Power-Law Fluid Pressure Behaviour in Homogenous and Naturally Fractured Reservoir with Spherical Flow

Abstract

Studies have revealed most wells are usually completed with limited or restricted-entry and it’s often characterized with spherical flow behaviour. High viscosity crude by their nature may also exhibit Non-Newtonian flow behavior. Fall-off test in polymer injection well with partial completion may also exhibit spherical flow. This paper therefore presents pressure transient analysis for spherical flow behaviour of non-Newtonian power-law fluids in Homogenous and Naturally Fractured Reservoir. In this work, skin and wellbore storage effect are incorporated into the Laplacian space analytical solution derived by Liu Ci-qun (1987). New pressure and pressure derivative type curves are developed for different flow behaviour index of power-law fluid in Homogenous and Naturally Fractured Reservoirs. The log-log plot of pressure derivative for the Homogenous system gives a slope of -0.5 at the spherical flow straight line, as expected for Newtonian fluid flow in porous medium; while the slope of non-Newtonian fluid at the spherical flow regime is a function of its flow behaviour index. The pressure derivative plot for Naturally Fractured Reservoir system shows the usual three (3) flow regimes typical of double porosity reservoir system. This work further develop equations to estimate reservoir, wellbore and power-law flow parameters using Type curve matching and Tiab’s Direct Synthesis technique (TDS) --- which uses analytical solution of long-time approximation in evaluating well test data from the log-log plot of pressure and pressure derivative. Equations are developed for both the Homogeneous and Naturally Fractured Reservoir.