Theoretical Research Of Unsteady Flow In Porous Media Related Start-up Pressure Gradients

The exploration and exploitation of the low reservoirs have wide prospects in China. It is one of important strategic direction of the industrial development of petroleum of our country to develop scientifically and rationally low-permeability reservoirs. It is important to enhance the recovery efficiently for developing oil industry and releasing short supply of energy resources.We know that the non-Darcy porous flow exists in low permeability reservoirs. Start-up pressure gradient exists and the special phenomenon that the moving boundary expands outwards constantly presents in fluid flow through low-permeability media. All these make stratum pressure distribute and bottom-hole pressure distribute in low permeability reservoirs are different from that of medium-high permeability and have their own characteristics. In order to guide practice of developing better, it is worthy of our discussion deeply. In view of this, this paper importantly studied the rule of flow in homogeneous low-permeability reservoir related start-up pressure.Firstly, we set mathematics model on the basis of the introduction of start-up pressure to describe the law of Non-Darcy porous flow. Around 1ow permeability flow, starting from start-up pressure gradients, basics differential equations are derived and initial conditions and boundary conditions are discussed. The basics differential equations, initial conditions and boundary conditions are then transformed into dimensionless representation. The mathematical model of fluid flow in porous media related to start-up pressure is established.Secondly, the essay uses mathematical knowledge to solve the model and obtained the analytical solution of the pressure distribution function. This part is the focus of the content of this article; mathematical model is derived in detail by knowledge of mathematical physics including Laplace transform, Boltzman transform, Green function, contour integration. Then we obtain the analytical simulation, asymptotic solution and Laplace space solution.At last, the paper analyzes solution composition. Results indicate start-up pressure gradients has a significant impact on fluid flow that the more star-up pressure gradients,the more affection degree.The article is more complete exploration of the law of unstable flow in low permeability reservoir, which provides a solid foundation for well test analysis.