A FULL APPROXIMATE ANALYTIC SOLUTION TO THE PROBLEM OF SPONTANEOUS IMBIBITION IN POROUS MEDIA

Spontaneous imbibition of water into matrix blocks because of positive capillary forces is an important mechanism for oil (or gas) recovery from fractured reservoirs during aquifer rise and most of the secondary and tertiary recovery processes. Li and Horne (SPE Reservoir Eval. Eng., vol. 9, no. 3, pp. 251-258, 2006) studied the problem of spontaneous imbibition in the systems where gravity is important and presented an implicit approximate analytical solution. In this short manuscript, using the Lambert W function we extend the work by Li and Horne to obtain the corresponding full approximate analytical solution. This solution enables us to express recovery explicitly as a function of time and other influencing parameters in the cases of nontrivial gravity. It can be seen that the full approximate analytic solution presented in this study has the same functional form as the literature analytic solutions for imbibition into porous media and single capillary tubes, although different approaches and assumptions have been used. The presented solution is furthermore used to derive a transfer function with applications to dual-porosity simulation.