OnPlan Comparison Study 1 Weng

Brief

The case study is based on Weng ^[1] paper published in 1992.

The onPlan calculates 12 cases described in the paper and shows reasonable agreement in results.

Inputs

Paper Summary

Pseudo 3D (P3D) hydraulic fracturing models often overpredict fracture height for a poorly contained fracture. This is caused partly by either the neglect of the fluid flow component in the vertical direction or a crude treatment of the 2D fluid flow in the fracture as 1D flow in the vertical direction in the fracture-height calculation. This paper presents a height-growth model that adopts a flow field more representative of the actual 2D flow in a fracture.
— Xiaowei Weng^[1]

Simulators

Terra Tek 3D - fully 3D simulator
U. of Texas 3D - fully 3D simulator
Original P3D - a commercial P3D simulator
Modified P3D - a commercial P3D simulator modified by replacing its original height-growth model with Weng 2D flow-height model

Cases

CASE	A	B	C	D	E*	I	J	K	L	M	N	O
Formation Properties
Young's modulus, psi	4.225E+06	4.225E+06	4.225E+06	4.225E+06	4.225E+06	7.50E+05	7.50E+05	7.50E+05	7.50E+05	5.19E+06	5.19E+06	5.19E+06
Poisson's ratio	0.3	0.3	0.3	0.3	0.3	0.2	0.2	0.2	0.2	0.29	0.29	0.29
Stress contrast, psi	200	400	800	400	400	100	100	100	500	900, 1400	900, 1400	900, 1400
Fracture toughness, psi in^0.5	1000	1000	1000	1000	1000	1000	1000	1000	1000	4920	4920	4920
Fluid Properties
K, (lbf-sec^n)/ft^2	0.0031	0.0031	0.0031	0.0016	0.0031	0.12	0.07	0.00002	0.07	0.00157	0.15	0.00002
n	1	1	1	1	1	0.39	0.75	1	0.75	1	0.4	1
Leak-off, ft/min^0.5	0.0006	0.0006	0.0006	0.0006	0.0006	0.000163**	0.000163**	0.000163**	0.000163**	0.000043***	0.000043***	0.000043***
Spurt loss, gal/ft^2	0	0	0	0	0	0.025	0.025	0.025	0.025	0.00035	0.00035	0.00035
Other Data
Pumping rate, bbl/min	20	20	20	20	20	40	40	40	40	25	25	25
Pumping volume, 1000 gal	25	25	25	25	25	66	64	63	71	5.6	10	2.5
Pupming time, min	29.8	29.8	29.8	29.8	29.8	39.3	38.1	37.5	42.3	5.3	9.5	2.4
Perforated interval, ft	80	80	80	80	80	180	180	180	180	16.4	16.4	16.4
Pay-zone thickness, ft	100	100	100	100	100	223	223	223	223	62	62	62

* - Case E is identical to Case B, except there is no fluid leakoff in the bounding layers.
** - In case spurt-loss is not an input a larger leak-off coefficient of 0.00065 is used which yields roughly the same efficiency as the other models.
*** - In case spurt-loss is not an input a larger leak-off coefficient of 0.0002 is used which yields roughly the same efficiency as the other models.