A New Solution Method for the Lietard Natural Fracture Width Prediction Model

When the Lietard natural fracture width prediction model is solved by means of the chart method, the solving velocity is low and human errors tend to occur. In order to quickly and accurately predict the natural width with lost circulation and provide a decision-making basis for plugging operations and shield temporary plugging operations, the numerical solution method for Lietard model was studied in this paper. It was shown from the analysis on Lietard model that there was an approximate straight line section in the theoretical leakage characteristics curve obtained from Lietard model and it could be linearized. Based on the measured leakage data during the lost circulation, the calculation model for the linear parameters of approximate straight line section in the actual drilling leakage characteristics curve was established by means of the least square method. After the theoretical leakage characteristics curve which was the only one corresponding to the actual drilling leakage characteristics curve was identified by using the adaptive search method, natural fracture width could be inversed on the basis of the dimensionless finite invasion factor. Based on experimental studies, the calculation model for the linear parameters of approximate straight line section in the actual drilling leakage characteristics curve was built up and automatic matching without blind area was realized with matching error less than 0.001%. And furthermore, human errors were avoided and the Lietard mode could be solved quickly. It was shown that the solution accuracy of Lietard model was proportional to the linear correlation of approximate straight line section in the actual drilling leakage characteristics curve. And for the same correlation, new method was faster and more accurate than the chart method.