The Integral Equation of the Micro-Fracture's Electrical Logging Response
On the condition that integral surfaces lie in instrument surface, well wall and fracture surface, we have deducted the integral equation for computing the logging response of micro-fracture. From the theoretical result we know that the integral value of the micro-fracture item is direct proportion to micro-fracture opening. To proof-test the deducted equation, we take the geological model as the infinite layered micro-fractured formation, and then compare the result computed by this method and one got by mirror image method, which is regarded as the precise value. The computation result show that with the decrease of the fracture opening h, the computation precision of the micro-fractured integral equation is improved, and when the micro-fracture opening less then 100um, the computation result owns higher precision, so the logging result computed by this method listed would meet with the computing requirement of practical project.
Zhijiu Ai, Xiaodong Zhang, Yun-Hae Kim and Prasad Yarlagadda
F. P. Liu et al., "The Integral Equation of the Micro-Fracture's Electrical Logging Response", Advanced Materials Research, Vol. 339, pp. 521-525, 2011