OnPlan Comparison Study 1 Weng

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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.


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]

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


Formation Properties             
Young's modulus, psi 4.225E+064.225E+064.225E+064.225E+064.225E+067.50E+057.50E+057.50E+057.50E+055.19E+065.19E+065.19E+06
Poisson's ratio0.
Stress contrast, psi 200400800400400100100100500900, 1400900, 1400900, 1400
Fracture toughness, psi in^0.5 100010001000100010001000100010001000492049204920
Fluid Properties             
K, (lbf-sec^n)/ft^20.00310.00310.00310.00160.00310.120.070.000020.070.001570.150.00002
Leak-off, ft/min^0.5 0.00060.00060.00060.00060.00060.000163**0.000163**0.000163**0.000163**0.000043***0.000043***0.000043***
Spurt loss, gal/ft^2000000.0250.0250.0250.0250.000350.000350.00035
Other Data            
Pumping rate, bbl/min 202020202040404040252525
Pumping volume, 1000 gal2525252525666463715.6102.5
Pupming time, min29.829.829.829.829.839.338.137.542.
Perforated interval, ft 808080808018018018018016.416.416.4
Pay-zone thickness, ft 100100100100100223223223223626262

* - 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.


The fracture shapes predicted by different models[1] 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.

Weng Case B

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

Net PressureHalf-length
HeightFluid Efficiency

Summary Table

CaseModel(1,000 gal)(psi)(ft)(ft)%
ATerra Tek2528033537148
AU. of Texas25275380380
AOriginal P3D2529131448544
AModified P3D2526834039351
BTerra Tek2542047925049
BU. of Texas25375500250
BOriginal P3D2536239434649
BModified P3D2538247924752
CTerra Tek2550659615754
CU. of Texas25480620150
COriginal P3D2547756217352
CModified P3D2548961014854
DTerra Tek2534853223247
DU. of Texas25590220
DOriginal P3D2533246430044
DModified P3D2535054022249
ETerra Tek2539352333368
EU. of Texas2537957031567
EOriginal P3D2538648437770
EModified P3D2537551533868
ITerra Tek6610037537578
IU. of Texas669838736272
IOriginal P3D668831047774
IModified P3D669833739575
JTerra Tek6410931439280
JU. of Texas6411133936875
JOriginal P3D649828348675
JModified P3D6410829540977
KTerra Tek633480625262
KU. of Texas
KOriginal P3D633661126757
KModified P3D632981023150
LTerra Tek7113739024683
LU. of Texas7114038324177
LOriginal P3D7112737927178
LModified P3D7113339123977
MTerra Tek5.684539310593
MU. of Texas5.677542311689
MOriginal P3D5.673538710886
MModified P3D5.673640810387
NTerra Tek1095544215391
NU. of Texas1092048917288
NOriginal P3D1089244719989
NModified P3D1095044016289
OTerra Tek2.54233768192
OU. of Texas
OOriginal P3D2.52985127078
OModified P3D2.53184446678


  1. 1.0 1.1 1.2 Weng, Xiaowei (1992). "Incorporation of 2D Fluid Flow Into a Pseudo-3D Hydraulic Fracturing Simulator" (SPE-21849-PA). Society of Petroleum Engineers.