Determination Of Principal Stresses And Confinement Of Hydraulic Fractures In Cotton Valley
Authors: Rosepiler Michael J. 
Published: December 2007

Abstract
In order to delineate formations that will inhibit the vertical growth of hydraulic fractures, the principal stresses within the formations must be known. The principal stresses can be calculated from density and acoustic logs. Overburden pressure is obtained by integrating density logs. The lithostatic gradient in Cotton Valley is approximately 1.07 psi/ft (2.4 × 10(4) Pa/m). Digitized acoustic wavetrains are processed to calculate Poisson's ratio. Poisson's ratio averages .16 in sands and .29 in shales. This implies that the average horizontal stresses in sands and shales at a depth of 10000' (3948 m) are 2038 and 4370 psi (1.4 × 10(7) and 3.0 × 10(7) Pa) respectively. Principal stresses are also calculated from acid treatments. The minimum horizontal principal stress (closure stress) closely agrees with the predicted value from logs. The second horizontal predicted value from logs. The second horizontal principal stress is much greater than the closure principal stress is much greater than the closure stress implying that an additional tectonic stress is present. Since the horizontal principal stresses are higher in shales than sands, overlying shales should tend to confine the vertical growth of fractures. Fracturing pressures should be limited so as to take advantage of the sand-shale closure stress differential.

Introduction
The Cotton Valley sand-shale sequence is upper Jurassic in age and is bounded by the "Z" limestone and Bossier shale. The sequence is approximately 1500' (457 m) thick and is found at depths ranging from 8000' (2438 m) to 10500' (3200 m) in Harrison, Rusk, and Panola Counties. (See Figure 1.)The Cotton Valley is arbitrarily divided into four zones: blue, green, orange, and yellow in order of increasing depth. Figure 2 is a resistivity log of the Davidson Foundation, Inc. #1 which is located in eastern Harrison County. The reservoir is characterized by low porosity (commonly less than 10%) and low permeability (on the order of microdarcies). In places the sands are well cemented with calcite. Due to the extremely low permeability of Cotton Valley sands, the wells are being stimulated by hydraulic fracturing. Beginning in August 1972, Amoco Production Company has performed 8 conventional fracs on 2 wells, and since March 1975, 60 massive hydraulic fracs have been performed on 50 wells. These stimulations have a cumulative volume of 23 million gallons of gel and 50 million pounds of sand. Immediately following the fracturing treatments, temperature surveys are run to profile the fractures. These show that a significant number of fractures have grown out of zone into overlying strata (Figure 3). Vertical growth causes two problems: First, overlying water bearing zones may be fractured, and second, tip to tip fracture length is decreased. Thus, vertical confinement of fractures is a problem in Cotton Valley, and methods are needed to predict when a fracture will grow out of zone and how such growth can be prevented. The fracturability of a formation is controlled by various elastic moduli and principal stresses within the earth. By calculating these moduli and stresses, the tendency for a fracture to propagate through various strata can be predicted. propagate through various strata can be predicted.

THEORY
In general, the underground state of stress is such that the magnitudes of the principal stresses are unequal. Various assumptions can be made in tectonically relaxed regions that simplify the problem of determining these stresses. The first problem of determining these stresses. The first assumption is that the greatest principal stress is vertical and that the intermediate and least principal stresses are horizontal. If the wellbore is principal stresses are horizontal. If the wellbore is vertical it will be parallel to the greatest principal stress and perpendicular to the intermediate principal stress and perpendicular to the intermediate and least principal stresses. Assuming that the stresses at depth are lithostatic, the vertical stress can be solved for as:
(1)