Investigation of Barree-Conway non-Darcy flow effects on coalbed methane production

Abstract

Coalbed gas non-Darcy flow has been observed in high permeable fracture systems, and some mathematical and numerical models have been proposed to study the effects of non-Darcy flow using Forchheimer non-Darcy model. However, experimental results show that the assumption of a constant Forchheimer factor may cause some limitations in using Forchheimer model to describe non-Darcy flow in porous media. In order to investigate the effects of non-Darcy flow on coalbed methane production, this work presents a more general coalbed gas non-Darcy flow model according to Barree-Conway equation, which could describe the entire range of relationships between flow velocity and pressure gradient from low to high flow velocity. An expanded mixed finite element method is introduced to solve the coalbed gas non-Darcy flow model, in which the gas pressure and velocity can be approximated simultaneously. Error estimate results indicate that pressure and velocity could achieve first-order convergence rate. Non-Darcy simulation results indicate that the non-Darcy effect is significant in the zone near the wellbore, and with the distance from the wellbore increasing, the non-Darcy effect becomes weak gradually. From simulation results, we have also found that the non-Darcy effect is more significant at a lower bottom-hole pressure, and the gas production from non-Darcy flow is lower than the production from Darcy flow under the same permeable condition.

Keywords

non-Darcy flow / Barree-Conway model / coalbed methane production / error estimate / numerical simulation

References

[1] LuM, ConnellLD. A dual-porosity model for gas reservoir flow incorporating adsorption behavior-part I. Theoretical development and asymptotic analyses [J]. Transp Porous Med, 2007, 68: 153-173

[2] PillalamarryM, HarpalaniS, LiuS. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs [J]. Int J Coal Geol, 2011, 86: 342-348

[3] ClarksonC R, BustinR M. Coalbed methane: current field-based evaluation methods [J]. SPE Reserv Eval Eng, 2011, 14: 60-75

[4] RanjbarE, HassanzadehH. Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media [J]. Adv Water Resour, 2011, 34: 627-639

[5] AminianK, AmeriS. Predicting production performance of CBM reservoirs [J]. J Nat Gas Sci Eng, 2009, 7: 25-30

[6] ZhangY-j, YangC-shuai. FEM analyses for influences of stress-chemical solution on THM coupling in dual-porosity rock mass [J]. Journal of Central South University, 2012, 19: 1138-1147

[7] ZhangY-j, YangC-shuai. Coupled thermo-hydromechanical- migratory model for dual-porosity medium and numerical analysis [J]. Journal of Central South University, 2011, 18: 1256-1262

[8] YoungG B C. Computer modeling and simulation of coalbed methane resources [J]. Int J Coal Geol, 1998, 35: 369-379

[9] UnsalE, MatthaiS K, BluntM J. Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions [J]. Computat Geosci, 2010, 14: 527-538

[10] ThararoopP, KarpynZ T, ErtekinT. Development of a coal shrinkage-swelling model accounting for water content in the micropores [J]. Int J Mining and Mineral Engineering, 2009, 1: 346-364

[11] ThararoopP, KarpynZ T, ErtekinT. Development of a multi-mechanistic, dual-porosity, dual-permeability, numerical flow model for coalbed methane reservoirs [J]. J Nat Gas Sci Eng, 2012, 8: 121-131

[12] WangJ G, KabirA, LiuJ S, ChenZ W. Effects of non-Darcy flow on the performance of coal seam gas wells [J]. Int J Coal Geol, 2012, 93: 62-74

[13] YeZ H, ChenD, WangJ G. Evaluation of the non-Darcy effect in coalbed methane production [J]. Fuel, 2014, 121: 1-10

[14] ClarksonC R, BustinR M, SeidleJ P. Production-data analysis of single-phase (gas) coalbed-methane wells [J]. SPE Reserv Eval Eng, 2007, 10: 312-331

[15] ZengF, ZhaoG. The optimal hydraulic fracture geometry under non-Darcy flow effects [J]. J Petrol Sci Eng, 2010, 72: 143-157

[16] GiraultV, WheelerM F. Numerical discretization of a Darcy-Forchheimer model [J]. Numer Math, 2008, 110: 161-198

[17] RuiH X, PanH. A block-centered finite difference method for the Darcy-Forchheimer model [J]. SIAM J Numer Anal, 2012, 50: 2612-2631

[18] BarreeR D, ConwayM W. Beyond beta factors: A complete model for Darcy, Forchheimer and trans-Forchheimer flow in porous media [C]. SPE Annual Technical Conference and Exhibition, 2004

[19] LopezH DExperimental analysis and macroscopic and pore-level flow simulations to compare non-Darcy flow models in porous media [D], 2007GoldenColorado School of Mines

[20] WuY S, LaiB T, MiskiminsJ L, FakcharoenpholP, DiY. Analysis of multiphase non-darcy flow in porous media [J]. Transp Porous Med, 2011, 88: 205-223