A material balance model based on mass conservation in the producing layer and gas and water injection in non-communicating gas-cap and aquifer layers

Abstract

In this work a material balance model has been developed, expanding the previous work of Borthne (1986), based on: the modified black-oil model, mass-conservation in the producing layer, gas and water injection in non-communicating gas-cap and aquifer layers and volume conservation between the producing, gas-cap and aquifer layers. The model takes as input produced surface quantities of oil (or gas) in time and voidage replacement ratios for gas and water injection and outputs reservoir pressure, associated surface quantities of gas (or oil), fluid saturations and surface volumes of aquifer and gas-cap.

The model is solved by converging the pore volume of the producing layer in each iteration of the Secant method, which is used to converge the oil or gas mass balance of the producing layer. The pore volume of the producing layer is converged by substitution and considers the expansion of gas-cap and aquifer, the injected volumes of gas and (or) water and compressibility of connate water and rock. Injection of gas and (or) water is allocated to a gas-cap or aquifer layer only thus not affecting the saturation and mobility of oil and gas in the producing layer.

The model successfully reproduces the results of the volatile-oil base case of Borthne and a dry gas case with a pot aquifer. Cases considering water and gas injection with different voidage replacement ratios are also simulated and discussed.