Multiple Interacting Continua Method Research Articles

A heat mining strategy for the potential Enhanced Geothermal System of the Acoculco Caldera Complex, Puebla (Mexico): A numerical approach based on Multiple Interacting Continua

As the world faces a transition to low-carbon electricity, energy markets have witnessed a fast expansion of Variable Renewable Energy, such as solar and wind power. In contrast, the installed capacity of geothermal electricity has increased with at a much lower rate. Continuous innovation is required to maintain geothermal electricity as a cost-competitive technology that helps building flexible power generation systems. Here we propose a heat mining setup for the promissory Enhanced Geothermal System (EGS) of the Acoculco caldera complex, which hosts a heat source in low permeability rocks. The conceptual model of the EGS reservoir consists of a fractured-porous layer between impermeable confining beds. An injection-production triplet is located in line with a fault plane that intersects the model area. Under the assumption of hydraulic stimulation to the fault zone, flow of the injection-production system restricts to a fracture network with secondary and variable permeability. Mass and heat transport is modeled following the Multiple Interacting Continua method with the software TOUGH2. We evaluate the performance of the heat mining system considering water and CO2 as working fluids for a given flow rate. We also evaluate the impact of fracture spacing in the reservoir performance. Results show that for a reservoir temperature of 300 °C, the CO2-based system experiences considerable adverse flow conditions that demands a higher pressure differential between the producer and injector (about 60 bar higher than the water-based reservoir). Likewise, the low heat capacity of CO2 imply a considerable limitation for heat mining. While for the water-based reservoir the cooling front extends throughout the entire reservoir at 30 yr of operation, for CO2 this happens in only about 60%. Additionally, the energy extracted per unit time in the water-based reservoir results more than twice the energy extracted with CO2. Finally, our numerical results show that fracture spacings in the range of 10 to 75 m behave similarly in terms of heat mining performance; decreasing the heat exchange area by increasing the fracture spacing from 10 to 75 m produces a minor impact under the assumption of high permeability fractures. Additional constrains for the fracture network, such as geometry, effective porosity and permeability of both fractures and rock matrix, have to be investigated in future research to better understand the possible performance of the production system.

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.

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 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.

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...

Numerical Analysis of Thermal Remediation in 3D Field-Scale Fractured Geologic Media.

Thermal methods are promising for remediating fractured geologic media contaminated with volatile organic compounds, and the success of this process depends on the coupled heat transfer, multiphase flow, and thermodynamics. This study analyzed field-scale removal of trichloroethylene (TCE) and heat transfer behavior in boiling fractured geologic media using the multiple interacting continua method. This method can resolve local gradients in the matrix and is less computationally demanding than alternative methods like discrete fracture-matrix models. A 2D axisymmetric model was used to simulate a single element of symmetry in a repeated pattern of extraction wells inside a large heated zone and evaluate effects of parameter sensitivity on contaminant recovery. The results showed that the removal of TCE increased with matrix permeability, and the removal rate was more sensitive to matrix permeability than any other parameter. Increasing fracture density promoted TCE removal, especially when the matrix permeability was low (e.g., <10(-17) m(2)). A 3D model was used to simulate an entire treatment zone and the surrounding groundwater in fractured material, with the interaction between them being considered. Boiling was initiated in the center of the upper part of the heated region and expanded toward the boundaries. This boiling process resulted in a large increase in the TCE removal rate and spread of TCE to the vadose zone and the peripheries of the heated zone. The incorporation of extraction wells helped control the contaminant from migrating to far regions. After 22 d, more than 99.3% of TCE mass was recovered in the simulation.

Modeling Two Phase Flow in Large Scale Fractured Porous Media with an Extended Multiple Interacting Continua Method

Modeling Two Phase Flow in Large Scale Fractured Porous Media with an Extended Multiple Interacting Continua Method

A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media

AbstractA multiple interacting continua (MINC) method is presented, which is applicable for numerical simulation of heat and multiphase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on. the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be controlled primarily by the distance from the fractures, which leads to the use of nested gridblocks. The MINC concept is implemented through the integral finite difference (IFD) method. No analytical approximations are made for the coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in a simulation are preprocessed from a specification of fracture spacings and apertures and the geometry of the matrix blocks.The numerical implementation of the MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems.