Universal Scaling of Counter-Current Spontaneous Imbibition Experiments Accounting for Sample Shape, Wettability, Saturation Functions and Other Input Parameters

Abstract Spontaneous imbibition (SI) refers to multiphase fluid flow driven by capillary forces. In particular, counter-current (COU) SI is a flow setting where the wetting phase invades the sample while the non-wetting phase flows in the opposite direction (counter-currently). This is facilitated by exposing all open sides of the sample to the wetting phase. COU SI is among the most common experiments performed on porous media core samples. An important application of those tests is to estimate the rate of SI and ultimate recovery on larger scale, e.g. in naturally fractured reservoirs for assessing oil production from the matrix blocks or to assess water losses during hydraulic fracturing in tight shales. This is performed by converting the time scale seen in the laboratory to a time scale corresponding to the metric dimensions in the field. Current approaches are based on taking a time scale obtained from the 1D (linear) capillary diffusion equation while applying a characteristic length to correct for flow into samples that do not have linear flow, such as cylindrical or otherwise. While a semi-analytical solution does exist that perfectly scales 1D flow tests for all conditions (although only at early time), the use of a characteristic length is only approximate and it is unclear how accurate or inaccurate the results can be. In a recent work it was demonstrated that imbibition into samples of arbitrary geometry could be accounted for in a highly accurate manner. While 1D flow results in recovery linear with the square root of time at early time, such linearity occurs until a much lower value of recovery for samples with flow from more sides open. This work aims to apply those results to assess different scaling approaches: In the first approach all samples have identical initial imbibition rate against scaled square root of time. While this works well for 1D samples, the rate of recovery declines soon for the complex geometry cases. An alternative, which still collects the 1D samples perfectly, focuses on giving similar recovery for all cases at a higher level of recovery. Both approaches are theory based and do not require any tuning parameters. The theory is tested on numerical simulations and experimental data. The scaling collects data on a unit slope line of recovery against square root of scaled time. It is demonstrated that experimental data that can be modeled consistently (using the same set of input parameters) can be scaled more successfully.