OnPlan Comparison Study 1 Weng

Brief

The case study is based on Weng 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

Hydraulic Fracturing 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.

Comparison

The fracture shapes predicted by different models at the end of pumping for Case B are plotted below. The overlapped onPlan fracture shape shown in green predicts 5% less height and 13% more length.

The cross plots for the 12 cases compare the onPlan vs reference simulators results:

Summary Table

		Volume	Pressure	Half-Length	Height	Efficiency
Case	Model	(1,000 gal)	(psi)	(ft)	(ft)	%
A	Terra Tek	25	280	335	371	48
A	U. of Texas	25	275	380	380	—
A	Original P3D	25	291	314	485	44
A	Modified P3D	25	268	340	393	51
A	onPlan	25	279.9	405.5	363	52.85
B	Terra Tek	25	420	479	250	49
B	U. of Texas	25	375	500	250	—
B	Original P3D	25	362	394	346	49
B	Modified P3D	25	382	479	247	52
B	onPlan	25	394.5	567.9	269	54.61
C	Terra Tek	25	506	596	157	54
C	U. of Texas	25	480	620	150	—
C	Original P3D	25	477	562	173	52
C	Modified P3D	25	489	610	148	54
C	onPlan	25	505.8	777.2	149.5	64.1
D	Terra Tek	25	348	532	232	47
D	U. of Texas	25	—	590	220	—
D	Original P3D	25	332	464	300	44
D	Modified P3D	25	350	540	222	49
D	onPlan	25	334.4	597.8	234.9	52.38
E	Terra Tek	25	393	523	333	68
E	U. of Texas	25	379	570	315	67
E	Original P3D	25	386	484	377	70
E	Modified P3D	25	375	515	338	68
E	onPlan	25	369.8	576.4	320.3	69.25
I	Terra Tek	66	100	375	375	78
I	U. of Texas	66	98	387	362	72
I	Original P3D	66	88	310	477	74
I	Modified P3D	66	98	337	395	75
I	onPlan	66	99.08	405.5	363	73.25
J	Terra Tek	64	109	314	392	80
J	U. of Texas	64	111	339	368	75
J	Original P3D	64	98	283	486	75
J	Modified P3D	64	108	295	409	77
J	onPlan	64	115.7	362.9	405.7	76.06
K	Terra Tek	63	34	806	252	62
K	U. of Texas	—	—	—	—	—
K	Original P3D	63	36	611	267	57
K	Modified P3D	63	29	810	231	50
K	onPlan	—	—	—	—	—
L	Terra Tek	71	137	390	246	83
L	U. of Texas	71	140	383	241	77
L	Original P3D	71	127	379	271	78
L	Modified P3D	71	133	391	239	77
L	onPlan	71	139.1	448.5	209.2	79.83
M	Terra Tek	5.6	845	393	105	93
M	U. of Texas	5.6	775	423	116	89
M	Original P3D	5.6	735	387	108	86
M	Modified P3D	5.6	736	408	103	87
M	onPlan	5.6	715.8	427.2	106.8	89.3
N	Terra Tek	10	955	442	153	91
N	U. of Texas	10	920	489	172	88
N	Original P3D	10	892	447	199	89
N	Modified P3D	10	950	440	162	89
N	onPlan	10	921	487.9	167.8	88.36
O	Terra Tek	2.5	423	376	81	92
O	U. of Texas	—	—	—	—	—
O	Original P3D	2.5	298	512	70	78
O	Modified P3D	2.5	318	444	66	78
O	onPlan	—	—	—	—	—