tip_inversion module

This file is part of PyFrac.

Created by Haseeb Zia on Tue Nov 01 15:22:00 2016. Copyright (c) “ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE, Switzerland, Geo-Energy Laboratory”, 2016-2020. All rights reserved. See the LICENSE.TXT file for more details.

tip_inversion.C1(delta)

tip_inversion.C2(delta)

tip_inversion.FindBracket_dist(w, Kprime, Eprime, fluidProp, Cprime, DistLstTS, dt, mesh, ResFunc, simProp)

Find the valid bracket for the root evaluation function.

tip_inversion.StressIntensityFactor(w, lvlSetData, EltTip, EltRibbon, stagnant, mesh, Eprime)

This function evaluate the stress intensity factor. See Donstov & Pierce Comput. Methods Appl. Mech. Engrn. 2017

Parameters

• w (ndarray-float) – fracture width

• lvlSetData (ndarray-float) – the level set values, i.e. distance from the fracture front

• EltTip (ndarray-int) – tip elements

• EltRibbon (ndarray-int) – ribbon elements

• stagnant (ndarray-boolean) – the stagnant tip cells

• mesh (CartesianMesh object) – mesh

• Eprime (ndarray) – the plain strain modulus

Returns

the stress intensity factor of the stagnant cells. Zero is returned for the

tip cells that are moving.

Return type

ndarray-float

tip_inversion.TipAsymInversion(w, frac, matProp, fluidProp, simParmtrs, dt=None, Kprime_k=None, Eprime_k=None, perfNode=None)

Evaluate distance from the front using tip assymptotics according to the given regime, given the fracture width in the ribbon cells.

Parameters

• w (ndarray) – – fracture width.

• frac (Fracture) – – current fracture object.

• matProp (MaterialProperties) – – material properties.

• fluidProp (FluidProperties) – – fluid properties.

• simParmtrs (SimulationParameters) – – Simulation parameters.

• dt (float) – – time step.

• Kprime_k (ndarray-float) – – Kprime for current iteration of toughness loop. if not given, the Kprime from the given material properties object will be used.

• Eprime_k (float) – – the plain strain modulus.

Returns

– distance (unsigned) from the front to the ribbon cells.

Return type

dist (ndarray)

tip_inversion.TipAsymInversion_hetrogenous_toughness(w, frac, mat_prop, level_set)

This function inverts the tip asymptote with the toughness value taken at the tip instead of taking at the ribbon cell.

Argument:

w (ndarray-float): fracture width frac (Fracture object): current fracture object matProp (MaterialProperties object): material properties level_set (ndarray-float): the level set values, i.e. signed distance from the fracture front

Returns

the inverted tip asymptote for the ribbon cells

Return type

ndarray-float

tip_inversion.TipAsym_Hershcel_Burkley_MK_Res(dist, *args)

Function to be minimized to find root for power-law fluid (see e.g. Bessmertnykh and Donstov 2019)

tip_inversion.TipAsym_Hershcel_Burkley_Res(dist, *args)

Function to be minimized to find root for Herschel Bulkley (see Bessmertnykh and Donstov 2019)

tip_inversion.TipAsym_MDR_Res(dist, *args)

Residual function for viscosity dominate regime, without leak off

tip_inversion.TipAsym_MK_deltaC_Res(dist, *args)

Residual function for viscosity to toughness regime with transition, without leak off

tip_inversion.TipAsym_MK_zrthOrder_Res(dist, *args)

Residual function for viscosity to toughness regime with transition, without leak off

tip_inversion.TipAsym_MTildeK_deltaC_Res(dist, *args)

Residual function for viscosity to toughness regime with transition, without leak off

tip_inversion.TipAsym_MTildeK_zrthOrder_Res(dist, *args)

Residual function for zeroth-order solution for M~K edge tip asymptote

tip_inversion.TipAsym_M_MDR_Res(dist, *args)

Residual function for viscosity dominate regime, without leak off

tip_inversion.TipAsym_PowerLaw_M_vertex_Res(dist, *args)

tip_inversion.TipAsym_Universal_1stOrder_Res(dist, *args)

More precise function to be minimized to find root for universal Tip asymptote (see Donstov and Pierce)

tip_inversion.TipAsym_Universal_zrthOrder_Res(dist, *args)

Function to be minimized to find root for universal Tip asymptote (see Donstov and Pierce 2017)

tip_inversion.TipAsym_k_exp(dist, *args)

Residual function for the near-field k expansion (Garagash & Detournay, 2011)

tip_inversion.TipAsym_m_exp(dist, *args)

Residual function for the far-field m expansion (Garagash & Detournay, 2011)

tip_inversion.TipAsym_mt_exp(dist, *args)

Residual function for the intermediate-field m expansion (Garagash & Detournay, 2011)

tip_inversion.TipAsym_power_law_MK_Res(dist, *args)

Function to be minimized to find root for power-law fluid (see e.g. Bessmertnykh and Donstov 2019)

tip_inversion.TipAsym_power_law_Res(dist, *args)

Function to be minimized to find root for power-law fluid (see e.g. Bessmertnykh and Donstov 2019)

tip_inversion.TipAsym_variable_Toughness_Res(dist, *args)

tip_inversion.TipAsym_viscLeakOff_Res(dist, *args)

Residual function for viscosity dominated regime, with leak off

tip_inversion.TipAsym_viscStor_Res(dist, *args)

Residual function for viscosity dominate regime, without leak off

tip_inversion.Vm_residual(dist, *args)

tip_inversion.f(K, Cb, Con)

tip_inversion.find_zero_vertex(Elts, level_set, mesh)

find the vertex opposite to the propagation direction from which the perpendicular on the front is drawn