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Natural Gas Geoscience ›› 2021, Vol. 32 ›› Issue (5): 695-702.doi: 10.11764/j.issn.1672-1926.2020.12.001

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Mathematical diffusion-filtration model of gas in deep and tight gas reservoir and analysis of influencing factors

Wei-yao ZHU(),Yu-bo SHA,De-bin KONG(),Lian-zhi YANG   

  1. College of Civil and Resource Engineering，University of Science and Technology Beijing，Beijing 100083，China
  • Received:2020-09-14 Revised:2020-11-02 Online:2021-05-10 Published:2021-04-27
  • Contact: De-bin KONG E-mail:weiyaook@sina.com;kongdb@ustb.edu.cn
  • Supported by:
    The Fundamental Research Funds for the Central Universities, China(FRF-TP-20-006A1)

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Abstract:

Deep and tight gas reservoir is one of the hot spots now. Because of the large burial depth and low permeability the existing diffusion-filtration model cann’t accurately predict the concentration distribution of the reservoir, thus affects the formulation of development schema. ZHU（1989） put forward the concept of expansion diffusion coefficient based on the principle of diffusion originating from the change of chemical potential gradient, and established a Diffusion-filtration model considering pressure effect. However, this model does not consider the phenomena of gas collision and slippage with the pore surface in the process of tight gas reservoir flow. Based on the original model, the absorption term is added, and the collision slip phenomenon of gas in tight reservoir is considered in the motion equation, so that the new model can describe the flow law of gas in tight reservoir, and the influencing factors of the new model are analyzed. The results show that the expansion diffusion coefficient caused by pressure can increase production of gas more than 10%. The lower the permeability is, the greater the influence is. Molecular diffusion plays a major role in the whole production process, and the diffusion caused by pressure mainly affects the early stage of production and near well zone. The diffusion caused by pressure has a greater impact on low-permeability and high-pressure gas reservoirs.

Key words: Deep gas reservoir, Mass concentration, Concentration distribution, Diffusion-filtration model, Expansion diffusion coefficient, Molecular diffusion coefficient

CLC Number: 

  • TE32

Table 1

Basic parameters of tight sandstone gas physical experiment in Sulige Gas Field, Ordos Basin[15-17]"

参数取值
岩心密度/（kg/m3）2 500
岩心渗透率/（10-3 μm2）0.1
岩心孔隙度/%3
岩心压缩系数/Pa-11.45×10-10
岩心长度/m0.05
岩心直径/m0.025
模拟流体甲烷
气体密度/（g/m3）716
Langmuir体积常数/(m3/kg)4.199×103
Langmuir压力常数/Pa4.55×106
气体扩散系数/（m2/s）12×10-7
气体膨胀扩散系数/[m2/(Pa·s)]5×10-5
气体黏度/（mPa·s）0.011

Table 2

Core simulation parameters of tight sandstone gas in Sulige Gas Field, Ordos Basin"

物理量取值
网格参数网格大小/m0.001
网格数量50
初始条件c(x,0)/%0
p(x,0)/Pa0
边界条件c(0,t)/%1
c(L,t)/%0
p(0,t)/Pa100 000
p(L,t)/Pa0

Fig.1

Simulation of variation character methane saturation in the core of filling test"

Fig.2

Basic schematic diagram of numerical model"

Table 3

One dimensional simulation parameters of tight sandstone gas in Sulige Gas Field, Ordos Basin"

参数取值
网格参数网格大小/m25
网格数量120
初始条件C(x,0)/（g/m3）200 480
p(x,0)/MPa28
边界条件c（0，t）0
p(0,t)/MPa22

Fig.3

Variation of formation methane concentration in different mining time"

Fig.4

Variation of formation methane concentration under different original formation pressures"

Fig.5

Variation of formation gas concentration under different permeability"

Fig.6

Variation of formation methane concentration under different bottom hole pressure"

Fig.7

Variation of formation methane concentration under different molecular diffusion coefficients"

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