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In this work the mathematical model developed by Aronovsky et. al. for predicting rates of free-water imbibition in naturally fractured oil reservoirs has been modified. The proposed model allows prediction of fractional oil recovery by spontaneous water imbibition in core samples with high accuracy.
The proposed modification involves development of an empirical correlation for the reservoir rock/fluid system-dependent parameter (l) used in Aronofsky model and defined as rate of convergence. The key reservoir rock and fluid physical properties considered in this work include absolute permeability of the rock, porosity, initial water saturation, interfacial tension between oil and water (IFT), viscosity of oil, viscosity of water, and length of core sample.
The accuracy of the modified model is evaluated using the results of laboratory imbibition tests on nine limestone core samples. All imbibition tests were conducted at 90 ° C. The absolute per cent error based on laboratory versus calculated values of (l) is found to range between 0.334 and 3.88.
The proposed model may also be applied for predicting fractured reservoir performance on field scale by simply replacing the core length by matrix block length when the block is totally immersed in water. Additional experimental work and/or field observations would be necessary to verify the reliability of the proposed modification.
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