A Review on Analytical Scaling Equations for Counter-Current Spontaneous Imbibition in Naturally Fractured Oil Reservoirs

Spontaneous imbibition is one of the main mechanisms for oil production in fractured reservoirs by which water due to the positive capillary forces imbibes into the reservoir rock and pushes oil into the fractures surrounding the matrix. For evaluation of the effectiveness of this mechanism, usually, laboratory tests at core scales are conducted. However, these core-scale laboratory experiments differ from a real reservoir situation by many aspects, including flow geometry, fluids properties, pressure, temperature, and sample dimensions. Thus, applying the laboratory results to reservoir scale needs appropriate scaling approaches. One of such approaches is the use of analytical scaling-up equation. In this paper, the fundamentals of such equations are reviewed, followed by discussing their limitations and advantages. This is done by evaluating the laboratory results (under various operational and sample conditions) by a set of universal equations published in our previous research. The results of this study can be useful in application of scaling equations for imbibition in fractured reservoirs.