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Energy Sources, Part A: Recovery, Utilization, and Environmental Effects

ISSN: 1556-7036 (Print) 1556-7230 (Online) Journal homepage: http://www.tandfonline.com/loi/ueso20

Coalbed methane reservoir dynamic prediction model by combination of material balance equation and crossflow-diffusion

Fengpeng Lai, Zhiping Li, Yining Wang & Yingkun Fu

To cite this article: Fengpeng Lai, Zhiping Li, Yining Wang & Yingkun Fu (2016) Coalbed methane reservoir dynamic prediction model by combination of material balance equation and crossflow-diffusion, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 38:2, 257-263, DOI: 10.1080/15567036.2013.763389

To link to this article: http://dx.doi.org/10.1080/15567036.2013.763389

Published online: 02 Feb 2016.

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Coalbed methane reservoir dynamic prediction model by combination of material balance equation and crossflow-diffusion Fengpeng Laia, Zhiping Lia, Yining Wangb, and Yingkun Fua

aSchool of Energy Resources, China University of Geosciences, Beijing, China; bCollege of Petroleum Engineering, China University of Petroleum, Beijing, China

ABSTRACT The proposed dynamic prediction model is based on the occurrence and migration law of coalbed methane and on the pseudo-steady state diffusion model. The model integrated multi-phase flow theory and material balance equation. It is established by considering not only desorption and diffusion but also crossflow. Moreover, the calculation results show the rationality of the method used. The research analyzes the effects of crossflow factor and diffusion coefficient on development effectiveness. The effect of crossflow factor is obvious in the late production stage but not in the early stage. The diffusion coefficient affects gas production during the exploitation stage.

KEYWORDS Crossflow; diffusion; dual media; dynamic prediction; material balance equation

1. Introduction

The porosity and permeability of coal matrix blocks are very small; thus, the Darcy flow of coalbed methane (CBM) is very weak in pores. The main transport mechanism of CBM in pores and coal matrix blocks is through diffusion, and Darcy flow can be ignored (Liang and Sun, 2006). The diffusion of CBM is essentially driven from a desorption zone to a permeable fracture by concentra- tion gradient, and it is one of the important regulatory characteristics of CBM. Following Fick’s law, the diffusion of a coal matrix in the micro-pore can be spread by non-steady-state and pseudo- steady-state modeling (Yang and Wang, 1986).

A coalbed is combined with matrix and fracture systems, and the crossflow between these two systems is obvious because of the different pressure distributions in pores. The current study did not consider this factor (Guo et al., 2004; Tong and Zhang, 2008; Shi et al., 2011). The proposed dynamic prediction model is based on the occurrence and migration law of CBM and on the pseudo-steady state diffusion model. Considering that the diffusion is from the matrix to the fracture, the method integrated multi-phase flow theory and material balance equation. A dynamic prediction model is established by considering not only the desorption and diffusion but also the crossflow. The calculation results are in line with the production changes law of CBM, reflecting the rationality of the method used. The effects of crossflow factor and diffusion coefficient on development effectiveness were also analyzed.

2. Gas transport equations in the matrix system

Non-steady-state modeling can more accurately reflect the temporal and spatial variation of methane concentration and diffusion, but the calculations are very difficult and slow. Pseudo-steady state modeling is a simplified diffusion. In the late exploitation stage, the results of these two models are significantly similar (Kolesar et al., 1990a, 1990b), but the calculation in pseudo-steady-state model- ing are more convenient compared with those in non-steady-state modeling.

CONTACT Dr. Fengpeng Lai [email protected] School of Energy Resources, China University of Geosciences, Beijing, No.29, Xueyuan Road, Haidian District, Beijing 100083, China. © 2016 Taylor & Francis

ENERGY SOURCES, PART A: RECOVERY, UTILIZATION, AND ENVIRONMENTAL EFFECTS 2016, VOL. 38, NO. 2, 257–263 http://dx.doi.org/10.1080/15567036.2013.763389

The crossflow between matrix and fracture systems can be regarded as the point source term and can be introduced into a desorption-diffusion model under the pseudo-steady state. The average concentration of methane in the matrix is affected both by the desorption of adsorbed gas and the crossflow of free gas. Hence, increasing the crossflow term in the desorption-diffusion equation is necessary to reflect the changes in the average concentration. The established new crossflow- diffusion equation in pseudo-steady state can more accurately describe the desorption transport process in the matrix system. Shi et al. (2011) established some equations to described gas concen- trations in the surface of the matrix element and gas average concentration in the matrix unit. The crossflow-diffusion equation at time n is calculated by:

qmfg � �nþ1 ¼ �FG

τ

VLpnfg pL þ pnfg

þ ϕmMpfg ρsczRT

� �n � Vnm

" # þ α0 FGβ

μnmg pnmg

� �2 � pnfg � �2�

; (1)

where qmfg is the diffusion from the matrix to the fracture, m 3/(m3.d); FG is the geometry-related

factor, Dimensionless; τ is the desorption time, d; VL is the Langmuir volume, m 3/m3; Pfg is the current

fracture pressure, MPa; PL is the Langmuir pressure, MPa; ϕm is the porosity in matrix, fraction; M is the molecular weight of methane; ρsc is the gas density under standard conditions, t/m

3; z is the gas compressibility factor, Dimensionless; R is the gas molar constant, J.mol–1.K–1; T is the temperature, K; Vm is the average gas concentration in matrix unit, m

3/m3; α0 is the unit conversion factor, 8.64 × 1010; β is the crossflow factor, KPa–1; μmg is the gas viscosity in matrix, mPa.s; and Pmg is the current matrix

pressure, MPa.

3. Material balance equation of the fracture system in CBM reservoir

3.1. Assumptions

(1) For CBM reservoir, the fluid properties in the matrix and fracture systems are uniform. (2) Free gas and water are present in the fracture system of an initial CBM reservoir, and only

gas is present in the matrix system. Adsorbed gas and dissolved gas are ignored. (3) A coal reservoir is a closed system, a water and coal reservoir are slightly compressible, and

free gas is real gas. (4) Pseudo-steady diffusion follows Fick’s law; adsorption and desorption of CBM can be

described by the Langmuir isothermal equation. (5) CBM production from a coal reservoir undergoes three stages, including seepage migration,

desorption, and diffusion, all of which are in an isothermal environment.

3.2. Establishment of the material balance equation

The amount of free gas in the coal fracture system and remains in the coal fracture system under average reservoir pressure can be calculated by volumetric method. The gas successively desorbs from the coal matrix and enters the fracture system by diffusion and crossflow during the exploita- tion of CBM. These gases, moving from the matrix system to the fracture system, can be treated as the source term in the continuity equation.

The cumulative gas production (Gp) at any time t is calculated by Eq. (2):

Gp ¼ 0:01Ahϕfi 1� Swið Þ PiZscTsc PscZiT

þ 0:01Ahqmfgt � 0:01Ahϕf 1� Sw � � PZscTsc

PscZT ; (2)

258 F. LAI ET AL.

where A is the CBM supply area, km2; h is the seam thickness, m; ϕfi is the original fracture porosity, fraction; Swi is the original water saturation in initial fracture, fraction; Pi is the reservoir initial pressure, MPa; Zsc is the gas deviation factor under standard conditions, Dimensionless; Tsc is the temperature under standard conditions, K; Psc is the pressure under standard conditions, MPa; Zi is the gas deviation factor under Pi, Dimensionless; ϕf is the fracture porosity under current pressure,

fraction; Sw is the average water saturation in fracture under current pressure P, fraction; and Z is the gas deviation factor under P, Dimensionless.

The matrix will swell when gas is adsorbed to the coal inner surface and will shrink when gas is desorbed from the surface. This phenomenon is called self-regulation. In drainage, the

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