大斜度井和水平井井地三维电阻率数值模拟和联合反演

井地电阻率成像法利用井套管作电流源向井下供入大功率直流电流，在地表测量由地下介质的电性变化形成的电位分布，通过反演可得到地下介质的电阻率分布.针对大斜度井和水平井开展井地三维电阻率数值模拟和反演研究，对油田注水及压裂效果监测具有重要意义.基于井地电阻率成像法原理，采用有限差分法和不完全切勒斯基共轭梯度法进行了三维正演模拟，研究了大斜度井和水平井的井地电位响应特征.提出了采用层状约束阻尼最小二乘法由浅到深地进行大斜度井和水平井的多层联合反演，并对实际水平井井地电位各个层段数据进行了三维反演.模拟结果表明，倾斜线源和水平线源会对地面电位响应产生明显影响，在反演中需要考虑线源形态.实际水平井井地电位反演成像表明，考虑倾斜线源或者水平线源的联合反演得到了准确的水平井三维注水层成像图，得出注水层的真电阻率分布，能够判断注水运移方向.

Numerical simulation and joint inversion of three-dimensional borehole-to-surface resistivity of high deviated or horizontal wells

Borehole-to-surface electrical imaging supplies the high-power direct current into the borehole through the well case, and the electric potential is measured formed by the electrical characteristics change of underground fluids on the surface to inverse the resistivity distribution of underground medium. It is of great significance for the monitoring of water injection and fracturing effect in oil fields to carry out numerical simulation and inversion research on three-dimensional resistivity of the high deviated or horizontal wells. Based on the principle of borehole-to-surface electrical imaging method, the finite-difference method and the incomplete Cholesky conjugate gradient (ICCG) method were used to simulate the surface response of the high deviated or horizontal wells. A multi-layer joint inversion method of the high deviated or horizontal well was presented by using the layered damped least square method from shallow to deep, and three-dimensional inversion was carried out for the actual potential data of each layer of horizontal well. The forward modeling results show that inclined and horizontal line sources have obvious influence on the surface potential response. The line source form should be considered in the inversion. The inversion imaging of the actual horizontal well data shows that, after considering the influence of inclined or horizontal line sources, a more accurate three-dimensional inversion imaging of horizontal wells can be obtained by the joint inversion of multi-layer observations. In this way, the true resistivity distribution of horizontal wells can be obtained to judge the direction of the water injection.