Comparison of experimental results and theory for two laboratory hydraulic fracture apparatus

II

Comparison of Experimental Results and Theory For

Two Laboratory Hydraulic Fracture Apparatus

by

TIMOTHY SEAN QUINN

Submitted to the Department of Mechanical Engineering

In Partial Fulfillment of the Requirements for the Degree of

MASTER of SCIENCE

in MECHANICAL ENGINEERING at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY January 1992

C Timothy S. Quinn 1992

The author hereby grants to MIT permission to reproduce and to distribute copies of this thesis in whole or in part.

Signature of Author

S

Signature Redacted

ignature

Signature

Dep ment of Mechanical Engineering

Redacted

Professor M. P. Cleary

Redacted

Professor Ain A. Sonin, Chairman Departmental Committee on Graduate Students

MA'%ACHUSETTS INSTITUTE

OF TE rW OGY

Comparison of Experimental Results and Theory For

Two Laboratory Hydraulic Fracture Apparatus

by

TIMOTHY SEAN QUINN

Submitted to the Department of Mechanical Engineering in January 1992

In partial fulfillment of the requirements for the degree of Master of Science

in Mechanical Engineering ABSTRACT

Two distinctly different experimental simulators of hydraulic fracturing are compared. Extensive experiments were performed using a crack interaction apparatus (CIA), which allows growth of one or more arbitrarily shaped fractures in 3-D space but involves a rigorous experimental procedure. The results were compared with a second hydraulic fracture experiment which more conveniently models planar underground fractures, using an interface separation technique (DISLASH). Numerous inaccuracies from previous studies were uncovered, and corrected, which significantly improved the match between the theoretical results and the experimental data. Comparisons were made with a 3-D leading edge simulator specially configured to model the experimental conditions; this showed good agreement, especially when leading edge dilatancy was modeled as non-penetrated zone squeezing.

Thesis Supervisor: Professor Michael P. Cleary Title: Associate Professor of Mechanical Engineering

Acknowledgments

I would like to take this opportunity to thank those individuals without whose assistance this work would never have reached completion.

First of all I would like to thank Professor Cleary for the opportunity to work on this project. Also thanks is due to all of the researchers at the Resource Extraction Laboratory who have given their guidance and assistance, namely, Forrest Patterson, and Dr. William Keat. They were kind enough to share their expertise and insights at critical junctures in the project.

I am also grateful to UROPs Edward Moore, and Christian Hamer for their dedication to the project. When testing was frustrating, the tasks became tedious, and the job at hand horribly filthy, their enthusiasm was unparalleled. This project would have been impossible without their assistance with testing and data reduction.

Dr. David Barr and Ed Johnson also provided crucial information concerning their work which is the basis for a good deal of the comparisons in paper. Dr. Dave Barr also deserves special thanks for running the A3DH simulator which provided added insight to the project.

In conclusion, I would like to thank my family for their continued moral support and encouragement. Without my their support I would not have been able to bring this project to completion.

Table of Contents

List of Figures... 6

List of Tables ... 7

N om enclature ... 8

1. Introduction ... 9

1.1 Discussion of H ydraulic Fracture... 9

1.2 Problem Statem ent... 9

1.3 Experim ental Discrepancies... 10

2. Background... 11

2.1 DISLASH and CIA ... 11

2.2 General Hydrafrac Theory and Models... 11

2.2.1 PK N and CGD ... 11

2.2.2 Pressure and Radii Equations... 13

2.2.3 Non-penetrated Zone Size and Possible Dilatancy Effects ... 13

2.3 Scaling Laws ... 14

3. Experimental Efforts and Current Theories ... ... 17

3.1 Experim ental Considerations... 17

3.1.1 Actual Flow Rates... 17

3.1.2 Constant Pressure Experiments ... 17

3.1.3 M aterial Toughness... 17

3.1.4 Viscosity... 19

3.2 Scaling Issues ... 19

3.3 Dilatancy Effects... 19

4. Experim ental Setup... 24

4.1 DISLASH ... 24

4.2 Crack Interaction Apparatus... 24

4.2.1 Apparatus ... 26 4.2.1.1 Pressure Vessel... 26 4.2.1.2 Oil Cart ... 26 4.2.1.3 W ater Cart ... 26 4.2.1.4 Data Acquisition ... 30 4.2.2 Special M odifications... 30 4.2.2.1 Pressure Vessel... 30 4.2.2.2 W ater Cart ... 31 4.2.2.3 Data Acquisition ... 31 4.2.2.4 Data Reduction ... 33 5. Results ... 35 5.1 M odulus Tests... 35

5.2 Overall Comparison of CIA and DISLASH... 35

5.3 N on-penetrated Zone Size ... 38

6. Conclusions... 46

6.1 Inaccuracies in Earlier CIA Tests ... 46

6.2 Comparisons of CIA and DISLASH ... 46

6.3 Leading-Edge Dilatancy ... 46

7. Recom m endations... 47

7.1 Apparatus ... 47

r"',

7.2 Experimental ... 47

7.3 Computational ... 48

References... 49

Appendix A: Experimental Parameters... 51

Appendix B: Experimental Procedure... 52

B. 1 M aking M olds ... 52

B. 1.1 Constructing Endplates ... 55

B.2 Constructing Reservoirs... 55

B.2.1 Constructing Reservoir Caps ... 56

B.2.2 Cutting Diaphragms ... 56

B.2.3 Constructing Aluminum Piston Disks... 56

B.2.4 Constructing Boreholes... 56

B.2.4.1 Preparing Precracks... 58

B.2.4.2 Attaching Precracks ... 58

B.3 Replacing the Bottom Ram End Pad ... 58

B.4 Preparing Molds for Casting ... 59

B.5 Casting... 63

B.6 Demolding Specimens ... 64

B.7 Preparing Specimens For Testing... 65

B.8 Procedure For Running CIA Tests... 66

B.8.1 Preliminary Set-Up... 66

B.8.2 Test Preparation... 67

B.8.3 Testing... 68

B.8.4 Biasing the Stress State to form a Marking Ring... 69

B.8.5 Test Shut-down... 69

Appendix C: Data Reduction Techniques ... 74

C. 1 Pressure and Flow Data... 74

C.2 Radius M easurement ... 74

C.2.1 X-Y Radius Graphs ... 76

C.2.2 Circular Curve Fitting ... 76

C.3 Associating Radii with Times... 79

C.4 Nondimensionalizing Curves. ... 79

Appendix D: RoXsf (Radial pOlar X2 (Chi Squared) Fit) ... 80

Appendix E: DISLASH Diagrams... 83

Appendix F: Leading Edge Dilatancy... 87

Figure 2.1 Figure 2.2 Figure 2.3 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure B.1 Figure B.2 Figure B.3 Figure B.4 Figure B.5 Figure B.6 Figure B.7 Figure C.1 Figure C.2 Figure C.3 Figure D.1 Figure D.2 Figure E.1 Figure E.2 Figure E.3 Figure F.1 Figure G.1 Figure G.2 Figure G.3 List of Figures PKN and CGD geometries ... 12

Non-penetrated zone size with dilatancy in the crack ... 15

Effects of Dilatancy in the non-penetrated zone compared to non-dilatant situation.. ... 15

Old CIA test with a flow rate recorded as 0.002 cc/sec. Actual flow rates are possibly greater by a factor of two... 18

Changes in viscosity of DC200 fluids under high pressures... 20

Changes in c* and a* over reasonable experimental pressures due to changes in viscosity... 20

Effect of viscosity dependance on pressure in nondimensionalized graphs... 21

Non-penetrated zone size measured after breakout... 23

DISLASH with fluid puddle at the interface... 25

Line diagram showing all 4 CIA subsystems ... 27

Diagram of Pressure Vessel ... 28

Diagram of Oil Cart... 29

Diagram of New W ater Cart... 32

Example of p, $, and R for circle displaced from origin ... 34

Modulus of Portland Type III cement measured every 6 hrs... 36

Nondimensionalized and shifted curve of radial crack growth in CIA and DISLASH detailing effect of viscosity's dependance on pressure. ... ₃₉

Nondimensionalized and shifted data for CIA constant flow tests and A3DH fracture simulator... 40

Excess pressure with respect to time to the 1/3 for two characteristic CIA tests... 42

Nondimensionalized and shifted pressure universal curves for three CIA tests. ... 43

Non-penetrated zone experimental data for CIA and quasi-static theoretical values ... 44

Schematic Views of Mold Assembly ... 54

Fracture Fluid Reservoir and Wellbore Assembly... 57

M old Ready for Casting... 61

Cut-Away View of Mold Ready for Casting ... 62

New W ater Cart Front View... 71

New W ater Cart Side View ... 72

New Water Cart Power Train and Control Panel... 73

Pressure and Cumulative Flow Graph for Specimen 20E ... 75

Graph of Radial Bias Data for Specimen 20E. ... 77

Polar Graph of Radial Bias Data for Specimen 20E. ... 78

M ain Program of RoXsf... 81

Subroutines for RoXsf... 82

Top view of DISLASH ... 84

Right side view of DISLASH... ... 85

Left side view of DISLASH ... ... ... 86

Non-penetrated zone showing dilatant effects ... 88

Pressure and Cumulative Flow for Test 161... 90

Pressure and Cumulative Flow for Test 181... 91

I4

List of Tables

Table 5.1 List of CIA tests with confining pressure,

flow rate, non-penetrated zone size, and *... 37

Table 5.2 Experimental parameters used by A3DH to model

a CIA experim ent ... 41

Table 5.3 Experimental effects compared to A3DH with

Nomenclature

E Young's modulus

E Crack-opening modulus

k Consistency index for power-law fluid

K,, Critical stress intensity factor

n Flow behavior index for power-law fluid

Pf Fluid pressure

Q,

r Fit bias-ring radius

R Crack tip radius

RW Wellbore radius

t Time

y4 Lumped-model gamma coefficients

A Crack opening width

0 Measured angle for polar bias-ring data acquisition

s

s

U Poisson's ratio

p Measured offset length for bias-ring data acquisition

a Excess pressure Pf

-a Confining pressure

a* Characteristic pressure for constant-flow-rate conditions

,r* Characteristic time for constant-flow-rate conditions

Measured offset angle for bias ring data acquisition

1. Introduction

1.1 _{Discussion of Hydraulic Fracture}

In simplest terms hydraulic fracturing, or "hydrafrac," is a technique commonly used to fracture rocks surrounding existing petroleum wells in order to allow fluids (usually oil or gas) to flow more readily to the wellbore. In practice, the technology involves pumping fluid into the well to produce pressures sufficient to overcome the existing underground pressures, fracture the rock, and create an opening wide enough to allow a sand proppant to be carried into the fracture which serves to hold the fracture open after the fluid pressure is removed.

Hydraulic fracturing is a widely used method of increasing the productivity of oil and natural gas wells. In the first thirty years after hydrafrac was introduced into the industry more than 800,000 wells have employed the technology [1] and as of 1983 about 35 to 40% of drilled wells use hydraulic fracture[2]. As the demand for oil and natural gas increases and drilling companies are forced to investigate less efficient geological areas with lower rock permeability, hydrafrac technology is increasingly in demand to aid in making oil extraction conditions more favorable. In order to create economically optimal fracture conditions, detailed modeling of the geological structure and fracturing process are necessary to provide insight into the proper pressures, flow rates, and pumping volumes.

The experimental apparatus at the Resource Extraction Laboratory has made significant contributions to the modeling of hydraulic fracture growth[3,4]. The principle developments have been accomplished using DISLASH (Desktop Interface Separation Laboratory Apparatus for Simulation of Hydraulic Fracture) and CIA (Crack Interaction Apparatus). DISLASH and CIA represent the two extremes of testing. In DISLASH there is no fracture toughness; growth of the fracture can be visually monitored, and a typical test can be run in 15-20 minutes. In CIA testing, there is a significant fracture toughness, elaborate steps must be taken to establish the actual fracture growth, and tests require approximately 12 person hours per specimen over a period of three days from specimen preparation to testing, with an additional four to five person hours for recording and analysis of the fracture growth data.

1.2 Problem Statement

Previous experimental work, especially the study of field data [51, has produced conflicts which point to a number of different mechanisms that may be present under hydraulic fracturing conditions (e.g. dilatancy and fracture

toughness). _{Past comparisons of CIA data and DISLASH data seem to imply that}

in constant flow rate tests, CIA's growth rate is slower while in constant pressure tests DISLASH's growth rate is slower[4]. Previous hypotheses for this behavior include the effect of the confining stress, toughness effects in CIA tests, and

nonlinearities, including dilatancy. Attempts at modeling underground fractures and experiments [6] have yielded promising reconciliations of the discrepancies but only through significant modification of the estimated test parameters.

A vast database of tests exists for the two primary laboratory apparatus (CIA

and DISLASH) but doubts about test conditions* have required retesting of several situations including constant flow rate studies to further broaden the database.

1.3 Experimental Discrepancies

Current investigation with CIA has uncovered additional possible errors, including significant viscosity changes as a function of pressure, variation of the modulus over time, flow rate inaccuracies, and data acquisition errors including

pressure, flow rate, and radius. _{The new experimental procedure has been}

redesigned to eliminate these errors and the significant differences will be discussed

in section 4.2.2. _{The previous work [4,5] indicated that under constant flow}

conditions a slower growth rate existed, which was attributed to dilatancy. To investigate the possibility of a dilatant effect in CIA, constant flow tests were performed under various conditions and compared against more ideal simulations, (i.e. DISLASH, which does not exhibit dilatant behavior), and theoretical models (i.e. A3DH, which is capable of simulating CIA test conditions with and without dilatant effects).

For instance, reference [7] stated that previous constant flow rate tests were run at 0.02 cc/sec an then, later in the same reference, at 0.002 cc/sec. This discrepancy was uncovered

2. Background

2.1 DISLASH and CIA

Aside from significant pressure and size scaling issues, fracture toughness would seem to be the principle difference between CIA and DISLASH when considering purely planar fracture growth*. The conclusion that fracture toughness is insignificant in deep underground fractures, so that DISLASH can serve as a valid model with no fracture toughness are based on energy arguments. Neglecting the effect of toughness is not completely without basis because the confining pressures underground are usually sufficient to neglect material toughness. CIA however, is incapable of producing pressures above 2200 psi confining stress, limiting the extent to which toughness can be neglected. By performing an order of magnitude analysis, it is possible to compare the effects of the toughness to the

confining pressure contributions. _{The K, of Portland Type III cement is}

approximately 200 psi _{, compared to the hydrostatic confining pressure effect}

which is of the order a R or (1400)

\J1i for the smallest confining stress. A factor

of 25 for CIA is small compared to field hydrafrac jobs where the factor is of order

100 or higher.** _{If fracture toughness played a dominant role in CIA, DISLASH}

would effectively model the opposite extreme from CIA because of the insignificantly small toughness of the mylar-PMMA interface*** and all data should be interpreted with this understanding.

2.2 General Hydrafrac Theory and Models 2.2.1 PKN and CGD

Early models for underground fracture growth include the Perkins, Kern, and Nordgren (PKN) and Christianovich, Geertsma, deKlerk, and Daneshy (CGD) models which assume the height of the fracture and then use many additional simplifying assumptions (visually depicted in Figure 2.1) in order to determine the CIA (Crack Interaction Apparatus) is so named because of the ability to study the interaction of mutiple cracks with assorted stresses, inclusions, and other propagating cracks. Narandren and others at the Resource Extraction Laboratory have extensively investigated the stresses and growth patterns of numerous cracks in a variety of orientations[8,9,10]. Dilation is a consideration in CIA because the Poisson's ratio of the cement is of order 0.2 whereas DISLASH uses a pliant block with Poisson's ratio of .4995 under significantly smaller pressures which minimizes dilatant effects.

** Field conditions based on a fracture toughness of 1000psi v, radius of approximately 300ft, and net pressures of order 1000 psi[6].

*** DISLASH does have some small "toughness" effect due to static forces between the

mylar and the PMMA and due to surface tension effects the residual silicon fluid that is never completely removed from the surface. These two contributions combine to produce a nonzero toughness factor which is several orders of magnitude lower than it is for CIA or for most underground fracturing situations, even after proper scaling.

PKN and CGD geometries [11] S(X, Z) 2H _L L 2 z L2 Figure 2.1

width and length of the fracture. Apart from the errors in there internal assumptions and solution methods, these models lose credibility when applied to most actual field conditions. Most obviously because, fracture height is rarely known and, in non-ideally contained fractures, the height is likely to change during the fracturing process.

2.2.2 Pressure and Radii Equations

Theories have since been developed[12] with a more accurate incorporation of the physics behind hydraulic fracturing. By combining the results of fully 3-D or cross-sectional fracture simulators with the governing equations through spatially-integrated results expressed as gamma (y) functions, very accurate descriptions of the hydraulic fracturing process are possible. To analyze the extensive sets of CIA and DISLASH data, the basic governing equations are first reduced to the solution for a circular fracture.

In order to simplify the presentation of the equations, several of the material properties are combined to form effective parameters. Viscosity of the fracturing

fluid is expressed in terms of the effective channel-flow viscosity ( ), given by

[

For example, a Newtonian fluid, k = . and n=1, therefore = 12g. For a

homogeneous, isotropic material, the modulus (E) and Poisson's ratio are combined

into a single term referred to as the crack opening modulus (E) where

- E

4(1 -) (2.2)

Using these combined terms to derive the form of the equations for circular fracture growth under constant flow conditions, the crack tip radius can be found as a function of time []

9(7127142 3) 3

4 71Y13 P 27 t

Similarly, the excess pressure (o=Pfac) and crack opening (A) can be expressed as functions of time and the material parameters, as follows:

1 .1 E 4 71713 3 1 E t - 3 (2.4)

71 9712714

2.2.2 Non-penetrated Zone Size and Possible Dilatancy Effects

During fracture propagation the fluid does not penetrate to the fracture tip, since that would require an infinite pressure gradient at the tip. Instead the fluid

front moves in an "equilibrium" relationship with the crack front, i.e. keeping the stress intensity factor, K, at the tip equal to a critical value (the fracture "toughness") K,, ; for quasi-static fracture propagation. The excess stress acting over the fluid penetrated region must balance with the confining pressure acting on the non-penetrated zone and the fracture toughness of the material[5], as follows.

a - (ac + a)

\r,,

By rearranging, it is straight forward to solve for (o:

(1 2

0) =

L

Nfi (0, + (Y)R

It appears to be well-established now that the material toughness is insignificant for deep underground fractures and for DISLASH, namely:

a >> Kc _(2.8)

Neglecting the Kc factor then,

2R 1 2

CO = - (2.9)

J(ac + a)] 29

In the non-penetrated zone it is believed that non-linear dilation may occur as illustrated in Figure 2.2[5,4] and dilatancy is suggested as a means of explaining the high net pressures seen in the field. As the crack faces are unloaded in the non-penetrated zone, the rock may dilate in a non-linear fashion, partially pinching

closed the crack tip. The effects of this behavior would appear as larger

non-penetrated zone size and shorter and wider fractures. Figure 2.3 below depicts the effect on the non-penetrated zone under dilatant and non-dilatant conditions. First mention of the possibility of dilatant effects was made by Cleary et. al. [3] to explain the differences in field data from model simulations. If dilatant effects are present in CIA experiments it reinforces the possibility that discrepancies in field data are the result of non-linear dilatancy and opens possibilities for further study and quantification of the effects.

A3DH, a simulator for axisymmetric fracture conditions [6], is capable of

simulating the effect of dilatant pinching near the crack tip by artificially squeezing the tip opening by a certain percentage and continuing that effect through several non-penetrated zone sizes back toward the wellbore. Although the actual response of the rock in such conditions is not simulated in detail, the effects of dilatancy can be simulated in the program.

2.3 Scaling Laws

In order to analyze hydraulic fracturing in the laboratory, it is necessary to design tests that can be performed on a smaller scale, yet retain relevance to the

field where fractures may extend up to hundreds of meters in length. If the

Ce2 0 cl Net Pressure Dilation Effect

/

Non-penetrated zone size with dilatancy in the crack

ih dtIn

with dilation

without dilation .4- (O

Effects of Dilatancy in the penetrated zone compared to non-dilatant situation. Figure 2.2 Figure 2.3 -P - aC2 R

necessary to perform dimensional analysis on the parameters involved and reduce the equations to nondimensionalized relationships that can relate laboratory conditions to field conditions.

Equation 2.3 above, which expresses radius as a function of time can be

nondimensionalized for radius and time using Rw, the wellbore radius and t* as

characteristic values, namely [4]

FZ*=( -~

'4

the relationship between radius and time is then reduced to R = f(2.10)

Following a similar procedure for a using a characteristic stress

(3* = - (2.11)

The excess pressure and time are related through

:a

From equations 2.11 and 2.12 it is evident that universal radius vs. time and pressure vs. time curves should exist for all materials and all Newtonian fluids at any constant flow rate, which is one benefit of using a nondimensionalized approach.

3. Experimental Efforts and Current Theories

3.1 Experimental Considerations

The Crack Interaction Apparatus (CIA) is very versatile, but care must be taken when interpreting the data generated by the data acquisition systems and when using the supporting programs that perform the data reduction. In general, misinterpretation of the data may have been a source of many discrepancies in the past. CIA does operate at high pressures, which requires other modifications in the data reduction process that are not necessary in DISLASH; for example, considerations of viscosity as a function of pressure.

3.1.1 Actual Flow Rates

In former publications, it has been stated that the water cart is capable of producing constant flow rates as low as 0.002 cc/sec.[4,5] Unfortunately, recent modifications in the water cart power-supply prohibited steady operation at rates below 0.02cc/sec when the water cart was attempting to pump against any pressure

head above 2000psi. _{Although this problem has been corrected and steady}

'pressurized' flow rates have been achieved in the range of 0.0005 cc/sec it was necessary to rerun the previous constant flow tests to verify the previous data. The

new system measures the actual flow rate throughout the duration of the test -not

just the cumulative flow at five or six times during the test, requiring extrapolation of the flow rate. In fact, reanalysis of one such previous test, where cumulative flow was recorded, uncovered possible errors by a factor of two in the flow rates which can be seen in Figure 3.1. Current flow rates show variations of less than 5% over the duration of the test.

3.1.2 Constant Pressure Experiments

CIA's original design involves a positive displacement pressure generator that is controlled manually through a powerstat. For a constant pressure test the operator need only make minor variations in the flow to maintain a pressure within one or two percent. For this reason the existing database of constant pressure data was considered sufficiently accurate, and the major effort was made to produce repeatable constant flow rate tests.

3.1.3 Material Toughness

Material toughness has always remained a poorly quantified parameter in the characterization of growth rates for specimens in CIA.[4] Complex geometries and varying degree of cure of the cement specimens bring the calculation of the toughness to a level of such complexity that often times the toughness is simply neglected or administered as an afterthought to account for discrepancies in the match between theory and experimental results. The estimates in section 2.1 seem to justify neglecting fracture toughness.

7

6

Q =0.003

5

- LinearFit

Flow rate (cc/sec)

- 0.0038042 .s 4 -Q=- 0.0042 3 Q=0.004 2 Cubic Fit Flow Rates 1 Q=0.0025 0 0 400 800 1200 1600 2000 Time (sec)

Figure 3.1 Old CIA test with a flow rate recorded as 0.002 cc/sec. Actual flow rates are possibly greater by a factor of two.

3.1.4 Viscosity

Previous researchers working with CIA have realized that the viscosity of Dow Corning 200 Silicon Fluid varies with pressure and they have reconciled variations by either ignoring the changes or by multiplying the effective viscosity R

by a factor of 1.6 [4,5,6]. The actual variation in the fluid is approximately a linear

relationship with pressure shown in Figure 3.2 below[13,14,15], which can easily be approximated in the calculation of r* and a*, as shown in Figure 3.3 below. A simple means of estimating the effect of the viscosity variation is to recompute c* at each time used to evaluate the radial growth rate of the fracture. While this value does not account for the variation between radial marks, recalculation at the discrete times produces significant improvements in agreement between CIA and DISLASH. Figure 3.4 below is one example where this correction factor was applied. The new curve produces a much closer match to the DISLASH curve, with the data verifying

the linear relationship between R/RW and t/'* raised to the 4/ power. For DISIASH

no viscosity modifications are necessary because of the low pressures involved.

3.2 Scaling Issues

The correlation between DISLASH and CIA requires the use of the proper non-dimensionalized variables to compare growth rates and excess pressure. Although the effect of variation of modulus is only of order 0.25, tests have shown that the modulus varies significantly over the first several days after casting. There is however, a time period of three days when the specimens have achieved an essentially constant value for the modulus. This is the time when conditions are right for testing of the specimens, i.e. after sufficient strength has developed in the cement and before the specimen becomes overly brittle with shrinkage cracks destroy the integrity of the specimen. Specifics of the modulus curve are discussed in section 5.1 and the effect is included in c*.

3.3 Dilatancy Effects

Unfortunately the scale of dilatant effects is too small to measure directly in CIA and its effect can be measured only indirectly. In the non-penetrated zone of a

CIA fracture, dilatancy would slow the growth rate below that of DISLASH, in

which there are no dilatant effects. If all other conditions are the same, any nonlinear effects due to rock dilatation would be evident in the growth response. Other differences between the two apparatus, beside Poisson's ratio and non-linear response near the fracture tip, complicate the analysis and disguise possible

dilatancy effects. Material toughness, discussed in section 2.1, could play a

ja Pressure p Atmospheric Pressure a a 2 1.5 I 0 1000 2NW 3Nd 4 50 a = o0 Pressure (psi)

Changes in viscosity of DC200 fluids under high pressures.

1.3 L25 1.2 1.15 1.1 1.05 1 0 1.3 1.25 1.2 1.15 1.1 1.05 I 1MX 2M0 M00 4M0 500 60 0 7M 0 Pressure (psi)

Changes in t* and ;* over reasonable experimental pressures due

to changes in viscosity. Figure 3.2 SPressure - * G Atmosph. T Pessure-r Atmosph. Figure 3.3 ... ...

60 . 1 1 1 1 f i l l 1 1 1 1 1 1 I f l i l y

0/

50 ... _{cu lyiiii-- ... ... ... --- ...}

With Viscosity Dependance on Pressure 4 0 ... ... ... -CIA Data 30 . ... ... NaXism aity-Depeadance ... -on Pressure 00 2 0 ... ... ... -0 0 10 ... _{q ... ...} 0 _{DISIASH Data} 0 0 J 0 2 4 6 8 10 12 14 t/T*

Effect of viscosity dependance on pressure in nondimensionalized graphs. Figure 3.4

Another possible method of establishing the presence of dilatant effects in CIA is to measure the non-penetrated zone size. Although the zone size cannot be monitored during the entire test, the final non-penetrated zone size is evident at specimen breakout. When the fracture tip reaches the outer edge of the specimen the confining oil rushes into the fracture staining the cement a dark brown. The only regions not stained are the areas covered with the silicon fracture fluid. By measuring the difference between the outer radius of the fracture at breakout and the portion protected with silicon fluid, the non-penetrated zone size can be measured. Figure 3.5 shows the oil-silicon marking pattern associated with the non-penetrated zone size at breakout.

Final crack edge

Width of nonpenetrated zone

Cement covered and soaked by oil

Cement covered and sealed by fracture fluid

4. Experimental Setup

4.1 DISLASH

This laboratory apparatus was designed to simulate negligible fracture toughness, based on the deductions in section 2.1 that fracture toughness plays an insignificant role in deep underground hydraulic fractures. DISLASH, shown in Figure 4.1 and Appendix E, is the latest version of this overall experimental approach.

DISLASH models the separation of the rock faces in fracture growth by

forcing a viscous silicon fluid into the interface between a pliant rubber block and comparatively rigid PMMA block to simulate half of a fractured body. Fracture toughness is almost zero, since the only bonding arises from surface tension effects and static electricity between the mylar and the PMMA, both of which are

insignificant. The apparatus is appealing for several reasons. Primarily

experiments may be carried out very quickly, lasting less than two minutes in most cases. Additionally, there is virtually no preparation time because the separation of the interfaces is non-destructive, and fracture growth can be measured visually.

When analyzing the DISLASH data it is important to realize that the fracture opening half the height of a full simulation. To account for the half crack nature of DISLASH, the equations must be modified by doubling the crack opening modulus based on a lumped model analysis.[4]

4.2 Crack Interaction Apparatus

In simplest terms, a CIA test involves externally pressurizing a cylindrical cement specimen and then pumping in a silicon fluid to initiate a crack growing from a cast-in precrack. Periodically, minor perturbations in the axial stress state are

generated, changing the crack tip growth direction. These changes in growth

direction leave "beach marks," commonly referred to as bias rings, and provide a

permanent history of the crack radius. Although the fracture toughness is

negligible, in comparison to the energy required to counteract the confining stress, it is significant in allowing natural determination of the fracture tip orientation and thus the crack growth direction.[16] [The biased stress state during the marking of rings is an interesting problem in mixed mode fracture quantified in numerous articles [17] and as such will not be discussed here]. The apparatus is very versatile in the simulation of multiple fractures and perforated wellbore conditions which can

be run under hydrostatic conditions or under a uniaxial biased state. For

comparison to DISLASH and other theoretical models, it is most appropriate to run

simple circular precrack geometries under hydrostatic conditions. A complete

experimental procedure can be found in Appendix B, which includes several new improvements in the casting and testing procedure. After enduring a number of failures, the system now runs dependably; only one unsuccessful test was

Transducers

qal

t m

T1

LL2i

DISLASH with fluid puddle at the interface.

L1KLJ

Figure 4.1

I I

I I

---experienced in the last 15 tests, due to cement in the borehole (we were still able to initiate a crack and mark rings but cement partially clogging the borehole made

actual pressures applied to the fracturing fluid impossible to determine). This

particular test proved that the water cart used to pressurize the silicon fluid in the reservoir is capable of functioning to at least twice its design specifications! Unfortunately, it is not safe to test the corresponding range of allowable confining stress. A line diagram of the system is shown in Figure 4.2.

4.2.1 Apparatus

The Crack Interaction Apparatus (CIA) is composed of four main components, each of which has undergone major changes since the pressure vessel was first installed late in 1979 [8]. It is necessary to know the history of the apparatus and the motivations behind some of the major changes in the past to understand the reasons for the current modifications and the forthcoming arguments concerning the comparisons between CIA and DISLASH experiments.

4.2.1.1 Pressure Vessel

The pressure vessel, shown in Figure 4.3, is the core of the system and,

unfortunately, the major limiting factor when rnnning tests. The pressure vessel

was constructed using two 900 lb. 12" Taylor Forge weldneck flanges which were welded together to provide the main body of the vessel. The top and bottom are two

similar blind flanges bolted to the main body with twenty 13I8" diameter bolts per

flange. This setup is rated to operate safely up to pressures of 2200 psi, which sets the upper operating pressure for tests. Very few modifications have been made to the pressure vessel, except for minor changes to the axial pressure generating system, which will be discussed in section 4.2.2.1. The design for the pressure vessel was strongly influenced by the need to find an inexpensive and immediately available method of conducting high pressure tests, there were no plans for extended use of the apparatus but after twelve years of service it has performed exceptionally well, considering the minimal initial investment.

4.2.1.2 Oil Cart

The second component, and the most temperamental of all, is the oil cart, shown in Figure 4.4, which provides the 1200 to 2000 psi confining pressure and the

1600 to 2600 psi axial pressure. The oil cart was last modified, at least in any major

fashion, in 1985 when the cart was reconfigured to run repeatable tests and the performance of the various subcomponents of the cart were quantified[8,9].

4.2.1.3 Water Cart

A unique feature of CIA is the reservoir pressurization system which uses

water to push a piston into the reservoir in the specimen, thus pressurizing the silicon fracturing fluid. This piston arrangement, with the water and silicon fluid separated, overcomes the problem of large pressure drops due to viscous forces in the

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Line diagram showing all 4 CIA subsystems Figure 4.2 SM PC I KeOft DA"S

SM*

Vessel top drain

(removes air)

Cover plate

Rubber diaphram

Vessel confining pressure line

(from oil cart)

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(from oil cart)

Bolehole pressur line

(from water cart)

esel drain line

(back pressure required)

Diagram of Pressure Vessel

1-Figure 4.3

I

Air line quick-connect on Dump reservoir

Reservoir pressure gauge Pump input pressure

Confining pressure gauge Ram pressure gauge

Confining regulator

Ram regulator

Ram supply line

Confining supply line

Pressure accumulato

Oil reservoir

Water trap

.Accumulator valve

-Main drain valve

- Pressure accumulator

Pump

- Filters

Diagram of Oil Cart Figure 4.4

pumping process, thus also allowing accurate measurement of the fracture driving pressure.

The water cart, originally designed for much simpler tests, has finally been rebuilt to overcome serious design problems that complicated maintenance and prevented the running of some desired tests. The water cart has probably been the most modified component of the entire CIA system. Originally, the cart required

230 volts AC and the pressure and flow rate system was controlled using a DEC

MINC-11 computer and a complex motor control subsystem. Almost every

modification, since its original development, has succeeded in reducing the effectiveness of the cart. When the original control system was designed in 1981, flow rates in the .002 cc/sec range were supposedly possible [7,16]. Before the current redesign, the lowest flow rate possible was .02 cc/sec, with significant fluctuations.

4.2.1.4 Data Acquisition

The final and most recent addition to the system is the Keithley Data Acquisition System. Although the computer does not control the system, as the MINC did, it does free the operators from trying to monitor and record pressures during the test. The few MINC files that are still accessible show readings that are approximately 300 seconds apart. The previous system required the operator to visually monitor the three different pressure gages while biasing and then manually

recording the data onto a testing sheet. The current system is a modified

configuration of the setup used for DISIASH. Some of the more specific details of the Keithley system can be found in other references where the entire DISLASH Data Acquisition is described in detail.[5] For CIA the confining, ram, and two A-Line pressures are recorded as well as the cumulative fluid flow.

4.2.2 Special Modifications

In order to address some of the specific issues surrounding the discrepancies in growth rates mentioned earlier, it was necessary to make some additions to CIA, the support systems, and the data acquisition and reduction techniques.

4.2.2.1 Pressure Vessel

The pressure vessel is still the limiting factor for high pressure testing [note that we have achieved water cart pressures up to 6500psi without damage to the water cart or leakage around the borehole] but some modifications have been made to better facilitate testing.

The axial pressure generator, commonly called the ram, consists of a bottom plate which connects to a fitting in the bottom of the pressure vessel, and a rubber inflatable end pad which is used to apply an axial pressure to the specimen. The axial pressure applied serves to mark the rings and is essential to collecting radius data. Unfortunately, the ring marking system had been unsuccessful for almost a year before modifications were made to counter the effects of an aging system.

Severe blockage of the piping system, fatigue of the pressure release valves, and

clogged accumulators were among the problems. Several additional problem

concerned the ram, which applies the axial bias stress to the specimen. The ram is composed of multiple aluminum rings to allow for the gripping of the end pad and uniform flow of oil over the surface. These rings had warped from years of use and the O-rings which isolated the ram oil from the confining pressure oil, failed preventing the isolation of ram pressure from confining pressure. In order to mark rings, the axial pressure must be approximately 400 psi higher than the confining pressure. The addition of a thicker O-ring gasket and increasing the torque on the 24 attachment screws has effectively isolated the ram. Although failure of the rubber end pad has limited the upper bias pressure, bias rings are now producible on a repeatable basis.

A second factor that prohibited the accurate marking of growth rings was an

unacceptable level of compliance in the ram system, due to the presence of air

trapped below the end pad. The solution in the past involved an attempt to

evacuate the ram after installation. The new method is to fill the vessel and ram with oil prior to assembly. A complete description of the new process can be found in Appendix B.

4.2.2.2 Water Cart

The previous water cart was incapable of steady flow rates below .02 cc/sec and even these flow rates were outside the abilities of the apparatus. Pulsing was unavoidable and stalling of the motor was common as the pressure increased during the test. Although the compliance of the rest of the system probably absorbed the effects of the flow pulsation, some effects of a non-continuous flow rate may have affected the fracture growth. With the new gear ratios of the redesigned water cart, shown in Figure 4.5, the lowest possible flow rates are of the order .0005 cc/sec, with only occasional pulsing at the lowest rates and highest pressures, well beyond normal testing specifications.

4.2.2.3 Data Acquisition

The freedom granted to the system operators to monitor test conditions and respond immediately without the burden of recording data during the test is the primary improvement in the Data Acquisition process. At any time during the test the operators must be able to monitor the wellbore, confining, and ram pressures in order to respond to changes in the test conditions. If the operators were also required to record the pressures and times, the data is likely to be incomplete, or small problems with the test could escalate while the operators are recording data, until the parameters of the test have strayed beyond acceptable bounds.

An additional benefit of the new system, which is a significant improvement over the older MINC Data Acquisition system, is the ability to monitor the system conditions at one second intervals, as opposed to 300 second intervals. Transients in the pressure or flow are immediately apparent and easily identifiable. In prior

Water reseroir Power stat I - ~ U, Limit switches Pressure generator

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cases, surges in the flow were possible but there was no way of recording their magnitude or duration. Now it is possible to verify the procedure of every test and discount any tests where perturbations in the flow or pressure fluctuations may have caused fracture growth instabilities.

4.2.2.4 Data Reduction

Data analysis for the rings is a multistage process. The first step involves getting the ring data into a machine-readable form. In the past this was done with an Advanced Space Graphics Space Tablet (which is no longer available commercially), capable of rapidly digitizing the X, Y, and Z coordinates of the bias rings from the fracture surface. This apparatus is currently not functional, and in the final stages of its operation there was doubt as to its ability to achieve accuracy greater than .25". The current technique relies on a much more manually intensive approach to gathering the data. For each ring the radial distance (p) is measured every 5 degrees along the arc where the ring is visible. This information is then entered into an ASCII file for the (RoXsf) program to fit the data to a circle offset from the center of the borehole: the program fits the data to the nonlinear equation below using a chi squared technique,

r = p cos(O - $) + JR2 + p2cos2(0 - . p2 (4.1)

hence its name (Radial pOlar X2 _{(Chi Squared) Fit: "Rocks").}

The rate of convergence for the current routine is very dependent on the initial guesses. A fairly accurate approximation of the angle $ has a profound impact on the speed while radius R and offset p, are less critical. It is easy to find good guesses from a polar graph generated prior to the curve fitting procedure. To estimate 0 it is usually sufficient to pick the correct quadrant.

This method produces results that are typically 1-9% different than previous methods of measuring the ring radius from the bore hole to the ring at 900 and 270*. Previous researchers[5] have used a different system where 0* and 180* are used to refer to 90* and 270*. The minor shifts are caused by nonuniform initiation from the precrack, which initially prejudices crack growth in a specific direction. During continued growth the relative magnitude of the deviation from the center is minimized due to a tendency for circular crack growth, allowing the crack front to recover from minor perturbations due to the restriction of fluid flow.

Example of p, $, and R for Circle Displaced From Origin (Distances are Greatly Enlarged to Show Detail).

5. Results

5.1 Modulus Tests

Although there is extensive data on the long term changes in strength of cement paste, there is no significant data on the modulus changes over the first 48 to 96 hours after casting for Portland Type III cement[19,20]. Modulus tests were performed beginning 24 hours after casting and then every six hours until 96 hours after casting. This encompasses the normal testing period with significant time before and after. As can be seen from Figure 5.1 the modulus reaches a plateau after 40 to 45 hours and maintains a fairly constant value. The relatively flat portion of the curve shows that the use of a constant value of 1.1 x 106 psi is correct for the modulus during the testing period. The limiting factor at the far end of the testing period is shrinkage cracks which begin to damage the integrity of the specimen after 96 hours.

5.2 Overall Comparison of CIA and DISLASH

A total of fourteen successful CIA, constant-flow tests were run at confining

pressures of 1400, 1600, and 1800 psi with flow rates between .000 1 and .007 cc/sec. Table 5.1 details each of the tests and the atmospheric r* and a* for each test. The

modulus was assumed at a constant value of 1.1 x10 6 psi for each specimen and

minor variations with time were neglected.

CIA tests still exhibits the slightly slower growth rate previously noted [5]

but by introducing the pressure dependence of viscosity, the curve makes a dramatic improvement. Figure 3.4 showed a sample growth curve from specimen 20E but all of the other specimens exhibit similar behavior.

Equation 2.3 states that the radius for circular growth should grow

approximately as t .^". DISLASH growth rates have been extensively studied and

closely match with a radius that grows at an exponent value of 0.42 for foam and 0.46 for rubber material which are within 4.5% of the theoretical value[5].

The start of the timer for a CIA test occurs when pressurization of the specimen begins, but initiation typically occurs after approximately 300 seconds. The reason for the significant time lag is due to the considerable level of compliance in the fluid pressurization system. By plotting R vs. t, the significant time lags are immediately apparent and time shifts, t, have significant effects on the form of

equation 2.3 which becomes is in valid for large values of to.

By shifting along the time axis and fitting the growth curve to equation 5.2, a

valid relationship is found for the nondimensionalized values

r~C2

=- t0+ C1[ RJ(5.1)

where C₂ would equal 9/4 for a perfect match to theory. CIA growth rates calculated

for the shifted values have an exponential value of 0.433 with scatter plus or minus

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10 5

Modulus of Portland Type III cement measured every six hours. Figure 5.1

Specimen Confining Flow Rate

Non-Pressure (cc/sec) Penetrated Atmospheric

(psi) Zone Size / R (sec)

16G 1600 0.0013 0.040 1.70548 16H 1600 0.00435 0.044 0.68935 161 1400 0.00219 0.034 1.15338 17D 1400 0.0083 * 0.42462 17E 1800 0.00703 0.045 0.48094 17F 1800 0.00107 0.033 1.97363 18G 1800 0.00268 0.035 0.99130 181 1800 0.00549 0.049 0.57893 19D 1400 0.0098 0.059 0.37487 19E 1600 0.0048 0.048 0.64028 20D 1600 0.00499 * 0.62191 20E 1600 0.00606 * 0.53759

Table 5.1 List of CIA tests with confining pressure, flow rate, non-penetrated

zone size, and V*

2.3%. The growth rate for CIA of 0.433 is significantly different from previous work

because of the more precise measurement of the crack front radius, and the compensation for viscosity increase with pressure

Figure 5.2 demonstrates the nondimensionalized and shifted data when compared with a constant flow DISLASH test. The first two points in Figure 5.2 are noticeably lower than the line that would result if the radius time relationship

was strictly of 9/4 dependance. This behavior is due to the compressibility of the

fluid and the compliance of the system. Figure 5.3 shows comparisons of five

characteristic CIA constant flow tests with the results of A3DH[6]; conditions required to match a typical CIA test are shown in Table 5.2. The CIA data shows the same slower growth as Figure 5.2 but once the system transients have subsided there is a close match between the computer simulation and experimental data.

Excess pressures also behave according to the equations in section two. Figures 5.4 and 5.5 show the 1/3 dependance with time and the universal curve for various flow rates and confining pressure. The significant scatter in the excess pressure is due to the pressure perturbations used to mark the bias rings.

5.3 Non-penetrated Zone Size

Figure 5.6 shows the nondimensionalized non-penetrated zone size R plotted verses the excess to confining pressure ratio. The solid line represents the upper limit based on a quasi-static approximation in equation 4.1. Table 5.3 shows information representing a single test condition from three different sources. Information was collected from CIA specimen 181 and compared with the values from a similar situation run on A3DH. Comparisons for A3DH are based on two methods. In the first case, no dilatant effects were incorporated, while in the later cases some squeeze at the crack tip was added to simulate dilatancy. The first column is the measured non-penetrated zone size to radius ratio, the second column is the measured excess pressure at breakout and, the third column is the approximate time between initiation and breakout. Table 5.3 shows that although good agreement exists between A3DH and CIA for the pressures and crack growth times when no dilatancy included, the non-penetrated zone size is too small by a factor of ten or more. When A3DH incorporates the crack tip squeeze to simulate dilatancy, the non-penetrated zone size agrees much more closely and the pressures are still close to the experimental values.

60 50 0 DISLASH ₀ ... ... 0 CIA (20E) ₀ 0 ... 0 00 ... ₉ ... * ... 0 0 0 0 ... 0 0 0 0 ... _{... ... -" ... --- ... ...} 0 0 30 W CD 20 10 0 2 4 6

8

10

Figure 5.2 _{Nondimensionalized and shifted curve of radial crack growth in}

0 R/Rw 161 ₊₀ 0 R/Rw 17F ₀ 5 0 ... ... - * ... ... **'** ... ... .... 0 ... 0 R/Rw 181 + x x R/Rw 20D 0 X + R/Rw 20E ₀ 40 ... - R /R w A 3 D H ... ... a ... 3 0 ... ... -2 0 ... ... -A3 0 0 X CY 0 0 + 10 ... ... -0 00 0 0 -600 -400 -200 0 200 400 600 800 1000 t/T* Shifted

Figure 5.3 _{Nondimensionalized and shifted data for CIA constant flow tests}

* Fluid viscosity is the channel fluid viscosity at higher pressures.

viscosity multiplied by 1.6 to simulate the

Table 5.2 _{Experimental parameters used by A3DH to model CIA experiment.}

Young's Modulus 1.0 x 106 psi

Poisson's Ratio 0.2

Confining Stress 1800 psi

Flow Rate 0.002 cc/sec

Fluid Viscosity 940,000 cp *

Fracture Toughness _{200 psi}

_4in

Surface Tension 21.5 dyne/cm

Specimen Size 12.4 cm radius x 35 cm height

. ... ... 9 Excess 181 0 Excess 20D ... . ... ... ... ... ... .. ... I ... .... ... 3000 _{I I I} 2500 2000 1500 to 1000 500 0

Excess pressure with respect to time to the 1/3 for two

characteristic CIA tests Figure 5.4

0.14 0.15 0.16 0.17 0.18 0.19

I I I I I I I I I I I I I I I ,- I I I I I I I I I I I . ... ... W IM ... . ... ... .... ... ... . ... .... .... ... .... . ... ... ... -. a I a I I a a j a I a 0.035 E) Sigma/Sigma* 181 B Sigma/Sigma* 20D - 0 Sigma/Sigma* 20E x Sigma/Sigma* 17D 0.03 0.025 0.02 0.015 0.01 I a I I a a I I I I I I I 1 1 0.005 -100 -50 0 100 150 200 tk* shifted

Nondimensionalized and shifted pressure universal curves for ClAtests. Figure 5.5

e WRAMH 0% LED ... ... . ... ... ... _{/R Experim ental} 0)/R Theory ... ... ... ... ... ... ... ... .... ... ... o A3DH 99% . ... ... ... ... 0 A3DH 95% LED 0 ::A3DH 90% LED . ... ... ... ...... ... 0 43DH 80% LED . ... ... ... ... 0: X3DH'*9S%*LED A3DH 0% LED 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 LED 0 0.2 0.4 0.6 0.8 I (Y/(y_C

Non-penetrated zone experimental data for CIA and quasi-static theoretical values

Table 5.3 Experimental effects compared to A3DH with and without LED Compared for test conditions for 181.

Squeeze acting over five co.

Max squeeze of approximately 95% produces good agreement if the effects of the self similar assumptions are noted.

co / R Experimental 0.048 value A3DH with 0% 0.009 LED A3DH with 50% 0.017 LED A3DH with 80% 0.032 LED A3DH with 90% 0.044 LED A3DH with 95% 0.055 LED A3DH with 99% 0.069 LED

6. Conclusions

6.1 Inaccuracies in Earlier CIA Tests

Inconsistencies in previous constant flow tests prompted the reevaluation of previous data and the rerunning of the tests using more consistent testing methods and improved accuracy in the data acquisition and reduction phases. For example, when the system was first brought back into service, the A-Line pressure gages were reading pressures approximately 2000 psi under the actual applied pressure. How long this error was present in the system is unknown, but all gages and transducers have since been replaced and/or recalibrated.

6.2 Comparisons of CIA and DISLASH

CIA and DISLASH are two very valuable, experimental fracture simulators

that produce comparable results using very different techniques. Each apparatus is uniquely suited to specific tasks and with careful analysis of the experimental data both CIA and DISLASH can be used to perform valid experiments in the areas where they excel. For example, CIA is capable of studying the growth on three dimensional curved fractures and crack interactions while DISLASH is suited to planar problems and interfacial crack growth. When run in similar configurations, (planar crack growth), both systems agree well with theoretical models and with

each other over a wide range of test parameters. Previous comparisons used

apparently faulty data and/or failed to include significant considerations such as the effect of pressure on viscosity.

6.3 Leading-Edge Dilatancy

Although a limited number of comparisons were made, it is apparent that the manner in which A3DH models the possible dilatant behavior of the cement, there is

close agreement with the experimental data. Because A3DH approximates an

unknown physical behavior with a presumed effect of squeezing the crack over a small distance near the tip, comparisons with CIA are not entirely conclusive. Without some physical basis behind the "dilatant" effect incorporated into A3DH it is possible to assign arbitrary values to the percent squeeze and arrive at broad ranges of numbers for the non-penetrated zone. While no definitive statement can be made about the existence of dilatancy from the A3DH model, it is possible to state with confidence that the A3DH model does adequately describe the behavior of measurable CIA parameters. If CIA does exhibit dilatant behavior, or if the effects of low confining stress to excess pressure produce behavior that is characteristic of the modeling method of dilatancy in A3DH, or some combination of the two, is impossible to determine from the current experimental apparatus. Neither the correctness of the A3DH model of dilatancy nor the existence of dilatancy in CIA can be verified at this point in time.