A comprehensive mathematical model is developed, which combines the fracture deformation and leak-off from the fracture faces, to describe the trend of mud loss in fractured formations. Also, an explicit approximate cubic equation is derived to predict the width of natural fracture from mud loss data for yield power-law drilling fluids, if the leak-off and fracture deformation can be neglected. The approach of the comprehensive method is based on a transient modeling of mud loss in permeable fractures when a yield power-law drilling fluid penetrates the fracture. It considers the leak-off from fracture faces, which is assumed perpendicular to the fracture face. The fracture deformation is described as a linear function of exerted differential pressure. A computer program is developed to solve the governing equations using implicit and explicit finite difference methods. The study also investigates the effect of fracture characteristics and rheology of drilling fluid on mud loss. The results of the approximate method is compared with the numerical method using field data that are available in the literature. The comparison indicates that the predicted fracture width of the approximate method only differs 5% from that of numerical method. The substantial new finding is that depending on the magnitude of leak-off coefficient, three major type-curves of mud loss can be expected. For high values of leak-off coefficient, the mud loss steadily increases with time. For low values of leak-off coefficient, the mud loss volume flattens as it is controlled by fracture ballooning and mud rheology characteristics. For moderate values of leak-off coefficient, the early time behavior of mud loss follows that of low leak-off values, where as in late times it follows that of high leak-off values.
A common characteristic of naturally fractured formations during drilling operation is sever mud losses, which often leads to non-productive time. In addition, subsequent problems may arise due to sever mud losses, such as formation damage, formation kick, and wellbore control issues. Fracture deformation can also play an important role in presence of high overbalance pressure. When fracture width is changing, the mud loss/gain sometimes is mistakenly interpreted as formation influx or drilling fluid loss. Such misinterpretation may worsen the situation and can create well control problems. Nevertheless, the losses through the matrix should be distinguished from the losses to natural fractures. Dyke et al. (1995) stated that the mud losses through pores begin slowly and gradually increases in time, whereas sever initial losses followed by a gradual decline in time is an indication of natural fractures. Knowing the location and width of fractures directly affects the success of drilling operation.