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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.
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 andZheltov/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 includes (1) compressional and shear wavevelocities from a long-spaced sonic or sonic digital tool to calculate rockelastic properties; (2) a transversely isotropic elastic model to computeproperties; (2) a transversely isotropic elastic model to compute minimumhorizontal stress using elastic properties and pore pressures; and (3) a 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.
Hareland, Geir (New Mexico Inst. of Mining and Technology) | Rampersad, Paul (New Mexico Inst. of Mining and Technology) | Dharaphop, Jirapong (New Mexico Inst. of Mining and Technology) | Sasnanand, Sunthan (New Mexico Inst. of Mining and Technology)
This paper uses a three-dimensional three stress layer hydraulic fracturing model in conjunction with a fractured reservoir production model to optimize hydraulic fracture design. The hydraulic fracturing model has varying widths along the fracture and has the option to choose constant, linear or parabolic fracture height growth criterion. The fracturing fluid rheology is modeled with a non-Newtonian pressure loss model in the fracture, with the special case being the Newtonian model. The fractured reservoir production model uses an equation formulated from a work by Guo and Evans . In this paper the specific reservoir properties were taken from a tight gas sandstone section of the Mesa Verde formation in Colorado . It should be noted that the fracturing and production of any oil or gas reservoir can be simulated with this procedure. The fracturing parameters optimized in this paper are fracture length and fracturing fluid pump rate. The economics show that this optimization approach has great promise and that it can predict net revenue.
A successful hydraulic fracturing stimulation treatment is dependent on numerous factors. Its design requires a number of considerations: (1) The prediction of well productivity for various fracture lengths and conductivities. (2) Parametric studies on fracture geometry requirements for particular type formations, (3) Selection of appropriate types of fracture materials and, (4) The determination of fracture design criteria based on maximum returns from the well. Key design parameters which must be carefully considered for a successful fracturing stimulation include:
* The augmentation of reservoir properties and fracture characteristics to achieve optimum reservoir deliverability,
* The formation rock in-situ stress distribution and mechanical properties,
* The fracturing fluid characteristics, and
* The pad volume, type and mode of injection of proppant, pump rate and treating pressures.
A combination of these factors can then be used to determine the entire economic viability of the proposed treatment.
The successful application of a stimulation treatment is complex and design projections are rarely achieved. Over the years hydraulic fracturing technology has unproved significantly, increasing the chances for a successful job.
This case study describes a unique logging suite used to design and evaluate a hydraulic fracture treatment. The combination of pre-frac and post-frac spectral gamma, full waveform sonic, and temperature logs provides an enhanced interpretation of the stimulation treatment.
The Yowlumne field is located at the southern end of the San Joaquin Valley, Kern County, California (Figure 1). Arco Oil and Gas Company has operated the field since 1988, when the field was purchased from Tenneco Oil Exploration and Production Company. Tenneco was operator of the field from its discovery in 1974 until late 1988.
In 1988, the field's waterflood was receiving approximately 54,000 barrels of water per day [8,585 m3 water per day] from 33 injection wells, and producing in excess of 16,000 barrels of oil per day [2,543 m3 oil per day] from 59 production wells.
The reservoir consists of upper Miocene turbidite sand deposits that are a combination of stacked high energy channel and fan facies sandstones. The lenticular gross sand interval has a maximum thickness of 450 ft [137 m], and ranges in width from 1/2 - 2 miles [0.8 - 3.2 km]. Individual turbidite beds range in thickness from 1/2 - 12 ft [0.2 - 3.7 m], averaging 2 ft [0.6 m]. Each bed has the potential of behaving as an isolated reservoir, but for simplicity the numerous beds are grouped into composite sand packages that are identified based on stratigraphic correlations and historical pressure data, Original oil in place is estimated to be 245 million barrels [39 million m3].
Hydraulic Fracture Height in Gas Shale Reservoirs Norman R. Warpinski, Pinnacle - A Halliburton Service While there are many decades of experience with hydraulic fracturing in the petroleum industry, the recent exposure of the general public to this technology, particularly as practiced with large volume water fractures in the gas shales, has resulted in considerable fear and misunderstanding of what is occurring downhole. Fortunately, the industry has been studying the problem of fracture height growth for several decades and has been monitoring fractures with tiltmeters for two decades and with microseismicity for over one decade. This compendium of knowledge and measurements shows that the common practice of multistage stimulations of shale reservoirs in horizontal wells is not a threat to groundwater via fracture pathways. There is a host of laboratory, analytical, numerical-modeling, mineback, and field studies that have examined the issue of fracture height growth. Such growth is obviously undesirable since it wastes fluid, proppant, and horsepower.
Summary Fracture height is a critical input parameter for 2D hydraulic-fracturing-design models, and also an important output result of 3D models. Although many factors may influence fracture-height evolution in multilayer formations, the consensus is that the so-called “equilibrium height belonging to a certain treating pressure” provides an upper limit. However, because of the complexity of the algebra involved, published height models are overly simplified and do not provide reliable results. We revisited the equilibrium-height problem, started from the definition of the fracture stress-intensity factor (SIF), considered variation of layered formation properties and effects of hydrostatic pressure, and developed a multilayer fracture-equilibrium-height (MFEH) model by use of the programming software Mathematica (2017). The detailed derivation of SIF and work flow of MFEH model are provided. The model is compared with existing models and software, under the same ideal geology condition. Generally, MShale (2013) calculated smaller height, and FracPro (2015) larger height, than the MFEH model. Most of the difference is attributable to the different interpretation of the “net pressure,” and the solving of the nonlinear equations of SIF as well. In the normally stressed case, they are both acceptable, although MShale is more reliable. The discrepancy is much larger when there is abnormally high or low stress in the adjacent layers of the perforated interval. The effects of formation rock and fluid properties on the fracture-height growth were investigated. Tip jump is caused by low in-situ stress, whereas tip stability is imposed by large fracture toughness and/or large in-situ stress. If the fluid density is ignored, the result regarding which tip will grow into infinity could be totally different. Second and even third and fourth solutions for a three-layer problem were found by Excel experiments and this model, and proved unrealistic; however, they can be avoided in our MFEH model. The full-height map with very-large top- and bottom-formation thicknesses shows the ultimate trend of height-growth map (i.e., when the fracture tip will grow to infinity) and suggests the maximum pressure to be used. To assess the potential effects of reservoir-parameter uncertainties on the height map, two three-layer pseudoproblems were constructed by use of a multilayer formation to create an outer- and inner-height envelope. The improved MFEH model fully characterizes height evolution amid various formation and fluid properties (fracture toughness, in-situ stress, thickness, and fluid density), and for the first time, rigorously and rapidly solves the equilibrium height. The equilibrium height can be used to provide input data for the 2D model, improve the 3D-model governing equations, determine the net pressure needed to achieve a certain height growth, and suggest the maximum net pressure ensuring no fracture propagation into aquifers. This model may be incorporated into current hydraulic-fracture-propagation simulators to yield more-accurate and -cost-effective hydraulic-fracturing designs.