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Abstract
At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant pressure outer boundary and closed outer boundary are compared with the analytical solutions. The calculation results show that it is reliable to solve the oil-gas seepage equation with the moving boundary nonlinear equation. To deal with the difficulty in solving analytical solutions for low-permeability reservoirs and numerical solutions of moving boundaries, a quasi-linear model and a nonlinear moving boundary model were proposed based on the characteristics of low-permeability reservoirs. The production decline curve chart of the quasi-linear model and the recovery factor calculation chart were drawn, and the sweep radius calculation formula was also established. The research results can provide a theoretical reference for the policy-making of development technology in low-permeability reservoirs.
Highlights
Classical Darcy’s law [1] has been widely used to describe seepage mechanics and numerical simulation for a long time
The moving boundary propagation mechanism is a difficult point in the study of low-permeability reservoirs, and the pressure sweep radius is the core indicator of lowpermeability reservoir development technology policy formulation
The nonlinear equation is solved by the quasi-Newton method, and the obtained nonlinear solution is compared with the analytical solution
Summary
Classical Darcy’s law [1] has been widely used to describe seepage mechanics and numerical simulation for a long time. Dou H E [7] stated that the experiment conditions, the experiment process and the core sample preparation process are the three main reasons for the obvious TPG measured from the low permeability core experiments This is necessary to determine the starting pressure gradient when the quasi-linear seepage model is used. In. 2008, Feng [12] studied the unstable radial seepage model in a low-permeability gas reservoir considering the start-up pressure gradient through the numerical approximate Green function method; the results show that the moving boundary can characterize the control radius of a single well. Are the main research methods and tools; the exact analytical solution of a porous media seepage flow boundary model with the starting pressure gradient, the proof of the existence of the solution and the moving law of the moving boundary are rarely studied. The results can provide a theoretical reference for low-permeability reservoir development technology policy formulation and numerical simulation of low-permeability reservoirs
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