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 techniques available to the petroleum engineer, is being used extensively in tight gas sandstones,1–5 coalbed methane,6 high-permeability sandstones in Alaska,7very weak sandstones off the U.S. gulf coast,8horizontal wells in chalks,9–10 and many other applications 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 hydraulic fracture model, yet there is very little comparative information 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 available 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 judging 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 problem that involves the mechanical interaction of the propagating fracture 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 geometry 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 not always reliably predict the observed behavior for a given treatment. This discrepancy has been attributed to many complex interactions 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 fractures and increasted frictional losses) and near the fracture tip (e.g., nonlinear formation behavior, microcracking, formation plasticity, 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 experience. 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 forum 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.

    • "Cell" approach: STIMPLAN of NSI Inc., ENERFRAC of Shell20,21 and TRIFAC of S.A. Holditch& Assocs. Inc.

    • Overall fracture geometry parameterization: FRACPRO of Reservoir Engineering Systems (RES) Inc.22-25and MFRAC-ll of Meyer & Assocs.26-29

  4. Classic Perkins-Kern-Nordgren (PKN) and Geertsma-deKlerk(GDK) models30-35: PROP of Halliburton,34-36 the Chevron 2D model, the Conoco 2D model, the Shell 2D 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 TerraFrac12–16 and the HYFRAC3D17 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 difference is in the numerical technique used to calculate fracture opening. 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 Models.

The TerraFrac12–16 and the HYFRAC3D17 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 difference is in the numerical technique used to calculate fracture opening. 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.

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