The Transient Well Test Analysis of Fractured-Vuggy Triple-Porosity Reservoir With the Quadratic Pressure Gradient Term

Abstract

Abstract This paper aims at triple porosity reservoir with fracture and vugs, according to basic percolation principle the nonlinear well testing model with quadratic pressure gradient is established, considering wellbore storage and skin, for both the unsteady interporosity flow of the matrix to fracture and the unsteady interporosity flow of vugs to fracture. By use of variable substitution, linearizing the flow equation, the model is solved, and the Laplace space analytic solution is obtained, and then the real space solution is procured by use of Stehfest numerical inversion. So the pressure and the pressure derivative log-log new type curves are drawn up. Sensitivities of the type curves affected by different parameters are analyzed, including the influence of the quadratic pressure gradient coefficient β, fluid capacitance coefficient and interporosity flow factor, which are the main parameters that can reflect the traits of fractured-vuggy triple porosity reservoir. The impact of (lower case beta) under certain conditions is extremely intense, and the dimensionless pressure error may be up to 20% and dimensionless pressure derivative error may be up to 30%. Especially for low permeability reservoirs and heavy oil reservoirs, there is a bigger β; therefore the deviation of type curves between the linear model and nonlinear model is much obvious. In the end, the example match explanation of a Carbonate well in Tarim oilfield is made, which shows that there are some differences in the explanation results between linear and nonlinear model, and the error of explanation results is very close to theoretical error, so the quadratic pressure gradient should not be neglected, and that the nonlinear percolation law is the actual flow law of oil in porous medium, and that the parameter values of nonlinear model explanation are more precise than those of linear model explanation, so the research on the nonlinear flow model and its application with quadratic pressure gradient should be undoubtedly strengthened and stressed. The results available in this paper can be further used in the study of the flow rule and the well test analysis of fractured-vuggy carbonate reservoir.