Fracture Height Prediction
Authors: Ahmed Usman 
Published: December 2007

Technology Today Series articles provide useful summary informationon both classic and emerging concepts in petroleum engineering. Purpose:To provide the general reader with a basic understanding of a significantconcept, technique, or development within a specific area of technology.

Introduction
The three basic types of vertical hydraulic-fracturing-treatment designmodels can be classified as two-dimensional (2D), pseudothree-dimensional(p-3D), and fully three-dimensional pseudothree-dimensional (p-3D), and fullythree-dimensional (3D) models. The 2D models that simulate 2D fracture geometryand one-dimensional (1D) fluid flow include the classic Khristianovic and Zheltov/Geertsma and de Klerk (KGD) and Perkins and Kern/Nordgren (PKN) typemodels. The p-3D models approximate 3D fracture geometry and assume 1D flow, whereas the 3D models simulate fully 3D geometry and rigorous 2D fluidflows.
The 2D models require fracture height as an input parameter. Thesophisticated 3D models adequately represent parameter. The sophisticated 3Dmodels adequately represent created fracture geometry (fracture height, width, and length), provided that detailed fluid rheology, formation in-situ stress, provided that detailed fluid rheology, formation in-situ stress, and mechanicalproperties at the wellbore and throughout the reservoir are available. Fordaily use by the completion and production engineer, such sophistication maylead to significant production engineer, such sophistication may lead tosignificant cost and complexity in use. Also, quite often the unavailabilityand quality of data do not warrant the sophistication these models provide. Moreover, a significant majority of fracturetreatment designs are performedwith 2D models. Therefore, the availability of a practical method to predictthe hydraulic fracture height effectively in conjunction with 2D models isimportant.

Fracture Height Prediction Procedure
Until the late 1970's, fracture height prediction methods were, at best, qualitative. A common method involved using the spontaneous potential and gammaray curves to identify shale from sand and to consider the location of thisshale to be the limit of the vertical extent. A common misconception, stillused to date, is that shale is an absolute barrier to fracture migration.
Several investigators used linear fracture mechanics models to predictfracture height. Stress input data were obtained through mini- or microfracturetests. Although the data were accurate, the frequency of the data, especiallyfor shales, was scanty. This resulted in inadequate predictions for mostcases.
The introduction of long-spaced sonic and sonic digital tools made itpossible to measure accurate compressional and shear velocities. This, in turn, allowed the calculation of stress and mechanical properties for every 6 in.[15.25 cm] over the entire logging depth.
A currently used, simple procedure includescompressional and shear wavevelocities from a long-spaced sonic or sonic digital tool to calculate rockelastic properties;a transversely isotropic elastic model to compute minimumhorizontal stress using elastic properties and pore pressures; anda linearfracture mechanics model using minimum horizontal stresses to predict fractureheight growth.
Each of these steps is briefly described below. Detailed discussion of thesesteps appears in Chap. 10 of Ref. 13.
Use of Compressional and Shear Velocities to Calculate Rock ElasticProperties. In traveling through a section of rock, an acoustic pulse deformsthe rock and, in turn, the rock alters the propagation characteristics of thepulse. By combining these data with bulk density, it is possible to calculatePoisson's ratio and other elastic properties of the rock.
With the introduction of a new generation of sonic logging tools(long-spaced sonic and sonic digital), it is now possible to detect routinelythe shear wave as well as the compressional wave. The transmitter and receiverspacings of these new tools are so designed that the compressional and shearwaves are sufficiently spread out in time. This procedure facilitates themeasurement of shear wave velocities as well as compressional velocities. Previously, use of the regular sonic tool made it impossible to detect theshear wave curve.

Calculation of Stress With a Transversely Isotropic Elastic Model.
With theknowledge of the elastic constants, overburden pressure, pore pressure, and anyunbalanced tectonic stresses, one can calculate the horizontal stress at anyparticular depth by means of a poroelastic relationship. particular depth bymeans of a poroelastic relationship. Horizontal stress measurement throughmini- or microfracture tests always should be made available to calibrate theelastic- model-derived values. In predicting fracture height, consistency inthe stress data, and therefore their differences, is more important than theirabsolute value.
Use of a Linear Fracture Mechanics Model To Predict Fracture Height Growth. During a fracturing job, the fracture fluid creates tension in front of thetip. The fracture will grow vertically if the induced stress exceeds theformation's inherent strength. The important variables in such calculations arefracture height, fluid pressure in the fracture, and the magnitude of theminimum horizontal stress, which varies with depth. Fig. 1 illustrates fracturegrowth in a 3-ft [0.91-m] cubic concrete block where the horizontal stressincreases with depth. Note the fracture height growth upward from theperforations located at the bottom, as expected. Several perforations locatedat the bottom, as expected. Several investigators have used the fundamentalresults of Muskhelishvili to predict fracture height growth. Simonson et al.obtained the exact solution of the integrals and Newberry et al. includedgravity effects within the fracture. The model is illustrated in Fig. 2. Themodel can be easily extended to n number of stress layers as required by thestress data. Details of the model can be found in Refs. 12 and 21. Stress andmechanical properties also may be made available through cores and a micro- andminifracture procedure.
Fig. 3 is an illustration of a fracture height prediction procedure thatuses log-derived mechanical properties. Note procedure that uses log-derivedmechanical properties. Note here that whenever possible the log-derived stressvalues should be checked with minifracture data for consistency. Use of staticlaboratory data also can be helpful, provided that sufficient core sampling isavailable. In Fig. 3, the depth is labeled every 100 ft [30.48 m]. Perforationsare flagged. Within the track of fracture height vs. net pressure on the leftis a step profile illustrating the fracture height migration at discrete netpressures. On the right is the increase in fracture height with continuousincrease in net pressure.
JPT
P. 813