Models for filtration during drilling, completion and stimulation operations

Filtration of solid suspensions is encountered in many operations during drilling, completing and stimulating oil and gas wells. Filtration of drilling muds, completion and fracturing fluids, gravel packing slurries are a few examples. Most of these applications involve the filtration of non-Newtonian fluids into a porous medium containing compressible fluids. Internal and external compressible filter cakes can form under static or dynamic filtration conditions.; Models for static filtration of solid-laden polymer fluids have been developed. These models solve the basic filtration equations to obtain the depth of invasion of solids and polymer into the formation. The buildup of an external filter cake is modeled after a transition time is reached when no more additional particles invade the formation. It is shown that a square root of time dependence is obtained during external filtration of polymer fluids. During the spurt loss period (internal filtration) the model allows us to calculate the extent of solids and filtrate invasion and the duration of spurt loss. The model for the first time presents a formulation where the spurt loss can be obtained from the model directly. Fluid compressibility effects as well as cake compressibility can be accounted for in the model. The results of the model allow us to better interpret leak-off data during the period in which the polymer is being squeezed into the formation. Comparisons with experiments show that fluid leak-off during the spurt loss period can be accurately estimated with the equations presented.; During drilling or when a fracture is created in a frac-and-pack operation, fluid leak-off occurs by a dynamic filtration process. In this process, particles are constantly sheared away by the flow of the polymer slurry parallel to the face of the fracture with fluid leak-off occurring into the rock. A new model for dynamic filtration has been developed which takes into account the particle size distribution of the wall-building fluid leak-off material. It is found that the permeability of the formation as well as the shear rate and the particle size distribution of the fluid leak-off material control the leak-off behavior. A relatively simple analytical expression is derived for leak-off during dynamic filtration. Comparisons with experimental data show excellent agreement with model predictions. Trends with increasing filtration pressure and formation permeability are consistent with those predicted by our model.; The dynamic filtration model developed in this dissertation is applied to the problem of hydraulic fracturing using a 3-dimensional hydraulic fracture simulator. It is shown that the leak-off behavior can play an important role in fracture propagation, both in classical hydraulic fracturing and in the fracturing of high permeability sands. Therefore, accurately modeling the static and dynamic filtration that occurs during fracture propagation is critical for an accurate prediction of fracture geometry.