In the reservoir which contains randomly distributed impermeable shale, the shale density and the size of each shale affect the production performance of a horizontal well.
In general, the oil recovery by water injection decreases with the increase of shale density and the shale correlation length. On the other hand, for the reservoir which has a bottom water, shale is considered to act as a barrier to the water encroachment, and the high shale density and large shale correlation length keep the oil production rate high.
For the practical reservoir simulation, not the explicit reservoir model, which is the realization describing in detail all the shale position and size, but the implicit reservoir model, which is a homogeneous and anisotropic reservoir model characterized by the effective vertical permeability, is in use. In this case, the implicit model should be the one that reproduces the production performance of the corresponding explicit model correctly.
In this study, three methods to construct the implicit model from the realizations which contain random shale ditribution are compared for both water injection and bottom water drive cases.