Application of MCMC Optimization Method to Estimate Relative Permeability of Carbonate Rocks from Unsteady-State Core Flood Experiments

Da Silva Moreira, Paulo Henrique (LRAP / Universidade Federal do Rio de Janeiro) | Gomes da Silveira, Thaís Márcia (LRAP / Universidade Federal do Rio de Janeiro) | Drexler, Santiago (LRAP / Universidade Federal do Rio de Janeiro) | Couto, Paulo (LRAP / Universidade Federal do Rio de Janeiro)

OnePetro 

Abstract

The reliable prediction of reservoir performance requires the cost effective implementation of oil recovery systems, and it is necessary to simulate the fluid flow processes in the reservoir and to measure the rock and fluid properties that determine reservoir behaviour. However, a good prediction relies on accurate values of reservoir physical properties. Carbonates rocks in Brazilian Pre-salt are known for their heterogeneity. Characterizing their physical represents a great challenge and the combination of experimental and computational techniques lead to a more comprehensive understanding of the reservoir behavior.

In the present work, the relative permeability curves of a carbonate core sample with respect to oil and water are calculated by matching the data obtained in a labscale unsteady-state core flood experiment carried out at high pressure high temperature characteristics of Brazilian Pre-salt reservoirs. Corey-type equations were used to model the relative permeability due to its simplicity and having fewer parameters involved. The Monte Carlo Markov chain (MCMC) method was used as optimization tool, taking the fluid production and pressure drop measurements collected during the core flood experiment as input data. An alalysis of the sensitivity cofficients was carried out in order to deal with eventual linear dependences among the terms to be estimated. The Markov chain was generated and its convergence observed. The posterior distributions of the constant terms in the Corey equations were calculated and their mean values applied in order to calculate the relative permeability curves for the oil and water phases. The range of water saturation in which the relative permeability curves describe the core conditions after the breakthrough time, due to the occurrence of capillary end-effects, was calculated. The history match of fluid production and pressure drop was carried out, showing a good fit between the pressure curves. A gap was observed between the production curves due to the fact that the experimental measurements accounted the cumulative volume of oil and water, while the theoretical curve accounted the oil volume only.