Hyfranc3d Reference

8/10/2019 Hyfranc3d Reference

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1 INTRODUCTION

This document is a user's guide for the hydraulic fracture simulator HYFRANC3D, aFRacture ANalysis Code for 3 Dimensional simulation of hydraulic fracturing. Itdescribes how to use the program and some of the concepts behind the program forperforming hydraulic fracture analysis. This assumes that the user is already familiar withFRANC3D, the basis of HYFRANC3D. Information for FRANC3D can be obtainedfrom the other FRANC3D reference documentation (www.cfg.cornell.edu/software/).The theory behind the coupled fluid flow - fracture propagation is available in severalpublications.

2 MENU REFERENCE

This section describes the additional menus that are added to FRANC3D for hydraulic

fracture. The first is Write HyFSys File,which is available from the Read/Write

Analysis Files (Figure 1).

Figure 1. Read/Write Analysis Files Menu.

2.1 Write .hyf File

The Write HyFSys File menu (Figure 2) is used to set fluid flow boundary conditions andto write the .hyf file, which contains the finite element data, boundary condition, and fluidand material properties.

Figure 2. Write .hyf File menu.


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Set Leakoff Coefficient

Set the leakoff coefficient for a region. The user is prompted to select a region ofthe model. Pick a point on the screen that falls within the region, rotate themodel, and then pick a second point along the displayed line such that theintersection point falls in the region. When a valid point in a region is defined, a

dialog box is displayed (Figure 3), which allows the user to set the Carter leakoffcoefficient. A coefficient of 0.0 implies an impermeable rock formation. This isthe default for all regions of the model.

Figure 3. Carter leakoff coefficient dialog box.

Set Initial Boundary ConditionsSet the fluid type and properties, the flow rate boundary conditions, closurepressure and crack type. These parameters must be set for the initial model (initialcrack model), but do not have to be set for subsequent models (steps ofpropagation). A submenu is presented first (Figure 4).

Figure 4. Set Initial Boundary Conditions submenu.

set closure, fluid & crack typeThe user is prompted to pick a point on the crack surface (on any face of the crack

surface). After picking a point on a crack surface, select FINISH. A dialog box(Figure 5) is displayed that allows the user to set the closure pressure, fluidproperties, crack type and initial crack size for that particular crack. If there aremultiple cracks, these parameters must be set for each crack.


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Figure 5. Initial boundary conditions dialog box.

The fluid type is either Newtonian or power-law. At this stage, Newtonian fluid isthe only supported fluid type due to the analytical crack front solution. Beware of

the unit of viscosity; it must be consistent with the unit of Youngs modulus, flowrate, and other properties and boundary conditions.

Two different initial crack types are supported, radial or slot. These typescorrespond to the two-dimensional radial and KGD types of hydraulic fracturegeometry. The hydraulic fracture solution procedure requires an initial estimate ofpressure and crack opening displacement to provide a starting point for theiterative solution procedure for the first time stage only (initial crack model). Thissolution is provided by an analytical estimate. The radius of the radial crack orthe length and height of the slot crack must be entered.

Finally, the closure stress must be entered. This is the far-field stress normal tothe crack surface and is only used for the initial analytical solution in order tocompute initial fluid pressure and crack opening displacement.

define point flow ratesThe user is prompted to pick a point on the crack surface. After picking a point

on the crack surface, select FINISH. The user is then prompted to pick vertices

on the crack where point flow boundary conditions exist. Select FINISHwhenall the points are chosen. A dialog box (Figure 6) is displayed that allows the userto set the flow rate. Note that we only allow one flow rate boundary condition tobe specified for each crack. The total flow rate specified for the crack is then

equally split between the selected vertices.

Figure 6. Flow rate boundary condition dialog box


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define edge flow ratesThe user is prompted to pick a point on the crack surface. After picking a point

on the crack surface, select FINISH. The user is then prompted to pick edges on

the crack where flow boundary conditions exist. Select FINISHwhen all the

edges are chosen. A dialog box (Figure 6) is displayed that allows the user to setthe flow rate. Note that we only allow one flow rate boundary condition to bespecified for each crack. The total flow rate specified for the crack is then splitbetween the selected edges according to the length of each edge.

Write .hyf FileWrite the finite element data, initial boundary conditions, fluid properties, andcrack type to a .hyf file. The finite elements correspond to the boundary elementsurface mesh. Essentially, a shell element is assumed to exist between the twocrack surfaces and the shell elements have a direct correspondence with boundaryelements on the crack surface. A file selector box is presented (Figure 7). Enter

the file name in the Filename: text entry field and select Accept. The .hyfextension is added automatically if you do not type it.

Create Extra Flex SetsThe user is presented with an additional menu (Figure 8). The extra flex sets areused to provide far-field loading that can be modified during the fluid flowsimulations. The usual static far field loading that is applied in FRANC3D cannotbe modified after the elastic boundary element solution. The procedure requires

that the user Open a Flex Set Fileand then select model faces to be added to theflex set. The faces in a flex set are subjected to the same load. Any number of

these flex sets can be created. The file must be closed by selecting Close Flex Set

Fileafter adding all the required faces.

Figure 7. File selector dialog box.


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Figure 8. Create Extra Flex Sets menu.

2.2 Hydraulic Fracture

The second menu that is added to FRANC3D is the Hydraulic Fracturemenu, which is

available from the Visualize/Analyze Resultsmenu. This menu (Figure 9) is used toread in the .hyf file, build up the shell finite element model, solve the coupled fluid flow -structure equations, view the response information, propagate the hydraulic fracture(s),and save the final equilibrium solution for the model.

Figure 9. Hydraulic Fracture menu.

Build Model From FileRead the shell finite element data along with the initial boundary conditions, fluidproperties, and crack type from the .hyf file. A file selector box showing all the.hyf files is presented. The user must select the appropriate .hyf file. The .flexfile produced by BES must exist in the same directory. The .flex file is read thefirst time; a .infl file, which combines all the flex solutions on the crack surface, isthen written automatically. This file is a binary file that compresses the data

making it much faster to read for subsequent solution trials. If this model issolved again later, the .infl file is read instead of the .flex file. Note that the .inflfile is binary and cannot be transported to other computer platforms. For theinitial crack model (i.e., the first model before any propagation occurs), a dialogbox is presented (Figure 10), which allows the user to set the parameters forsolving the coupled fluid flow - structure equations.


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Figure 10. Hydraulic fracture simulation parameters dialog box.

Set Solve ParametersA dialog box similar to that shown in Figure 10 is presented, which allows theuser to adjust the parameters that are used to control the solution process, such astolerances and relaxation factors. The parameters in this dialog box can beadjusted to improve the iterative non-linear solution.

The flow rate as defined in the .hyf file can be altered by selecting the all cracks

usetoggle button and setting a new value under flow rate. The fluid type can bealtered in a similar manner. The next set of parameters controls the solutiontolerance and convergence criteria.

During the iterative solution, the crack opening displacement (cod) is computed.The solution has converged when the difference in cod between the current andprevious iterations is less than the prescribed tolerance. The true solution iscontrolled by the global mass balance also, i.e., the volume of fluid flowing intothe crack must equal the volume of the crack opening. The solution is convergedwhen the global mass balance is less than the prescribed tolerance.

Part of the solution is the time, which controls the volume of fluid pumped intothe crack. The pumping time must be altered to achieve convergence for thecurrent crack configuration. Because the solution is highly non-linear, we need tocontrol the rate at which we alter the time step. This is done using the global timestep relaxation factor. In addition, the initial starting time can be altered so thatthe solution converges more rapidly.


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The maximum number of iterations controls how long the solution is allowed toiterate. This number is based on the global mass balance iterations. Within eachof these iterations, we iterate on cod as well. This maximum number can beincreased on the terminal window if the solution appears to be converging and the

maximum is exceeded.

The remaining two parameters control the solution in the case of leakoff. Wesolve for leakoff using the one-dimensional empirical leakoff coefficient. Toimprove the solution procedure, we ramp up the leakoff starting from zero leakoffand ending at the proper solution. The user controls the number of steps and therate at which the leakoff is ramped-up.

Solve Current ModelSolve the set of coupled fluid flow and structural equations. The iterative processis displayed on the terminal window as the solution proceeds. The user canmonitor the convergence (or lack of convergence). If the solution processconverges within the specified number of iterations, the iterations terminate andcontrol is passed back to the user. At this stage, the user can examine the results,save the solved model, and/or propagate the crack. If the solution does notconverge, the user can increase the allowable number of iterations and/or modifythe parameters in the dialog box that control the iterative solution procedure.

Display Response InfoA submenu is presented (Figure 11).

Figure 11. Display Response submenu.

Global equilibriumPrints to the terminal window the global equilibrium parameters such as totalcrack volume and total fluid volume.

Crack equilibriumPrints to the terminal window the equilibrium data for a specific crack. The useris prompted to select the crack by picking a point on the crack surface.

Color contoursPresents a new window for displaying contours. The user is prompted to enter aninitial magnification factor for displaying the color contours on the deformed


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crack surfaces. A new window is then presented. This window is similar to theDeformation/Contour window in FRANC3D. However, only the crack surface(s)are displayed by default. The deformed surfaces and color contours can only beshown for the crack surfaces.

Line plotsPresents a new window for displaying data in x-y form. The user is prompted topick lines on the crack surface. Multiple lines can be given by picking the first

point and last point of the lines until the user selects FINISH. A new window ispresented showing the line(s) on the model surface and the user can then select theresponse value to be plotted. The normalized length of the lines is plotted on thex-axis while the data is plotted on the y-axis. This window is similar to the LinePlot window in FRANC3D.

Point responseDisplays response data for a surface point. The user is prompted to select a pointon the crack surface. The data is printed on the terminal window.

Node responseDisplays response data for a node on the crack. The user is prompted to select anode on the crack surface. The data is printed on the terminal window.

Write and Read .besout FileA submenu is presented (Figure 12).

Figure 12. Write and Read .besout File submenu.

write and read .besout fileWrites out the .besout file then reads it back in; see the next two submenu entries.These two steps are necessary for crack propagation and to determine globaldisplacements combining both far field loading and fluid pressure in the crack.

write .besout filePrompts the user to select the .flex file. The influence matrices are combined with

the equilibrium fluid pressures and the equilibrium displacements in the entiremodel are determined. The user is then prompted to enter the .besout file name inthe file selector box. The displacements and tractions are then written to the.besout file.

read .besout filePrompts the user to select the .besout file; the data is read in as it would be if the

user selected Read BES Filefrom the Read/Write Analysis Filesmenu.


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Advance Crack FrontOnce the coupled fluid flow solution is found, the crack can be advanced to createthe geometry of the next time stage. A submenu is presented (Figure 13).

Figure 13. Advance Crack Front submenu.

stress intensity factorsPrompts the user to select a point on the crack front and then presents a dialog box(Figure 14). The dialog box allows the user to select parameters for displaying thestress intensity factors. See the FRANC3D Menu and Dialog reference for further

details.

Figure 14. The Stress Intensity Factors dialog box.

show new front pointsPrompts the user to select a point on the crack front and then presents a dialog box(Figure 15a,b). The dialog box allows the user to select the crack growthdirection model and the maximum extension. See the FRANC3D Menu andDialog reference for further details.

Figure 15a. The Crack Propagation Models dialog box.


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Figure 15b. The Crack Extension Models dialog box.

fit polynomial to frontPrompts the user to select a point on the crack front and then presents a dialog box(Figure 16). The dialog box allows the user to fit the new crack front points witha polynomial to smooth the new crack front points. See the FRANC3D Menu andDialog reference for further details.

Figure 16. The Polynomial Fitted Data dialog box.

propagate crackPrompts the user to select a point on the crack front. The crack is thenpropagated.

Write/Read .hyd FileA .hyd file contains nodal widths, pressures, fluid speeds and crack advance dataassociated with the equilibrium solution and the crack advance. A submenu ispresented (Figure 17).

Figure 17. Write/Read .hyd File submenu.

write current modelPrompts the user to save the current solved model (after propagating the crack) toa file so that it can be used to solvethe next model (step of propagation). A fileselector box is presented; enter the file name in the text entry box. It is importantthat this file be saved after propagating the crack because part of the solution isthe crack front advance. The amount of crack front advance is required to solve


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the fluid flow - structure equations in the subsequent model. The advance, fluidor crack front speed, and time step must be consistent.

read solved modelReads a previously saved solved model to use as the initial solution for the current

model. A file selector box is presented; select the appropriate .hyd file. A solvedmodel must read into HYFRANC3D before solving for the second and subsequentmodels where the crack has been propagated.

Apply Constant PressureA constant pressure is applied to the crack surfaces. This feature allows the userto quickly check to see if the model and starting fluid pressure are reasonable. Aninitial constant pressure is applied to all nodes of the crack. The resulting crackopening displacements are then computed. The results can be viewed using thefeatures described above.

Delete All ModelsDelete the models and free the associated memory. This feature is only needed ifthe user is examining a number of different models with HYFRANC3D in asingle session.

3 Example Simulation Steps

This section is designed to give a brief overview of the series of steps that are required inorder to do a hydraulic fracture simulation using HYFRANC3D.

1. Create the model with an initial crack and boundary conditions and then save theHYFRANC3D (.fys) file.

2. Write the .bes file from the Read/Write Analysis Filesmenu.

3. Write the .hyf file. Select Write .hyf Filefrom the Read/Write Analysis Filesmenu.

Set theleakoff coefficient, set theinitial boundary conditions, and then Write the .hyf

File.

4. From the terminal window, start BES running:> runbes ocqr quad flex file_name &

where ocqr is the out-of-core QR solver, flex and quad tells BES to create the influencematrices, file_name is the .bes file name without the .bes extension. The & runs the job inthe background.

5. When BES is finished running (check the .q.out file to monitor the progress), you willhave a .flex file. Assuming that HYFRANC3D is running and the model is available,

from HYFRANC3D, select the Hydraulic Fracturemenu button from the

Visualize/Analyze Resultsmenu.


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The mesh on the crack surface is constrained by the fact that a boundary between the

near-front region of the crack and the bulk of the fracture surface must exist. The near-

front region is governed by the analytical linear elastic hydraulic fracture (LEHF)

equations (SCR Geomechanics Group, 1994). It is necessary to keep track of the element

edges that form this boundary along with the orthogonal distance between the crack front

and the boundary. The near-front analytical solution implicitly provides for a fluid lagand a singular pressure distribution without having to perform prohibitive discretization

of the crack front region.

The set of nodal widths and pressures from the previous solution must be mapped onto

the mesh of the current fracture. This is a trivial procedure if the mesh has remained

fixed. If the mesh has been modified, the nodal widths and pressures for the new mesh

must be interpolated from the previous mesh. These procedures are implemented in

HYFRANC3D and are invoked automatically when reading in the propagated crack

models.

4.1.2 Computation of the Flexibility Matrix

Given the fracture geometry *(tn+1) , the elastic properties of the model, and the

corresponding boundary conditions, BES is used to compute the flexibility matrix. (The

flexibility matrix is a set of resulting displacements and tractions for the body assuming a

unit traction load on a node of the crack surface.) Using the flexibility matrix, one can

convert the nodal pressures inside the fracture into nodal fracture widths. This reflects

the influence of the geometry of the fracture, the geometry of the model, the elastic

properties of the model, and the boundary conditions on the model. The computation of

the elastic flexibility matrix is by far the most time consuming part of the analysis and

guided the earlier choice of fixing the geometry instead of the time.

4.1.3 Iterative Solution of the Fluid Flow

The results from the previous time stage, tn , are used as starting values for the solution

process. Given an initial set of values for crack opening displacement, fluid pressure and

crack front speed, the iterative scheme proceeds at two levels. First, the set of nonlinear

equations describing the fluid flow inside the fracture coupled to the structural response

of the model is solved in an iterative manner. Once convergence is achieved based on the

crack opening displacements, the global mass balance and the crack front speeds are

considered in the following way to determine the absolute time corresponding to thecurrent geometry. The total volume of fluid injected should be equal to the volume of the

fracture minus the volume of fluid that has leaked away into the formation. Also, the

fluid speed at each point of the crack front should equal the crack propagation speed, i.e.

the crack advance divided by the time step. Note that, within the framework used here,

these two relationships both express satisfaction of global mass balance. If these two

relationships are not satisfied, the time step is adjusted and the fluid flow equation is


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solved iteratively again. This process continues until the solution has converged on both

the nodal values and the time, therefore satisfying both elasticity and fluid flow.

4.1.4 Fracture Propagation

Before a crack can be propagated, the total model displacements must be determined.

This is done by combining the displacements due to the far-field applied loading with the

displacements produced by the fluid pressurization in the fracture.

The process of propagating a crack in FRANC3D has been described elsewhere. The

only difference in this case is that the crack is propagated using an ad-hocpropagation

criterion for hydraulic fracturing. (More research is needed in this area.)

The local extension of the fracture propagation along the crack front is proportional to the

speed of the fluid at that point. It is scaled by a maximum propagation length L0 (input

by the user) so that the point where the maximum speed is attained is propagated by L0 .Indeed, a reasonable value for L0 will depend on the model and crack geometry as well as

the desired accuracy but, because of the linear interpolation in time, should not be greater

than 10% of the fracture penetration into the formation.

The direction of fracture propagation at each point is determined according to the

maximum circumferential stress criterion. The criterion is evaluated at discrete points

along the front in a plane normal to the crack front tangent (Figure 8). The angle iscomputed using the mode I and II stress intensity factors K1 and K2 . Quasi-static

propagation of the fracture requires that the mode I stress intensity factor be equal to the

fracture toughness of the rock K1c at each point. The assumption underlying the special

solution used here at the fracture front is that, although not explicitly taken into account, afluid lag would exist and automatically adjusts its length to satisfy this condition.

Therefore, (x) is taken to satisfy:

K1c sin(( )) +K2(x)(3cos((x)) 1) = 0

Once the crack has been propagated, the model can be remeshed for the next stage of

analysis.

4.2 Special Case for the First Time Stage

As described in the previous section, the solution process requires the results of a

previous step. This is achieved for the first model through approximate analytical

solutions. These solutions are used to produce the complete description of a "dummy"

crack that is smaller than the initial crack, which is then considered as the previous model

by the iterative solver. This provides the initial values to be used for the real fracture

geometry, and the solution scheme then proceeds as described above.

Two solutions have been developed covering most initial crack geometries in hydraulic

fracturing, one for a slot crack and one for a penny-shaped crack (or radial crack). The


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main assumption behind these solutions is that the pressure profile near the crack front is

governed by a singular field and that the resulting stress intensity factor is zero. This

allows one to obtain a pressure profile from which all other quantities are derived. These

solutions, therefore, produce time, crack opening displacements, crack front speeds and

fluid pressure inside the crack as a function of fracture extension, elastic parameters, and

pumping parameters.

4.2.1 Initial Solution for a Radial Crack

We start with the following pressure profile for a radial crack

P(r )=c + 3.72 PhL1

R

1 3

PhL1

1 3

with Ph = 31 3

E and L1 =v

Ewhere c is the stress acting normal to the fracture

surface, R is the fracture radius, is the distance from the fracture tip, v is the fracturespeed, is the viscosity, and E is the effective modulus. At the wellbore (= R), thisgives a pressure Pwequal to

Pw =c +1.89 E2 3 v

R

1 3

To keep the initial solution simple, consider a width profile w(r) resulting from a

constant pressure profile of value Pw

w(r) = wo

1r

R

2

; wo=

8PwR

3=Q t

Assuming a constant flow rate Q , we can eliminate the speed in favor of the flow rate to

get

v = 0.0962 Q3 4E

1 4

R5 4

This provides us with the speed at the near-crack front boundary and an initial pressuredistribution on the crack surface. Using the flexibility (influence) matrix, we cancompute the equilibrium crack opening displacement. The dummy crack is smaller

than the actual crack. We can compute the pseudo-crack advance to arrive at the actualcrack front geometry. All data necessary to start the iterative solution procedure for theactual crack geometry are thus provided.

4.2.1 Initial Solution for a Slot (KGD) Crack

We start with the following pressure profile for a slot crack


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+=

31

31

31

2 1126

3)(

xL

vEP c

where c is the stress acting normal to the fracture surface, L is the fracture length, is

the distance from the fracture tip, v is the fracture speed. At the wellbore ( =L ), this

gives a pressure Pwequal to

31

32

179.1

+=

L

vEP cw

Assuming a constant flow rate Q , one can derive an expression for fracture length as a

function of time

326

1

21

0656.0)( tE

QtL

=

from which the crack front speed is obtained

21

41

43

0354.0

= L

EQv

The rest of the solution follows that for the radial crack.

4.2.3 Initial Solution Convergence

Depending on the model, the first solution may not converge to the desired accuracy interms of mass balance error and fluid - crack speed error. The convergence is oftenimproved by reducing the time step relaxation factor to a very small value. This willincrease the number of iterations required.

In general, the iterative solution converges better from an over-pressurized condition. Bystarting from a larger initial time step, we can over-pressurize the crack. We then relaxthe time step to converge to the correct solution. There are times when the mass balanceerror is still large, but the crack front - fluid speed error changes from positive tonegative. The over-pressurized condition produces a positive error in speed. If the speederror changes to negative, the solution becomes incorrect even though the mass balanceerror continues to decrease; i.e., it is converging to the wrong solution.


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4 Tutorial Example

This section provides a step by step tutorial guide for modeling a radial type hydraulicfracture in 3D from an uncased wellbore. The modeling procedures to create the initialmodel, place the initial crack, and apply static boundary conditions will not be described.If the user is unfamiliar with these topics, he/she should follow through the FRANC3Dtutorial and learn how to use FRANC3D first.

The initial crack modeling including the crack is shown in Figure 18. We are usingsymmetry conditions and modeling a half-radial crack from an uncased wellbore. Thematerial properties consist of Youngs modulus = 7.5e6 psi and Poissons ratio=0.25.The fracture toughness is 700 psi. The far field loading consists of uniform pressures of9090 psi parallel to the wellbore, 10100 psi perpendicular to the crack surface, and 12820psi parallel to the crack. The wellbore pressure is 10500 psi. The initial crack radius is10 inches. The closure stress is 10100 psi. The fluid viscosity is 0.0001 cP. The flow

rate along the crack mouth is 0.2 bpm; this is applied to the edges of the crack mouth.This data is written to the .hyf file.

Figure 18. Initial model of radial crack.

The .fys and .bes files are written from HYFRANC3D. BES is used to perform theelastic analysis and produces a .flex file containing the base solution for the far fieldloading and the influence matrices for the unit tractions on the crack surface. The BES


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solution for this model requires about half an hour on a DEC ALPHA workstation. (Thismesh is much coarser than would normally be used for an actual simulation).

Once BES has finished, we read the .fys file into HYFRANC3D. We proceed to the

Hydraulic Fracturemenu and select Build Model From File. We select the proper .hyf

for this model (it should have been written previously). HYFRANC3D reads the .hyf fileand the corresponding .flex file. Once finished, the solution parameter dialog box is

displayed. To begin, just select Accept on this dialog and proceed to Solve Current

Model. The iteration steps are displayed on the terminal window and should be similar tothe following information. (Only the final set of iterations starting from the time stepprior to negative speed error is shown.)

Decreasing starting time factor 0.0188639 to 0.017149.Time step set to: 0.039861; Speed at one node: 50.1743COD Iteration #1COD Error (target = 0.001 ): 0.0137515COD Iteration #2COD Error (target = 0.001 ): 0.000891194

Mass balance error: 0.367349.Crack/fluid speed error: 0.10807.

Starting iterations from last solution.Time step set to: 0.0478333; Speed at one node: 41.8119COD Iteration #1COD Error (target = 0.001 ): 0.0253502COD Iteration #2COD Error (target = 0.001 ): 0.00128419COD Iteration #3COD Error (target = 0.001 ): 2.94335e-05

Global Iteration #1Mass Balance Error (target = 0.01 ): 0.331611Crack/Fluid Speed Error : -0.196452

Speed error is -0.196452 and mass balance error is 0.331611.Do you want to continue iterating (y/n) :n

Global mass balance convergence achieved - system solved

The speed error changes from 0.10807 to -0.196452 in one set of iterations. The massbalance error is 0.331611. This is clearly not a very good solution. We can improve on

this by adjusting the relaxation factor in the dialog box. Select Set Solve Parametersto

view the dialog box. Set the global time step relaxation factorto 0.001, set the

maximum number of iterationsto 500, and then select Accept. Select Solve CurrentModelto obtain the equilibrium solution again. This time, the solution procedure takes alot longer to converge. After 349 global iterations, the speed error is reduced to a valueof -0.00016398. The mass balance error is 0.35311. It is not possible to achieve a goodmass balance in this case. The starting solution is not good enough; the mass balanceerror should decrease significantly for the subsequent steps of propagation because westart from better starting solutions.


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The next step is to Write/Read the .besout file. You can display the response informationfirst if desired. HYFRANC3D reads the .flex file again, combines the base solution dueto the far field loading along with the fluid pressure and influence matrices to produce theequilibrium displacements and tractions which are stored in the .besout file. The .besoutfile is read as soon at it is written so that we can proceed to propagate the crack.

Select the Advance Crack Front menu button and then select stress intensity factors. Pick

the crack front and the Stress Intensity Factorsdialog is displayed. Select Accept. Youcan keep or destroy the plots that are displayed. The next step is to calculate the newcrack front points. Select show new front points from the submenu. In the dialog boxes(Figure 15a,b) set the extension to 2 and select Accept. You are prompted to enter atolerance on the terminal window for partial propagation (this is temporary). Enter 0.001and press the Return key. The new points for the new crack front are displayed. Fit apolynomial to these points by selecting the proper submenu entry; a single third orderpolynomial is appropriate. Finally, propagate the crack. The crack should be propagatedfor you. It will have to be meshed, but we will do that after saving the solution. Select

Write/Read .hyd Filesand select write current model. Save the data using the defaultfile name.

Now, subdivide the edges and mesh the surfaces. You can use a similar mesh to that forstep 1. Save the HYFRANC3D model (.fys) file, save the BES input (.bes) file, and savethe .hyf file. Note that you do not have to reset any far-field boundary conditions. Theprevious solution (.hyd file for step 1) provides most of the necessary fluid flow boundarycondition data and fluid properties for step 2. The flow rate boundary conditions must bereapplied to the crack mouth edges, however.

Perform the BES analysis using the same command as for step 1, but change the filename to that for step 2. The solution requires a little longer than step 1 because of the

additional crack surface elements. Once the .flex file is generated, proceed with readingthe model back into HYFRANC3D. Then proceed to the Hydraulic Fracturemenu.This time, we need to read in the .hyd file for the previous step before reading the current

model .hyf file. Select Write/Read .hyd Filesand select read solved model. Select the.hyd file for step 1.

Now, select Build Model From Fileand select the .hyf file for step 2. The .flex file isread in along with the .hyf file and a .infl file is written. Once the model has been read in,proceed to solve it using the default parameters. From this initial solution, decide on therelaxation factor and maximum number of iterations and resolve. In this case, arelaxation factor or 0.01 and maximum number of iterations of 500 should suffice. The

final converged solution after 174 global iterations has a speed error of -0.00088 and amass balance error of 0.0802. This is a vast improvement from the initial solution. Theerror could be reduced somewhat by reducing the relaxation factor and performing moreiterations. For this tutorial, the solution is adequate. The mass balance error shouldcontinue to decrease with each step if the amount of propagation is not too large.

The user is encouraged to continue the simulation on his/her own. The responseinformation can be examined at each step or at the end of the simulations. The user can


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read in all the solved models in succession and then display animated sequences ofimages showing the evolving crack and the fluid pressures or crack openingdisplacements at each step of propagation. For instance, Figure 19 shows the pressurecontours on the crack surface for step 2.

Figure 19. Fluid pressure contours on the deformed crack surfaces for step 2.

5.0 Bibliography

Abass, H.H., Hedayati, S. and Meadows, D.L. (1996)Nonplanar fracture propagation from a horizontalwellbore: experimental study, SPEPE, August, p. 133-137.

Advani, S.H., Lee, T.S. and Lee, J.K., (1990) Three dimensional modeling of hydraulic fractures in layered

media: Finite element formulations, J. Energy Res. Tech., 112, p. 1-18.Bahat, D. (1991) Tecton-fractography. Springer-Verlag Publishers.Barree, R.D. (1983)A practical numerical simulator for three-dimensional hydraulic fracture propagation

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