Insights into the solution of counter-current spontaneous imbibition for tight unconventional reservoirs

Oil production from fractured reservoirs is challenging due to tendency of water to flow through the fractures causing reservoir oil to be bypassed and captured in the matrix. The spontaneous imbibition is a key mechanism to recover these captured reservoir hydrocarbons. This study brings pressure loss calculations to be an addition to the semi-analytical solution of counter-current imbibition. The magnitude of pressure loss was shown to be quite considerable for tight unconventional reservoirs contrary to its insignificancy for conventional reservoirs. The validity of the semi-analytical solution for unconventional reservoirs is discussed in this respect. A material balance check methodology is introduced and implemented to check the accuracy of the calculation by means of semi-analytical method. Comparison of the results of semi-analytical and numerical solutions reveals that the efficiency of the numerical solution is poor in respect to requirement of model partition and computation time. In this connection, error analysis is conducted for both numerical and semi-analytical solution to clarify the reasons for this observation. Invariance of the minimum and maximum phase pressures, the circumstance of pressure losses to be higher in the oil phase, extended variations in pe pressures due to greater capillary pressures are the considerable outcomes of the solution of the counter-current spontaneous imbibition.