Comparison Study of Hydraulic Fracturing Models-Test Case: GRI Staged Field Experiment No. 3 N.R. Warpinski, SPE, Sandia Natl. Labs; Z.A. Moschovidis, SPE, Amoco Production Co.; C.D. Parker, SPE, Conoco Inc.; and 1.5. Abou-Sayed, Mobil E&P Technical Center

Summary. This study is a comparison of hydraulic fracture models run using test data from the GRI Staged Field Experiment No. 3. Models compared include 2D, pseudo-3D, and 3D codes, run on up to eight different cases. Documented in this comparison are the differences in length, height, width, pressure, and efficiency. The purpose of this study is to provide the completions engineer with a practical comparison of the available models so that rational decisions can be made as to which model is optimal for a given application.

Introduction Hydraulic fracturing, one of the most important stimulation tech-niques available to the petroleum engineer, is being used exten-sively in tight gas sandstones, 1-5 coalbed methane,6 high-perme-ability sandstones in Alaska,7 very weak sandstones off the U.S. gulf coast, 8 horizontal wells in chalks, 9.10 and many other appli-cations from waste disposal to geothermal reservoirs. Because of this diversity of application, hydraulic fracture design models must be able to account for widely varying rock properties, reservoir properties, in-situ stresses, fracturing fluids, and proppant loads. As a result, fracture simulation has emerged as a highly complex endeavor that must be able to account for many different physical processes.

The petroleum engineer who must design the fracture treatment is often confronted with the difficult task of selecting a suitable hy-draulic fracture model, yet there is very little comparative infor-mation available to help in making a rational choice, particularly on the newer 3D and pseudo-3D models. The purpose of this paper is to help provide some guidance by comparing many of the avail-able simulators.

The Fracture Propagation Modeling Forum held Feb. 26-27, 1991, near Houston provided the origin for this paper. This forum, sponsored by the Gas Research Inst. (GRI), was open to all known hydraulic fracturing modelers. Participants were asked to provide fracture designs based on the Staged Field Experiment (SFE) No. 3 fracture experiment. After the fracture designs presented at this meeting were compared, a final, revised data set was given to all participants. The results presented in this paper are derived from that data set. To publish the results, a four-member committee (the authors) was chosen from forum participants. In assembling this comparison, committee members purposely attempted to avoid judg-ing the relative values of the different models. Only the results and quantifiable comparisons are given.

Background-Basic Modeling Discussion In recent years, fracturing simulators used in the oil industry have proliferated. This proliferation was intensified by the availability of personal computers and the need for fast design simulators for use in the field. Applying these models as "black boxes," without knowledge of the underlying assumptions, may lead to erroneous conclusions, especially for unconfined fracture growth.

Hydraulic fracturing is a complex nonlinear mathematical prob-lem that involves the mechanical interaction of the propagating frac-ture with the injected slurry. Several assumptions are commonly made to render the problem tractable: plane fractures, symmetric with respect to the wellbore; elastic formation; linear fracture mechanics for fracture propagation prediction; power-law behavior of fracturing fluids and slurries; simplification of fracture geome-try and its representation by few geometric parameters; etc. Ref. 11 gives a detailed description of the governing equations. Although the models predict' 'trends" of treating pressure behavior, they may

Copyright 1994 Society of Petroleum Engineers

SPE Production & Facilities. February 1994

not always reliably predict the observed behavior for a given treat-ment. This discrepancy has been attributed to many complex in-teractions between the injected fluids and the formation that are not well understood.

An attempt to characterize phenomenologically some of these complex processes occurring within the fracture (e.g., mUltiple frac-tures and increased frictional losses) and near the fracture tip (e.g., nonlinear formation behavior, microcracking, formation plastici-ty, dilatancy, and plugging) was made in various simulators by the introduction of additional ad hoc parameters ("knobs"). The choice of values for these parameters is based only on the modeler's ex-perience. These knobs, used to match model predictions with field-observed behavior, result in the lack of a standard model response for a given physical problem. This issue was addressed in the fo-rum by having different participants (discussing several different models) simulate common test cases derived from the actual SFE No.3 fracturing treatment. These models can be categorized in order of decreasing complexity as follows.

1. Planar 3D models: TerraFrac of TerraTek Inc. 12-16 run by Arco and HYFRAC3D by S.H. Advani of Lehigh U.17

2. GOHFER, a unique finite-difference simulator by Marathon Oil Co. 18.19

3. Planar pseudo-3D models. A. "Cell" approach: STIMPLAN of NSI Inc., ENERFRAC

of Shell,20,21 and TRIFRAC of S.A. Holditch & Assocs. Inc. B. Overall fracture geometry parameterization: FRACPRO of

Reservoir Engineering Systems (RES) Inc. 2225 and MFRAC-II of Meyer & Assocs. 26-29

4. Classic Perkins-Kern-Nordgren (PKN) and Geertsma-deKlerk (GDK) models30-35 : PROP of Halliburton, 3436 the Chevron 2D model, the Conoco 2D model, the She1l2D model, and pseudo-3D models run in constant-height mode.

A discussion of the basics of these models is given to provide some insights on the model assumptions and their expected effect on results.

Planar 3D Models. The TerraFrac 12-16 and the HYFRAC3D 17 models incorporate similar assumptions and formulate the physics rigorously, assuming planar fractures of arbitrary shape in a linearly elastic formation, 2D flow in the fracture, power-law fluids, and linear fracture mechanics for fracture propagation. Their differ-ence is in the numerical technique used to calculate fracture open-ing. TerraFrac uses an integral equation representation, while the Ohio State model uses the finite-element method. Both models use finite elements for 2D fluid flow within the fracture and a fracture-tip advancement proportional to the stress-intensity factor on the fracture-tip contour.

Planar 3D Finite-Difference Model (GOHFER). Besides the nu-merical technique used, this model 18,19 is different from the previ-ous models in two fundamental ways: (1) the fracture opening is calculated by superposition using the surface displacement of a half-

7

space under normal load (Boussinesq solution); (2) the fracture prop-agates when the tensile stress normal to the fracturing plane ex-ceeds the tensile strength of the formation at some distance outside the fracture by enforcing the tensile criterion at the centroid of the cells "outside" the fracturing contour. This model predicts higher treating pressures and shorter, wider fractures than the previous 3D model predictions.

Pseudo-3D Models. These models were developed from the PKN model by removing the requirement of constant fracture height. They use equations based on simple geometries (radial, 2D, and elliptical) to calculate fracture width as a function of position and pressure and to apply a fracture propagation criterion to length and height. Furthermore, they assume 1D flow along the fracture length.

These models can be divided into two categories: (1) models that divide the fracture along its length into "cells" and use local cell geometry (2D crack or penny crack) to relate fracture opening with fluid pressure and (2) models that use a parametric representation of the total fracture geometry. As a result of these assumptions, each class is expected to have a different fracture geometry, even for the simple case of a confined fracture.

The pseudo-3D simulators are used extensively for fracture de-sign because of their efficiency and their availability on personal computers. However, they are directly applicable only for the ge-ometries that are not significantly different from the basic model assumptions (e.g., models based on a PKN geometry should have large length/height ratios to be appropriate). Thus, for relatively unconfined fracture growth in a complex in-situ stress profile, a 3D model is more accurate in predicting "trends" of fracture ge-ometry. To avoid this problem, some pseudo-3D models attempt to include truly 3D fracture behavior in terms of "history" match-ing or "lumped" parameters determined from fully 3D solutions of simpler problems or determined from simulations with 3D models. Classic PKN and GDK Models. The difference in treating pres-sure behavior and fracture geometry of the PKN and GDK models is well documented 11.37 and is not repeated here.

Fracture Models This section describes the individual fracture models in this com-parison. The modelers or the companies that ran commercially avail-able models provided short descriptions of the models.

Marathon (GOHFER). Marathon Oil CO.'s Grid Oriented Hy-draulic Fracture Extension Replicator (GOHFER) 18,19 is a planar 3D fracture geometry simulator with coupled multidimensional fluid flow and particle transport. As the name indicates, the model is based on a regular grid structure used for the elastic rock displace-ment calculations and as a planar 2D finite-difference grid for the fluid flow solutions. The areal pressure distribution obtained from the fluid flow equations, including proppant transport, is iterative-ly coupled to the elastic deformation solution. Using the finite-difference scheme for fluid flow allows modeling of mUltiple dis-crete fluid entry points, representing perforations at various loca-tions. Each grid node can be assigned an individual value of net stress, pore pressure, permeability, porosity, wall-building coeffi-cient, rock strength, Young's modulus, and Poisson's ratio, as well as variables describing fracture-wall roughness and tortuosity. Dis-placement of the fracture face at each node is determined by in-tegration of the pressure distribution over all nodes, including the computed tensile stress distribution in the unbroken rock surrounding the fracture. The fracture width equation used is the general for-mula given by Boussinesq for displacement of a semi-infinite half-space acted upon by a distributed load. The solution is general enough to allow modeling of multiple fracture initiation sites si-multaneously and is applicable to any planar 3D geometry from perfect containment to uncontrolled height growth.

Halliburton (PROP). The PROP program34-36 is a 2D fracture design model based on Daneshy's34,35 numerical solution. Its nu-merical nature makes the model much more flexible than most an-

8

aiytical models. For example, the program was recently modified for use of multiple fluids and rates within a single treatment, each fluid with its own set of time- and temperature-dependent rheolog-ical parameters. In addition to the power-law model normally used to characterize gelled fracturing fluids, PROP uses the three-parameter Herschel-Bulkley model for fluids containing a nitrogen or carbon dioxide phase. The program's proppant transport calcu-lations are of similar capability. Although the model originally presented by Daneshy was based on the Khristianovic-Zheltov width equation (designated GDK in this paper), the PROP program has since been expanded to include a similar numerical solution of PKN-type geometry with a width profile based on calculated local pres-sures. The results presented here are for the GDK-type solution only.

S.A. Holditch & Assocs. (TRIFRAC). TRIFRAC is a pseudo-3D model of fracture propagation and proppant transport that com-putes created and propped fracture dimensions with a finite-difference numerical approach. It can handle multiple nonsymmetric stress layers with unique values for Young's modulus, Poisson's ratio, fracture toughness, permeability, porosity, and fluid-Ieakoff coefficients for each layer. Currently, properties for a maximum of 22 layers can be entered. The apparent viscosity of the fractur-ing fluid is computed from the shear rate inside the fracture and changes in flow-behavior index, n' , and consistency index, K', ow-ing to variations of temperature and time. Thus, a temperature cal-culation model is part of TRIFRAC. The choice of initiating the hydraulic fracture from 10 different layers simultaneously is avail-able. Special options are available to enter the pump schedule for nitrogen-foam treatments. The created geometry computation mod-ule is coupled with a rigorous finite-difference proppant transport simulator that solves simultaneously for proppant distribution, trans-port, and settling, along with fracture growth. Depending on the fluid velocity along the fracture height and the proppant settling rate, the model computes the proppant profIle at each timestep during the job. TRIFRAC also has the simpler 2D geometry computational finite-difference GDK and PKN models. Horizontal fracture ge-ometry calculation with the GDK method is also available. All these models are coupled with proppant-transport-calculation modules.

RES (FRACPRO). FRACPR022-25 uses measured values of flow rate, proppant concentration, and fluid rheology parameters to cal-culate the pressure drop down a wellbore of variable deviation and diameter. The time histories of the fracture growth and the net frac-ture pressure are calculated. The wellbore model handles non-Newtonian fluids and corrects for the effects of nitrogen foam, car-bon dioxide, and proppant phases. The model also accounts for fric-tion variation from entrained proppant. The fracture model is 3D in that spatial variations in reservoir stress, modulus, pressure, and flow distribution are taken into account.

However, FRACPRO does not need to calculate the variations at specific points in the fracture. Instead, the effects are integrated into functional coefficients of governing differential equations, great-ly simplifying the calculation of fracture dimensions. The module can therefore run many times faster than real time, as required for on-site history matching. The coefficients necessary to calculate the spatial variations are calculated from a fully 3D model and checked against experimental and field test data. FRACPRO han-dles up to 3 modulus zones, up to 50 stress zones, and up to 50 permeable (Ieakoff) zones. Fluid loss is modeled as 1D flow per-pendicular to the fracture face, following Darcy-law behavior, in-cluding spurt loss, filter-cake buildup on the fracture face, and a compressible reservoir-fluid region. The rise in confining stress ow-ing to poroelastic effects (backstress) is included. Heat transfer modeling assumes that there is a cubic-fit temperature distribution between the fracture and the end of the heat transfer region. FRAC-PRO models proppant convection and settling in a fracture. In prop-pant convection, heavier treatment stages (e.g., proppant stages) displace rapidly downward from the perforations to the fractury bottom. Then the pad or low-concentration proppant stages replace those stages. FRACPRO also can be used to model proppant settling. The proppant is carried with the fracturing fluid and settles. The model takes into account the effects of non-Newtonian fluids, hin-dered settling rates, and settled bank buildup.

SPE Production & Facilities. February 1994

TABLE 1-ROCK AND RESERVOIR DATA

Zone In-Situ Young's Depth Thickness Stress Poisson's Modulus Fracture Toughness

Interval (ft) (ft) (psi) Ratio (million psi) (psi/Jin. ) --- --

Single-Layer (2D) Case

1 9,170 to 9,340 170 5,700 0.21 8.5 2,000

Three-Layer (3D) Case

1 8,990 to 9,170 180 7,150 0.30 6.5 2,000 2 9,170 to 9,340 170 5,700 0.21 8.5 2,000 3 9,340 to 9,650 310 7,350 0.29 5.5 2,000

Five-Layer (3D) Case

1 8,990 to 9,170 180 7,150 2 9,170 to 9,340 170 5,700 3 9,340 to 9,380 40 7,350 4 9,380 to 9,455 75 5,800 5 9,455 to 9,650 195 8,200

Chevron 2D Fracturing Simulator. This model can predict the, propagation of constant-height, hydraulically induced, vertical frac-tures for a power-law fluid. The simulator also includes a prop-pant transport model with proppant settling and a production model. The simulator can predict the created fracture geometry based on the PKN and GDK models. It is most suitable to design fractures where the geologic conditions restrict height growth. In fracture propagation models, the equations describing conservation of mass, conservation of momentum, continuity of fluid flow, and linear elas-tic deformation of the rock in plane strain are used to calculate mass flux, fracture width, pressure, and length as functions of time. Given a settling velocity, the proppant transport model calculates the fi-nal propped concentration, width, and bank height. It also can predict possible problems caused by proppant bridging or screenout.

Shell (ENERFRAC). ENERFRAC20,21 is a hydraulic fracture model that predicts fracture dimensions for uncontained (circular) and contained (rectangular) fractures. ENERFRAC incorporates fracture-tip effects and the other interacting processes of viscous fluid flow, elastic rock deformation, and fluid loss. Fracture-tip effects are accounted for through direct input of the rock's appar-ent fracture toughness or the fracture-tip net pressure (overpres-sure). This overpressure, defined as the instantaneous shut-in pressure minus the closure pressure, can be determined in the field from a microfracture or minifracture test. Shell also provided 2D PKN and GDK model results. The ENERFRAC results provided a useful comparison of the effect of free model parameters (knobs) on the results. Shell provided results for typical fracture toughness values measured in laboratory tests (designated ENERFRAC-1) and for a tip overpressure of 1,000 psi (ENERFRAC-2). This compar-ison shows the effect of fracture-tip overpressure on fracture ge-ometry and net pressure.

Meyer & Assocs. (MFRAC-II). MFRAC-II26-29 is a pseudo-3D hydraulic fracturing simulator. MFRAC-II also includes options for the penny-, GDK- and PKN-type 2D fracturing models. This study was run with MFRAC-II, Version 6.1. MFRAC-II accounts for the coupled parameters affecting fracture propagation and prop-pant transport. The major fracture, rock, and fluid mechanics phe-nomena include (1) multilayer, asymmetrical confining stress contrast, (2) fracture toughness and tip/overpressure effects, (3) rock deformation, (4) variable injection rate and time-dependent fluid rheology properties, (5) multilayer leakoff with spurt loss, and (6) 2D proppant transport. The fracture propagation model cal-culates fracture length, upper and lower heights, width, net pres-sure, efficiency, and geometry parameters as functions of time. The width variation as a function of height and confining stress also is calculated. To provide applicability over the broadest range of circumstances, MFRAC-II offers numerous options. These options and other free parameters (knobs) allow customization in the model-

SPE Production & Facilities, February 1994

0.30 6.5 2,000 0.21 8.5 2,000 0.26 5.4 2,000 0.20 7.9 2,000 0.30 4.0 2,000

ing approach adopted. MFRAC-II was run in two different modes to demonstrate the effects of some of these parameters. In one case, the base model using system defaults was run (designated MEYER-1); in a second case (MEYER-2), additional parameters (such as greater friction drop in the fracture) were applied. In both cases, the viscous thinning assumption was made as a default. Without viscous thinning, the effective friction factor would have increased, resulting in higher net pressures, greater widths, and shorter lengths. In addition, the fully implicit coupled model for height growth (Ver-sion 7.0) results in increased development of fracture height and net pressure for certain multilayer formations.

Advani (Lehigh U. HYFRAC3D). The three- and five-layer model results (Cases 5 through 8) are obtained from the HYFRAC3D code. 17 This finite-element code is based on a set of coupled mass conservation, fluid momentum, constitutive elasticity, and fracture mechanics equations governing planar hydraulic fracture propaga-tion in a multilayered reservoir. A mapping technique of the base-line mesh (88 triangular elements representing one-half the fracture) defined in a unit circle to arbitrarily shaped fracture geometries is used in the numerical scheme to track the moving fracture front. The PKN model results (Cases 1 and 2) also are based on a 2D finite-element model simulator with standard PKN model equations, including vertical stiffness and 1 D fluid flow. These simulation re-sults are obtained with 20-line elements for the normalized, time-dependent fracture half-length.

NSI (STIMPLAN). STIMPLAN is a state-of-the-art 3D hydrau-lic fracture simulator for fracture design and analysis in complex situations involving height growth, proppant settling, foam fluids, tip screenout, etc. The model has complete fluid/proppant track-ing that allows optimum fluid selection and scheduling based on time and temperature histories. Fracture height growth is calculat-ed through multiple layers and includes proppant settling and bridg-ing calculations. A fracture analysis/history matching module provides history matching of measured net treating pressures to yield the most accurate possible estimation of actual fracture geometry and behavior. Also, simulations during fracture closure (pressure decline) aid in pressure-decline analysis for fluid loss in complex geologic situations.

Arco (Using TerraFrac). TerraFrac Code 12-16 is a fully 3D hy-draulic fracture simulator. Initiated at Terra Tek in 1978, its com-mercial availability was announced in Dec. 1983. The model's overall approach is to subdivide the fracture into discrete elements and to solve the governing equations for these elements. These governing equations consist of (1) 3D elasticity equations that re-late pressure on the crack faces to the crack opening, (2) 2D fluid flow equations that relate the flow in the fracture to the pressure gradients in the fluid, and (3) a fracture criterion that relates the

9

TABLE 2-TREATMENT DATA

Bottomhole temperature, of Reservoir pressure, psi Spurt loss Fluid-Ieakoff height Fluid-Ieakoff coefficient, tt/.JiTiTr1 Viscosity-Case A, cp Viscosity-Case B

n' K'

Fluid volume, bbl Injection rate, bbl/min Proppant

246 3,600

0.0 Entire fracture height

0.00025 200

0.5 0.06

10,000 50

None

intensity of the stress state ahead of the crack front to the critical intensity for Mode 1 fracture growth. TerraFrac provides many distinctive features: 2D fluid flow for both proppant and tempera-ture distribution; multiple stages having different fluids, proppants, and rates, with fluid and proppant properties as functions of tem-perature if desired; multiple layers, each having different in-situ stresses, Young's moduli, fracture toughnesses, Poisson's ratios, and leakoffs; poroelastic and thermoelastic capabilities for water-flooding and other applications; a robust mesh generator to handle a wide variety of fracture geometries and a quasi-Newton method to solve the nonlinear system of equations for the fluid pressures (this approach provides fast convergence and high accuracy); and a post-shut-in calculation capability for which no additional assump-tions are made (only the injection rate changes).

Texaco (Using FRACPRO). Texaco also ran FRACPRO for six different cases. These include single-layer PKN and GDK models, a three-layer case with constant fracture-fluid viscosity, and five-layer cases for constant fluid viscosity, power-Iaw-fluid behavior, and power-Iaw-fluid behavior with the tip-dominated rheology be-havior not operating. The five-layer runs provide a good compari-son of tip-dominated vs. conventional rheology results with FRACPRO.

Conoco. Conoco's fracture design program is a constant-height (2D) model where either PKN or GDK geometry can be selected. 38 It has single inputs for n', K', and leakoff coefficient. However, the model can calculate the positions and concentrations of progres-sive fluid/proppant stages. Fracture area can be calculated by either the Howard and Fast model or by Crawford's39 extremely accurate simplification.

SFE3 Formation and Treatment Data The input data for the fracture modeling comparison are based on the results obtained at the GRI-sponsored SFE-3 experiment. 3,40 Well SFE-3 was drilled as the Mobil Cargill Unit No. 15 well in the Waskom field, Harrison County, TX. The well was spudded in Sept. 1988 and drilled to a total depth of 9,700 ft. Of particular interest was the Cotton Valley Taylor sand, which was perforated between 9,225 to 9,250 ft and 9,285 to 9,330 ft. An extensive log program and detailed core analyses were done on this well. Both pre fracture well testing and postfracture production testing were performed. Two minifracs and one full-scale treatment were con-ducted as part of the stimulation program.

TABLE 3-20 RESULTS AT END OF PUMP

200 cp Length Height Pressure Maximum Width Efficiency

Model ~ ~ (psi) (tt) b' E, * (%) --SAHt (GOK) 2,542 170 62 0.848 0.849 0.605 85.5 SAH (PKN) 4,855 170 1,094 0.502 0.394 0.289 72.3 Marathon 2,584 204 1,685 0.91 0.76 0.73 93

Meyer-1 (GOK) 2,659 170 70 0.79 0.79 0.62 83.1 Meyer-1 (PKN) 4,507 170 1,188 0.55 0.43 0.32 72.2 Meyer-2 (GOK) 2,288 170 97 0.94 0.94 0.74 85.4 Meyer-2 (PKN) 3,803 170 1,474 0.68 0.53 0.4 76.6

Shell (GOK) 2,724 170 53 0.78 0.78 0.61 84 Shell (PKN) 4,039 170 1,377 0.59 0.46 0.37 75

Texaco-FP (GOK) 2,480 200 71 0.74 86 Texaco-FP (PKN) 4,157 200 925 0.50 77 Chevron (GOK) 1,347 170 81.9 0.77 0.77 0.6 81.9 Chevron (PKN) 2,029 170 1,380 0.63 0.36 73

Advani 4,595 170 1,182 0.54 0.43 0.32 73.8 Halliburton 2,212 170 82 0.98 0.98 0.77 85.9

Conoco (GOK) 2,716 170 0.767 0.6 82.5 Conoco (PKN) 3,986 170 0.554 0.37 74.4 ENERFRAC-1 3,866 170 1,595 0.627 0.492 0.387 75 ENERFRAC-2 3,556 170 1,684 0.704 0.553 0.434 78

n', K'

SAH (GOK) 2,542 170 61.8 0.85 0.85 0.6 61.8 SAH (PKN) 4,629 170 1,167.5 0.54 0.42 0.28 73.6 Marathon 2,516 204 1,824 0.98 0.82 0.75 93

Meyer-1 (GOK) 2,098 170 117 1.04 1.04 0.82 86.4 Meyer-1 (PKN) 4,118 170 1,397 0.64 0.5 0.36 74.3 Meyer-2 (GOK) 1,808 170 161 1.24 1.24 0.97 88.3 Meyer-2 (PKN) 3,395 170 1,774 0.831 0.64 0.46 79

Shell (GOK) 2,142 170 89 1.03 1.03 0.81 89 Shell (PKN) 3,347 170 1,754 0.75 0.59 0.47 79

Advani 4,046 170 1,474 0.68 0.53 0.38 76.9 Halliburton 2,031 170 97 1.07 1.07 0.84 86

Conoco (GOK) 2,304 170 0.933 0.933 0.733 85.2 Conoco (PKN) 3,656 170 0.622 0.415 76.5 ENERFRAC-1 3,396 170 1,880 0.738 0.58 0.456 78 ENERFRAC-2 3,155 170 1,986 0.817 0.641 0.504 81.7

'b = average width at the wellbore. "b, = overall average fracture width. t S.A. Holditch & Assocs. Inc.

10 SPE Production & Facilities, February 1994

TABLE 4-THREE-LAYER RESULTS AT END OF PUMP

200 cp

Length Height Pressure Maximum Width Efficiency Model ~ ~ (psi) (ft) b b , (%) --SAH 3,408 318 1,009 0.65 0.35 0.3 77 NSI 3,750 903 283 0.56 0.32 0.25 66 RES 1,744 544 1,227 0.9 0.54 0.36 80

Marathon 1,360 442 1,387 1.04 0.68 0.64 96 Meyer-1 3,549 291 987 0.58 0.35 0.29 70.3 Meyer-2 2,692 360 1,109 0.72 0.41 0.34 74.3

Arco-Stimplan 3,598 306 992 0.57 0.31 0.25 67 Texaco-FP 1,938 435 1,132 0.72 68

Advani 2,089 357 1,113 0.66 0.33 0.25 43

n', K'

SAH 3,259 371 1,093 0.75 0.38 0.31 77.6 NSI 3,289 329 1,005 0.67 0.35 0.26 68 RES 902 596 1,428 1.1 0.74 0.49 62

Marathon 1,326 442 1,433 1.08 0.71 0.66 96 Meyer-1 2,915 337 1,094 0.69 0.4 0.32 72.7 Meyer-2 2,120 413 1,212 0.86 0.48 0.4 76.9

Arco-Stimplan 3,235 353 1,083 0.65 0.33 0.26 69 Advani 2,424 435 1,171 0.74 0.34 0.21 47

TABLE 5-FIVE-LAYER RESULTS AT END OF PUMP

200 cp

Length Height Pressure Maximum Width Efficiency Model (ft) (ft) (psi) (ft) b b, (%) --SAH 2,905 394 960 0.72 0.42 0.31 80.1 NSI 3,709 361 852 0.63 0.38 0.25 66 RES 1,754 501 1,119 0.83 0.6 0.4 82

Marathon 1,224 476 1,250 1.03 0.7 0.65 97 Meyer-1 2,962 328 669 0.5 0.36 0.28 70.5 Meyer-2 2,407 327 768 0.6 0.46 0.35 74.8

Arco-Stimplan 3,399 394 944 0.64 0.36 0.24 68 Texaco-FP 2,011 428 1,008 0.68 69

Advani 1,594 438 1,129 0.81 0.45 0.36 58.1

n', K'

SAH 2,642 430 1,035.5 NSI 2,765 388 935 RES 1,042 600 1,358

Marathon 1,156 476 1,262 Meyer-1 2,535 330 766 Meyer-2 1,980 349 891

Arco-Stimplan 2,926 405 968 Arco-Terrafrac 3,124 449 1,160

Texaco-FP 1,125 602 1,270 Texaco-FPNOTIP 2,636 391 934

Advani 1,870 458 1,151

The SFE-3 data set was specifically chosen to ensure that the model comparison would be performed with actual field data, not for a contrived data set that might favor one type of model. In ad-dition, the SFE-3 data set is one of the most complete sets of well information available. It includes stress, rock, and reservoir and well-performance results.

Table 1 shows the relevant rock and reservoir information for this initial study. As described in the next section, three different physical configurations were considered: a single layer, three lay-ers, and five layers. Stress and rock property measurements were averaged over the appropriate depths for each interval to yield the physical data in Table 1. Most importantly, the stress contrasts range from 1,450 to 1,650 psi, although the lower barrier is only 40 ft thick for the five-layer configuration. Young's modulus and Pois-son's ratio were obtained from sonic measurements, thus account-ing for the elevated values of Young's modulus.

The actual SFE-3 treatment was a 13-stage procedure using primarily a 40-lbm/l ,OOO-gal crosslinked gel with sand stages vary-ing from 1 to 8 Ibm/gal. For this comparison, the treatment was simplified to a single, constant-property fluid with no proppant,

SPE Production & Facilities, February 1994

0.82 0.46 0.31 81.8 0.71 0.42 0.25 70 1.18 0.9 0.6 87 1.04 0.71 0.66 93 0.6 0.46 0.37 73.7 0.75 0.57 0.42 77.8 0.7 70 0.74 62 1.11 76 0.49 62 0.85 0.47 0.34 64

primarily because changes in fluid properties owing to tempera-ture or proppant addition cannot be quantified easily and any re-sulting comparisons would be of questionable value.

Test Cases As noted, most models can accommodate and process a much broad-er range of complex data than presented in this data set (i.e., mul-tiple rock properties, leakoff coefficients, n', and K'). Table 1 and Table 2 give the complete set of data input. However, the data set was arbitrarily restricted to limit as many discretionary inputs as possible to allow more direct comparison of model performance. The input also should not be construed as optimum design parame-ters. As mentioned, the data for the cases approximates that from SFE No.3.

Each participant could model a total of eight possible cases. These were GDK, PKN, three-layer, and five-layer cases, with separate runs for a constant Newtonian viscosity and a constant n/ and K' power-law fluid. The PKN and GDK cases were run with a con-stant height (2D) set at 170 ft. The three- and five-layer cases were run with a 3D or a pseudo-3D model, allowing fracture height to

11

CONSTANT HEIGHT MODELS

g ::: r7a'" ,-~-o-. '~-"~-""-~-;-'-'~-G-_-~-\-.. _-_-----._-..... -2-' --11'---.. '-----,'"

lr 1>"'-''''' I 3,000 I-C} Z 2,000 W oJ

1,000

~~

GDK -200cp --GDK - n'=O 5, K'=O 06 ---.-_. PKN -200cp 0

PKN - n'=0.5, K'=O.06 --0--

01H':~~.~CP

OTHER 20 - 0'=0.5, K'=O.06 ---{~--

Fig. 1-Fracture length-2D models.

'r;; c. ;u- 1,500 II: => ~ 1,000 W II: Il.

Iii 500 Z

.CONSTANT HEIGHT MODELS GDK-200cp --GDK - n'=0.5, K'=O.06 ---.-_. PKN-200cp ...... 8 ..

PKN - n'=O.S, K'=O.06 --0--

OTHER 20 - 200 cp _ .. -6.-.. -

OTHER 20 - n'=0.5, K"=O.06 - . ..,:.,....-

Fig. 2-Net pressure-2D models.

3-LAYER MODELS g 4,000 ,------------------, I I-C} Z 3,000 W oJ LL ;;t 2,000 I W g; 1,000

,a

~ OU-__ L-~ __ _L __ ~~ __ _L __ J_ __ ~ LL f#v"I ~"I 9,,?-O"l [c"'~ ,.J-~ .1

3-LAYER MODELS: n', K' 600~------------------~--------~

f-I

"

500

~ 300

200

-e-SAH --&-NSI ---!'l--RES ---+-- MARATHON -+-ARCO(STIM)

~----+------------il ->

5-LAYER MODELS: n', K' 700

----e-SAH ----NSI

600 ---e--RES ---+-MARATHON --+-ARCO(STIM)

500 ~ARCO(TERR)

,,-.... -----E- MEYER-1 - ______ MEYER-2 ..... '-" ---+-ADVANI f- 400 _______ TEXACO(FP) :r: 0 _______ TEX-FPNOTP w :r:

300

200

100~ __ ._--~---r---.----r---.---~--~ o 25 50 75 100 125 150 175 200

TIME (min)

Fig. 13-Height vs. time-five-Iayer models.

Three-Layer Results. The three-layer results (Table 4) show con-siderably more variability than results from the 2D cases. In Fig. 3, the fracture half-length varies from < 1,000 ft for FRACPRO to >3,000 ft for the conventional pseudo-3D models. The differ-ences between MEYER -1 and -2 again show that the options avail-able to the analyst can significantly affect results. Many such options have probably been used in the other models but were not identi-fied for this comparison.

running FRACPRO show that consistent results can be obtained from a given model even if run by different organizations.

The fracture height comparison in Fig. 4 shows that much great-er height growth is obtained by FRACPRO than by other models. Net pressures (Fig. 5) are particularly high in FRACPRO and GOH-FER. Efficiencies vary from 40% to >95%, as given in Table 4.

Also of interest are the length, height, and pressure development with time, as Figs. 6 through 8 show for the case with non-Newtonian rheology. Height growth is extremely fast in FRAC-PRO but much better contained in most other models.

The favorable comparison between Arco and NSI running Stim-plan and a similar favorable comparison between Texaco and RES

14

5- LAYER MODELS: n' , K' 1600~--------------------------------~

1400

,,-.... 1200 (f)

0.. '-"

w a:: ::>

1000

(/) 800 (/) w a:: 0... 600 f-W Z 400

200

----e-SAH ----NSI

I~~:::::!~~~~::::::===::===+---e--RES ~ ---+-MARATHON --+-ARCO(STIM)

~'----=" ~ARCO(TERR)

,;::::===~;:;::::;!::=:t====:e::-::t=l-----E- M EYER-1

~*-~~~~~~~~$:i:2::=~ ------ MEYER-2 ~ ---+-ADVANI _______ TEXACO(FP)

,,",-_~----:l~-t _______ TEX - FPNOTP

O __ --~--~---r--~----r---._--._--~ o 25 50 75 100 125 150 175 200

TIME (min)

Fig. 14-Pressure vs. time-five-Iayer models.

SPE Production & Facilities, February 1994

Five-Layer Results. The five-layer results (Table 5) are similar to the three-layer comparison, except that fractures in some models are shorter because the height breaks through the lower barrier. Fig. 9 shows the half-lengths; Fig. 10 shows the fracture heights. Net pressures range from'" 700 to '" 1 ,400 psi (Fig. 11). Efficien-cies range from about 60 % to 97 % .

Fig. 12 shows fracture lengths as a function of time. The length development in this case is not uniform because height breakthrough into the lower barrier limits growth in some models. The height growth is shown in Fig. 13 and the net pressure in Fig. 14. By comparing these results with the three-layer results of Figs. 6 through 8, we can see the effect of breakthrough into the lower low-stress region.

Discussion and Conclusions The completion engineer now has a wide array of hydraulic models available for both design and analysis of hydraulic fracture treat-ments. However, these models calculate widely different fracture geometries for the same input parameters, and choosing a model that meets the engineer's needs becomes important. We hope that this comparison study provides sufficient information to make a studied choice.

Some models clearly predict results that are significantly differ-ent from the majority. Considering the five-layer cases shown in Figs. 9 through II, FRACPRO calculates very short fractures, high net pressures, and large heights. GOHFER also predicts short frac-tures and high net pressures, but the height growth is not as se-vere. TRIFRAC, STIMPLAN, TERRAFRAC, and MFRAC-II are all in general agreement, with longer fractures, less height, and somewhat lower net pressures. Advani's model is midway between the two end cases.

MFRAC-II (in 2D, three-layer, and five-layer cases), ENER-FRAC (in 2D cases), and Texaco's FRACPRO cases (five-layer) were run in two different modes and thus provide a useful assess-ment of the importance of the options available to the fracture designer. In the original formulation of this study, the modelers were asked to run their models in both a base mode (no options) and then with a best-option mode-i.e., a mode that reflected their expectations of the options needed to provide the closest simula-tion of true fracture behavior. Such options may have included tip effects, higher frictional pressure drops in the fracture, multiple fracture strands, or enhanced toughness.

In the three cases mentioned above, the modelers provided such a comparison, and these results can be used to estimate how sig-nificantly the engineer can modify the fracture design by incorporat-ing his or her estimate of the best physics possible for a given reservoir. Presumably, such an estimate would be guided by expe-rience with the reservoir. For the five-layer case with non-Newtonian viscosity, best-physics results for fracture length differed by about 22 % for MFRAC-II and 57 % for FRACPRO run by Tex-aco. For the 2D case with non-Newtonian rheology, ENERFRAC results differed by about 7 %. Because many models have such op-tions, these results should be a useful guideline for estimating the differences in model designs that can be obtained.

The 2D models, both PKN and GDK, generally provide self-consistent results (Figs. I and 2), and the differences between these types of models are discussed elsewhere. 11 ,37 Chevron's 2D model, however, yields considerably shorter lengths than the other PKN and GDK models. GOHFER is also of note because it yields a length typical of the GDK models with the net pressure typical of the PKN models. Other differences in these 2D models are minor.

This particular case was chosen because it was a realistic field situation for which detailed data were available. The committee and modelers recognize that other formations, with different stress and lithology data, may provide a considerably different comparison. Good examples would be cases with either minimal or extremely large stress contrasts. It would be beneficial if future model com-parisons investigated those cases as well.

Finally, in assembling this comparison, we have purposely at-tempted to avoid making any value comparisons between the vari-ous models. Only the results and quantifiable comparisons (e.g.,

SPE Production & Facilities, February 1994

Model A fracture length is greater than Model B fracture length) are given. It would take a committee with greater powers than this one has to truly know how the fracture is evolving in the subsur-face and thus to decide which model is better.

Acknowledgments We thank the GRI for its support of this modeling endeavor. We also thank our respective companies for allowing us to perform this comparison. The modelers who participated in the forum and pre-pared data for this paper also deserve special thanks for their ef-forts. Most importantly, Steve Holditch of S.A. Holditch & Assocs. Inc. should be singled out for special mention as the prime mover of the forum and this follow-up paper. He is not an author because his firm submitted a model, but this study would never have hap-pened without his efforts. Thanks also go to Bill Whitehead of S.A. Holditch & Assocs. for his work in the forum and in data gathering.

References 1. Holditch, S.A. et al.: "The GRI Staged Field Experiment," SPEFE

(Sept. 1988) 519. 2. Robinson, B.M., Holditch, S.A., and Peterson, R.E.: "The GRI's Sec-

ond Staged Field Experiment: A Study of Hydraulic Fracturing," paper SPE 21495 presented at the 1991 SPE Gas Technology Symposium, Houston, Jan. 22-24.

3. Robinson, B.M. et al.: "Hydraulic Fracturing Research in East Texas: Third GRI Staged Field Experiment," JPT (Jan. 1992) 78.

4. Saunders, B.F. et al.: "Hydraulic Fracturing Research in the Frontier Formation through the GRI's Fourth Staged Field Experiment, " paper SPE 24854 presented at the 1992 SPE Annual Technical Conference and Exhibition, WashingtoI), Oct. 4-7.

5. Northrop, D.A. and Frohne, K-H.: "The Multiwell Experiment-A Field Laboratory in Tight-Gas Sandstone Reservoirs," JPT(June 1990) 772.

6. Cramer, D.D.: "The Unique Aspects of Fracturing Western U.S. Coal Beds," JPT (Oct. 1992) 1126; Trans., AIME, 293.

7. Martins, P.J. et ai. : "Deviated Well Fracturing and Proppant Produc-tion Control in the Prudhoe Bay Field," paper SPE 24858 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washing-ton, Oct. 4-7.

8. Monus, F.L. et al.: "Fracturing Unconsolidated Sand Formations Off-shore Gulf of Mexico," paper SPE 24844 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, Oct. 4-7.

9. Owens, K.A., Andersen, S.A., and Economides, M.J.: "Fracturing Pressures for Horizontal Wells," paper SPE 24822 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, Oct. 4-7.

10. Meehan, D.N.: "Stimulation Results in the Giddings (Austin Chalk) Field," paper SPE 24783 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, Oct. 4-7.

11. Recent Advances in Hydraulic Fracturing, J.L. Gidley et al. (eds.), Monograph Series, SPE, Richardson, TX (June 1989) 12.

12. Clifton, R.J. and Abou-Sayed, A.S.: "On the Computation of the Three-Dimensional Geometry of Hydraulic Fractures," paper SPE 7943 presented at the 1979 SPEfDOE Low Permeability Gas Reservoir Sym-posium, Denver, May 20-22.

13. Clifton, R.J. and Abou-Sayed, A.S.: "A Variational Approach to the Prediction of the Three-Dimensional Geometry of Hydraulic Fractures," paper SPE 9879 presented at the 1981 SPEfDOE Low Permeability Reservoir Symposium, Denver, May 27-29.

14. Clifton, R.J. and Wang, J.J.: "Multiple Fluids, Proppant Transport, and Thermal Effects in Three-Dimensional Simulation of Hydraulic Frac-turing," paper SPE 18198 presented at the 1988 SPE Annual Techni-cal Conference and Exhibition, Houston, Oct. 2-5.

15. Clifton, R.J. and Wang, J.J.: "Modeling of Po roe las tic Effects in Hy-draulic Fracturing," paper SPE 21871 presented at the 1991 SPE Rocky Mountain Regional/Low Permeability Reservoir Symposium, Denver, April 15-17.

16. Clifton, R.J. and Wang, J.J.: "Adaptive Optimal Mesh Generator for Hydraulic Fracturing Modeling," Proc., 32nd U.S. Rock Mechanics Symposium (1991).

17. Advani, S.H., Lee, T.S., and Lee, J.K.: "Three-Dimensional Model-ing of Hydraulic Fractures in Layered Media: Part I-Finite Element Formulations," ASME J. Energy Res. Tech. (1990) 112, 1-9.

18. Barree, R. D.: "A Practical Numerical Simulator for Three Dimensional Fracture Propagation in Heterogeneous Media," paper SPE 12273 presented at the 1983 SPE Reservoir Simulation Symposium, San Fran-cisco, Nov. 15-18.

IS

Authors

Warpinski Moschovidis Parker

Norm Warplnskl is a distinguished member of the techni-cal staff at Sandia National Laboratories in Albuquerque, where he specializes in fluid and rock mechanics with in-terests in hydraulic fracturing, in-situ stresses, geomechan-ics, and natural fracture systems. He holds a PhD degree in mechanical engineering from the U. of Illinois and has been with Sandia since 1977. Warpinski was a 1990-92 Review Chairman for JPT and was a member of the Editorial Review Committee. Zlssls Moschovidis is currently a research as-sociate at the Amoco Research Center in Tulsa. A member of the Wellbore Stability Team, he works primarily in well bore stability, cuttings injections, hydraulic fracture propagation, modeling, and rock mechanics. Moschovidis received a diplo-ma in civil engineering from the Natl. Technical U. of Athens, Greece, an MS degree in structural engineering from the Im-perial C. of Science and Technology in London, and a PhD degree in engineering mechanics from Northwestern U. in Evanston, 1L. Cecil D. Parker is a senior staff engineer for Conoco in the Well Completions Group in Houston. He has spent 25 years designing and executing stimulation treat-ments worldwide, including the North Sea, Middle East, and North America. He holds a degree in chemistry/biology from Abilene Christian U., Abilene, TX. Photograph and biograph-ical sketch of 1.5. Abou-Sayed are unavailable.

19. Barree, R.D.: "A New Look at Fracture-Tip Screenout Behavior," 1PT (Feb. 1991) 138; Trans., AIME, 291.

20. Shlyapobersky, J.: "Energy Analysis of Hydraulic Fracturing," Proc., 26th U.S. Symposium on Rock Mechanics, Rapid City (June 1985).

21. Shlyapobersky, J., Wong, G.K., and Walhaug, W.W.: "Overpressure Calibrated Design of Hydraulic Fracture Simulations, " paper SPE 18194 presented at the 1988 SPE Annual Technical Conference and Exhibi-tion, Houston, Oct. 2-5.

22. Cleary, M.P.: "Analysis of the Mechanisms and Procedures for Produc-ing Favorable Shapes of Hydraulic Fracturing," paper SPE 9260 present-ed at the 1980 SPE Annual Technical Conference and Exhibition, Dallas, Sept.

23. Cleary, M.P.: "Comprehensive Design Formulae for Hydraulic Frac-turing," paper SPE 9259 presented at the 1980 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 21-24.

24. Cleary, M.P., Wright, C.A., and Wright, T.B.: "Experimental and Modeling Evidence for Major Changes in Hydraulic Fracturing De-sign and Field Procedures," paper SPE 21494 presented at the 1991 SPE Gas Technical Symposium, Houston, Jan. 22-24.

25. Cleary, M.P. and Fonseca, A.: "Proppant Convection and Encapsu-lation in Hydraulic Fracturing: Practical Implications of Computer Lab-oratory Simulations," paper SPE 24825 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, Oct. 4-7.

16

26. Meyer, B.R.: "Design Formulae for Two- and Three-Dimensional Ver-tical Hydraulic Fractures: Model Comparison and Parametric Studies," paper SPE 15240 presented at the 1986 SPE Unconventional Gas Tech-nology Symposium, Louisville, May 18-21.

27. Meyer, B.R.: "Three-Dimensional Hydraulic-Fracturing Simulation on Personal Computers: Theory and Comparison Studies," paper SPE 19329 presented at the 1989 SPE Eastern Regional Meeting, Morgan-town, Oct. 24-27.

28. Meyer, B.R., Cooper, G.D., and Nelson, S.G.: "Real-Time 3D Hy-draulic Fracturing Simulation: Theory and Field Case Studies," paper SPE 20658 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 23-26.

29. Hagel, M. and Meyer, B.: "Utilizing Mini-Frac Data To Improve De-sign and Production," paper CIM 92-40 presented at the 1992 Annual Technical Conference of the Petroleum Soc. of CIM, Calgary, June.

30. Kristianovic, S.A. and Zheltov, Y.P.: "Formation of Vertical Frac-tures by Means of Highly Viscous Liquid," Proc., Fourth World Pet. Cong., Rome (1955) II, 579-86.

31. Perkins, T .K. and Kern, L.R.: "Widths of Hydraulic Fractures," 1PT (Sept. 1961) 937; Trans .. , AIME, 222.

32. Geertsma, J. and deKlerk, F.: "A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures," 1PT (Dec. 1969) 1571; Trans., AIME, 246.

33. Nordgren, R.P.: "Propagation of Vertical Hydraulic Fractures," SPEJ, (Aug. 1972) 306; Trans., AIME, 253.

34. Daneshy, A.A.: "On the Design of Vertical Hydraulic Fractures," 1PT (Jan. 1973) 83; Trans., AIME, 255.

35. Daneshy, A.A.: "Numerical Solution of Sand Transport in Hydraulic Fracturing," 1PT (Jan. 1978) 132.

36. Poulsen, D.K. and Lee, W.S.: "Fracture Design With Time- and Temperature-Dependent Fluid Properties," paper SPE 12483 present-ed at the 1984 SPE Formation Damage Control Symposium, Bakers-field, Feb. 13-14.

37. Geertsma, J. and Haafkens, R.: "A Comparison of the Theories for Predicting Width and Extent of Vertical Hydraulically Induced Frac-tures," ASME 1. Energy Res. Tech. (March 1979) 101, 8.

38. McLeeod, H.O.: "A Simplified Approach to Design of Fracturing Treat-ments Using High-Viscosity Cross-Linked Fluids," paper SPE 11614 presented at the 1983 SPE Low Permeability Symposium, Denver, March 14-16.

39. Crawford, H.R.: "Proppant Scheduling and Calculation of Fluid Lost During Fracturing," paper SPE 12064 presented at the 1983 SPE An-nual Technical Conference and Exhibition, San Francisco, Sept. 5-8.

40. "Staged Field Experiment No.3," GRI-9110048, GRI final report, Chicago, IL (Feb. 1991).

41. Warpinski, N.R.: "Hydraulic Fracture Model Comparison Study: Com-plete Results," GRI-93/0109, GRI topical report , Chicago, IL (Feb. 1993) 163.

51 Metric Conversion Factors bbl x 1.589873 E-Ol m3 ep x 1.0* E+OO mPa's ft x 3.048* E-01 m

OF (OF-32)/1.8 C gal X 3.785412 E-03 m3

in. x 2.54* E+OO em Ibm x 4.535924 E-01 kg psi x 6.894757 E+OO kPa

Conversion factor is exact. SPEPF Original SPE manuscript received for review April 26, 1993. Revised manuscript received Nov. 17, 1993. Paper accepted for publication Nov. 16, 1993. Paper (SPE 25890) first presented at the 1993 SPE Rocky Mountain Regional/Low Permeability Reservoirs Sym posium held in Denver, April 12-14.

SPE Production & Facilities, February 1994

Discussion of Comparison Study of Hydraulic Fracturing Models-Test Case: GRI Staged Field Experiment No. 3 Michael P. Cleary, SPE, Massachusetts Inst. of Technology

Warpinski et al. deserve commendation for selflessly undertaking the task of compiling their paper and maintaining an independent approach to the process, which was initiated and supported by the GRI to assist them (and others) in evaluating the relative perform-ance of various "models" -e.g., in making decisions for their future funding choices. Because I was at least partly responsible for one or more of their nominations to this relatively thankless effort, I hope that they will bear with me now as I make some comments. I will try to be dispassionate in my comments, but it should be clearly understood by readers that I do have a vested interest in one of the modeling approaches (contained in the FRACPRO system).

My comments may be divided into three categories: (1) the limited comparisons offered by the material in the paper alone; (2) the issues of matching data from related field operations; (3) the relevance/im-pact for overall hydraulic fracturing technology. I will treat these somewhat individually, and with limited space, I will try to make simply some important points.

1. Limited Comparison of Models in Paper The approach here was based on an "established" (SPE) approach of defining a limited "test problem" and comparing the predictions of the various models. This was deemed especially necessary (e.g., by GRI) because there had been such an extraordinary proliferation of "models" for hydraulic fracturing during the 1980's, most of them claiming some kind of "3D" capability. I feel partly (perhaps especially) responsible for this because I "opened Pandora's box" with my 1980 papers, 1-4 in which I ruminated/formulated different approaches, including most relevant modeling methods.

Although I understand all the obvious reasons for this comparison exercise-apart from common observations that some models might not even satisfy basic requirements (like mass conservation)-I had to invent for myself some analogy/metaphor for the process. I guess I stayed as professor a little too long and have gotten the habit of teaching my students in metaphors/parables. The most immediate comparison that popped into my head was the gizmo/robot test: we run design competitions at the Massachusetts Inst. of Technology (MIT) (which you may see on public TV every year, including inter-national competing teams) in which the objective is to perform some simple function-e.g., he/she who collects the most ping-pong balls wins. Such a simple, well-defined test allows us to eliminate the most obvious failures (e.g., machines that do not work) and even to declare a clear winner, in most cases.

The objective of Warpinski et at.'s paper was, obviously, not to declare such a winner (although I would have welcomed such an objective, as discussed in Points 2 and 3). But could it have been possible to eliminate the obvious failures? The answer is yes (e.g., see Point 2), but not when based on the "rules of engagement," which merely report the model calculations for the specified input parameters. The readers must decide for themselves which model(s) they believe. This situation generates my only major objection to the phraseology: because of the artificial test environment, the paper does not "provide the completions engineer with a practical com-parison of the available models," because no way is provided for engineers to judge the results in any way, unless they resort to the kind of divine inspiration (translate: personal predisposition, or what they have been telling their company for years), which still seems all too pervasive in this industry. So the general question arises: how should the engineer decide on a model choice?

2. Matching Data From Related Field Operations The best way to check these models would be to compare their pre-dictions with definitive physical observations. We began this process about 15 years ago, starting in the laboratory at MIT5-9 and con-tinuing with extensive field work over the past 10 years. 10-20 The laboratory tests served mainly to check the physical and mathemati-

SPE Production & Facilities. February 1994

cal consistency of our models, but they also served to eliminate some specUlative models. For instance, the protuberant shapes calcu-lated by the pseudo-3D Hydrafrac (P3DH) models, which Ioriginal-ly proposed as a tentative simplistic approach, 1 were shown to be completely wrong, even under ideal circumstances where all the as-sociated physical assumptions should have been justified (if ever). Although we then (1984) publicly disavowed these models and re-fused to publish associated papers (including Refs. I and 2) injour-nals, as a result perhaps achieving pariah status (successfully achieved later with other publications), many companies continued to use them and some still even sell them commercially. At least three of the models compared in the subject paper (and one other commercial model, not included) are of this kind and are demon-strably wrong at the most basic level. (This is not often made so obvious: they generally avoid publicly displaying their seductively long protuberances along the pay zone and/or the associated net pressure behavior).

What is more often ignored (and even omitted in Warpinski et al. 's paper, despite extensive data, 10) is the behavior of the true net fracturing pressure, which can be measured on every job, with different injection volumes and different fluids. 11-20 We have in-deed found field measurements to show dramatically different response (vs. laboratory behavior and also vs. all conventional models like those in the subject paper). We also have identified the major probable causative reasons, establishing the credibility of the resulting models by matching very many data sets for many complex and variable reservoir environments. We have done this without resorting to "knobs" like fracture-fluid rheology or even without very questionable manipulation of stress. In fact, we have established such credibility, beyond subjective evaluation, by pre-dicting the results of fracture treatments and successfully executing the jobs without screenouts and with excellent matching of pressure predictions, as recently reported by numerous users at the first GRI Real-Time Conference (Houston, Oct. 1993).14-20

We did not even insist on the application of the latter stringent condition (i.e., prediction) to the evaluation process now reported in the subject paper. Although such a blind experiment would truly have been the proper approach to the overall undertaking, we had already correctly predicted the response to the job in question (GRI SFE No.3, Ref. 10), and our work on this was already provided or available to the other modeling participants (along with all of the post job data) before the "contest" was held. However, matching ofthis available data was not required of the participants, so many of the models' calculations did not (even with such hindsight) match the net pressure data (e.g., Figs. 9 and 15 of Warpinski et al. 's paper). This explains many of the major differences between models. There are even two different results by two FRACPRO users: RES used the physically realistic default model in FRACPRO, while Tex-aco presumably used one of the many conventional model options, which are actually provided in FRACPRO to clearly demonstrate that such models do not match the pressure data.

At risk of (being libelled for) excessively belittling expensive soft-ware sold by certain vendors, I may point out that the general story of most models in the paper may be summarized in a simple equation for fracture-wing length, L, and half-height, h:

U+ 1h2- 1 =gEVI/(PI-uc), ...................... (D-la)

where VI = volume of fluid remaining in the fracture (efficiency, e X volume pumped, V), E = Young's modulus, PI = fracture pres-sure (e.g., determined carefully from instantaneous shut-in pres-sure), uc=closure stress, and g (of order 0.25)="garbage collector" (which depends on fracture geometry, with ridiculuously high values for aforementioned protuberances). The variable 1 al-lows for variable fracture geometries (/=0 for L>h and/or PKN-type geometries, 1= I for L

This equation is simpler when reduced to oilfield units:

L l+ l h 2 - 1 2V E / net 100 100 == e 100 106 PlOO' .................. (D-Ib)

in which L lOO and hloo=length and height in l00-ft units and V lOO =pumped volume in l00-bbl units (while PI?:} =net pressure in units of 100 psi and E I06 =Young's modulus in units of 106 psi). To achieve ultimate simplicity, we can plug in actual data from SFE No.3 (in round terms: Plog ==16; E I06 ==6; Vloo ==I(0) to get a very approximate mnemonic result:

2Llooh l00 2 == 100 ............................... (D-lc)

Clearly, variation of p net (which in turn, along with artificial stress profiles, should greatly affect h in all the models in Warpinski et al.'s paper) will affect the resulting length. For example, Figs. 9 and 15 show that FRACPRO and the only other considered 3D model (Marathon) calculate higher net pressures (closer to the ex-cellent agreement achieved with actual data), greater fracture heights, and therefore shorter fracture lengths.

Ironically, despite the incredulous reaction to our early work, matching of production data shows even shorter fracture lengths, (e.g., Ref. 10, which typifies the reality of post fracture production matching on many jobs in low-permeability reservoirs). This reality is finally dawning on some in the industry. The "ballpark" ex-pressed in Eq. D-lc may be optimistic, even with nonoptimistic geometry. For instance, Llh == 3 - L - 800 ft should produce greater production than actually observed, if proppant was placed effectively opposite pay zones. 13 The latter comment represents the crux of the whole matter: all the models calculate fracture lengths that are excessively optimistic in terms of the actual production, unless ridiculous games are played with kh, damage, etc. , and a more realistic estimate of actual production could have been obtained with the simplest possible assumptions: L==h-L-400 ft.

Indeed, this comment applies more generally to most jobs pumped in this industry: if all treatments were just able to achieve an effec-tively circular fracture with the proppant placed effectively (Ref. 13), the overall average production throughout the industry would probably be much better and overall job costs would generally be substantially reduced.

3. Relevance to Overall Hydraulic Fracturing Technology Practically speaking, what matters to the completions engineer is how he/she can reduce cost and make better wells. Any effort that claims to be a (supporting) technology must contribute to one or both of these goals. Our efforts, over the past 5 years at least, have demonstrated that dramatic cost reductions and greatly improved production (beyond conventionally designed jobs) can be achieved confidently only with the use of appropriate real-time technology. An intrinsic part of such a system is a reliable general physical model that allows accurate predictions, rapid on-site evaluation, and desigp. or redesign and execution of the most effective fracturing treatments. Such a capability provides a reliable, cost-effective, and credible approach that may be contrasted with costly and misleading efforts commonly used to justify continued inappropriate procedures. Ex-treme examples are the use of fracture-height logs (e.g., sonic, tem-perature, and/or tracer), which we need not even condemn for the thoughtful reader. Neither need we explain limitations of shallow (e.g., "big dig") or near-wellbore observations.

What we do need to point out is that the kind of data-isolationist modeling represented by the subject paper has been used by vested interests to mislead the industry for many years. This process con-tinues at some companies. Rather than going out on each individual job, finding out what is happening (with instant analysis and feed-back in real time), and pumping the appropriate job, some personnel still insist on rendering a grave financial disservice to their company by using such models or surveys as a crutch to support their own pre-dispositions (e.g., about fracture dimensions). Such "blind-man's bluff" (BMB) hurts all of us, including its practitioners, as careful evaluation on the long term shows; it renders vast resources uneco-nomical, with associated negative effects on the U.S. reserve base.

However, I am happy to report that the tide has turned: sensible practical field-oriented personnel at many companies have grown tired of BMB and have demanded and obtained change. Spurious

18

modeling and capability claims have been exposed (and discarded) because of continuous failure in the field, and most companies are now turning to real technology. It may be hoped that Warpinski et al. 's paper might serve to accelerate rather than retard that process.

References 1. Cleary, M.P.: "Comprehensive Design Fonnulae for Hydraulic Fractur-

ing," paper SPE 9259 presented at the 1980 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 21-24.

2. Cleary, M.P.: "Analysis of Mechanisms and Procedure for Producing Favorable Shapes of Hydraulic Fractures, " paper SPE 9260 presented at the 1980 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 21-24.

3. Cleary, M.P., Keck, R., andMear, M.: "Microcomputer Models for the Design of Hydraulic Fractures," paper SPE 11628 presented at the 1983 SPE Symposium on Low Permeability Gas Reservoirs.

4. Cleary, M.P., Kavvadas, M., and Lam, K.Y.: "Development ofa Fully Three-Dimensional Simulator for Analysis and Design of Hydraulic Fracturing," paper SPE 11631 presented at the 1983 SPE Symposium on Low Permeability Gas Reservoirs, March.

5. Cleary, M.P.: "Theoretical and Laboratory Simulation of Underground Fracturing Operations," MIT UFRAC Annual Reports, Cambridge, Sept. 1981-87.,

6. Crockett, A.R., Okusu, N.M., and Cleary, M.P.: "A Complete Inte-grated Model for Design and Real-Time Analysis of Hydraulic Fractur-ing Operations," paper SPE 15069 presented at the 1986 SPE California Regional Meeting, Oakland, April.

7. Cleary, M.P., Barr, D.T., and Willis, R.M.: "Enhancement of Real-Time Hydraulic Fracturing Models With Full 3D Simulation," paper SPE 17713 presented at the 1988 SPE Gas Technology Symposium, Dallas, June 13-15.

8. Cleary, M.P.: "The Engineering of Hydraulic Fractures-State of the Art and Technology," JPT (Jan. 1988) 13.

9. Johnson, D.E. and Cleary, M.P.: "Implications of Recent Laboratory Experimental Results for Hydraulic Fractures," paper SPE 21846 . presented at the 1991 SPE Rocky Mountain Regional Meeting/Low Per-meability Symposium, Denver, April.

10. Gas Research Institute Staged Field Experiments (SFE) I through 4; No.3 finally published as Report No. GRI-9110048, Feb. 1991.

11. Wright, T.B., Johnson, D.E., and Cleary, M.P.: "Real-Data/On-Site Analysis of Hydraulic Fracturing and Procedures for Design Optimi-zation," paper presented at the IntI. Gas Research Conference, Orlando, FL, Nov. 1992.

12. Cleary, M.P., Wright, C.A., and Wright, T.B.: "Experimental and Modeling Evidence for Major Changes in Hydraulic Fracturing De-sign and Field Procedures," paper SPE 21494 presented at the 1991 SPE Gas Technology Symposium, Houston.

13. Cleary, M.P. and Fonseca, A. Jr.: "Proppant Convection and Encapsu-lation in Hydraulic Fracturing: Practical Implications of Computer and Laboratory Simulations," paper SPE 24825 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, Oct. 4-7

14. Cipolla, c.L., Meehan, D.N., and Stevens, P.L.: "Hydraulic Frac-ture Perfonnance in the Moxa Arch Frontier Formation," paper SPE 25918 presented at the 1993 SPE Rocky Mountain Regional Meetingl Low Permeability Reservoirs Symposium, Denver, April 26-28.

IS. Martinez, A.D., Wright, C.A., and Wright, T.B.: "Field Application of Real-Time Hydraulic Fracturing Analysis," paper SPE 25916 present-ed at the 1993 SPE Rocky Mountain Regional Meeting/Low Penneability Reservoirs Symopsium, Denver, April 26-28.

16. Wright, T.B. et al. : "Identification and Comparison of True Net Frac-turing Pressures Generated by Pumping Fluids With Different Rheology Into the Same Formations," paper SPE 26153 presented at the 1993 SPE Gas Technology Symposium, Calgary, June 28-30.

17. Johnson, D.E. etal.: "On-Site Real-Time Analysis Allows Optimal Propped Fracture Stimulation of a Complex Gas Reservoir," paper SPE 25414 presented at the 1993 SPE Production Operations Symposium, Oklahoma City, March.

18. Johnson, D.E. et al.: "Real-Data On-Site Analysis of Hydraulic Fractur-ing Generates Optimum Procedures for Job Design and Execution," paper SPE 25920 presented at the 1993 SPE Rocky Mountain Regional Meet-ing/Low Permeability Reservoirs Symposium, Denver, April 26-28.

19. Cleary, M.P. et al.: "Field Implementation of Proppant Slugs To Avoid Premature Screenout of Hydraulic Fractures With Adequate Proppant Concentration," paper SPE 25892 presented at the 1993 SPE Rocky Mountain Regional Meeting/Low Penneability Reservoirs Symposium, Denver, April 26-28.

20. Cleary, M.P. et al.: "Critical Issues in Hydraulic Fracturing of High Per-meability Reservoirs," paper SPE 27618 to be presented at the 1994 SPE European Production Operations Conference, Aberdeen, March 15-17.

(SPE 28158) SPEPF

SPE Production & Facilities, February 1994