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.
Highlights
Material balance models are simplified numerical approximations to estimate the evolution of oil and gas reservoirs when undergoing depletion and injection
Material balance models are typically derived by applying volume conservation on the container, considering, e.g.: gas cap expansion, gas released from oil or condensate dropout from gas, rock and water expansion, aquifer expansion and influx, water and gas injection
The model development pursued as main premise to keep to a min imum modifications to the mass balance equations and procedures to model and solve the producing layer presented by Borthne (1986)
Summary
Material balance models are simplified numerical approximations to estimate the evolution of oil and gas reservoirs when undergoing depletion and injection. Material balance models are typically derived by applying volume conservation on the container, considering, e.g.: gas cap expansion, gas released from oil or condensate dropout from gas, rock and water expansion, aquifer expansion and influx, water and gas injection. The rate is integrated to the simulation step where a new reservoir pressure and flowing gas-oil (or condensate-gas) ratio and water cut are computed with the surface produced volumes and the material balance model. The original model of Borthne (1986) did not include, nor discussed the inclusion of gas-cap or aquifer and injection and the treatment of connate water compressibility. The present work expands the original model of Borthne to include the presence of gas-cap and aquifer (if an oil reservoir) an aquifer (if a gas reservoir) and to consider injection with an input voi dage replacement ratio. The derived model still has the characteristics inherent to material balance models, but it could still be used in the classroom (or elsewhere) to demonstrate a larger variety of scenarios than the original model of Borthne (1986)
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