Dual-continuum Models Research Articles

Exploring Health Literacy and Psychological Resilience as Moderators of Symptoms of Mental Illness Among Australian Men.

Although highly related, mental illness may not fully determine perceived well-being, a distinction captured by dual-continuum models. Separating mental illness and well-being into related but separate constructs prompted investigation into potential buffers to reduce the impact of mental illness on perceived well-being. This study explored two such buffers in health literacy and psychological resilience among Australian men. Using the Ten to Men Australian Longitudinal Study on Male Health, this secondary data analysis of n = 8,408 men between 18 and 60 years of age assessed the moderating effect of three components of health literacy (feeling supported by health care providers, ability to find health information, and active engagement with health care providers) and psychological resilience on the relationship between mental illness and well-being. Mental illness symptoms were negatively associated with well-being, whereas psychological resilience, active engagement with health care, and health care provider support (β res = .65, β eng = .28, and β sup = .25) had positive significant relationships with the outcome (all p ≤ .001). Ability to find health information (p = .25) and psychological resilience (p = .43) were not significantly associated with well-being. Of the four interactions tested, health literacy relating to health care worker support was the only significant moderator between mental illness and well-being (β sup = .03). This study identified that meaningful support and understanding from health care providers for Australian men aged between 18 and 60 years may somewhat ameliorate the impact of mental illness on well-being. Further related investigation may reveal specific interventions that improve perceptions of support among men.

Analytical modification of EDFM for transient flow in tight rocks

The commercial development of unconventional resources with multiply fractured horizontal wells has been in the spotlight over the last ten years because of the significant contribution of unconventional oil and gas (UOG) reservoirs to the total US oil and gas production. UOG reservoirs contain multiscale fractures with heterogeneous properties, so the focus has been on efficient and accurate models that can account for these fractures individually. One of such models is the embedded discrete fracture model (EDFM), which has been applied to various types of fractured reservoirs. This work shows that the application of EDFM in fractured tight rocks yields significant errors because it cannot account for the expected transient flow between the matrix and fractures. To address the limitation when EDFM is used in tight rocks with structured Cartesian grids, we modified the matrix/fracture non-neighboring connection (NNC) flux in EDFM by multiplying it with a transient factor. We obtained this factor as in the transient matrix/fracture transfer term for dual-continuum models and implemented it in in our open-source shale simulator. We simulated a single vertical fracture in the middle of a tight reservoir with and without this EDFM modification and show the importance of the proposed modification. We also simulated cyclic gas enhanced oil recovery (CGEOR) in a fractured Bakken shale oil well and analyzed the model results using standard rate-transient analysis plots to evaluate the significance of the proposed modification. The results show that the standard EDFM underestimates oil and gas production by up to 73% at early times. This work presents the first analytical modification of EDFM to account for the nonlinear pressure drop expected near fracture surfaces. Comparing the modified and standard EDFM model results to a reference solution shows that the modified EDFM matches it. In contrast, the standard EDFM cannot match the reference solution when we use structured Cartesian grids with linear spacing. Additionally, by timing the simulation of a representative Bakken shale oil reservoir with 256 fractures, we show that the analytical modification proposed is only 1.5% slower than the standard EDFM.

On the parameterisation of dual-continuum models for reactive transport modelling in fractured media

In sparsely fractured rocks, the rock matrix is an important geochemical buffer and provides significant retardation to contaminants advected through the flowing fractures. Accounting for geochemical reactions and mass exchange between these two regions is key to properly capture the overall buffering capacity and the related hydrogeochemical evolution of a fractured medium. Reactive transport modelling in these kinds of fractured media is routinely performed using Equivalent Continuous Porous Media (ECPM) models: i.e. continuum models based on permeability and porosity fields that somehow preserve the underlying fracture properties, which are in turn described by companion Discrete Fracture Network (DFN) models. However, the proper parameterisation of these models, in terms of mass exchange between fractures and the bordering matrix, is still a largely unresolved issue. Here, we leverage the Dual Continuum Disconnected Matrix Model (DCDMM) formulation included in the massively parallel code PFLOTRAN to propose a novel parameterisation approach that honours the local volumetric fracture density (P32). The proposed approach is first benchmarked against a semi-analytical solution with a problem that entails flow and transport along two different and consecutive fractures. Two demonstrative large-scale reactive transport problems are also presented and discussed: the first is related to the generation and migration of radiogenic helium and the second assesses the buffering capacity of a realistic fractured medium against the infiltration of acidic water. The latter simulation, which includes more than three hundred million transport degrees of freedom is one of the largest subsurface reactive transport models ever formulated and solved. This simulation was made possible by the highly efficient implementation of the DCDMM in PFLOTRAN, which makes the solution of the secondary continuum equations embarrassingly parallel.

A new approach for modeling three-dimensional fractured reservoirs with embedded complex fracture networks

In the last decades, the study of fluid flow through discontinuities such as fractures has received significant attention from the petroleum industry owing to the discovery of highly productive naturally fractured reservoirs. Several approaches based on an explicit or implicit representation of fractures have been adopted for modeling fluid migration in fractured rocks. The explicit approach is the most accurate for such a purpose; however, it is computationally expensive. Alternatively, the implicit representation is very attractive because fracture properties, such as stiffness and permeability can be introduced in the model through dual continuum models. Therefore, the modeling of fluid flow through fractured porous media has been performed through conceptual models, while the modelling of more realistic scenarios is still an open question. This paper proposes a new embedded fracture approach for fluid flow in highly fractured porous media. This approach includes the fracture contribution into the continuum element using a condensation technique based on the multi-constrain method. The main advantage of this approach is the guarantee of compatibility between fracture and porous matrix within a standard finite element mesh. Several fractured rock reservoir cells are analyzed to demonstrate the robustness of the proposed approach and its applicability to highly fractured rocks with random fracture orientation. The pore pressure field obtained with the proposed embedded approach is very close to the predictions provided by the explicit approach with zero-thickness interface elements. Despite the simplicity of the method, the results are promising.

Foundations and Their Practical Implications for the Constitutive Coefficients of Poromechanical Dual-Continuum Models

A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.

Differences in Performance of Models for Heterogeneous Cores during Pulse Decay Tests

Shale and fractured cores often exhibit dual-continuum medium characteristics in pulse decay testing. Dual-continuum medium models can be composed of different flow paths, interporosity flow patterns, and matrix shapes. Various dual-continuum medium models have been used by researchers to analyze the results of pulse decay tests. But the differences in their performance for pulse decay tests have not been comprehensively investigated. The characteristics of the dual-permeability model and the dual-porosity model, the slab matrix, and the spherical matrix in pulse decay testing are compared by numerical modeling in this study. The pressure and pressure derivative curves for different vessel volumes, storativity ratios, interporosity flow coefficients, and matrix-fracture permeability ratios were compared and analyzed. The study found that these models have only a small difference in the interporosity flow stage, and the difference in the matrix shape is not important, and the matrix shape cannot be identified by pulse decay tests. When the permeability of the low permeability medium is less than 1% of the permeability of the high permeability medium, the difference between the dual-permeability model and the dual-porosity model can be ignored. The dual-permeability model approaches the pseudo-steady-state model as the interporosity flow coefficient and vessel volume increase. Compared with the dual-porosity model, the dual-permeability model has a shorter horizontal section of the pressure derivative in the interporosity flow stage. Finally, the conclusions were verified against a case study. This study advances the ability of pulse decay tests to investigate the properties of unconventional reservoir cores.

Vertically integrated dual-continuum models for CO2 injection in fractured geological formations

Various modeling approaches, including fully three-dimensional (3D) models and vertical-equilibrium (VE) models, have been used to study the large-scale storage of carbon dioxide (CO2) in deep saline aquifers. 3D models solve the governing flow equations in three spatial dimensions to simulate migration of CO2 and brine in the geological formation. VE models assume rapid and complete buoyant segregation of the two fluid phases, resulting in vertical pressure equilibrium and allowing closed-form integration of the governing equations in the vertical dimension. This reduction in dimensionality makes VE models computationally much more efficient, but the associated assumptions restrict the applicability of VE models to geological formations with moderate to high permeability. In the present work, we extend the VE models to simulate CO2 storage in fractured deep saline aquifers in the context of dual-continuum modeling, where fractures and rock matrix are treated as porous media continua with different permeability and porosity. The high permeability of fractures makes the VE model appropriate for the fracture domain, thereby leading to a VE dual-continuum model for the dual continua. The transfer of fluid mass between fractures and rock matrix is represented by a mass transfer function connecting the two continua, with a modified transfer function for the VE model based on vertical integration. Comparison of the new model with a 3D dual-continuum model shows that the new model provides comparable numerical results while being much more computationally efficient.

Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties

Here, we present some Reduced Basis (RB) methods for fluid infiltration problems through certain porous media modeled as dual-continuum with localized uncertainties. We apply dimension reduction techniques to construct a reduced order model. In the RB methods, to perform the offline–online computation decomposition, the model inputs need to be affinely dependent on the uncertainties. We develop a Proper Orthogonal Decomposition and Greedy (POD-Greedy) RB method for stochastic dual-continuum models. In the POD-Greedy RB framework, for heterogeneous porous media, we need to solve the stochastic dual-continuum models many times using very fine grid to construct a set of snapshots for building optimal reduced basis. This offline computation may be very expensive. To improve the offline computational efficiency, we further develop a local–global RB method, which integrates the coupled multiscale and multicontinuum approach using Generalized Multiscale Finite Element Method (GMsFEM) to the POD-Greedy RB method. To illustrate the efficiency of the proposed methods, we present two numerical examples for stochastic dual-continuum models. Our numerical results show that both the POD-Greedy RB method and the local–global RB method greatly improve the computation efficiency with high approximation accuracy.

Multi-component transport of BTX in a discretely fractured aquifer with fracture–skin: numerical investigation and sensitivity analysis

Monitoring of BTX natural attenuation in a fractured rock aquifer is highly challenging due to lack of knowledge about the influence of interaction of heterogeneous domains on transport processes. Contaminant transport in a fractured rock is commonly investigated using dual continuum models by considering fracture and its surrounding rock–matrix as two different continuums. In this study, a numerical multi-component transport model based on a triple continuum modeling approach is developed to investigate the transport of dissolved BTX in a discretely fractured aquifer with fracture–skin. A residual BTX source zone is considered to be present at the fracture inlet. A multi-component dissolution model is coupled with the present numerical model to simulate the dissolution of benzene, toluene and xylene at the residual BTX source. Dissolved BTX components are considered to undergo sorption and biodegradation in addition to advection and dispersion within the fracture. Dissolved BTX components diffusing to fracture–skin and rock–matrix are considered to undergo sorption and biodegradation in fracture–skin and rock–matrix. A novel sensitivity analysis approach based on spatial moments is introduced in the manuscript to investigate the sensitivity of various flow and transport parameters of fracture–skin and rock–matrix on dissolved BTX mass retained in fracture and matrix. The presence of fracture–skin is found to significantly affect the concentration distribution and mass retention of dissolved BTX components in a fractured aquifer.

Numerical simulation of CO2 huff-n-puff in complex fracture networks of unconventional liquid reservoirs

Horizontal drilling and hydraulic fracturing produce Unconventional Liquid Reservoirs (ULRs) economically. One of the characteristics of the ULRs is high production declining rate, and thus enhanced oil recovery techniques such as Huff-n-Puff will ensue. In addition, the existence of complex fracture network has been proven by both field and simulation work. This study investigated the potential of CO2 huff-n-puff in ULRs with complex fracture networks. Two fracture characterization techniques for complex fracture network such as fractal-based, and microseismic-based were applied to reduce uncertainties of fracture networks and thus improve the accuracy of simulation input. In order to study complex CO2 recovery mechanism, lab-measured data was upscaled to the field-scale, and then used for evaluating production performance of a simple fracture network. Detailed sensitivity analysis showed that diffusion in the field scale is negligible compared with other recovery mechanisms such as oil swelling, gas expansion, viscosity reduction, etc. The following comparison between dual continuum and the explicit fracture modeling approaches highlights the importance of heterogeneity due to the explicit fractures. Dual continuum models yields less accurate pressure behavior than explicit discrete fracture models even though production behavior could be history matched.

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

Discrete-Fracture and Dual-Permeability Models for Multiphase Flow in Naturally Fractured Reservoirs

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 142295, ’Comparison of Discrete-Fracture and Dual-Permeability Models for Multiphase Flow in Naturally Fractured Reservoirs,’ by Ali Moinfar, SPE, University of Texas at Austin, and Wayne Narr, SPE, Mun-Hong Hui, SPE, Bradley Mallison, SPE, and Seong H. Lee, SPE, Chevron Energy Technology Company, prepared for the 2011 SPE Reservoir Simulation Symposium, The Woodlands, Texas, 21-23 February. The paper has not been peer reviewed. Two discrete-fracture models (DFMs) based on different numerical techniques have been developed for studying the behavior of naturally fractured reservoirs (NFRs). One model uses unstructured gridding with local refinement near fractures, while in the second model, fractures are embedded in a structured matrix grid. Both models capture the complexity of a typical fractured reservoir better than conventional dual-permeability models. Introduction Regarding flow behavior, NFRs can be considered as comprising two media (rock matrix and fractures) with very different properties. Generally, the rock matrix provides primary storage of hydrocarbons while fractures serve as highly conductive flow paths. Fracture apertures are very small compared to matrix dimensions (often 0.1 mm or less in petroleum reservoirs); hence, fractures hold very little fluid, yet the permeability can be very high (e.g., hundreds of darcies). The large contrast between matrix and fracture permeability, coupled with small fracture volumes, makes numerical simulation of fluid flow in NFRs challenging. A dual-porosity model presumes that flow occurs in fractures, and that the rock matrix acts only as fluid storage. Interconnected fractures provide the flow path to injection and production wells. In this model, matrix and fracture domains are linked through an exchange term that connects each fracture cell to its corresponding matrix cell in a gridblock. The dual-porosity model is a simplistic representation of a geologically complex reservoir. Consequently, considerable effort has been devoted to make the dual-porosity model more realistic. DFMs were developed to reduce the number of nonphysical abstractions inherent in dual-continuum models. Most DFMs rely on unstructured grids to represent a fracture network explicitly. Compared with dual-porosity models, DFMs can simulate realistic fracture-system geometry; hence, they account explicitly for the effect of individual fractures on fluid flow. DFMs are not overly constrained by grid-defined fracture-geometry constraints; hence, the fracture model is adaptable and updatable. Specification of the exchange between matrix and fracture is more straightforward because it depends directly on fracture geometry. A disadvantage, however, is that DFMs typically lead to discrete systems of equations that have a complex structure and that are difficult to solve numerically. However, advances in numerical-solution methods have helped to minimize this disadvantage. The accuracy of two recently developed DFMs was studied. Sensitivity of DFMs to background-grid orientation was tested. Comparisons were made of the two new modeling methods with dual-permeability modeling in sparsely fractured reservoirs and in highly and more variably fractured systems.

Status of Dual-Continuum Models for Naturally Fractured Reservoir Simulation

Naturally fractured reservoirs (NFR) contain significant portions of the world's proven reserves of conventional oil. However, their simulation is one of the most challenging and computationally intensive problems in reservoir engineering. Most commercial reservoir simulators use dual-continuum models to predict performance of an NFR where two overlapping continua for the fracture and matrix medium are considered. Then transfer of multiphase fluid between the two media is taken into consideration by a source-sink transfer function (Zhang and Sun, 2000). After review of different conceptual models to simulate an NFR, major pitfalls related to dual-porosity and dual-permeability models for simulation of such reservoirs will be discussed briefly within this article.

Time-dependent matrix-fracture shape factors for partially and completely immersed fractures

The modeling of multiphase flow in fractured porous media relies on the accurate description of fracture-to-matrix transfer of water. Calculation of this rate, within dual-continuum models, depends on matrix-fracture transfer functions incorporating the so-called shape factor. Typically, matrix-to-fracture transfer functions are obtained by assuming all fractures to be instantaneously immersed in water (instantly-filled), with a uniform fracture pressure distribution under pseudo-steady state conditions. The result is constant, time-independent, shape factors. Clearly, this is not necessarily true. Partially immersed fractures and other unsteady-state conditions do not lead to constant shape factors. A new time-dependent matrix-fracture transfer shape factor formulation and transfer functions for both filling- and instantly-filled fracture transfer are derived based on dimensional analysis of experimental data. The dimensional analysis of full-physics data avoids simplifications that may lead to expressions that do not represent accurately matrix-fracture transfer. The new shape factor carries information about the transient behavior of the water saturation, S w, and so it leads to more accurate description of the matrix-fracture transfer. Good agreement was found between experimental data, an analytical model, and a proposed modified dual-porosity formulation with the new time-dependent shape factor and transfer function.

Abstract: Linking Dual Porosity Continuum and Discrete Feature Network Models for Fractured Reservoirs

Abstract: Linking Dual Porosity Continuum and Discrete Feature Network Models for Fractured Reservoirs