Analytical Time-Dependent Shape Factor for Counter-Current Imbibition in Fractal Fractured Reservoirs

Abstract

Summary The fluid exchange behavior for counter-current imbibition in fractured reservoirs can be quantitatively characterized by the transfer function in numerical simulation. The time-dependent shape factor (TDSF) in the transfer function is one of the main factors controlling fluid transport, which directly affects the result of ultimate oil recovery prediction. In practice, fractured reservoirs with different microscopic pore structures often have varied flow laws under the same flow conditions. However, the current TDSFs proposed for counter-current imbibition assume that the microscopic pore structure has no impact on the fluid inter-porosity flow behavior, which is inconsistent with the actual situation. In this work, the fractal theory is used to establish the TDSF of counter-current imbibition, which is related to the microscopic pore structure. First, the analytical solutions of average water saturation and imbibition rate are obtained under different conditions related to the maximum pore diameter and tortuosity fractal dimension of the matrix. The validity of the new analytical solution for strong water-wet and moderate water-wet reservoirs is ascertained by a single-porosity model and experimental data. Subsequently, the proposed analytical solution is applied to the two-phase transfer function to develop the new TDSF for counter-current imbibition, and the sensitivity analysis is carried out. The results demonstrate that the unsteady-state duration of the TDSF is proportional to the characteristic length and tortuosity fractal dimension of the matrix, and it is negatively proportional to the maximum pore diameter of the matrix. The influence of the characteristic length, tortuosity fractal dimension, and maximum pore diameter of the matrix on a constant shape factor (SF) under quasi-steady-state is exactly the opposite. This work provides an enhanced clarification of the fluid exchange behavior of counter-current imbibition in strong water-wet and moderate water-wet fractured reservoirs.