Summary
An improved method of calibrating in-situ stress logs was validated with data from two wells. Horizontal stress profiles are useful for hydraulic fracture design, wellbore stability analysis, and sand production prediction. The industry-standard method of estimating stresses from logs is based on overburden, Poisson's ratio, and pore pressure effects and gives an estimate of minimum horizontal stress. The model proposed here adds effects of temperature and tectonics and outputs of minimum and maximum horizontal stress magnitudes, which are particularly important to the successful completion of horizontal and deviated wells. This method was validated using data collected from a GRI research well and a Mobil well. Seven microfrac stress tests in GRI's Canyon Gas Sands Well of Sutton County, Texas, provided a means of comparing the predictive capability of different methods. First, one of the seven stress tests was selected as a calibration standard for the stress log. Then the results obtained from the two calibration methods were compared to stress magnitudes from the other six stress tests. This process was repeated using each of the seven stress tests as a calibration standard and comparing predictions to the other six. In every case, the method incorporating tectonic strain and thermal effects produced significantly more accurate values. The Mobil well is located in the Lost Hills Field in California, and pre-frac treatment breakdown tests were used to calibrate a log-derived stress profile. All of the data were used simultaneously to get a best fit for the log-derived stress. The log and its fracture height growth implications compared favorably with available fracture diagnostic data, and maximum horizontal stress values were consistent with published values for a similar, nearby reservoir.
Introduction
Advances in well completion technology have made accurate profiles of horizontal stresses more important to successful field development. Data on in-situ stress have always been important to hydraulic fracture design, wellbore stability analysis, and sand production prediction. More recent work has shown that accurate stress profiles can be used to optimize fracturing of horizontal wells and designing multizone fracture treatments. In fracturing horizontal wells, stress profiles can be used to select zones for the horizontal section that optimize fracture height.1 For multizone fracturing, the success of advanced limited-entry techniques depends on having accurate profiles of horizontal stresses.2
Theory
Conventional Method.
The industry-standard method3-9 of calculating stresses from logs is based on the following equation:
σ h m i n = μ 1 − μ ( σ v e r t − α p p ) + α p p . ( 1 )
The shmin formula is obtained by solving linear poroelasticity equations for horizontal stress with vertical stress set equal to the overburden and horizontal strains set to zero. The only deformation allowed is uniaxial strain in the vertical direction. Overburden stress, svert, is determined from an integrated density log. Poisson's ratio, m, is calculated from compressional and shear wave velocities given by an acoustic log.
When independent measures of horizontal stress magnitudes are available from microfracs or extended leak-off tests, there is often a discrepancy between the log-derived and measured values, leading to the conclusion that the uniaxial strain assumption inherent to Eq. (1) is inadequate. In order to improve the estimated stress values, an adjustment (calibration) is made by adding an additional stress term to Eq. (1), thereby shifting the profile to match the measured values.4-8 For the purposes of this article, a constant shift with depth is used, stect which in some cases has been referred to as tectonic stress.5 Eq. (1) then becomes what we term here the conventional method stress equation:
σ h m i n = μ 1 − μ ( σ v e r t − α p p ) + α p p + σ t e c t , ( 2 )
where
σ t e c t = { σ h m i n ′ − μ ′ 1 − μ ′ ( σ v e r t ′ − α p ′ p ′ ) − α p ′ p ′ } . ( 3 )
The primes indicate parameter values at the calibration depth, z¢ where a measure of the minimum horizontal stress, σhmin′, is available. When measured values are available for several zones, slightly different calibration techniques are used, such as multiplying the log-based stress by a constant factor and adding a "tectonic" gradient.6
These calibrations have physical implications. When horizontal stress is applied as in Eq. (2), the zero lateral strain boundary conditions used to derive Eq. (1) are no longer appropriate. If we assume the strain in the direction orthogonal to the applied tectonic stress is zero (plane strain), the normal strain in the direction of the applied calibration stress, [epsiv] (z), can be written as
ε ( z ) = E ( z ) 1 − μ ( z ) 2 σ t e c t , ( 4 )
where E and m are functions of depth. Given that typical geologic sequences are layered in elastic moduli, Eq. (4) implies that a constant tectonic stress calibration [exemplified in Eqs. (2) and (3)] results in horizontal strains that may be discontinuous across layer boundaries, which is a nonphysical consequence of the conventional log-derived stress calibration approach.
Spatially Varying Stress State in the Central U.S. From Bayesian Inversion of Focal Mechanism and In Situ Maximum Horizontal Stress Orientation Data