OnPlan Comparison Study 2 Warpinski

Brief

The case study is based on Warpinski ^[1] paper published in 1994.

The onPlan calculates 6 cases described in the paper and shows good agreement in results.

Inputs

Paper 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.
— Warpinski et al ^[1]

Simulators

Planar 3D models:

TerraFrac of TerraTek Inc.
HYFRAC3D by S.H. Advani of Lehigh U. - Planar 3D model
GOHFER by by Marathon Oil Co. - a unique finite-difference simulator

Planar pseudo-3D models:

STIMPLAN of NSI Inc.
ENERFRAC of Shell
TRIFRAC of S.A. Holditch & Assocs. Inc.
FRACPRO of Reservoir Engineering Systems (RES) Inc.
MFRAC-II of Meyer& Assocs.

Classic Perkins-Kern-Nordgren (PKN) and Geertsma-deKlerk (GDK) model:

PROP of Halliburton
Chevron 2D model
Conoco 2D model
Shell 2D model
pseudo-3D models run in constant-height mode

Cases

CASE	1	2	3	4	5	6
Formation Properties
Resesvoir and rock data	Single-Layer	Single-Layer	3-Layer	3-Layer	5-Layer	5-Layer
Fluid Properties
Viscosity, cP	200		200		200
K, (lbf-sec^n)/ft^2		0.06		0.06		0.06
n		0.5		0.5		0.5
Leak-off, ft/min^0.5	0.00025	0.00025	0.00025	0.00025	0.00025	0.00025
Spurt loss, gal/ft^2	0	0	0	0	0	0
Other Data
Pumping rate, bbl/min	50	50	50	50	50	50
Pumping volume, bbl	10000	10000	10000	10000	10000	10000
Pupming time, min	200	200	200	200	200	200
Proppant	None	None	None	None	None	None

Rock and reservoir data:

Interval	Depth (ft)	Zone Thickness (ft)	In Situ Stress (psi)	Poisson's Ratio	Young's Modulus (10^6 psi)	Fracture Toughness (psi/in^0.5)
Single-Layer Case
1	9170-9340	170	5700	0.21	8.5	2000
3-Layer Case
1	8990-9170	180	7150	0.3	6.5	2000
2	9170-9340	170	5700	0.21	8.5	2000
3	9340-9650	310	7350	0.29	5.5	2000
5-Layer Case
1	8990-9170	180	7150	0.3	6.5	2000
2	9170-9340	170	5700	0.21	8.5	2000
3	9340-9380	40	7350	0.26	5.4	2000
4	9380-9455	75	5800	0.2	7.9	2000
5	9455-9650	195	8200	0.3	4.0	2000

Perforations data:

The well was perforated between 9225 to 9250 ft and 9285 to 9330 ft.

Comparison

The fracture net pressure, half-length, width and height predicted by different simulators^[1] are plotted below in dots. The overlapped onPlan fracture net pressure, half-length, width and height shown as lines.

Single-Layer cases 1 and 2 show good agreement between onPlan and paper results.

3-Layer and 5-Layer cases 3 - 6 show that onPlan generally predicts less height thus more length and less width.

These comparisons show that differences in calculated fracture lengths can be large, as much as a factor of three difference. Fracture heights, for the multi-layer cases, can differ by more than 50%. Net pressures also differ by a factor of two.
— Warpinski et al ^[1]

Case 1 (Single-Layer 200cp). Net Pressure	Case 1 (Single-Layer 200cp). Half-length	Case 1 (Single-Layer 200cp). Width	Case 1 (Single-Layer 200cp). Height
Case 2 (Single-Layer K&n). Net Pressure	Case 2 (Single-Layer K&n). Half-length	Case 2 (Single-Layer K&n). Width	Case 2 (Single-Layer K&n). Height
Case 3 (3-Layer 200cp). Net Pressure	Case 3 (3-Layer 200cp). Half-length	Case 3 (3-Layer 200cp). Width	Case 3 (3-Layer 200cp). Height
Case 4 (3-Layer K&n). Net Pressure	Case 4 (3-Layer K&n). Half-length	Case 4 (3-Layer K&n). Width	Case 4 (3-Layer K&n). Height
Case 5 (5-Layer 200cp). Net Pressure	Case 5 (5-Layer 200cp). Half-length	Case 5 (5-Layer 200cp). Width	Case 5 (5-Layer 200cp). Height
Case 6 (5-Layer K&n). Net Pressure	Case 6 (5-Layer K&n). Half-length	Case 6 (5-Layer K&n). Width	Case 6 (5-Layer K&n). Height