Analytical solution of the Boltzmann transient line sink for an oil reservoir with pressure-dependent formation properties

This paper gives an analytical solution for the transient line sink for oil reservoirs assuming that the porosity, permeability, viscosity, rock compressibility and reservoir height (bulk compressibility) are pressure dependent. The solution is obtained by a perturbation method, improving a procedure initially proposed for real gas flow. Traditionally, these parameters have been assumed constant in the Boltzmann solution for the transient line sink, whereas this oversimplification has to some extent been taken into account in numerical simulators. tory-obtained reservoir property data are fitted to a function used to obtain an analytical solution. The results can be expressed as the sum of the traditional Boltzmann solution and a correction term, which asymptotically behaves as a transient skin. lution can replace numerical simulators to evaluate field data. In particular, it has application to well test analysis, because it is found that the transient skin effect may contribute significantly in drawdown well tests. y, using laboratory-obtained rock compressibility data, the perturbed solution is applied to a well drawdown test case to demonstrate the error introduced by assuming constant rock properties.