The Theory And Application Of One Kind Of Gas Non-linear Porous Flow Problems

With the growing energy demand and the rising awareness of environmental protection, natural gas as a clean, efficient and high-quality fuel has gradually become a major force in the energy structure. The development and utilization of natural gas is paid more and more attention. In this paper, the study on the gas flow is to guide the efficient development of gas reservoir.Natural gas is a multi-component, low-density, low viscosity, high compressibility of fluid, and viscosity-compressibility product is a function of pressure which results in the gas flow equation with strongly nonlinear. In this paper, integrating of common modeling conditions and according to the mass conservation equation, the real gas state equation and Darcy's law, the gas non-linear flow mathematical model is established. Based on this, we improve the nonlinear item step by step. Three major models and their solving process are researched: (1) Fetkovich / Arps combination production decline model; (2) Carter type curve model; (3) Gas non-linear flow model (taking into account the viscosity-compressibility product as a function of the pressure). The model do not consider the non-linear at the beginning and finally we obtain the result of considering the nonlinear term as a function of pressure. It reflects a complete idea about studying on gas nonlinear problems.Laplace transform and Stehfest numerical inversion methods are used to solve Fetkovich/Arps combination production decline model to get production decline curves in this article. When we solve the Carter type curve model, we use the pseudopressure which is presented by Al-Hussainy to linearize the equation at first and then calculate the Carter type curves with the same method as before. These two methods can be used to predict production performance, analyze the production data and estimate the gas reservoir properties, such as formation permeability, wellbore damage and reservoir size and so on. When we solve the third model, we consider two situations: constant rate and constant pressure. In the process, we seek a new method to solve problems, that is, we use the pseudopressure which is presented by Russell to linearize the equation at first and then use convolution and gas material balance methods to account for the nonlinear term as a function of pressure in Laplace domain. At last, combined with Stehfest numerical inversion method, we can get the analytical solution in real domain. In verifying our new gas flow solution we use a finite-difference simulator to get a numerical solution and both of their solutions achieve a good consistency. At the same time, we compare the liquid solution with the gas analytical solution and find the difference between them in the steady-state. Therefore, it is proved that the existence of the gas nonlinear term impact on the results. It is relatively accurate that we solve the gas nonlinear model using this method, and the resultant rate curves and pressure curves can be applied to predict gas production performance and gas well test analysis.