Study On The Electrical Anisotropy Of Crack Model And It's Application On The Prediction Of Reservoir Water Saturation

Fully understanding the physical properties of the shale are of great significance for benefiting the unconventional oil and gas exploration quality,as well as the development efficiency and cost reduction.The research on the cracked shale model with electrical anisotropy provides a significant theoretical basis for the interpretation of electrical well logging and reservoir evaluation.However,most classic theories and impirical models employ scalar to represent the electrical properties of formation,which makes them not capable of profiling the anisotropy when there are cracks impact the effective resistivity tensor along different directions.As a consequence,those classic models are not reliable for water saturation prediction in reservoirs with strong anisotropy.To further investigate the crack-induced anisotropy on the effective electrical properties of reservoir in terms of the crack shape and alignment variations,an analysis method adopting electrical tensor matrix is conducted through a large number of numerical simulation on various cracking models.Based on the tensor analysis,we propose a method to characterize the orthogonal electrical anisotropy with the extracted tensor invariant parameters.Furthermore,we modify the classic scalar Archie's Law into a tensor form with the tensor invariants.Therefore,an electrical model for water saturation prediction in anisotropy reservoir is established.The research is carried out as follows:(1)The crack effects on the effective electrical tensor of shale model are analyzed through numerical experiments.By using COMSOL Multiphysics(?) software,the idealistic ellipsoidal crack models are simulated.The Finite Element Method(FEM)and electrical tenor analysis are utilized to simulate the shale models with cracks,respectively.The crack effects on the effective electrical tensor are systematically discussed and summarized.(2)The responding resisitivity tensors of crack model in the orthogonal coordinate are computed through a three-component electrical logging simulation.The water saturation of crack model is inversed and verified using Archie's law.As the conventional Archie's law fails to obtain an accurate water saturation due to the anisotropy,a method using three orders of tensor invariants to characterize the orthogonal resistivity tensor matrix is proposed to modify the conventional Archie' law into a tensorial form.The prediction accuracy of water saturation are validated with two-phase,three-phase crack model as well as the randomly distributed crack models.(3)To further validate the numerial result,a few crack samples are designed and 3D printed,so the electrical properties can be measured in laboratory.The orthogonal electrical tensors of the samples containing prolate and oblate cracks are obtained by rotating the crack samples in the virtual measurement system.The results show that: the existence of the crack could induce strong anisotropy to the shale formation,as different crack shape and alignment impacts the effective electrical tensor differently;The conventional Archie's law may fail in accurately predicting the water saturation in antistropic models,while the modified tensorial Archie's law can well capture the electrical respondings in all directions,thus improving the prediction accuracy of water saturation in anisotropic reservoir.The results have significant theoretical and practical value for electrical well logging as well as the oil/gas evaluation in unconventional reservoir.