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**Abstract**

Fracture ballooning usually occurs in naturally fractured reservoirs and is often mistakenly regarded as an influx of formation fluid, which may lead to misdiagnosed results in costly operations. In order to treat this phenomenon and to distinguish it from conventional losses or kicks, several mechanisms and models have been developed. Among these mechanisms under which borehole ballooning in naturally fractured reservoirs take place, opening/closing of natural fractures plays a dominant role. In this study a mathematical model is developed for mud invasion through an arbitrarily inclined, deformable, rectangular fracture with a limited extension. A governing equation is derived based on equations of change and lubrication approximation theory (Reynolds’s Equation). The equation is then solved numerically using finite difference method. Considering an exponential pressure-aperture deformation law and a yield-power-law fluid rheology has made this model more general and much closer to the reality than the previous ones. Describing fluid rheology with yield-power-law model makes the governing equation a versatile model because it includes various types of drilling mud rheology, i.e., Newtonian fluids, Bingham-plastic fluids, power-law, and yield-power-law rheological models. Sensitivity analysis on some parameters related to the physical properties of the fracture shows how fracture extension, aspect ratio and length, and location of wellbore can influence fracture ballooning. The proposed model can also be useful for minimizing the amount of mud loss by understanding the effect of fracture mechanical parameters on the ballooning, and for predicting rate of mud loss at different formation pressures.

ballooning, boundary, dip angle, Drilling, effect, Fig, Flow, fracture, fracture aperture, geomechanics, loss, model, mud loss, mud loss rate, pressure, pressure distribution, rate, time, wellbore integrity

SPE Disciplines:

Fracture ballooning usually occurs in naturally fractured reservoirs and is often mistakenly regarded as an influx of formation fluid, which may result in misdiagnosed costly operations. Several models have been developed to treat this phenomenon and distinguish it from conventional losses or kicks. Among these borehole ballooning models and mechanisms, opening/closing of natural fractures is considered to have the main role in naturally fractured reservoirs.

In this study a mathematical model is developed for mud invasion through a disk-shaped and deformable fracture with two impermeable walls and a limited extension. A governing equation is derived based on the lubrication approximation theory (Reynolds's Equation) for radial flow in a single fracture. Considering an exponential deformation law to describe the pressure-aperture relationship, and a yield-power-law model to describe mud rheology, makes this model more general and much closer to the reality than the previous ones. Describing the fluid rheology with yield-power-law model turns the governing equation into a versatile model as it includes various types of drilling mud rheology.

The governing equation is solved numerically using finite difference method. Results show how different parameters can affect fracture ballooning and volume and rate of mud loss/gain. The effects of several parameters related to the mechanical properties of the fracture are analyzed. Shortcomings of the proposed model are outlined.

**1. Introduction**

Drilling through naturally fractured formations causes significant mud loss. The mud loss happens mainly due to the flow into the fractures and a small amount of leak-off into the matrix or wall of the fracture; the leak-off through the matrix depends on the porosity of the matrix but more or less it can be ignored in comparison with the amount of loss through the fractures. Fracture ballooning/breathing or fracture deformation is one of the main mechanisms under which the mud loss/gain occurs while drilling fractured formations. Fracture ballooning corresponds to inflating of a balloon; it occurs when the bottom hole is pressurized and drilling fluid flows into the fracture. Fracture breathing occurs when the rate of mud circulation is decreased and drilling fluid flows out of the fracture. Usually any flow during drilling is interpreted as an influx of the formation fluid and the common cure is to increase the mud weight and to insure an adequate overbalance (Majidi, et al, 2008); but if this influx is due to the mud gain, this kind of treating and controlling not only is not appropriate but also will worsen the situation. Therefore a quantitative analysis of mud gain/loss based on a mathematical model, which describes the physical phenomenon and mechanism under which flow within the fractures happens, is necessary to distinguish mud gain from flowing of formation fluid.

annular pressure drilling, ballooning, blowout flow modeling, borehole, deformation, effect, Figure, Fluid Dynamics, formation, fracture, fracture aperture, fracture ballooning, geomechanics, logic programming, loss, mud loss, mud loss rate, rate, reservoir simulation, time, value, well control equipment, wellbore integrity

SPE Disciplines: