Open Access

ARTICLE

Modeling Oil Production and Heat Distribution during Hot Water-Flooding in an Oil Reservoir

Chinedu Nwaigwe^1,2,*, Abdon Atangana²

1 Department of Mathematics, Rivers State University, Port Harcourt, 5080, Nigeria
2 Institute for Ground Water Studies, University of the Free State, Bloemfontein, 9300, South Africa

* Corresponding Author: Chinedu Nwaigwe. Email:

(This article belongs to the Special Issue: Fluid and Thermal Dynamics in the Development of Unconventional Resources II)

Fluid Dynamics & Materials Processing 2025, 21(5), 1239-1259. https://doi.org/10.32604/fdmp.2025.059925

Received 20 October 2024; Accepted 21 January 2025; Issue published 30 May 2025

Abstract

In the early stages of oil exploration, oil is produced through processes such as well drilling. Later, hot water may be injected into the well to improve production. A key challenge is understanding how the temperature and velocity of the injected hot water affect the production rate. This is the focus of the current study. It proposes variable-viscosity mathematical models for heat and water saturation in a reservoir containing Bonny-light crude oil, with the aim of investigating the effects of water temperature and velocity on the recovery rate. First, two sets of experimental data are used to construct explicit temperature-dependent viscosity models for Bonny-light crude oil and water. These viscosity models are incorporated into the Buckley-Leverette equation for the dynamics of water saturation. A convex combination of the thermal conductivities of oil and water is used to formulate a heat propagation model. A finite volume scheme with temperature-dependent HLL numerical flux is proposed for saturation, while a finite difference approximation is derived for the heat model, both on a staggered grid. The convergence of the method is verified numerically. Simulations are conducted with different parameter values. The results show that at a wall temperature of 10°C, an increase in the injection velocity from to increases the production rate from to . Meanwhile, with an injection velocity of , an increase in the temperature of the injected water from 25°C to 55°C increases production rate from to . Therefore, it is concluded that an increase in either or both the temperature and velocity of the injected water leads to increased oil production, which is physically realistic. This indicates that the developed model is able to give useful insights into hot water flooding.

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Keywords

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