Fast Inversion Of Array Laterolog Logging Based On Nonlinear Inversion Algorithm

Resistivity logging can be used to qualitatively identify the oil and water layers,and can also be used to quantitatively calculate the water saturation.Due to its inherent working mode,the array laterolog logging instrument will inevitably be affected by mud invasion,surrounding rock,borehole and other environmental factors.In the field,the measured apparent resistivity is often used directly as the reservoir's true resistivity,resulting in severe deviations in oil-water layer identification and oil-gas saturation calculations.Therefore,it is necessary to invert the apparent resistivity data by resistivity inversion to extract the true resistivity information of the reservoir and ensure the accuracy of the reservoir evaluation.The array laterolog logging instrument can provide four apparent resistivity curves?MLR1-MLR4?with detection depths of 9 in,13in,19 in,and 37 in.It helps to solve the problem of multi-solution existing in the inversion using traditional logging data?dual laterolog,dual induction,etc.?and improve the inversion accuracy.Using the finite element method to construct a three-parameter forward model(r_xo,R_xo,R_t)for the forward response calculation of array laterolog logging.The characteristics of array lateral logging response under different mud invasion,wall thickness and borehole conditions are summarized.Based on the definition of laterolog logging pseudo-geometric factors,the characteristics of?varying with mud invasion depth under different R_t/R_xo conditions are calculated,and a pseudo-geometric factor data table corresponding to MLR1-MLR4 is made.In the actual inversion process,the linear table interpolation is used instead of the strict forward calculation to improve the inversion efficiency under the premise of ensuring the accuracy of the forward calculation.In view of the characteristics of the linear inversion method,such as the Marquardt algorithm,which has serious dependence on the initial value and the poor global search ability,three-parameter inversion of array laterolog logging was performed using the Simulated Annealing algorithm and Differential Evolution algorithm with global optimization capability,and corresponding algorithm improvement measures were proposed.Using the theoretical stratum model,the improved algorithm is compared with the classical Simulated Annealing algorithm,the classical Differential Evolution algorithm and the Marquette algorithm.It is found that the improved algorithm has obvious advantages in terms of optimization success rate,convergence speed,and noise immunity.The improved nonlinear inversion algorithm optimization success rate is up to 91%,and the convergence speed is lower than that the Marquette algorithm,but it is about twice that of the classical nonlinear inversion algorithm.At the same time,the inversion accuracy has also been significantly improved,and the fitness can be controlled to less than 0.5%.The noise immunity of the improved algorithm is also strong.When the Gaussian noise reaches 10%,the parameter inversion error can still be controlled within 20%.The improved inversion algorithm is used to invert the actual well data.By comparing the results with the existing software,it is found that the inversion results of washing zone radius,formation resistivity are basically the same,but there are burrs in a few layers.Washing zone resistivity compliance is relatively poor,but the trend is consistent and the error is within the acceptable range In order to further verify the correctness of the improved inversion algorithm,the inversion results are compared with sampling data and test oil data.The results show that the water saturation calculated by inversion resistivity is consistent with core data and test oil data.However,there is some deviation in the calculation of water saturation by using apparent resistivity,which proves the applicability and superiority of the improved inversion algorithm.