Green's Function And Source Function In Well Test Analysis

The reservoir types and its boundary conditions are complicated in our country. Most of them have gas cap, bottom water, edge water or impermeable fault. Double porosity reservoir and triple porosity reservoir are common in China. It is very difficult to exploit those reservoirs. Therefore it is very important to research the flow in porous medial of those reservoirs. Source and Green's function is an effective mathematic tool to resolve the flow in porous medial in oil and gas reservoir. In this article, based on the theory of fluid mechanics in porous medium, we founded the bottom hole pressure dynamic response mathematic modal of vertical well or horizontal well or fracture well in homogeneous reservoir, double porosity reservoir and triple porosity reservoir. By using the mathematic tool of Source and Green's function, and applying the techniques of laplace transformation, mirror image, principle of superposition, Stehfest numerical inversion synthetically, we obtained the analysis solution in laplace domain. By using VC++ program we obtained the academic type curve. And we analyzed the characters of fluid flow through porous medium and its influencing factor of those type wells. The main research domains are as follows:1) According to the conservation of mass principle, using the idea of tiny cell we founded the mathematic modal of fluid flow in porous medial in reservoir. Using the S function and laplace transformation we obtained the fundamental solution of fluid flow through porous medium differential equation for instantaneous source.2) Using the method of Source and Green's function, we founded the bottom hole pressure dynamic response mathematic modal in homogeneous reservoir or double porosity reservoir which consider different types of top and bottom or cylindrical boundary and resolve it. We obtained the type curve of dimensionless pressure response in bottom hole .We analyzed the character of fluid flow through porous medial and its influence factors.3) Integrating with respect to the horizontal well, we obtained the horizontal well testing interpreting mathematic modal in homogeneous reservoir or double porosity reservoir which consider the influence of boundary. We obtained the type curve of dimensionless pressure response in bottom hole. We analyzed the fluid flow through porous medial of horizontal welland the influence of such parameters as the length and location of horizontal well, reservoir pollution, the boundary characters to the bottom hole pressure.4) Integrating along the fracture plane, then along the well, we obtained the fracture vertical or horizontal well pressure dynamic response mathematic modal which consider the influence of boundary. We calculated the reflection of dimensionless pressure versus to dimensionless time. We analyzed the character of fluid flow through porous medial and its influence factors of the fracture vertical or horizontal well.5) Using the Warran-Root modal to found the horizontal well welltesting interpreting mathematic modal in triple porosity reservoir, which consider the influence of boundary, Using the method of Source and Green's function to obtain the analysis solution in laplace domain, we obtained the type curve of dimensionless pressure response in bottom hole. And we analyzed the influence of triple porosity reservoir character parameter to fluid flow in porous medial of the horizontal well.After the research we have founded a set of theories, which use Source and Green's function to resolve the well test interpreting mathematic modal in complex reservoir.