# Numerical solution of single-phase flows in karstified heterogeneous carbonate rocks

## Palavras-chave:

Conduit, Karst Index, carbonate rocks, Darcy flow## Resumo

Oil reservoirs in carbonate porous media are usually composed of several structures such as matrices,

fractures and cavity systems, which impact properties like porosity, permeability and fluid transport behavior [1].

In this context, the problem of flow through a reservoir in the presence of karsts is rather challenging, and therefore

the predictive capabilities related to the flow and transport processes remain severely limited. In this work, we

perform simulations of a quarter of a five spot problem in a domain Ω ⊂ R

2

to numerically describe an incom-

pressible single-phase flow in a karstified carbonate rock. The methodology is based on the geometric treatment

and simulation data proposed in [2], and on the application of the Karst Index (KI) concept presented by [3]. The

use of the KI follows a similar approach to the application of the Well Index presented in [4]. Given the lack of

knowledge of the precise geometry of karst network shape, we test different arrangements with branching (such as

in [2, 5]). The mathematical model used includes equations that describe the fluid flow through a conduit, and a

mass conservation equation for each component. The domain is discretized by cartesian grids with different con-

figurations of homogeneous and high-contrast heterogeneous media, while the governing equations are discretized

by conservative finite volume methods. Results are verified in terms of conservation of mass. We compare the

generated results by using Darcy’s law changing the parameters of the conduit to assess its influence on the overall

simulation.