Audit of Available Models for Use in Consolidated Formations

Introduction

Common fracturing models, either public domain, commercial, or proprietary to individual operators were compared and contrasted. The bases for the comparison were:

• Basic Capabilities: This included whether the model it nonisothermal, whether it can represent matrix and/or fracturing behavior, whether it can consider poroelastic and thermoelastic stress changes, the dimensionality of a fracture if present, the degree of coupling with the reservoir, and the plugging mechanisms that are considered.
• Fracturing Criterion: Is the model two-dimensional (constant height), pseudo-three-dimensional, or planar three-dimensional? What is the basis for increase in the dimensions of the fracture (critical stress intensity factor, or tensile stress?
• Reservoir Model: What is the degree of coupling with and the sophistication of the reservoir model that interfaces with the fracture?
• Damage Model: How is damage due to solids and oil represented? Is there an internal and external filter cake, some sort of combination, and can material in the fracture be mobilized if the shear rate becomes large enough?

Summary of PWRI Model Capabilities (part 1 of 2)

[1]	http://www.mfrac.com/mwflood.html - Developed and marketed by Meyer and Associates, Inc. with specifications provided by Elf.
[2]	The thermal back stress can be transient. A back stress is applied in accordance to . is the difference between the fracture temperature (specified and constant) and the virgin reservoir temperature (specified and constant). Regardless of fluid loss or fracture length or time, this back stress is constant if the coefficient b is constant. b is the Perkins and Gonzalez shape parameter. It is defined by b (semi-minor axis of thermal front perpendicular to the fracture) and a (semi-major). For b/h (fracture height is h) < 0.01, . For b/h > 10, b approaches 1.0.
[3]	Multiple fractures (in different zones) can be considered.
[4]	Using Perkins and Gonzalez semi-analytical relationship.
[5]	Pseudo-analytical/numerical.
[6]	But fracture is contained in one zone.
[7]	Only uses an oil displacement factor and routines like Perkins and Gonzalez for the flood front position.
[8]	As skin.
[9]	Using PEA-23 formulation.
[10]	TIF is thermally-induced fracturing. HF is hydraulic fracturing (sometimes referred to as forced fracturing).
[11]	With capability for reactivation of propagation after fracture growth has stagnated.

Summary of PWRI Model Capabilities (part 2 of 2)

[12]	Matrix and fixed fracture length.
[13]	Not all PEA-23 participants have the thermal version.
[14]	Various KGD and radial models.
[15]	Constant height with a “square” fracture option to approximate radial growth.
[16]	Weakly represented by fault elements and zones of elevated strain.
[17]	Uses fluid loss, source functions for poroelasticity and Biot, Medlin, Massé solution for thermal stresses.
[18]	Different properties (viscosity, relative permeability, saturation can be represented in specific elliptical zones around the fracture.
[19]	V.I.P.S. indicated that this could be done.  However, they were not able to do this in the simulations that were carried out for this project on a well in Alaska.
[20]	This is accomplished by a permeability reduction associated with constitutive behavior but macro fractures are not specifically propagated.
[21]	Damage is represented as a fracture face skin or reduction in the effective conductivity of the fracture. Weakly represented (internal filter cake only).
[22]	This is accomplished by a permeability reduction associated with constitutive behavior and does not represent plugging-related damage.
[23]	Solids only??
[24]	TIF is thermally-induced fracturing. HF is hydraulic fracturing (sometimes referred to as forced fracturing).
[25]	Channeling implemented.
[26]	University of Texas at Austin PWRI Consortium.

Comparison of Fracturing Model

Case studies show that fracture height growth can be substantial in many cases (see for example, the cases presented by Elf for an offshore field in West Africa, and cases presented by Maersk for the Dan field). P3D or 3D fracturing models are required to simulate these PWRI-induced fractures.

One opinion is that a fracture criterion based on fracture toughness and stress intensity factor is preferred as non-linear effects such as in soft formations can be modeled by adopting results from non-linear fracture mechanics. Another school argues that the nonlinear aspects are too difficult to represent and that a stress-based criterion is appropriate, particularly for soft formations.

The intrinsic equations for the three-dimensional fracturing models in BPOPE and TerraFrac are the same.

The reservoir model in the BPOPE model is a three-dimensional finite difference model for heat transfer and two-phase fluid flow.

The reservoir model in the Duke model is a one-dimensional (perpendicular to the fracture face) finite difference model for heat transfer and two-phase fluid flow.

Coupling between fracturing simulation and reservoir simulation is necessary in PWRI modeling.

Comparison of Fundamental Damage

Few models are available to characterize formation damage, both internal and external, due to solids and oil in water.

Model Descriptions

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This download contains the theory and all of the models listed in the audit.

References

1. Clifford, P.J., Berry, P.J., and Gu, H.: “Modelling the Vertical Confinement of Injection Well Thermal Fractures: paper SPE 20741 presented at the 1990 (65th) Annual Technical Conference and Exhibition, New Orleans, LA, September 23-26.
2. PWRI ToolBox
3. SPE 54773 [describing external filter cake behavior and methodologies for measurements of their characteristics]
4. Settari, A. and Warren, G.M.: “Simulation and Field Analysis of Waterflood Induced Fracturing,” paper SPE/ISRM 28081 presented at the Eurorock 94 – Rock Mechanics in Petroleum Engineering, Delft, The Netherlands, August 29-31, 1994.
5. SPE 36916
6. SPE 68974 [Formation Damage Conference, The Hague, The Netherlands, May 21-22, 2001]
7. http://www.mfrac.com/mwflood.html
8. Perkins, T.K. and Gonzalez, J.A.: “The Effect of Thermoelastic Stresses on Injection Well Fracturing,” SPE Journal, February 1985, pp. 78 – 88.
9. Detienne, J-L., Creusot, M., Kessler, N., Sahuquet, B., and Bergerot, J-L.: “Thermally-Induced Fractures: A Field Proven Analytical Model,” paper SPE 30777 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, TX October 22-25.
10. PEA-23 Reports
11. “Fracture Propagation, Filter Cake Build-up and Formation Plugging During PWRI,” PWRI News Letter, Feature Article, Volume 1, No. 3, October 1999.
12. Ovens, J. and H. Niko, H.: “A New Model for Well Testing in Water Injection Wells Under Fracturing Conditions,” SPE 26425, presented at the 1993 SPE Annual Technical Conference and Exhibition held in Houston, Texas, October 3-6.
13. Koning, E.J.L.: “Waterflooding Under Fracturing Conditions,” PhD thesis, Technical University of Delft, 1988.
14. Ovens, J., Larsen, F.P. and Cowie, D.R.: “Making Sense of Water Injection Fractures in the Dan Field,” paper SPE 38928 presented at the 1997 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, 5-8 October 1997.
15. van den Hoek, P.J., Matsuura, T., de Kroon, M., and Gheissary, G.: “Simulation of Produced Water Re-Injection Under Fracturing Conditions,” SPE 36846, paper presented at the SPE European Petroleum Conference, Milan, Italy (October 22-24, 1996).
16. Gheissary, G., Fokker, P.A., Egberts, P.J.P., Floris, F.J.T., Sommerauer, G., and Kenter, C.J.: “Simulation of Fractures Induced by Produced Water Re-Injection in a Multi-Layer Reservoir,” paper SPE 54735 presented at the SPE/ISRM Eurorock ’98, Trondheim, Norway, July 8-10.
17. Clifton, R.J.: “Three-Dimensional Fracture-Propagation Models,” Chapter 5 in Recent Advances in Hydraulic Fracturing, SPE Monograph Vol. 2, edited by J.L. Gidley, S.A. Holditch, D.E. Nierode and R.W. Veatch, Jr.
18. Morales, R.H., Abou-Sayed, A.S., Jones, A.H. and Al Saffar, A.: “Detection of Formation Fracture in a Waterflooding Experiment,” paper SPE 13747, presented at the 1985 SPE Middle East Oil Technical Conference and Exhibition held in Bahrain, March 11-14, 1985.
19. Visage
20. Pang, S., and Sharma, M.M.: “A Model for Predicting Injectivity Decline in Water Injection Wells,” SPE 28489, paper presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 25-28.
21. Stevens, D.G., Murray, L.R. and Shah, P.C.: "Predicting Multiple Thermal Fractures in Horizontal Injection Wells; Coupling of a Wellbore and a Reservoir Simulator," paper SPE 59354 presented at the 2000 SPE/DOE Improved Oil Recovery Symp., Tulsa, OK, April 3-5.