Dual-porosity Dual-permeability Model Research Articles

A Practical probabilistic history matching framework for characterizing fracture network parameters of shale gas reservoirs

Simulating fluid flow in complex fracture systems encountered in subsurface systems, such as those encountered in tight or shale gas reservoirs, presents considerable challenges. Sophisticated numerical techniques and characterization approaches are required to integrate static and dynamic data from multiple sources to account for the intricate interplay between fractures and the surrounding rock matrix. A novel workflow using an indicator-based probability perturbation method (PPM) is applied to characterize uncertain discrete fracture network parameters. The posterior probability distributions of primary and secondary fracture transmissivity, aperture, length, height, and intensity of the secondary fracture are estimated according to the production (flow) histories. A case study based on the Horn River shale gas reservoir is presented. A pilot point scheme is formulated to update the distributions of P32L. The forward modelling entails upscaling each fracture model into a dual-porosity dual-permeability model and performing multiphase flow simulation. This approach produces an ensemble of history-matched discrete fracture and upscaled models by incorporating static and dynamic data. The results demonstrate the utility of the developed method for estimating secondary fracture parameters, which are not inferrable from other static information alone. The inference of both primary and secondary fractures offers a more comprehensive characterization of the fracture networks in tight or shale gas reservoirs. Integrating a pilot point parameterization technique and a sequential simulation approach into the PPM framework presents significant novelties in contributing to a comprehensive and effective method of simulating fluid flow in complex fracture systems, addressing the challenges associated with non-linear relationships between fracture model parameters and the corresponding flow response.

An improved dual-porosity dual-permeability modeling workflow for representing nonplanar hydraulic fractures

The Dual-Porosity Dual-Permeability (DPDK) model is commonly used for upscaling and simulating fractured reservoirs. However, many common upscaling approaches lead to disconnected fracture, particularly when simulating Discrete Fracture Networks (DFN) and nonplanar hydraulic fractures that are not aligned with the axes of corner-point grids supported by most reservoir simulation packages using the Two-Point Flux Approximation (TPFA) technique for flow and mass transfer calculations. This misalignment could result in inaccurate computed fluxes when fractures are disconnected in the upscaling process. Our previous works attempted to address this problem in DFNs by detecting misalignments and adjusting DPDK fracture parameters locally. However, such methods required explicit knowledge of the fracture coordinates. This paper introduces a novel approach based on area interpolation, which identifies disconnected fractures from fracture images without extracting fracture coordinates, significantly improving detection efficiency. This study primarily focuses on nonplanar fractures, aiming to simulate them using the DPDK model accurately. The simulations are compared with those obtained using the Embedded Discrete Fracture Model (EDFM). This work illustrates how nonplanar hydraulic fractures can be effectively simulated in a DPDK model. Our results demonstrate that the adjusted/corrected DPDK model can offer superior or comparable performance to an EDFM for simulating nonplanar fractures. The proposed method is flexible and readily applied in commercial simulation software.

A discrete unified gas kinetic scheme for simulating transient hydrodynamics in porous media with fractures

Tight gas reservoirs have typical characteristics of well-developed natural fractures, extremely low permeability, and low porosity. The flow in such media can be described by a dual-porosity dual-permeability (DPDP) model with the consideration of gas slippage and real gas effects. Based on this model, in this study, a discrete unified gas kinetic scheme is developed to describe the transient hydrodynamic behaviors in porous media with fractures. With an interporosity term, two kinetic equations are employed to capture the pressure propagation in matrix and fracture sub-systems, respectively. The proposed DUGKS can correctly recover the DPDP model through the Chapman–Enskog analysis. Unlike the traditional numerical methods, the velocity in DUGKS can be calculated locally by the non-equilibrium distribution functions. The presented method is verified by three typical problems, including the flow in a fractured porous medium, the flow around a vertical production well, and the flow around a fractured horizontal production well. The numerical results are in good agreement with the reference data. In the test, the global relative errors in pressures are on the order of 10−3. Moreover, the transient hydrodynamics in porous media with fractures are evaluated. The simulation results show that the slippage mainly occurs in the matrix, and this effect may result in a 20% increase in permeability. With the consideration of slippage and real gas effects, the predicted production is higher than that predicted by Darcy’s law. In addition, the results indicate that hydraulic fractures have a great impact on production.

Improved Permeability Model of the Binary Gas Interaction within a Two-Phase Flow and its Application in CO2-Enhanced Coalbed Methane Recovery.

In this paper, we develop a dual-porosity dual-permeability model for binary gas migration to explore the permeability evolution in the matrix and fracture in the process of a gas–water two-phase flow during CO2-enhanced coalbed methane (CO2-ECBM) recovery in coal reservoirs. This mechanistic model accommodates the effects of elastic deformation caused by the effective stress change in the matrix and fracture, the swelling/shrinkage deformation of the matrix caused by adsorption/desorption, the convection and diffusion of gas, and the discharge of water. Specifically, the time-dependent matrix swelling, from initially completely reducing the fracture aperture to finally affecting the coal bulk volume, is considered by the invaded volume fraction involving binary gas intrusion. The model is validated through laboratory data and applied to examine the permeability evolution of CO2-ECBM recovery for 10 000 days. Furthermore, we analyze the sensitivity of some selected initial parameters to capture the key factors affecting CO2-ECBM recovery. Our modeling results show that the permeability evolution can be divided into two stages during the process, where stage I is dominated by effective stress and stage II is dominated by adsorption/desorption. Increasing the injection pressure or initial permeability advances the start of stage II. The decrease in initial water saturation causes the permeability to change more drastically and the time of stage II to appear earlier until a time long enough, after which little effect is seen on the permeability results.

Application of an Accurate and Efficient Modeling Approach to a Multiscale Fractured Reservoir in South China Sea

Carbonate reservoirs in the South China Sea mostly contain natural fractures with various length scales and different intensities, which causes great challenges in efficient reservoir modeling and flow simulation. Existing efforts based on dual-porosity and dual-permeability models could not reflect the characteristics of production data in certain wells. To accurately and efficiently characterize multiscale fractures, a hybrid fracture characterization method is proposed. Firstly, fractures are divided into two types according to the geometrical size and interpretation approach. Then, small-scale fractures, characterized mainly by image log interpretations, are modeled by the traditional dual-porosity/dual-permeability (DP) method. And large-scale fractures, which are characterized by seismic interpretations and dominate the flow regime, are modeled by the embedded discrete fracture method (EDFM) to achieve both accuracy and efficiency. Lastly, transmissibilities among these three types of grid mediums are calculated to generate the hybrid DP+EDFM model for flow simulation. The proposed approach is applied to a carbonate, fractured reservoir in the South China Sea. The overall procedure is fast and reliable, and water cut matches of both field and specific wells are dramatically improved. Comparing the simulation results with the conventional DP model, the proposed approach yields much more accurate predictions on rapid water breakthrough and high water cut in fractured reservoirs.

Smart Proxy Modeling of a Fractured Reservoir Model for Production Optimization: Implementation of Metaheuristic Algorithm and Probabilistic Application

Numerical reservoir simulation has been recognized as one of the most frequently used aids in reservoir management. Despite having high calculability performance, it presents an acute shortcoming, namely the long computational time induced by the complexities of reservoir models. This situation applies aptly in the modeling of fractured reservoirs because these reservoirs are strongly heterogeneous. Therefore, the domains of artificial intelligence and machine learning (ML) were used to alleviate this computational challenge by creating a new class of reservoir modeling, namely smart proxy modeling (SPM). SPM is a ML approach that requires a spatio-temporal database extracted from the numerical simulation to be built. In this study, we demonstrate the procedures of SPM based on a synthetic fractured reservoir model, which is a representation of dual-porosity dual-permeability model. The applied ML technique for SPM is artificial neural network. We then present the application of the smart proxies in production optimization to illustrate its practicality. Apart from applying the backpropagation algorithms, we implemented particle swarm optimization (PSO), which is one of the metaheuristic algorithms, to build the SPM. We also propose an additional procedure in SPM by integrating the probabilistic application to examine the overall performance of the smart proxies. In this work, we inferred that the PSO had a higher chance to improve the reliability of smart proxies with excellent training results and predictive performance compared with the considered backpropagation approaches.

Fluid Displacement in a Dual-Permeability Medium with Local Capillary Equilibrium

The solution to the Buckley–Leverett problem in fractured porous media is investigated by applying the dual-porosity dual-permeability model. It is shown that the dual-permeability medium is equivalent to an upscaled homogenized medium at long injection times when local capillary equilibrium is established. Simple analytical relationships for the petrophysical properties and saturation functions of the equivalent medium are derived. The upscaled relative permeability and the fractional flow function can exhibit kinks, resulting in more complicated solutions to the Buckley–Leverett problem as compared to the classical case. It is found that immiscible displacement in fractured porous media leads to the appearance of saturation profiles with several displacement fronts and rarefaction waves. Up to four solution types are possible, which are constrained in a solution map constructed in the space of the dimensionless parameters of the problem. It is shown that, for particular parameters, the displacing fluid moves faster through the matrix than through the fractures.

A dual-porosity dual-permeability model for acid gas injection process evaluation in hydrogen-carbonate reservoirs

The Pre-Caspian basin is one of the most prolific in terms of oil and gas exploration and hydrogen and carbon compounds energy production around the world. The major hydrogen and carbon compounds reservoirs are Carboniferous reef and platform hydrogen-carbonate rocks. The original fluids under subsurface conditions contain 15% hydrogen sulfide and 4% carbon dioxide. Acid hydrogen and carbon compounds reinjection is not only an environmentally friendly solution for disposal of produced greenhouse gases but also enhances oil recovery and supplies more fuel energy. On the other hand, the presence of fractures makes hydrogen-carbonate reservoir characteristics nature more complicated than conventional sandstone reservoirs, which leads to a tremendous challenge to evaluate the gas injection process. In this work, a dual-porosity dual-permeability formulation was used to model the dual-medium nature incorporating matrix system with high porosity and low permeability and fracture network with low porosity and high permeability. After matching PVT experiments, a ten pseudo-components fluid model was generated for running compositional simulation. The miscible hydrogen and carbon compounds injection was simulated as an effective enhanced oil recovery approach. Sensitivity analysis such as timing of injection gas, injection rate, well spacing and completion interval have proposed the optimal condition for the miscible hydrogen and carbon compounds flooding. The recommended optimum hydrogen and carbon compounds injection scenario is twice higher oil recovery compared with natural depletion. The results of this study illustrate further the practicability of pseudo-components splitting and lumping for compositional simulation to evaluate the performance of hydrogen and carbon compounds injection processes, and are of great importance using the dual-porosity dual-permeability method performing numerical simulation of naturally fractured hydrogen-carbonate reservoirs.

Hydrodynamics Behaviour of Single and Multi Fracture with Different Orientations in Petroleum Reservoir

The studying of fluid flow throughout fracture in the reservoir is one of the most vital subjects attracted much attention from engineers and geologists. In the present paper, the Dual Porosity-Dual Permeability (DPDP) model has been applied to represent the fluid flow within the fractured reservoirs. This work aimed to demonstrate the utility of the fractures in the petroleum reservoir and how could be used the positive effect of these fractures on the productivity as well. The productivity of single-phase fluid flow within the single horizontal fracture, multi horizontal fractures, and inclined fracture with different orientations (20o, 30o, 45o, and 70o) have been implemented by using ANSYS-CFX program and compared with the productivity of conventional (without fractures) reservoirs. In addition to, visualize the velocity streamlines within fracture and matrix zones for the DPDP model. To verify this work the comparison has been made with published paper, which studies the fluid flow through fractures, and a good agreement has been obtained with each other. The study indicates that the presence of macro scale fractures in petroleum reservoirs contributes to increasing the total productivity of these reservoirs. Clearly, the productivity index of multi-horizontal fractures domain is more than twice of nonfractured domain. It is also clear that, when comparing the fractured and nonfractured reservoir, the improvement percentage of the productivity index reaches to (71.8) for a single horizontal fracture with 9 ft length. While this percentage would be about (116.88) if the fracture is inclined with 20o.

Comparative study of shale-gas production using single- and dual-continuum approaches

In this paper, we explore the possibility of specifying the ideal hypothetical positions of matrices blocks and fractures in fractured porous media as a single-continuum reservoir model in a way that mimics the dual-porosity dual-permeability (DPDP) configuration. In order to get an ideal mimic, we use the typical configuration and geometrical hypotheses of the DPDP model for the SDFM. Unlike the DPDP model which consists of two equations for the two-continuum coupled by a transfer term, the proposed single-domain fracture model (SDFM) model consists of a single equation for the single-continuum. Each one of the two models includes slippage effect, adsorption, Knudsen diffusion, geomechanics, and thermodynamics deviation factor. For the thermodynamics calculations, the cubic Peng-Robinson equation of state is employed. The diffusion model is verified by calculating the total mass flux through a nanopore by combination of slip flow and Knudsen diffusion and compared with experimental data. A semi-implicit scheme is used for the time discretization while the thermodynamics equations are updated explicitly. The spatial discretization is done using the cell-centered finite difference (CCFD) method. Finally, numerical experiments are performed under variations of the physical parameters. Several results are discussed such as pressure, production rate and cumulative production. We compare the results of the two models using the same dimensions and physical and computational parameters. We found that the DPDP and the SDFM models production rate and cumulative production behave similarly with approximately the same slope but with some differences in values. Moreover, we found that the poroelasticity effect reduces the production rate and consequently the cumulative production rate but in the SDFM model the reservoir takes more time to achieve depletion than the DPDP model. The normal fracture factor which appears in the transfer term of the DPDP model is adjusted against the SDFM.

A multi-continuum multi-phase parallel simulator for large-scale conventional and unconventional reservoirs

Reservoir simulation is considered as the core of data analysis during the development of an oilfield. With higher requirements from reservoir engineers, high-resolution geological model problems are commonly used in reservoir simulation. To simulate this kind of large-scale reservoir problems, based on black-oil models and compositional model, a parallel simulator is developed in this paper. Cartesian and corner point grids are supported by our simulator to describe complex geology, including faults and pinch-outs. The multi-continuum models (including a dual-porosity model, a dual-porosity dual-permeability model, and a multiple interacting continua model) are used to simulate fractured reservoirs. Geomechanics effects are successfully involved through a flexible and convenient interface provided by our simulator. Krylov subspace linear solvers, restricted additive Schwarz method, incomplete LU factorization (ILU) preconditioner, and a family of CPR (constrained pressure residual)-type preconditioners are implemented to provide flexibility of the linear system solution processes. Moreover, a new adaptive preconditioning strategy, which can automatically select and change preconditioner between a CPR-type preconditioner and an ILU preconditioner, is designed to accelerate the solution processes and is considered as the most efficient preconditioning technique to our knowledge. MPI-based parallel implementation is employed for each module of the simulator. With the simulator we developed, various conventional and unconventional reservoir simulation problems with large-scale geological models can be achieved on parallel computers within practical computational time. The computational efficiency and parallel scalability are achieved by our high-quality parallel implementation and efficient nonlinear and linear solution techniques.

Effective Local-Global Upscaling of Fractured Reservoirs under Discrete Fractured Discretization

The subsurface flow in fractured reservoirs is strongly affected by the distribution of fracture networks. Discrete fracture models, which represent all fractures individually by unstructured grid systems, are thus developed and act as a more accurate way for fractured reservoir simulation. However, it is usually not realistic to directly apply discrete fracture models to simulate field scale models for efficiency reasons. There is a need for upscaling techniques to coarsen the high resolution fracture descriptions to sizes that can be accommodated by reservoir simulators. In this paper, we extended the adaptive local-global upscaling technique to construct a transmissibility-based dual-porosity dual-permeability model from discrete fracture characterizations. An underlying unstructured fine-scale grid is firstly generated as a base grid. A global coarse-scale simulation is performed to provide boundary conditions for local regions and local upscaling procedures are carried out in every local region for transmissibility calculations. Iterations are performed until the consistency between the global and local properties is achieved. The procedure is applied to provide dual-porosity dual-permeability (DPDK) parameters including coarse-scale matrix-matrix, fracture-fracture and matrix-fracture flux transmissibilities. The methodology is applied to several cases. The simulation results demonstrate the accuracy, efficiency and robustness of the proposed method.

NUMERICAL SIMULATION OF A NATURALLY FRACTURED RESERVOIR.

This research is concerned with the development of a numerical model for stratified normally fractured reservoirs. Three dimensional three phase flow black oil simulation model is adopted. The dual porosity-dual permeability model is used. The IMPES (Implicit Pressure Explicit Saturation) method is used to solve the difference equations. The Tertiary trap in K oil field (an Iraqi oil field) was simulated by the numerical model. The trap consists of six layers having different properties. Equally spaced Cartesian grids were used to divide each layer into 1600 cells in the x-y plane with the thickness as the dimension of each grid block in z direction. Applying the two IMPES pressure equations to each grid of the simulated domain resulting in a block seven diagonal coefficient matrix.