Core Scale Simulation of Spontaneous Solvent Imbibition from HPAM Gel
Authors: Andersen Pål Østebø , Lohne Arild , Stavland Arne , Hiorth Aksel , Brattekås Bergit 
Published: March 2018

Abstract
Capillary spontaneous imbibition of solvent (brine bound in gel) from formed polymer gel into an adjacent, oil-saturated porous medium was recently observed in laboratory experiments. Loss of solvent from the gel by spontaneous imbibition may influence the blocking capacity of the gel residing in a fracture, by decreasing the gel volume, and may contribute to gel failure, often observed in water-wet oil fields. Formed gel cannot enter significantly into porous rock, which has important implications for spontaneous imbibition: the gel particle network itself is not imbibed, and remains close to the rock matrix surface, while gel solvent can leave the gel and progress into the matrix due to capillary forces. Polymer gel is an inherently complex fluid and modelling of its behavior is, as such, complicated. Accurate description and quantification of gel properties and behaviour on the laboratory scale is, however, necessary to predict the performance of gel placed in an oil field, particularly in fractured formations. In this work, we present an original modelling approach, to simulate and interpret spontaneous solvent imbibition from Cr(III)-Acetate HPAM gel into oil-saturated chalk core plugs. A theory describing solvent flow within a gel network is detailed, and was implemented into an in-house simulator. Simulations of spontaneous imbibition from gel was performed, and compared to free spontaneous imbibition of water. A good overall match was achieved between experiments and simulations on the core scale, which validates the proposed gel model.
All Faces Open (AFO) and Two Ends Open - Free Spontaneous Imbibition (TEOFSI) boundary conditions were used in the experiments, and formed the basis for simulation. Spontaneous imbibition occurs at the core end faces that are open to flow and exposed to gel (different for the two boundary conditions). The gel surrounding the core was discretized and included as a part of the total grid to capture transient behavior. The surrounding gel is treated as a compressible porous medium where the gel's polymer structure constitutes the matrix having constant solid volume while the gel porosity is a function of pore pressure. The gel permeability is modelled as function of gel porosity using a Kozeny-Carman approach. The flow equations for the gel and core domains were solved simultaneously by implementing the proposed description into the core scale simulator IORCoreSim. Two properties were identified to control the transport of water from gel into the adjacent matrix: the permeability and compressibility of the gel. The flow of water from the gel was observed in simulations to occur in a transient manner, driven by the coupled gradients in gel fluid pressure and gel porosity, where the gel porosity initially decreases in a layer close to the core surface due to reduced aqueous pressure. Gel porosity continued to decrease in layers away from the core surface; the propagation rate was controlled by two main gel parameters: (i) Gel compressibility controlled the pressure gradient within the gel network, and the amount of water transported from the outer part of the gel towards the core surface to balance the pore pressure. (ii) Gel permeability limited how fast water could flow within the gel at a given pressure gradient, thus increasing the time scale of the overall imbibition process.