Modeling of anomalous gas transport in heterogeneous unconventional reservoirs using a nonlinear generalized diffusivity equation

Garcez, Jonathan; Zhang, Miao; Ayala, Luis F.

doi:10.1016/j.fuel.2023.127519

Cited by 5 publications

(2 citation statements)

References 45 publications

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“…To treat these nonlinearities, the pseudo-variable approach [123,124] is predominantly adopted to remove the nonlinearity caused by the dependence of gas properties on pressure, while the perturbation technique proves applicable in treating the nonlinearities caused by stress-sensitive permeability [60,61]. Other methods for solving nonlinear differential equations also include Green's function approach [83,125] and the piecewise constant diffusivity approach [81].…”

Section: Analytical and Semi-analytical Methodsmentioning

confidence: 99%

A Review of Macroscopic Modeling for Shale Gas Production: Gas Flow Mechanisms, Multiscale Transport, and Solution Techniques

Liu,

Zhang,

Zhang

et al. 2023

Processes

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The boost of shale gas production in the last decade has reformed worldwide energy structure. The macroscale modeling of shale gas production becomes particularly important as the economic development of such resources relies on the deployment of expensive hydraulic fracturing and the reasonable planning of well schedules. A flood of literature was therefore published focused on accurately and efficiently simulating the production performance of shale gas and better accounting for the various geological features or flow mechanisms that control shale gas transport. In this regard, this paper presents a holistic review of the macroscopic modeling of gas transport in shale. The review is carried out from three important points of view, which are the modeling of the gas flow mechanisms, the representation of multiscale transport, and solution techniques for the mathematical models. Firstly, the importance of gas storage and flow mechanisms in shale is discussed, and the various theoretical models used to characterize these effects in the continuum scale are introduced. Then, based on the intricate pore structure and various pore types of shale gas reservoirs, this review summarizes the multiple-porosity models in the literature to represent multiscale gas transport, and discusses the applicability of each model. Finally, the numerical and analytical/semi-analytical approaches used to solve the macroscopic mathematical model governing shale gas production are reviewed, with a focus on the treatment of the complex fracture network formed after multistage hydraulic fracturing.

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Section: Analytical and Semi-analytical Methodsmentioning

confidence: 99%

A Review of Macroscopic Modeling for Shale Gas Production: Gas Flow Mechanisms, Multiscale Transport, and Solution Techniques

Liu,

Zhang,

Zhang

et al. 2023

Processes

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“…Other researchers have addressed these distance-dependent properties in unconventional reservoirs using more complex fractal models. − , However, parameters in such models, such as the fractal dimension, factional derivative order, and anomalous diffusion exponent, are not easily determined and explicitly understandable. Li developed a new analytical model accounting for multiphase flow, reservoir heterogeneity, anomalous diffusion, and pressure-dependent fluid properties by introducing a new Boltzmann transformation.…”

Section: Introductionmentioning

confidence: 99%

Rate Transient Analysis of Heterogeneous Unconventional Reservoirs Exhibiting Deteriorated Induced-Fractures with Exponential Permeability Profile

Fan

2024

ACS Omega

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Deterioration of induced fractures is common in hydraulically fractured tight or shale reservoirs due to the energy dissipation of the fracturing operation. New models that account for stimulated reservoir heterogeneity are needed for the rate transient analysis of unconventional formations. In this study, we present a practical and straightforward solution for heterogeneous fractured reservoirs by introducing the concept of dynamic average permeability (DAP). An explicit equation of average permeability for linear flow in heterogeneous formation is derived by integrating the solution of the linear flow diffusivity equation and exponential permeability profile function into the Darcy flow model. Methodologies for performance forecast and evaluation of the distance of investigation (DOI) for heterogeneous unconventional reservoirs are proposed based on the DAP concept. Early deviation from the straight line of reciprocal-of-production-rate versus square-root-of-time plot occurs in highly heterogeneous reservoirs, in contrast to the departure caused by the boundary-domination effect. Meanwhile, the study results show that the DOI is significantly reduced in severely permeability-deteriorated unconventional formations. The accuracy and applicability of the new solution have been validated through real examples and synthetic numerical simulations. The analytical solution for transient linear flow in heterogeneous formation with an exponential permeability profile in the Laplace domain is also provided for the verification of the DAP method. The method proposed in this work can be readily applied to rate transient analysis and production forecasting of heterogeneous unconventional reservoirs, avoiding the complex Laplace solution and numerical inversion process.

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Flow behavior of a coupled model between horizontal well and fractal reservoir

Lian,

Sun,

Zhang

et al. 2024

Energy Geoscience

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Modeling of anomalous gas transport in heterogeneous unconventional reservoirs using a nonlinear generalized diffusivity equation

Cited by 5 publications

References 45 publications

A Review of Macroscopic Modeling for Shale Gas Production: Gas Flow Mechanisms, Multiscale Transport, and Solution Techniques

A Review of Macroscopic Modeling for Shale Gas Production: Gas Flow Mechanisms, Multiscale Transport, and Solution Techniques

Rate Transient Analysis of Heterogeneous Unconventional Reservoirs Exhibiting Deteriorated Induced-Fractures with Exponential Permeability Profile

Flow behavior of a coupled model between horizontal well and fractal reservoir

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