Analytical Solutions for Pressure Transient Analysis of Injection, Falloff and Flowback Data for Two-Phase Flow Problem

In the petroleum industry, well testing is a common practice. A well test consists of wellbore pressure and flow rate data acquisition to estimate parameters that govern flow in the reservoir rock. Well tests give insight into the oil and gas field production potential and profitability, allow the estimation of reservoir parameters and inform the decision of whether a well needs to be stimulated. Multiphase flow is the norm in petroleum reservoirs, where water---but also gas and gas dissolved in or alternated with water---injection is commonly used to displace oil to a producing well. An injection-falloff test consists of a period of fluid injection into an reservoir, followed by a period of shut-in (zero flow rate). Injection-falloff testing is particularly important for offshore reservoirs containing high amount of harmful gases like carbon dioxide and sulfur dissolved in the oil. In this environment, a conventional test (production test) on an exploratory well cannot be run because the emission of these gases to the atmosphere is harmful to the environment; hence, there is a need to develop techniques for analyzing pressure data from injection-falloff tests. If we can return a well to production subsequent to an injection-falloff test, then during the flowback period, the sandface will be exposed to a range of water saturations. Consequently, the wellbore pressure during the flowback period must be influenced by the changing water saturation in the near wellbore region and hence must contain information about the two-phase oil-water relative permeability and capillary pressure curves. This work presents a procedure to generate analytical solutions to model multiphase tests involving different physical processes to provide an accurate and fast forward-model for well test analysis of injection-falloff and injection-falloff-production tests, considering hysteresis and capillary pressure effects on the wellbore pressure response.