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

Abstract 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.

[1]  L. Klinkenberg.  The Permeability Of Porous Media To Liquids And Gases , 2012 .

[2]  D. W. Peaceman.  Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability , 1983 .

[3]  W. Kast,et al.  Mass transfer within the gas-phase of porous media , 2000 .

[4]  A. Dehghani,et al.  Even and odd $\lambda$λ-deformed binomial states: minimum uncertainty states , 2017 .

[5]  A. Radwan,et al.  Analytical solution for fractional derivative gas-flow equation in porous media , 2017 .

[6]  F. Javadpour,et al.  Nanoscale Gas Flow in Shale Gas Sediments , 2007 .

[7]  Shahab D. Mohaghegh,et al.  Full field reservoir modeling of shale assets using advanced data-driven analytics , 2016 .

[8]  M. Belayneh,et al.  Control-volume finite-element two-phase flow experiments with fractured rock represented by unstructured 3D hybrid meshes , 2005 .

[9]  R. M. Bustin,et al.  Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications , 2009 .

[10]  R. Arnett,et al.  Modelling fluid flow in fractured‐porous rock masses by finite‐element techniques , 1984 .

[11]  Rajagopal Raghavan,et al.  Modeling of Fluid Transfer From Shale Matrix to Fracture Network , 2010 .

[12]  Faruk Civan,et al.  Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms , 2011 .

[13]  G. David,et al.  Gas productive fractured shales; an overview and update , 2000 .

[14]  M. Meyyappan,et al.  Modeling gas flow through microchannels and nanopores , 2003 .

[15]  Farzam Javadpour,et al.  Numerical Simulation of Shale-Gas Production: From Pore-Scale Modeling of Slip-Flow, Knudsen Diffusion, and Langmuir Desorption to Reservoir Modeling of Compressible Fluid , 2011 .

[16]  Kamy Sepehrnoori,et al.  Optimization of Multiple Hydraulically Fractured Horizontal Wells in Unconventional Gas Reservoirs , 2013 .

[17]  George J. Moridis,et al.  Analysis of Mechanisms of Flow in Fractured Tight-Gas and Shale-Gas Reservoirs , 2010 .

[18]  H. Kazemi,et al.  NUMERICAL SIMULATION OF WATER-OIL FLOW IN NATURALLY FRACTURED RESERVOIRS , 1976 .

[19]  Ruben Juanes,et al.  A general and efficient formulation of fractures and boundary conditions in the finite element method , 2002 .

[20]  M. Biot,et al.  THE ELASTIC COEFFICIENTS OF THE THEORY OF CONSOLIDATION , 1957 .

[21]  Zhongmin Wang,et al.  A Retrospective Review of Shale Gas Development in the United States: What Led to the Boom? , 2013 .

[22]  Xiaoming He,et al.  Improved Numerical Simulation for Shale Gas Reservoirs , 2014 .

[23]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[24]  Turgay Ertekin,et al.  DYNAMIC GAS SLIPPAGE: A UNIQUE DUAL-MECHANISM APPROACH TO THE FLOW OF GAS IN TIGHT FORMATIONS. , 1986 .

[25]  Amgad Salama,et al.  Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media , 2012 .

[26]  Yu-Shu Wu,et al.  A Unified Mathematical Model for Unconventional Reservoir Simulation , 2011 .

[27]  F. Javadpour.  Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone) , 2009 .

[28]  M. F. E. Amin.  Analytical solution of the apparent-permeability gas-transport equation in porous media , 2017 .

[29]  Hossein Kazemi,et al.  Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution , 1969 .

[30]  Amanda M. M. Bustin,et al.  Importance of Fabric on the Production of Gas Shales , 2008 .

[31]  Thomas K. Sherwood,et al.  The Flow of Gases in Pipes at Low Pressures , 1946 .

[32]  J. S. Aronofsky,et al.  A Simplified Analysis of Unsteady Radial Gas Flow , 1954 .

[33]  Amirmasoud Kalantari Dahaghi,et al.  Numerical Simulation and Modeling of Enhanced Gas Recovery and CO2 Sequestration in Shale Gas Reservoirs: A Feasibility Study , 2010 .