HOU Shaoji, ZHU Weiping, LIU Yuewu, ZHEN Huaibin, GAO Dapeng, LI Qi. A Semi-Analytical Model for Moving Boundary of Radial Non-Darcy Flow in Low Permeability Reservoir[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1115-1127. doi: 10.21656/1000-0887.380330
 Citation: HOU Shaoji, ZHU Weiping, LIU Yuewu, ZHEN Huaibin, GAO Dapeng, LI Qi. A Semi-Analytical Model for Moving Boundary of Radial Non-Darcy Flow in Low Permeability Reservoir[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1115-1127.

# A Semi-Analytical Model for Moving Boundary of Radial Non-Darcy Flow in Low Permeability Reservoir

##### doi: 10.21656/1000-0887.380330
Funds:  The National Science and Technology Major Project of China（2011ZX05038-003）
• Rev Recd Date: 2018-04-19
• Publish Date: 2018-10-01
• The threshold pressure gradient (TPG) generally exists in the seepage process of low permeability reservoir. In view of characteristics of low permeability seepage, the mathematical model for the moving boundary of non-Darcy flow was established, and the formula for calculating the moving speed of the boundary was given. The Laplace transform and the infinite series method were used to obtain the model’s general solution, and the Stehfest numerical inversion was conducted. The characteristics of moving boundary problems, the boundary change and propagation were discussed and explained in detail, and the phenomenon of TPG extending outward was explicated. The TPG effects on the bottom pressure and the pressure derivative were calculated, and the Gringarten-Bourdet charts under different conditions were given. The results show that, the low pressure percolation model is significantly different from the Darcy seepage model. For low permeability cases, the pressure drop expands with time and the pressure distribution curve is of compact support. The study on the low permeability problem with moving boundary, considering the influence of the TPG and the moving boundary, provides a theoretical basis for the seepage mechanism and production performance, interpretation and numerical simulation of low permeability oil reservoirs.

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