A New Solution Method for the Lietard Natural Fracture Width Prediction Model
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摘要: 采用图版法求解Lietard天然裂缝宽度预测模型时速度慢、易产生人为误差,为迅速准确地预测井漏时的天然裂缝宽度,给堵漏作业和屏蔽暂堵作业提供决策依据,开展了数值解法研究。研究Lietard模型发现,用Lietard模型计算得到的理论漏失特征曲线存在近似直线段,可作线性化处理,因此,基于井漏时实测得到的漏失数据,采用最小二乘法建立实钻漏失特征曲线近似直线段线性参数的计算模型,并运用自适应搜索法找出与实钻漏失特征曲线唯一对应的理论漏失特征曲线,根据该曲线的无因次有限侵入值反演出天然裂缝宽度。经过试验研究,建立了实钻漏失特征曲线近似直线段线性参数的计算模型,实现了无盲区自动匹配,将匹配误差控制在0.001%以内,克服了人为误差,并能快速完成Lietard模型求解。研究结果表明,Lietard模型的求解精度与实钻漏失特征曲线近似直线段的线性相关度呈正比关系,在同一相关度下,新方法比图版法求解速度更快、精度更高。Abstract: 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.
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Keywords:
- fractured leakage /
- fracture width /
- prediction model /
- errors /
- automatic matching
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