Pressure Transient Analysis of Bingham Fluids using Tiab’s Direct Synthesis Approach

Abstract

This study investigated transient flow response of heavy oil that exhibit Bingham fluid characteristics. Four wellbore conditions in naturally fractured reservoirs were considered which include horizontal well, hydraulically fractured well, partially penetrating and fully penetrating vertical wells. Physical models were established and corresponding mathematical models were presented taking cognizance of minimum threshold pressure,𝜆𝐵. The model was solved analytically by successive application of Laplace and Fourier transforms. The solution was inverted from Laplace space to real domain by using Stehfest algorithm and was extended to obtain solutions for all the four wellbore conditions. Also, equations used for Tiab’s Direct Synthesis (TDS) technique were derived, considering𝜆𝐵. It was established that the pressure derivative on log-log plot of a heavy oil reservoir with 𝜆𝐵𝐷is higher than that for oil behaving like Newtonian fluid by a factor of (𝜆𝐵𝐷 + 1) at any time on pressure derivative curve for all four wellbore conditions.