# Finite-Volume Simulation of Capillary-Dominated Flow in Matrix-Fracture Systems using Interface Conditions

## TL;DR

This paper develops a finite-volume simulation approach with discrete interface conditions to accurately model capillary-driven flow in fractured porous media, improving flux estimation without fine grid refinement.

## Contribution

It introduces a novel application of interface conditions in finite-volume schemes to enhance flux accuracy in multiphase flow simulations in fractured media.

## Key findings

- Interface conditions improve flux accuracy at coarse grid resolutions.
- The method accurately captures capillary-driven imbibition dynamics.
- The approach effectively models flow with viscous, buoyancy, and capillary forces.

## Abstract

In numerical simulations of multiphase flow and transport in fractured porous media, the estimation of the hydrocarbon recovery requires accurately predicting the capillary-driven imbibition rate of the wetting phase initially present in the fracture into the low-permeability matrix. In the fully implicit finite-volume scheme, this entails a robust methodology that captures the capillary flux at the interface between the matrix and the fracture even when very coarse control volumes are used to discretize the matrix. Here, we investigate the application of discrete interface conditions at the matrix-fracture interface to improve the accuracy of the flux computation without relying on extreme grid refinement. In particular, we study the interaction of the upwinding scheme with the discrete interface conditions. Considering first capillary-dominated spontaneous imbibition and then forced imbibition with viscous, buoyancy, and capillary forces, we illustrate the importance of the interface conditions to accurately capture the matrix-fracture flux and correctly represent the flow dynamics in the problem.