Analytical Forward Modelling and Response Analysis of Array Induction Logging Tool in Horizontal Well

ABSTRACT In this paper, we present a stable analytical method to simulate responses of an array induction tool in a horizontal well and analyse the vertical detection sensitivity in a planar‐stratified anisotropic formation. The electromagnetic field excited by a horizontal magnetic dipole is first derived by using the generalised transmission/reflection method. The measuring field with a dipole receiver is fixed on the same plane as the transmitter. To avoid the overflow problem in numerical integral, the boundary positions are introduced in the expressions. The background field is abstracted from its total field and calculated using its algebraic form. The rest of the expressions are related reflection field. It has the advantage of a small convergence domain and weak oscillation compared with its total field, which improves the stability and efficiency of the numerical integral. Combining with the proposed forward modelling method, a difference formula is defined for the vertical detection sensitivity of the array induction logging tool in horizontal wells. It is a fundamental investigation for tool response analysis and data processing. Finally, we validate our new formulas compared with the numerical method and analyse the effects on tool responses from anisotropy and layer thickness.