A modified Boltzmann Annealing Differential Evolution algorithm for inversion of directional resistivity logging-while-drilling measurements

Abstract

Being introduced in the last decade for proactive geosteering, directional resistivity logging-while-drilling (DRLWD) measurements have been used to predict and invert formation boundary, which provides more confidence to geosteering engineers in steering a well towards reservoirs’ sweet spots. However, the strong non-uniqueness of the inversion problems in the data processing in the DRLWD measurements requires a robust algorithm having a global optimization capability. We propose a modified Boltzmann Annealing Differential Evolution (BADE) algorithm to optimize the inversion problem in the DRLWD measurements. The algorithm combines a multi-population Differential Evolution (DE) algorithm with an annealing strategy. Controlled by the annealing temperature, a bad solution may be accepted probabilistically to avoid the local minima. Moreover, different differential strategies are employed at different stages of annealing to improve the convergence as well as to save computation time. The proposed algorithm is suitable for parallel implementation and it can be accelerated drastically. Synthetic and field examples are presented to showcase the effectiveness and accuracy of the BADE algorithm. Compared to the standard DE algorithm, the modified algorithm converges faster and finds global optimization easier. Combined with a multi-layer model, the BADE algorithm can be used to predict multiple formation boundaries and to evaluate the anisotropic formation resistivities, which will be of great help for proactive geosteering and well placement.