matrix interaction accurately; it can hence be easily applied in any reservoir simulator with MINC capabilities. Results from the fine-scale SP model are translated into an equivalent MINC model that yields more accurate results compared with a classical DP model for oil recovery by spontaneous imbibition; for example, in a water-wet (WW) case, the root-mean-square error (RMSE) improves from 0.123 to 0.034. In general, improved simulation results can be obtained when selecting five or fewer shells in the MINC model. However, the actual number of shells is case specific. The largest improvement in accuracy is observed for cases where the matrix permeability is low and fracture/matrix transfer remains in a transient state for a prolonged time. The novelty of our approach is the simplicity of defining shells for a MINC model such that the chemical-component-transport process in naturally fractured reservoirs can be predicted more accurately, especially in cases where the matrix has low permeability. Hence, the improved MINC model is particularly suitable to model chemical-component transport, key to many CEOR processes, in (tight) fractured carbonates.

Modeling of Matrix/Fracture Transfer with Nonuniform-Block Distributions in Low-Permeability Fractured Reservoirs

Summary Unconventional shale–gas and tight oil reservoirs are commonly naturally fractured, and developing these kinds of reservoirs requires stimulation by means of hydraulic fracturing to create conductive fluid–flow paths through open–fracture networks for practical exploitation. The presence of the multiscale–fracture network, including hydraulic fractures, stimulated and nonstimulated natural fractures, and microfractures, increases the complexity of the reservoir simulation. The matrix–block sizes are not uniform and can vary in a very wide range, from several tens of centimeters to meters. In such a reservoir, the matrix provides most of the pore volume for storage but makes only a small contribution to the global flow; the fracture supplies the flow, but with negligible contributions to reservoir porosity. The hydrocarbon is mainly produced from matrix/fracture interaction. So, it is essential to accurately model the matrix/fracture transfers with a reservoir simulator. For the fluid–flow simulation in shale–gas and tight oil reservoirs, dual–porosity models are widely used. In a commonly used dual–porosity–reservoir simulator, fractures are homogenized from a discrete–fracture network, and a shape factor based on the homogenized–matrix–block size is applied to model the matrix/fracture transfer. Even for the embedded discrete–fracture model (EDFM), the matrix/fracture interaction is also commonly modeled using the dual–porosity concept with a constant shape factor (or matrix/fracture transmissibility). However, in real cases, the discrete–fracture networks are very complex and nonuniformly distributed. It is difficult to determine an equivalent shape factor to compute matrix/fracture transfer in a multiple–block system. So, a dual–porosity approach might not be accurate for the simulation of shale-gas and tight oil reservoirs because of the presence of complex multiscale–fracture networks. In this paper, we study the multiple–interacting–continua (MINC) method for flow modeling in fractured reservoirs. MINC is commonly considered as an improvement of the dual–porosity model. However, a standard MINC approach, using transmissibilities derived from the MINC proximity function, cannot always correctly handle the matrix/fracture transfers when the matrix–block sizes are not uniformly distributed. To overcome this insufficiency, some new approaches for the MINC subdivision and the transmissibility computations are presented in this paper. Several examples are presented to show that using the new approaches significantly improves the dual–porosity model and the standard MINC method for nonuniform–block–size distributions.

Numerical Modeling of Reactive Transport and Self-Sealing Processes in the Fault-Controlled Geothermal System of the Guide Basin, China

Strong chemical reactions in the geothermal systems may cause sealing of fractures, which reduces the permeability in the reservoir and subsequently affects the heat production. However, it is difficult to reveal the sealing range in a deeply buried reservoir based on a limited number of downhole logs. This study recreated the sealing processes of the fault-controlled geothermal system in the Guide Basin, China, by reactive transport modeling. The modeling domain was discretized based on multiple interacting continua (MINC) approach, to address the nonequilibrium heat transport processes between the matrix and conduit in the fractured fault damage zone. Once the model was validated by observations of major ions in spring water and downhole temperature logs in the discharge area, it was used to determine the coupled processes of fluid, heat, and chemical transport in the reservoir and the resultant sealing ranges. It was found that the dissolution of albite and K-feldspar leads to the precipitation of smectite-Ca and illite in the middle and bottom of the fault under the condition of high concentration of Ca2+ and Mg2+ in the recharge water. Calcite veins were formed in discharge zone, because the horizontal fast flow in shallow subsurface zone supplied abundant Ca2+ and HCO3-. As a consequence, the permeability in the discharge zone reduced by 15% when compared to the original permeability of 100 mD. Moreover, another three self-sealing areas were formed near the recharge zone, the deep upgradient zone, and the downgradient area where the fast upward fluid flow occurred. Self-sealing subsequently prevented the deep circulation of the flow and heat absorption, which tends to make the fault-controlled geothermal system inactive.

A simulator for production prediction of multistage fractured horizontal well in shale gas reservoir considering complex fracture geometry

Shale gas is becoming an increasingly supplementary energy source because of its clean-burning and abundance. Economic gas production in shale requires the techniques of horizontal drilling and multistage hydraulic fracturing to create complex fracture network (CFN). How to accurately describe the characteristics of geometry and flow mechanisms of the CFN and select the most efficient approach for modeling are challenging. In this paper, a production forecasting model for multistage fractured horizontal well (MFHW) with CFN in shale is proposed based on the multiple interacting continua (MINC) theory (organic/inorganic matrix, natural fractures system) and lower-dimensional discrete fracture network (DFN) model (hydraulic fractures system). The model is designed to describe the unconventional flow mechanisms in shale system, such as fractal porous media and non-Darcy multiscale flow in ultra-tight matrix, ad-desorption on organic materials’ surface, rock un-consolidation within natural fractures, high-velocity turbulent flow near well range, and multiphase behaviors. We also propose a novel hybrid control volume finite element (CVFE) and finite-difference (FD) simulation method to obtain the numerical results of the model based on the unstructured 3D tri-prisms. The accuracy of the simulator is successfully validated and sensitivity analysis of some key factors (e.g.: fractal model permeability, Langmuir volume, heterogeneities of reservoir and fractures, well platform) are conducted to evaluate the impacts on production performance. Combing with the micro-seismic monitoring (MSM) data and engineering analyses, the DFN model is applied in Longmaxi shale formation to obtain the history matching with the field data and predict the production.

Flow modelling of unconventional shale reservoirs using a DFM-MINC proximity function

Due to their initial low permeability, unconventional plays can be economical only through hydraulic fracturing. This process, in order to be controlled needs to rely on a solid representation of the natural fracture geometry, an accurate stimulation model which considers the interaction with natural lineaments, and a physical reservoir model which can account for the different flow regimes occurring during production. The stimulated volume drainage can be evaluated using either Decline Curves Analysis/Rate Transient Analysis (DCA/RTA) techniques or reservoir simulation. In both cases, the geometry of the final Discrete Fracture Network (DFN) issued from the natural characterization and the stimulation, is very important, and for practical purposes is either overly idealized (Warren & Root approach) or oversimplified (Bi-wing). The models have shown their limitations when confronted with measurements in the field, opening up ways to use DFN geometries within integrated reservoir studies.The present work addresses some of the issues above, developing a hierarchical Discrete Fracture Model (DFM) based on the “filtering” of a stimulated DFN, realistically obtained by the characterization step and the stimulation process. This leads to a triple-continuum representation, consisting of: (1) the matrix media, (2) a high conductive stimulated fracture network and (3) a low conductive stimulated fracture network.The method consists in homogenizing low conductive networks, keeping a user defined backbone of high conductive fractures as the main “reservoir” DFN. One of the main advantages of this DFM relies on the way we compute the well-known Multiple Interacting Continua (MINC) approach, using a “proximity function” formalism, able to simulate transient effects. Using practical examples, this paper demonstrates applicability capacities of this method, enabling the integration of more complex geometries within a “quick” simulation framework.

Compositional modeling of shale condensate gas flow with multiple transport mechanisms

Shale condensate gas has gained great attention in recent years due to the production of profitable liquid hydrocarbons. The fluid flow in shale matrix is complex and influenced by multiple transport mechanisms, such as stress sensitivity, Knudsen diffusion, adsorption, molecular diffusion, and confined phase behavior. In addition, the coexistence of multiscale pore space, including hydraulic fractures, micro-fractures in simulated reservoir volume (SRV) and nanopores in matrix further increases the fluid flow complexity. Conventional models cannot commonly consider all the factors. In this work, we develop a hybrid model for condensate gas reservoir, where fluid flow is described by compositional model coupled with transport mechanisms, micro-fractures and hydraulic fractures are handled by multiple interacting continua (MINC) model and embedded discretized fracture model (EDFM). Then based on the proposed model, the effects of gas transport mechanisms on a multi-stage fractured horizontal well production are analyzed, where simulations are conducted with and without SRV to investigate the importance of SRV. Furthermore, some important reservoir parameters, such as SRV properties, hydraulic fracture length and bottom-hole pressure are also investigated with the proposed model.

Transport of barium in fractured dolomite and sandstone saline aquifers

To understand the advective-dispersive transport of Ba in fractured dolomite and sandstone saline aquifers, we conducted core-flooding experiments and reactive transport simulations. We used intact and synthetic fractured dolomite and sandstone cores collected from formations where hydraulic fracturing (HF) wastewater is disposed in Oklahoma, USA. The core-flooding experiments were conducted using saline water containing typical concentrations of NaCl (90 g/L), Ca (5 g/L), Mg (1 g/L), and Ba (100 mg/L) in HF wastewaters. At typical concentrations of NaCl, Ca, and Mg in HF wastewater, our experimental results show similar Ba transport rates in both intact and fractured dolomites but faster Ba transport rates in intact than in fractured sandstones. We found a match between measured and simulated breakthrough curves of Ba in intact and fractured sandstones. This supports the hypothesis that the inhibitory effect of salinity on Ba sorption increases Ba transport through matrix pores bordering the fracture while reducing its transport through the fracture. This is reflected by a reduction of the overall rate of Ba transport through fractured dolomites and sandstones. We found that the effect of salinity in retarding Ba transport through fractured dolomites and sandstones increases with increased matrix porosity and/or fracture aperture size. We implemented the multiple interacting continua (MINC) method developed for modeling fluid flow in fractured porous media to successfully capture the effect of salinity, matrix porosity and fracture aperture size on Ba transport in fractured sandstones. The measured and simulated results have significant implications on efforts of field-scale simulations of Ba transport in dolomite and sandstone saline aquifers where HF wastewater is disposed.

Numerical simulation of electricity generation potential from fractured granite reservoir using the MINC method at the Yangbajing geothermal field

Field tests indicate that after hydrofracturing the fracture spacing in an Enhanced Geothermal System (EGS) reservoir may be within 0.33–300 m. For EGS reservoirs with large fracture spacing, it is unreasonable to assume the local thermodynamic equilibrium between water and rock when simulating the heat production process, and temperature gradient between the rock and circulating water must be considered. The multiple interacting continua (MINC) model is an effective method for calculating the temperature gradient between the rock and the circulating water in the EGS reservoirs. In this work we evaluated the electricity generation potential from the 950–1350 m deep fractured granite reservoir at the Yangbajing geothermal field by the MINC method with TOUGH2 software, and analyzed the main factors influencing the system production performance. The results indicate that the system attains an electric power generation potential of 22.2–19.3MW, a reservoir impedance of 0.25–0.39 MPa/(kg/s), a pump power of 0.93–1.78 MW and an energy efficiency of 23.92–10.82 during an exploitation period of 30 years under reference conditions, showing good heat production performance. The main factors influencing the production performance are fracture spacing, fracture permeability, injection temperature and water production rate. Within a certain range, measures to improve the electricity generation performance are to reduce the average fracture spacing, to increase the fracture permeability, or to adopt more reasonable injection temperature and water production rate.

Simulation of Matrix/Fracture Interaction in Low-Permeability Fractured Unconventional Reservoirs

Summary Unconventional reservoirs, such as shale-gas or tight oil reservoirs, are generally highly fractured (including hydraulic fractures and stimulated and nonstimulated natural fractures of various sizes) and embedded in low-permeability formations. One of the main production mechanisms in unconventional reservoirs is the flow exchange between matrix and fracture media. However, because of extremely low matrix permeability, the matrix/fracture exchange is very slow and the transient flow may last several years to tens of years, or almost the entire production life. The commonly used dual-porosity (DP) modeling approach involves a computation of pseudosteady-state matrix/fracture transfers with homogenized fluid and flow properties within the matrix medium. This kind of model clearly fails to handle the long-lasting matrix/fracture interaction in very-low-permeability reservoirs, especially for multiphase flow with phase-change problems. Moreover, a DP model is not adapted for the simulation of matrix/fracture exchange when fractures are described by a discrete-fracture network (DFN). This paper presents an embedded discrete-fracture model (EDFM) dependent on the multiple-interacting-continua (MINC) proximity function to overcome this insufficiency of the conventional DP model.

A Comprehensive Model Coupling Embedded Discrete Fractures, Multiple Interacting Continua, and Geomechanics in Shale Gas Reservoirs with Multiscale Fractures

Shale gas has become one of the primary energy resources during the past few years, and its impact has been profound in many countries. Hydraulic fracturing treatments are required for the development of shale gas reservoirs, and the consequent hydraulic fractures usually connect with the original small-scale natural fractures forming complex fracture networks in these reservoirs. Therefore, a model for numerical simulation, which is capable of accurately modeling naturally and hydraulically fractured reservoirs, is essential in optimization and management of such reservoirs. In this paper, we develop a comprehensive model that couples embedded discrete fractures, multiple interacting continua, and geomechanics to accurately simulate the fluid flow in shale gas reservoirs with multiscale fractures. Large-scale hydraulic fractures are described by an embedded discrete fracture method, while middle-scale and small-scale natural fractures are modeled by a multiple interacting continua method. Usually, the co...

Fractional diffusion modeling of heat transfer in porous and fractured media

Fracture–matrix interactions strongly affect anomalous heat transfer in geological sites. This study investigates effects of the interactions between fractures and rock matrix by using the method of multiple interacting continua (MINC). The MINC generates different temperature histories for varied fracture spacings. Two analytical solutions of each porous model and fracture model are used to fit the numerical results for temperature histories due to cold-water injection. The porous model is good agreement with the result for small fracture spacing, while a solution of the fracture model fits the result for large fracture spacing. The MINC yields intermediate behaviors in between a porous medium and a single fracture. A fractional heat transfer equation (fHTE) has been developed to describe anomalous thermal diffusion in a fractured reservoir. The fHTE accounts for heat flux from fracture into matrix by using a temporal fractional derivative. The fHTE can capture numerical results for temperature histories with different fracture spacings. The fracture spacing has correlations to the fHTE best-fit parameters (i.e., the orders of fractional derivatives and the retardation parameters). The fHTE with varying time fractional derivatives can cover descriptions of subdiffusion, Fickian diffusion, and superdiffusion.