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Analytical aquifer model for interference analysis in reservoirs with bottom-water drive or water injection, An
MartÃnez Bernardino, Vladimir
MartÃnez Bernardino, Vladimir
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2022
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Abstract
This work develops a new 3-dimensional analytical model to estimate the water influx in reservoirs with bottom-water drive incorporating source and sink terms representing the presence of producing or injecting wells in the aquifer. This model also applies to reservoirs sharing an aquifer. The solution was obtained by solving the diffusivity equation employing Laplace and Fourier cosine transforms. The general solution is presented in Laplace space and requires a numerical inversion method to obtain the results in the real domain. The work demonstrates that the use of Euler's algorithm provides accurate numerical inversion of the results from Laplace transform domain to time domain.
The functionality of the analytical solution is evaluated with reservoir numerical simulation and communicating well models. The applications presented in this work focus on analyzing the feasibility of implementing water injection processes through subsurface connectivity between different formations (aquifer-reservoir or aquifer-aquifer), performed through communicating wells, allowing the water to flow from a source aquifer to a depleted formation. The water injection
flow rate is function of the pressure dfference between the formations and the pressure drop components: porous media, partial penetration, hydrostatic pressure and frictional forces. The study focuses on solving the lack of energy in reservoirs and considers the geological conguration of offshore fields located in the Gulf of Mexico, but can also be found in other hydrocarbon producing fields. Results show that implementing this solution brings important advantages because the
ultimate recovery factor improves signicantly. Additionally, it delays the water encroachment in reservoirs adjoined to the source aquifer and reduces water production.
The use of the analytical model provides significant advantages by comparison with numerical simulation since it allows computing the pressure at the points of interest of the aquifer, such as the water-oil contacts and the location of the water injecting/producing wells. Therefore, there is no need to calculate the pressure distribution along the entire aquifer, as required with the numerical simulation models; hence, the computing time reduces considerably.