Method for Fracture-Gradient Prediction for Vertical and Inclined Boreholes

Abstract

Summary. A new method for the prediction of fracture gradients in deeper wells has been developed. The method is based on the principles of mechanics but uses a correlation method in the application of field data. The new, improved methodgives both leakoff and lost-circulation pressures;works for vertical and inclined boreholes; andidentifies lithological effects. The result is given as a simple equation where only well depth, pore pressure, borehole angle, and lithology are needed to predict the fracture pressure. Because borehole inclination is included, the method can be used during both production and vertical-well drilling. The method was applied in a field study offshore Norway. The results show a remarkably good correlation with field observations. Introduction Detailed knowledge of formation pore pressure and fracture strength is considered the most essential element in the achievement of a successful drilling program. This becomes even more critical in the drilling of high-angle wells. Methods to predict fracture gradients are typically based on empirical correlations between fracture data, overburden data, and depth. Refs. 1 through 7 give different methods of this nature. Daines' method in particular has been successfully applied in Norway by several oil companies. All these methods work for vertical wells. Bradleys and Aadnoy and Chenevert used the equations for the stress field around the borehole and were thereby able to study inclined boreholes by means of stress transformations. The mathematical model used, the "Kirch solution" for stresses in a plate with a hole in the middle, has certain limitations. It assumes homogeneous and isotropic rock properties, linear elasticity, and a plane/strain condition. The model works well for wells deeper than 600 m f 1,970 ft]. Real rock can be described as heterogeneous and anisotropic with both spatial and directional variations in all its physical properties. Because of this complexity, a mathematical model that perfectly describes real rock does not exist. It has become evident that the ideal mathematical model does not work well for field calculations because it gives too-extreme results. In view of the complexity of modeling real rocks, it is easily understood that the model is too simple. This new method is derived to bridge the gap between field measurements and the principles of mechanics. The idea is to use the principles of mechanics but to adjust certain parameters to obtain a good fit to the field-measured fracture data. The criteria for these adjustments are based on observed behavior and are not always rational from a rigorous continuum mechanics point of view. The method, however, gives good results. The new method considers borehole inclination. Therefore, fracture data from production, wildcat, and delineation wells can all be used as input. The model is well suited for computers and may be updated continuously as new fracture data become available. Overburden Stress Because of compaction effects, the overburden gradient as a function of depth varies. Bourgoyne et al. summarize previous work on overburden-stress modeling. Experience shows that the porosity as a function of depth typically exhibits an exponential behavior. Because the weight of the overburden depends on the porosity, this curve is also exponential. To obtain the overburden stress at any depth, Bourgoyne et al. define (1) Integration of this equation and substitution of D, =D -D, depth below the surface of sediments, yields (2) Assuming that all densities are constant, Eq. 2 has a linear part and one correction term inside the last parentheses. The true overburden-stress curve for a field is obtained from density logs. When a field curve is given, the constants 00 and K in Eq. 2 can be determined by curve-fitting methods. As will be seen later, however, Eq. 2 is not always a good model for real field data. For cases that do not behave exponentially, any function can be used. The key is to find a function that is simple and that will reasonably describe the real overburden stress vs. depth. In-Situ Stresses Knowledge of all in-situ stresses is necessary to apply the principles of continuum mechanics to borehole stability problems. The horizontal in-situ stresses can be found indirectly by use of fracture data. Aadnoy and Chenevert show that the horizontal in-situ stress can be found with the equation (3) Eq. 3 is derived from the Kirch solution but is modified with a correlation coefficient, A, to accommodate field data. Also, the horizontal in-situ stress is assumed equal in all directions. In its application, the tensile strength of the rock is set to zero, assuming that an existing crack is merely reopened when the hole is fractured. Experience shows that when the horizontal in-situ stress is calculated from field data, different values are found, depending on the local pore pressure at which the fracture test is performed. Tins questions the validity of the Kirch solution. Some of the discrepancies, however, are known to be caused by anisotropic rock properties, simplified effective-stress concept, and mudcake quality. The last factor indicates that the pressure transition through the mudcake is seldom an ideal step function because some leakoff occurs, thereby increasing the pore pressure locally in the rock surrounding the borehole. Another assumption is that the horizontal in-situ stresses are equal, which is probably not correct for many oil fields. Despite the discrepancies found by the application of Eq. 3, we state that the overall stress behavior at the borehole is described by the Kirch solution, and we use the discrepancy constructively to adjust the model to field data. Eq. 3 is strictly valid for a vertical hole only. The failure criterion is that fracturing occurs when the effective tangential (hoop) stress exceeds rock strength. For inclined boreholes, the mathematics becomes more complicated because shear effect come into account. Aadnoy shows, however, that for deeper boreholes, the fracture will always be confined to extend along the axis of the hole. This shows that the tangential stress is the governing parameter, regardless of borehole inclination.