Audit of Available Models for Use

Audit of Available Models for Use in Consolidated Formations

Summary of PWRI Model Capabilities (part 1 of 2)

Capabilities	BPOPE	BP Spreadsheet	DE&S Model	Diffract	Hydrfrac	Hydfrac V3	MWFlood [1]	Perkins Gonzalez
Wellbore Temperature Profile	ü					ü
Matrix Injection Before Fracturing	ü	ü	ü		ü	ü
Thermal Stresses	ü	ü	ü		ü	ü	ü [2]	ü
Poroelastic Stresses	ü	ü	ü		ü	ü	ü	ü
2-D Fracturing Model		ü [3]	ü	ü	ü	ü		ü
P3D Fracturing Model							ü
3-D Fracturing Model	ü
Fully Coupled with Reservoir Model	ü		ü		ü	ü
Partially Coupled with Reservoir Model		ü[4]		ü			ü [4]	ü [5]
Not Coupled with Reservoir Model		ü
Multiple-Layer Formation	ü	~[3]	ü		~[6]	~ [6]	ü
Variable Saturation in the Invaded Zone	ü		ü		ü	ü	ü
Two Phase Flow	ü		ü		ü	ü	-[7]
Changing Viscosity with Temperature	ü	ü	ü		ü	ü
Secondary Fracture Considered								ü
Damage	ü	ü	ü	ü		ü		ü
Internal Formation Damage Considered	?	~[8]		ü		ü
External Filter Cake Considered	ü	~[9]		ü		ü		ü
Injection Regime [10]	TIF, HF	HF	HF	TIF, HF	TIF, HF	TIF, HF	HF	TIF, HF
Tip Plugging Enabled				Yes [11]	No	Yes [4]	No	No
Reference(s)	1, 21	2	4	3	5	6	7	8
Used By or Available To	BP	PWRI Toolbox	DE&S, Taurus	TFE	TFE, IFP	TFE, IFP	TFE and Various	Various

[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 ®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)

Capabilities	Predictif	PWFRAC	Shell/ Maersk	Shell 1	Shell 2	TerraFrac	Visage	WID
Wellbore Temperature Profile	ü						ü
Matrix Injection Before Fracturing	ü						ü	ü [12]
Thermal Stresses	ü	ü [13]	ü	ü	ü	ü	ü
Poroelastic Stresses	ü	ü	ü	ü	ü	ü	ü
2-D Fracturing Model	ü		ü [14]	ü [15]			- [16]	ü
P3D Fracturing Model					ü
3-D Fracturing Model						ü	- [16]
Fully Coupled with Reservoir Model							ü
Partially Coupled with Reservoir Model	ü	ü	ü	ü	ü	~ [17]		ü
Not Coupled with Reservoir Model
Multiple-Layer Formation				ü	ü	ü	ü
Variable Saturation in Invaded Zone							ü
Two Phase Flow	ü						ü
Changing Viscosity with Temperature	ü	?		~ [18]	~ [18]		- [19]
Secondary Fracture Considered							ü [20]	ü
Damage	ü	ü	~ [21]	ü [21]	ü		- [22]	~[23]
Internal Formation Damage?		ü		ü	ü [38]			~[23]
External Filter Cake Considered		ü		ü	ü [25]			~[23]
Injection Regime [24]	TIF	TIF, HF	TIF, HF	TIF, HF	TIF, HF	HF	TIF, Matrix	Matrix
Tip Plugging Enabled	No	Yes		Yes	~[25]			?
Reference(s)	9	10, 11	12, 13, 14	15	16	17, 18	19	20
Used By or Available To	TFE	PEA-23	?	Shell	Shell	Various	V.I.P.S.	U.T. PWRI [26]

[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

Model List	Fracturing Model			Fracture Criterion
Model List	2D	P3D	3D	Fracture Criterion
BPOPE			ü	S.I.F.
BP Spreadsheet	ü			Stress [27]
Diffract	ü			Stress
DE&S Model		ü		Stress
Hydfrac	ü			S.I.F.
Hydfrac V3	ü			S.I.F.
MWFlood		ü		S.I.F.
Perkins and Gonzalez				Stress and S.I.F. [28]
Predictif				Stress
PWFRAC	[29]			S.I.F.
Shell/Maersk Model				S.I.F.
Shell 1				S.I.F.
Shell 2				S.I.F.
TerraFrac				S.I.F.
VISAGE				Effective stress, but no fracture growth.
WID				Proprietary

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.

[27] Friction pressure input from experience.

[28] Length iteration until both satisfied.

[29] With adequate tip plugging, fracture propagation terminates and in current versions it is not possible to reactivate propagation.

Comparison of the Reservoir Model

Model List	Coupled Reservoir Model			Two-Phase Flow	Saturation Computed	Temperature Computed
Model List	No	Partially	Fully	Two-Phase Flow	Saturation Computed	Temperature Computed
BPOPE			ü	ü	ü	ü
BP Spreadsheet		ü[30]
Diffract		ü
DE&S Model			ü	ü	ü	ü
Hydfrac			ü	ü	ü	ü
Hydfrac V3			ü	ü	ü	ü
MWFlood				~	~	~ [31]
Perkins and Gonzalez				~	~	~ [32]
Predictif		ü		ü		ü
PWFRAC		ü				~[33]
Shell/Maersk Model		ü
Shell 1		ü
Shell 2		ü		~
TerraFrac	ü
VISAGE			ü	ü	ü	ü
WID (proprietary)		?

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.

[30] Weakly, using Perkins and Gonzalez type considerations.

[31] Elliptical fluid loss and Perkins and Gonzalez type of methodology (pseudo-analytical).

[32] Pseudo-analytical.

[33] A customized version was developed for two of the PEA-23 participants.

Comparison of Fundamental Damage

Model List	Internal Damage	External Filter Cake	Compound Damage	Dynamic Filter Cake [34]
BPOPE			ü
BP Spreadsheet		ü [35]	ü [35]
Diffract	ü	ü
DE&S Model	ü	ü		ü
Hydfrac	ü	ü		ü [36]
Hydfrac V3	ü	ü		ü [36]
MWFlood
Perkins and Gonzalez		ü	ü
Predictif			ü
PWFRAC	ü	ü		ü
Shell/Maersk Model			ü [37]
Shell 1	ü	ü
Shell 2	ü [38]	ü [39]
TerraFrac
VISAGE	~ [40]
WID (proprietary)	? [41]	? [41]		? [41]

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

[34] When the velocity in the fracture width is sufficiently high, material on the surface of the filter cake can be dislodged and swept along the fracture (often known as dynamic filtration).

[35] Skin is incorporated for radial flow as is the PEA-23 relationship for fracturing.

[36] Refer to Figure 4, SPE paper 68974.

[37] Weakly represented.

[38] Mobility representation.

[39] Channeling.

[40] Damage is due to mechanical effects related to effective stress levels, not plugging.

[41] Speculated based on the modelling methodology used in the radial flow version of WID – NOT CONFIRMED.

BPOPE	BP Spreadsheet
Duke Engineering Model	Hydfrac / Hydfrac V3
MW Flood	Perkins and Gonzalez
Predictif	PWFRAC
Shell / Maersk	Shell 1
Shell 2	TerraFrac
Visage	WID