Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Abstract

Spontaneous countercurrent imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO 2 storage, and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a onedimensional domain. In 1-D, for incompressible fluids and homogeneous rocks, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with ffiffi t p . At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here we present a new approach to approximate the whole imbibition process semianalytically. The onset is captured by a semianalytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with ffiffi t p . This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a selfsimilarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO 2 sequestration. We show that this concept improves common first-order approaches that heavily underestimate early-time behavior and note that it can be readily included into dual-porosity models. Key Points: New physically based model for spontaneous imbibition Model captures transition from earlytime to late-time imbibition Model validated for different applications Correspondence to: R. March, rafael.march@pet.hw.ac.uk Citation: March, R., F. Doster, and S. Geiger (2016), Accurate early-time and latetime modeling of countercurrent spontaneous imbibition, Water Resour.

A Practical Methodology to Screen Oil Recovery Processes Involving Spontaneous Imbibition

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Modelling shale spontaneous water intake using semi‐analytical and numerical approaches

“…The constant A can be measured using core‐scale imbibition experiments and by drawing log‐log plots of cumulative water production versus time, or be estimated applying modern modelling techniques. Our perspective is to model the countercurrent spontaneous imbibition and predict what the imbibition rate parameter entails using the integral solution of McWhorter and Sunada for the unsteady flow of two immiscible and incompressible fluids in a semi‐infinite, one‐dimensional domain . The flow process involves the piston‐like imbibition of water in a linear system perpendicular to the fracture face.…”