Quantitative analysis of mud losses is a direct method for prediction of fracture width, which offers a criterion for designing lost preventive materials and guides early remedial actions. This study presents a mathematical model for prediction of mud loss in naturally fractured formations in two parts. First, a mathematical model is developed considering the fracture deformation and leak-off from the fracture faces to describe the trend of mud loss in fractured formations. The fracture deformation is described as a linear function of exerted differential pressure. An explicit approximate equation is also proposed to predict the fracture width from mud loss data for yield power-law drilling fluids. Second, a mathematical model is developed, which describes mud losses in fractured formations taking into account the pressure drops in mud bank and formation fluid bank. The governing equations are solved numerically using an implicit finite difference method for the first part and an iterative method with variable time-step for the second part.

The comparison of approximate equation with the complete model indicates that the predicted fracture width of the approximate equation only differs 5% from that of complete numerical model. The substantial new finding is that depending on the magnitude of leak-off coefficient, three major type-curves of mud loss can be identified. It is found that formation fluid viscosity can affect mud loss volume in early times and thinner drilling fluids tend to increase the mud losses in fractured formations. However, the ultimate mud loss volume is governed by the mud-invasion factor, which is a direct function of drilling fluid yield stress. The validity of the model is examined using published data of mud loss measurement in the Gulf of Mexico. Automatic curve-fitting technique is adapted to find the fracture width by matching the model prediction with mud loss data. The results of this study is beneficial to predict the volume of mud loss for qualitative purposes during well planning and more importantly to quantify the conductive fractures for design of effective blend of lost circulation materials.

泥浆流失的定量分析是预测裂缝宽度的直接方法，它为设计损失的预防材料提供了标准，并指导早期的补救措施。这项研究提出了一个数学模型，用于预测两部分自然裂缝地层中的泥浆流失。首先，建立了考虑裂缝变形和裂缝面渗漏的数学模型，以描述裂缝地层中泥浆流失的趋势。断裂变形被描述为施加的压差的线性函数。还提出了一个明确的近似方程，根据屈服幂律钻井液的泥浆流失数据预测裂缝宽度。其次，建立数学模型 它描述了裂缝地层中的泥浆损失，其中考虑了泥浆库和地层流体库中的压降。第一部分采用隐式有限差分法，第二部分采用具有可变时间步长的迭代方法，以数值方式求解控制方程。

近似方程与完整模型的比较表明，近似方程的预测断裂宽度与完整数值模型仅相差5％。一项实质性的新发现是，根据泄漏系数的大小，可以确定出三种主要的泥浆流失曲线。发现地层流体粘度会在早期影响泥浆流失量，而较稀的钻井液往往会增加裂缝性地层中的泥浆流失量。但是，最终的泥浆流失量受泥浆侵入因子控制，这是钻井液屈服应力的直接函数。使用公布的墨西哥湾泥浆流失数据，检验了模型的有效性。通过将模型预测与泥浆流失数据进行匹配，自动曲线拟合技术可以找到裂缝宽度。这项研究的结果有益于预测定井过程中定性的泥浆流失量，更重要的是，为了设计有效的漏失循环混合物，量化导流裂缝的数量。