Transient divergent flow and transport in an infinite anisotropic porous formation

When seeking to predict plume geometry resulting from fluid injection through partially penetrating wells, it is common to assume a steady-state spherically diverging flow field. In reality, the flow field is transient. The steady-flow assumption is likely to cause overestimation of injection plume radius since the accommodation of fluid by increases in porosity and fluid density is ignored. In this paper, a transient solution is developed, resulting in a nonlinear ordinary differential equation expressing plume radius as a function of time. It is shown that the problem can be fully described by one type curve. A critical time, t(c), is identified at which the percentage error of the steady-state flow solution compared to the fully dynamic problem is less than 1%. Only for large injection rates and low permeabilities, does t(c) become greater than 1 h. Nevertheless, an improved approximate solution is obtained by a simple linearization procedure. The critical time, t(c) for the new approximate solution is 0.3% of that required for the steady-state flow solution.