Model and Calculation of In-Situ Stresses in Anisotropic Formations
Authors: Wang Y.Z. , Huang L.X. , Li Z.J. 
Published: December 2007

Abstract
In-situ stress has great influence on wellbore stability, well trace controlling and hydraulic fracturing design, therefore its estimation is considerably important. Previous work has been based upon simple isotropic, so these results were observed difference between practical stresses and calculated stresses. In this paper, according to sedimentary rocks having a laminated structures, the formations are considered as transversely isotropic material. The calculating equations of three horizontal principal in-situ stresses and a new formation fracture pressure model are to be presented. It is also introduced that how to determine elastic parameters of anisotropic rocks in lab. Meanwhile the above methods are applied in Tuha oilfield of China to detect formation fracture pressure. The results show that errors between the theoretic calculating pressures and practical formation fracture pressures are smaller that obtained by isotropic method. This has important significance for increasing the effectiveness of drilling.

Introduction
In situ stress is a widely existing natural force. The orientations and magnitudes of in-situ stresses strongly influence several reservoir characteristics related to geology, drilling, stimulation, and production. During drilling operations, for example, the building profiles of formation pressure aand formation fracture pressure, mud weight limits required to avoid wellbore collapse, and calculation of creep rate in creep formation such as shale, all these have relations to the magnitudes and orientations of in-situ stresses. During production, determinations of fracturing parameters, forecast of sanding problems and optimization of sand control, work out development plan, rational pattern arrangement, all these have close relations to them.
In the past, formation rocks are considered as isotropic material in nearly all investigations of in-situ stresses, many calculating equations of in-situ stresses and their applied equations are derived 1. Although these have guiding significance in practical work, calculating results have some errors as compared to practical values, one of the reasons is that rock anisotropy is not considered. Chenevert's work 2 showed that sandstones can be classified as very anisotropic, the shales as moderately anisotropic, and limestones as isotropic. Rahn's work 3 also showed that the moduli of elasticity of a foliated rock can vary by about 50% if measured normally and parallel to the bedding plane. In China, most formations of drilling sections are anisotropic sandstones and shales. Because of their depositional features, they have distinct beddings. This can be best described as transversely isotropic material.
Theories of in-situ stresses in anisotropic rock formations are well documented. Leknitskii 4, in his pioneering work, provided a comprehensive analytical solution for anisotropic elastic bodies. Amadei further studied wellbore stability in anisotropic formations. Andnoy 5 presented a model of anisotropic stress to study the fracture and collapse behaviour of boreholes. Recently, See Hong Ong 6 on the Andonoy's 8 work developed a wellbore-stability "design code" that can be used to drill, complete inclined wells optimally so as to keep wellbore-stability. In addition, Inversion presented some mechanical conceptions of in-situ stresses in anisotropic formations. The deficiency of above studies lies in that there is not an easily mastered method in field like istropic formations, most are qualitative equations.
The purpose of this paper is to present calculating equations of in-situ stresses in condition of considering rock anisotropy, practical distribution law of in-situ stresses by means of laboratory method and field data. Meanwhile, the above methods are applied in oilfield to detect formation fracture pressure, thereby field problems can be solved.

Mechanical Model

Calculating Equations of In-Situ Stresses.
It is assumed that the formations are transversely isotropic type of anisotropy and are horizontal flat determined as XOY flat(Fig. 1). The forces acting on the rock formation are only gravity and tectonic stress. According to the theory of elastic mechanics, first step must take into account affluence of rock gravity, then it is analyses according to Anderson's method.

Calctitlelating Equations of In-Situ Stresses.
It is assumed that the formations are transversely isotropic type of anisotropy and are horizontal flat determined as XOY flat(Fig. 1). The forces acting on the rock formation are only gravity and tectonic stress. According to the theory of elastic mechanics, first step must take into account affluence of rock gravity, then it is analyses according to Anderson's method.