Transient analysis of mud loss in fractured formations

Abstract

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.