Transient production analysis of gas-water two-phase flow of gas wells using a pseudo-pressure function based approach
In order to analyze gas/water two phase flow of gas wells in depletion-driven reservoirs,this work,based on the constitutive relationship between pressure and saturation,proposes the gas/water phase integral transformations including pseudo-pressure and β factor to linearize the two-phase diffusivity equation for a closed cylindrical reservoir with one vertical well.A pseudo-pressure based approach was described,which can generate the required benchmark analytical solution for single-phase liquid case,and the rescaled well performance equations subject to constant bottomhole pressure(BHP),con-stant rate,and step-BHP constraints were presented.A rigorous equation for variable BHP/rate constraints was also derived by using the Duhamel convolution,and the application conditions on the use of liquid type curves were studied with the defi-nition of a two-phase material-balance pseudo-time.The results show that the pseudo-pressure based approach and β factor can account for the change in saturation and gas/water PVT properties with pressure,and capture the path inter-dependency of pressure and saturation throughout the production life of the well.The material balance pseudo-time can convert variable rates/BHPs in gas-water two-phase cases into an equivalent constant rate solution for single-phase liquid case.In a boundary-dominated flow regime,the material-balance pseudo-time is strictly a rigorous solution,regardless of well specification con-straints.Nevertheless,the material-balance pseudo-time works fairly well in infinite acting flow regimes,which is an approx-imate solution for the constraint of step like decline drawdown and continuous non-monotonic drawdown.In a dimensionless way combined with the concepts of pseudo-pressure and material balance pseudo-time,the gas-phase equation has exactly the same form as the water phase,which means the dimensionless gas production data overlay with those of water production.The other unknowns such as formation parameters,original gas in place(OGIP)and original water in place(OWIP)can be ex-plicitly calculated using a simple,direct and fast way of a classical type-curve matching.
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