Well Test Analysis Of Nonlinear Seepage Model In Two-layer Gas Reservoir

Due to deposition,the natural gas reservoirs are usually composed of multiple layers,which have different physical characters.Considering the economic benefits,many multi-layer natural gas reservoirs are always developed by using commingled wells.In this way,the natural gas will flow to the wellbore from each layer,but the performance of wellbore pressure and production in every layer will affect each other at the same time.Therefore,we can't use the method of homogeneous single-layered gas reservoir model to solve two-layered gas reservoirs.Based on the study of flow mechanism of two-layered gas reservoirs,in this paper we have established the mathematical models of two-layer gas reservoirs in three different outer-boundary conditions considering the skin effect and wellbore storage.For the great influence of the compressibility of natural gas,parts of the control equation such as viscosity,compression coefficient,and deviation coefficient are related to pressure.Therefore,the control equation is nonlinear.In fact the control equation can be linearized by using quasi-pressure functions.But even if we can use pseudo-pressure functions to linearize the control equation of natural gas into the same form of the liquid control equation,the diffusion coefficient of the control equation is still related to pressure.By defining the pseudo-time factor,the control equations of the two-layer gas reservoirs considering the diffusion coefficient can be linearized.This paper uses the method of Laplace transform and the Bessel functions to solve the dimensionless mathematical models of two-layer gas reservoirs in three different outer-boundary conditions considering the skin effect and wellbore-storage coefficient under the consideration of diffusion coefficient.This paper presents the solutions of wellbore pressure and fractional production responses of two-layer reservoirs,which are in three different outer-boundary conditions with constant-rate production under the consideration of the skin factor and wellbore-storage coefficient.This paper have discussed the effects of different factorssuch as wellbore-storage coefficient,skin factor,inter-layer flow coefficient ratio,inter-layer storage ratio,initial formation pressure and radius of the reservoir on wellbore pressure and gas production of each layer.This paper presents the well test analysis method and typical curves,which can be used to analyze and estimate the properties of two-layer gas reservoirs.