Laboratory study of gas permeability changes in rock salt during deformation

Int. J. RockMech.Min.Sci. &Geomech.Abstr.Vol.29. No. 4, pp. 325-M2, 1992 Printed in Great Britain.All rights reserved

0148-9062/92$5.00+ 0.00 Copyright~) 1992PergamonPressLtd

Laboratory Study of Gas Permeability Changes in Rock Salt During Deformation J. C. S T O R M O N T , J. J. K. D A E M E N , Gas permeability and porosity measurements have been made during hydrostatic and triaxial quasi-static, stress-rate controlled compression tests. The permeability and porosity of the as-received samples decrease significantly as a result of hydrostatic loading. These changes are largely irreversible, and are believed to "heal" or return the rock to a condition comparable to its undisturbed state. The permeability can increase more than 5 orders of magnitude over the initial (healed) state as the samples are deformed during deviatoric loading. The gas permeability and porosity changes are consistent with a flow model based on the equivalent channel concept. A model of microcrack initiation and growth based on the frictional sliding crack suggests the flow paths initially develop along grain boundaries and then along axial intragranular tensile cracks. Post-test visual observations support the model predictions.

INTRODUCTION

Previous laboratory measurements of rock salt permeability have focused on sampling-induced disturbThe very low permeability of rock salt is its principal ance. Because rock salt is damaged or disturbed during advantage as a medium for hydrocarbon storage and sample collection and preparation [2, 3], as-received waste disposal. However, in the so-called disturbed rock core samples have a relatively large permeability [3, 4]. zone (DRZ) adjacent to most excavations in bedded Hydrostatic loading reduces the permeability to some rock salt, the permeability is dramatically increased [1]. low value, usually below the resolution of the test system The D R Z includes dilated rock salt and the discontinu(typically <1 to 5 x 10-2°m2). Subsequent hydrostatic ous response (separations, fracture and shear slip) of unloading indicates that the majority of the permeability thin, periodic anhydrite and clay layers often present in reduction is irreversible [3], although Peach et al. [4] bedded salt deposits. There is little understanding of the suggest that the permeability is recoverable upon mechanisms involved in the development of the DRZ. unloadirlg for short-term tests. The permanent perWe propose gas permeability measurements as a means meability reduction is referred to as "healing" and has to provide insight into the development of disturbance been attributed to plastic flow along grain boundaries by or damage in rock salt. Because permeability is Sutherland and Cave [3]. a function of the interconnected pore structure, The few measurements on rock salt subjected permeability changes can be interpreted in terms of the to deviatoric loading during conventional triaxial structural changes the material experiences. The gas compression tests reveal that the permeability may permeability of intact rock salt is effectively zero, so increase, depending on the magnitude of the deviatoric measurable gas permeability will be directly related and confining stresses. Peach et al. [4] found that to the creation of new pore structure (i.e. damage). under 5 MPa confining pressure the gas permeability can In situ gas permeability measurements have been used increase by more than four orders of magnitude as the successfully to delineate the extent of the D R Z [1]. axial strain increases to 10%. Donath et al. [5] report a single test on domal salt in which brine permeability fRepository Isolation Systems Division, Sandia National increases two orders of magnitude after being deformed Laboratories, Albuquerque, NM 87185, U.S.A. ~:Mackay School of Mines, University of Nevada, Reno, NV 89557, to 5% axial strain under a confining pressure of about U.S.A. 6MPa. At confining pressures of 14 and 20MPa, 325

326

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

Sutherland and Cave [3] found deviatoric loads of more than 40 MPa resulted in measurable gas permeability of previously healed samples. From numerous liquid permeability tests on a domal rock salt under various stress states, Lai [6] found the permeability to increase with decreasing mean stress and increasing deviatoric stress. The magnitude of the permeabilities Lai found are consistently many orders of magnitude greater than those from other measurements. The difference between the results of Lai with others may be due to considerable differences in intrinsic permeabilities for different rock salts, or may be related to the method used to heal the samples. In this study we investigate gas permeability changes in terms of the structural changes of the rock salt samples under two stress paths: hydrostatic compression (HC) and conventional triaxial compression (CTC). The purpose of the hydrostatic tests is to investigate the amount of sampling disturbance experienced by the samples, and how to reverse this disturbance. The purpose of the triaxial tests is to determine how the gas permeability changes with deformation as a function of confining pressure and deviatoric load. Porosity is also measured so the experimental results can be evaluated in terms of a flow model based on pore structure. A model of microcrack initiation and growth is used to provide insight into the changes in pore structure. Visual observations of cracks within the samples are made at the conclusion of testing. MEASUREMENT SYSTEMS AND METHODS The measurements are conducted on 9.5-cm dia., 20cm long samples of rock salt obtained from the underground workings of the Waste Isolation Pilot Plant (WIPP), a U.S. Department of Energy research and development facility located 650 m below ground surface in a bedded salt formation in southeastern New Mexico. The rock is clear to greyish orange-pink halite (rock salt) with a nominal grain dimension of I cm. The primary elements of the measurement system include a Hoek cell to provide sample confinement, a load frame to apply the axial load, and a permeameter for the gas permeability tests. The confining pressure in the Hoek cell is controlled by either a hand pump or a gas-over-oil pressure intensifier. The intensifier is used for HC tests where the confining pressure must be frequently and accurately changed. For CTC tests, once the cell pressure is brought to the desired value by means of a hand pump, excess cell oil induced by the subsequent deformation of the sample is bled to a buret by means of a pressure relief valve. The platens used to transmit the axial load are machined to allow fluid to be injected to or removed from the top or bottom of the sample. A linear voltage displacement transducer (LVDT) measures axial displacement. The axial stress, confining pressure, axial strain, lateral strain and volumetric strain are calculated from the hydraulic ram pressure, axial displacement of the sample and the load frame, confining pressure and change in oil volume in

either the buret or the intensifier. The calculated stresses and strains are true or current values as the changing dimensions of the sample are taken into account. In order to ensure that the pore fluid is made available to the entire cross-sectional area of the sample, porous metal disks are placed between the platens and the samples. One or two thin pieces of perforated teflon are placed between the sample and the porous metal because the porous metal disks can generate shear stresses at the end piece/sample interface, which in turn can inhibit sample dilation near the end pieces. These end effects may be a particular problem for permeability measurements as the presence of a low-permeability zone (undilated compared to the rest of the core) will cause the measured permeability to be lower than that of the bulk of the sample. The permeameter consists of gauges, transducers, valves and tubing mounted in a portable control panel which can be attached to the platens on the top and bottom of the sample by means of quick-connections. Analogue pressure gauges and pressure transducers measure the pressures which are applied to the top (upstream) and bottom (downstream) of the sample. In addition, a differential pressure transducer measures the pressure difference across the sample. A digital thermometer measures the gas temperature in the upstream line. The permeameter, including external tubing, is insulated to minimize temperature changes. The permeameter is capable of measuring permeabilities as great as 10 -t4 m:. The lower limit of the resolution of the permeameter is defined by the test duration: for a 24 hr test, the permeameter can detect permeabilities of about 5 x 10 -22 m 2. Transient permeability tests require that a constant pore pressure first be established in the sample. A pressure pulse (increment or decrement) is then applied to one side of the sample, and transient flow through the sample is induced. When the storativity of the sample is small (as is the case for these measurements on rock salt), the permeability of the sample can be determined directly from the measured pressure history [7] without resorting to type curves or numerical simulations. Such flow is termed quasi-steady. During some transient tests, the sample permeability is so small that no pressure changes are measured during the test. An upper bound permeability is determined by assuming a pressure change corresponding to the transducer accuracy. In these cases, the test duration defines the minimum detectable permeability. For permeabilities in excess of 10-17m 2, the permeameter is configured for steady-state flow. A supplemental 1.1 1. reservoir is attached to the upstream side of the permeameter to provide a nearly constant pressure to the top of the sample. The downstream side is vented to atmospheric pressure. From the measured flowrate, the permeability is determined by applying Darcy's law for steady-state flow of a compressible fluid. Hydrostatic stress tests were conducted to heal the samples to a condition comparable to intact rock salt for subsequent deviatoric stress testing as well as to provide

STORMONT and DAEMEN: GAS PERMEABILITY IN ROCK SALT

insight into the healing process. Four samples were tested only under hydrostatic stresses; the remaining 10 samples were tested first under hydrostatic stresses and then triaxial or deviatoric loading. The procedure for hydrostatic tests is as follows. A hydrostatic stress of 2.4 MPa is applied to the sample. A 0.7 MPa pore pressure is immediately established in the sample and at least one permeability test is performed. The hydrostatic stress is then increases, and another permeability test performed. Some samples are subjected to cycles of loading and unloading accompanied by permeability tests. As the final step of the hydrostatic testing phase, all samples are held for a minimum of 10 hr at about 14.5 MPa hydrostatic stresss, near the isotropic virgin stress state measured at the WIPP facility horizon [8]. Triaxial tests were performed on 10 samples which had been previously healed under hydrostatic stress conditions. The confining pressure is reduced from the final hydrostatic value (14.5MPa) to the constant confining pressure desired in the CTC test (2.4-7.6MPa). The axial stress is then increased to produce the deviatoric load on the sample. At prescribed axial strains (typically every 2%), the loading is halted and a permeability test conducted. The samples are deformed a total of 10-20% axial strain. During the triaxial tests, the samples are deviatorically loaded at a

327

rate of 0.2 MPa/min. This rate is comparable to that used by Wawersik and Hannum [9], Mellegard et al. [10] and Desai and Varadarajan [11]. The resulting axial strain rate is between 10-~ and 3 x 10-5 sec -~, comparable to that used for most strain-rate controlled quasi-static compression tests on rock salt. As a result of dilation during deviatoric loading, gas pressure in the permeameter decreases. Employing a mass balance of gas in the permeameter and the sample at the beginning and conclusion of each episode of deviatoric loading, changes in the gas-accessible porosity can be calculated. This method is equivalent to the gas expansion method for measuring porosity [12]. TEST RESULTS

Hydrostatic loading results Mechanical results. Typical hydrostatic stress vs volumetric strain data are given in Fig. 1. The volumetric strain is calculated from the axial strain assuming isotropic deformation (i.e. ~,,I = 3Eu) as well as from the change in oil volume in the cell. The generally good agreement between the two largely independent measurements confirms the isotropic nature of the volumetric response. A similar conclusion was reached by Wawersik and Hannum [9].

16

At =70 hr

J

12

II . i

0,.

ul

DI

DO

2

10 -t-

:

,

o.

to#

n° o .

,ff

r 0

-0.002

F

,~=°

I

I

I

!

I

-0.000

0.002

0.004

0.006

0.008

0.010

V o l u m e t r i c Strain Fig. I. Hydrostatic stress vs volumetric strain data. Volumetric strain is calculated from axial strain assuming isotropic deformation (N) and from cell oil volume (Q).

328

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

Table 1. Hydrostatic loading data

Sample number

As-received or initial porosity (%)

Permanent reduction in porosity (%)

Residual or final porosity (%)

Peak unloading modulus (MPa)

HUA3 HUA4 TUA5 TUA6 TUA7 TUA8 TUA9 TUAI0 TUA13 TUAI4 TUAI5 TUAI6 TUAI8 TUAI9

0.7 0.7 0.9 1,0 0.4 0.9 1.4 1.6 0.7 0.4 0.7 0.7 0.4 0.7

0.6 0.5 0.8 0.8 0.3 0.7 1.3 1.4 0.5 0.2 0.5 0.5 0.3 0.5

0.1 0.2 0. I 0.2 0.1 0.2 0. l 0.2 0.2 0.2 0.2 0.2 0. I 0.2

8.6 13.8 9.6 27.6 34.5 20,7 28.7 16.6 20.7 28.7 34.5 34.5 13.1 28.8

[9, 11, 17].

Table 1 provides the porosity data from the hydrostatic loading tests. Estimates of the residual porosity--the porosity which remains after healing--are derived from the unloading response by the technique of Walsh [13]. The residual porosity is 0. I-0.2% for all the samples, confirming the very low porosity of healed rock salt. The inelastic volume strain which accumulates during a complete hydrostatic load-unload healing cycle is equivalent to the permanent reduction in the porosity of the sample. The sum of the residual porosity and the porosity decrease during the healing process is the porosity of the as-received samples. The porosities of the as-received samples given in Table 1 are consistent with the porosity of unstressed (and presumably unhealed) samples reported by Others: 0.6% for a bedded salt from

10 -16

t

t

near Carlsbad, NM [9] and 0.59% [14] and 1.0% [15] for a bedded salt from near Hutchinson, KS. Unloading bulk moduli are also given in Table 1. The unloading bulk modulus is calculated from the slope of the hydrostatic stress vs volumetric strain data while unloading from the maximum hydrostatic stress (about 14MPa), following the suggestion of Wawersik and Preece [16]. The unloading bulk moduli in Table 1 are consistent with values reported for rock salt by others

Gas permeability results. The permeability results from the hydrostatic portion of the triaxial tests are summarized in Fig. 2. For clarity, only three permeability values are given for the hydrostatic loading portion of each test: the initial permeability at 2.4 MPa hydrostatic stress, the permeability immediately after the hydrostatic stress is increased to 14.5 MPa and the final permeability after the stress is held at 14.5 MPa for 10 hr or more. Complete results are given by Stormont [18]. At the initial hydrostatic stress state of 2.4 MPa, the permeabilities of all samples fall in the range of 10-17-10-JSm 2. The increase of the hydrostatic stress from 2.4 to 14.5 MPa causes an immediate decrease of the permeability by about 50%. The permeability typically decreases more than four orders of magnitude in less than 24 hr under a sustained 14.5 MPa hydrostatic stress. In fact, in all but three cases, no pressure changes were detected for some time and the final permeability given represents a conservative upper bound or maximum value. Permeability as a function of hydrostatic stress for a sample subjected to repeated loading and unloading

I

I

I

10 -16

I

10 -17

10 -17

10"18

10-18

10-19

10 -19

10 -20

10 -20

& >., JO

10"21

I! ToA,I rU'lSl TUA16

i Tu*s I TUA8 TUA19

10 -22 0

5

f

I

10

15

Hydrostatic Stress (MPa)

(a)

20

0

10 -21

:

TUA18

I

I

I

5

10

15

Hydrostatic Stress (MPa)

(b)

20

0

I

I

I

5

10

15

Hydrostatic Stress (MPa)

(c)

Fig. 2. Permeability vs hydrostatic stress data from tests on all triaxial samples during hydrostatic healing phase. Three data only are given for each sample: the initial permeability at 2.4 MPa hydrostatic stress, the permeability immediately after the hydrostatic stress was increased to about 14 MPa and the final permeability after the stress was held for some period of time (typically overnight).

10 -22 20

STORMONT and DAEMEN: 1 0 "17

329

GAS PERMEABILITY IN ROCK SALT

,

,

,

,

1 0 -18

hr

At = 10

1 0 -19

g es Ca

D.

At = 5 h r

1 0 -20

1 0 -21 w

1 0 -22 0

I

I

I

!

3

6

9

12

15

Hydrostatic Stress (MPa) Fig. 3. Permeability vs hydrostatic stress data from tests on sample HUA4. Dashed line indicates assumed permeability decrease as the hydrostatic stress was held constant but no permeability test was conducted.

is given in Fig. 3. The permeability decreases upon increases in the hydrostatic stress, and with time at a constant hydrostatic stress. Unloading to previous levels of hydrostatic stress reveals that the permeability changes have both recoverable and non-recoverable components. Comparison of the initial and final permeabilities under the same hydrostatic stress shows large, permanent permeability reductions.

Deviatoric loading results Mechanical results. Typical stress vs strain data are given in Fig. 4. The periodic decrease in the deviatoric stress is a result of the axial strain being held constant for permeability tests, during which the axial stress relaxes. In a few cases, the deviatoric stresses are completely removed. The rock salt strain hardens under all confining pressures. The greater the confining pressure, the greater the deviatoric stress necessary to reach a given axial strain, and the steeper the deviatoric stress vs axial strain response. All the samples dilate; the lower the confining pressure, the sooner the dilation is initiated and the steeper the volumetric strain vs axial strain response during dilation. The stress vs strain response is similar to that reported for comparable measurements [9, 10, 19].

Gas porosity and permeability results. Changes in the permeameter reservoir pressures during deviatoric loading are interpreted in terms of newly created gasaccessible porosity. These results are presented in Fig. 5. The creation of gas-accessible porosity is shown to be a function of confining pressure: the porosity develops at lesser values of axial strain and increases at a greater rate for lower confining pressures. Once communication through the sample is achieved, permeability tests are performed. The gas permeability vs axial strain data are given for similar confining pressures in Figs 6-9. The initial values shown on these figures are from the final measurements during the hydrostatic healing phase and are often below the resolution at the measurement system. The changes in permeability as the samples are axially deformed show consistent trends for the different confining pressures. At 2.4 MPa confining pressure, the permeability increases rapidly until about 4% axial strain, after which only modest increases in permeability are experienced. The limiting permeability is on the order of 10-~4m ~. The permeability increases during tests at 4.1 MPa confining pressure are similar to those at 2.4 MPa confining pressure, except that the limiting permeability is closer to 10-~Sm 2. At 5.9 MPa confining pressure, the

330

STORMONT and DAEMEN: GAS PERMEABILITY IN ROCK SALT

permeability levels off at about 10-17m 2 by 6% axial strain. At 7.6 MPa, the permeability increases at a slower rate with respect to axial strain than at lower confining pressures, and a leveling off of the permeability is not evident. Also, there is more variability in the response at this confining pressure. At the conclusion of many of the triaxial tests, a final permeability test is conducted after the axial stress is reduced to produce a hydrostatic state of stress. These results compare well with the single measurement reported by Peach et al. [4]. They found the gas permeability of a domal rock salt during a conventional triaxial test at 5.0 MPa confining pressure to approach a limiting permeability of 3 x 10-t6m z by about 6% axial strain.

DISCUSSION OF T E S T R E S U L T S

Discussion of hydrostatic loading results The as-received samples possess a small porosity (about 1%) in the form ofcracks, most likely along grain boundaries. Hydrostatic stress permanently closes some

cracks and reduces the porosity to the very low residual value of less than 0.2%. The healing of these cracks affects the sample properties. The bulk or effective compressibility, the inverse of the bulk modulus, decreases as the sample heals. Consider the test results given in Fig. 1. The compressibility decreases after the first substantial hold period (18 hr) as a result of permanent crack closure. The results in Fig. 1 also indicate that the compressibility is a function of the hydrostatic stress even when samples are healed. At low pressures, the compressibility is greater; it tends toward a constant value as the hydrostatic stress is increased. This response, which is typical for many rocks, is attributable to the residual porosity which remains after the sample has healed [13]. These results suggest that the effective elastic moduli depend on the amount of damage (cracks) as well as the stress state, and imply that constant moduli may not be appropriate for rock salt for all applications. The permeability also responds to the decrease in sample porosity. The permeability decreases more than 50% when the hydrostatic stress is increased from 2.4 to 14.5 MPa. For an elastic material containing random

60 7.6 MPa

50

5.9 M P a EL

40 (/)

P N

3o

(la)

0 0

-~

2o 10

-0.02

•/4

MPa

_c

-0.01

¢d

(lb)

h.

E

>0

7.6 M P a

0.00

0.01 0.00

x

I

I

I

0.04

0.08

O. 12

0.16

0.20

Axial Strain Fig. 4. Deviatoric stress and volumetric strain vs axial strain data for tests conducted at four different confining pressures.

STORMONT

and D A E M E N :

G A S PERMEABILITY IN R O C K SALT

microcracks, the permeability (k) and the effective hydrostatic stress (a,) are related by [20]: k y oc log ~,,

(1)

where y is a constant. The exponent y has been derived to be 1/3 [20] and 1/2 [21]. Experimentally, y has been found to be between 1/3 [22] and 1/2 [23]. We found y = 1 best fits our data, indicating that conventional models of rnicrocracks based on elastic contact of opposing crack surfaces are not adequate to describe permeability changes in rock salt. This, in turn, suggests that inelastic processes are significant and probably dominant on the microcrack scale for rock salt. The healing of rock salt is stress- and time-dependent. To investigate the influence of time of permeability, successive permeability measurements were made under nearly-constant applied hydrostatic stress and pore pressure. There are two groups of measurements, those made at about 2.4 MPa confining pressure and those made at about 14.5 MPa confining pressure. Typical data given in Fig. 10 for confining pressures of 2.4 and 14.5 MPa reveal the dramatic influence of hydrostatic stress on permeability changes with time. For the test duration less than 1 hr, a hydrostatic stress of 14.5 MPa 0.03

I

331

induces orders of magnitude changes in permeability. At a hydrostatic stress of 2.4 MPa the permeability changes are much less. Because bedded rock salt is probably subjected to nearly hydrostatic stresses for geologic times, healed samples are most representative of the in situ condition prior to disturbance from nearby excavation. Therefore, we use healed samples for the triaxial tests to make the results most relevant to intact rock salt.

Discussion of triaxial loading results Comparison of inelastic volume strain and gasaccessible porosity. During the deviatoric loading, the samples dilate as a result of the formation of microcracks. The inelastic volume strain is a measure of the dilatancy. If the void volume which is created is well-connected, then the gas-accessible porosity is also a measure of the dilatancy. The inelastic volume strain is determined for each test by subtracting the calculated elastic volume strain from the measured total volume strain during deviatofic loading. An example of the inelastic volume strain and the gas-accessible porosity data is given in Fig. 11. The inelastic volume strain remains near zero for small axial

I

I

Y •1 t I

¢n

2

O Q.

o c = 2.42 MPa:

¢I

,~ t

0.02

0 TUA10 r-] TUA13

oa U~ (/) 0 0

<

G c = 4 . 1 4 MPa:

• • A •

0.01

m

<3

./-" [ ~

-

o-;Z,--;,

...

-~

TUA6 TUA7 TUA8 TUA14

, I

0.00

0.05

0.00

0.10

0.15

0.20

Axial Strain

0.03

l

I

I

I

G c = 5.56 MPa: ¢/3

2

O O.

• TJAt9 0.02 O c = 7.59 MPa:

_= O O O

0.01

-

• I"} A •

TUA9 TUA15 TUA16 TUA18

o 0.00 0.00

0.05

,~'~ /

~ " ~ k ~ _ _.Z~-"

0.10

.A,, . o- . : D

0.15

43

0.20

Axial Strain Fig. 5. Gas-accessible porosity vs axial strain data from all triaxial tests. Data are grouped according to confining pressure.

332

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

strains. In this region, the response is dominated by elastic deformation, non-linear compaction and isovolumetric plastic deformation. In general, this initial response is sustained to larger values of axial strain for greater confining pressures. Eventually, the sample begins to dilate and the inelastic volume strain increases. The rate of dilatancy increase remains farily constant, increasing somewhat as the axial strain increases. The inelastic volume strain and the gas-accessible porosity compare very well. For all tests, the trend of the dilatancy changes as estimated by these two fundamentally different methods are similar. The onset of dilatancy measured by both methods coincides, and the absolute values of the dilatancy during deformation are within about 0.1%. These results imply that the porosity which develops during deviatoric loading is largely interconnected. The connectivity which develops in the samples at very small porosities is consistent with the flow paths modelled as narrow microcracks due to the relatively large probability of the intersection of microcracks when the crack opening is small compared to the lateral dimension [24]. Flow model evaluation. The fundamental difficulty in predicting permeability and permeability changes is a result of the extremely complicated 3-D pore structure of

porous media. It is desirable to find a model which includes the essential nature or character of the pore structure yet is simple enough to be useful. In this spirit, models based on the hydraulic radius concept have been used with some success. The essential feature of these models is that the pore structure is represented by an equivalent channel, which has a characteristic dimension referred to as the hydraulic radius. The particular hydraulic radius model we will use was originally proposed by Wyllie and Rose [25] and subsequently rederived and analyzed by Paterson [24] and Walsh and Brace [26]. The expression for the permeability is given as: m2q~ k = -~- r- ~ ,

(2)

where m is the hydraulic radius of the equivalent channel, b is a constant which depends on the shape of the channel, ~ is the porosity and r 2 is the tortuosity. The hydraulic radius is defined as the ratio of the pore volume to solid-fluid interfacial area. Equation (5) has been reduced to a form involving changes in permeability and porosity [18], the quantities measured during the tests: k oc ~ .

(3)

10-13 Final Measurement Made at Hydrostatic Stress State

10 -14

"'~,

..A

10-15

10-16

i

10"17

10-18

!

10"19

• • •

10 -20 InitialValueRelaruertta

Maximum

TUA10 TUA13

Initial Value

Upper Bound of Permeability

10-21 0.00

I 0.05

I 0.10 Axial Strain

Fig. 6. Permeability vs axial strain from triaxial tests at 2.4 MPa confining pressure.

0.15

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

333

10 "14

10"15

10 -16

¢4

10 "17

=>, J~ 10"18 o.

10"19

• • • •

iI

10 -20 i1 I iI

Initial Values Represent Mnxlmum Upper Bound of Permeability

iI

TUA7 TUA8 TUA14 Initial Value

I

10-21

t 0.00

t

0.05

0.10

0.15

Axial Strain Fig. 7. Permeability vs axial strain from triaxial tests at 4.1 MPa confining pressure.

The exponent x describes how the changes in porosity are manifested as changes in permeability, and is given as:

x = 2a + s.

(4)

The parameter a reflects the relation between the flow path aperture and the porosity: a varies from 0 where changes in porosity are due solely to changes in the crack area per unit volume to 1 where changes in porosity are due solely to changes in the aperture of the flow controlling porosity [27]. The value of s is related to the tortuosity of the flow paths through the sample, s is also known as the cementation factor in Archie's Law relating electrical resistivity and porosity, and has been found to be between 1 and 3 for a wide range of rocks including rock salt [28]. x, therefore, is expected to vary from 1 to 5. This range for x is consistent with empirical relations for changes in permeability and porosity developed for various materials (e.g. [29]). We next consider our experimental results in terms of changes in permeability and porosity. Because porosity increases nearly linearly with axial strain (refer to Fig. 5), the trends for permeability and porosity will be similar to that for the permeability and axial strain given in Figs 6-9. As expected, the data show the general trend of increasing permeability as the porosity develops. The

permeability and porosity changes show a similar response at 2.4, 4.1 and 5.9 MPa confining pressure: permeability increases very quickly from the healed condition (<10 -~ m 2) by many orders of magnitude until it levels off. Further changes in porosity result in relatively small increases in permeability. These results are generalized in Fig. 12 in which the response is divided into two regions. Region I is defined by relatively large permeability changes with porosity. In Region II, the permeability changes are considerably smaller. A transition porosity and permeability can be defined at the demarcation between these regions. The permeability and porosity data have been fit to the two-region model. From the data from all tests at a given confining pressure, a transition permeability and porosity are estimated. The data which fell into Regions I and II are separately fit to equation (3). Results are given in Table 2. The Region I exponent x, the transition porosity and the transition permeability all decrease as the confining pressure is increased. The Region II exponent is near 1 for tests conducted with 2.4 and 4. I MPa confining pressures, and lower for the single test at 5.9 MPa confining pressure. Results from tests at 7.6 MPa confining pressure do not fit the two-region response of the generalized model given in Fig. 12, and were therefore fit with a single equation.

334

S T O R M O N T and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

In Region I, the permeability changes are a function of the confining pressure. At 2.4 MPa confining pressure, the exponent x is near 5 which indicates that both a and s are near their maximum values. As the confining pressure is increased, x decreases. At 5.9 and 7.6 MPa confining pressure, x is nearly 1. This requires both a and s to be near their minimum values, 0 and 1, respectively. The decrease of a with increasing confining pressure indicates that confining pressure suppresses the dilation of the flow paths. Further, the decrease of s indicates that the flow paths are relatively more aligned in the flow direction as the confining pressure is increased. In Region II, a value of x near 1 for confining pressures of 2.4 and 4.1 MPa indicates well aligned flow paths in the axial or flow direction and apertures that do not change appreciably as the sample is deformed further. At 5.9 MPa confining pressure, the Region II exponent is below the lower limit of the flow model. It may be that a simple equivalent channel cannot describe the pore structure of this sample, perhaps because the developing pore structure is non-homogeneous or unconnected. Another explanation is that the confining pressure is sufficiently great so that significant healing is competing with the developing damage. Microcrack model eraluation. To further investigate the connected pore network which develops during

deviatoric loading, we evaluate our results with a simple model of microcrack initiation and growth based on the sliding frictional crack. The sliding or shear crack proposed by Brace et al. [30] has been extensively used as the basis for mechanistic models of rock behaviour (e.g. [31, 32]). Compressive loading induces shear stresses along the crack. With increasing load the frictional strength of the crack is overcome and sliding is induced. Continued loading results in secondary tension cracks initiating near the tips of the sliding crack and propagating sub-paraUel to the maximum compressive stress. The sliding crack is an idealization for most rocks. Horii and Nemat-Nasser [32] suggest the term "microflaw" as a more appropriate description of the sliding crack. Indeed, secondary crack initiation and propagation can be due to a geometric and/or stiffness mismatch between grains, interaction between glide lamella and grain boundaries, a stiff or plastic inclusion, or crystal cleavage in addition to a frictional crack [30, 33, 34]. In most models, it is the propagation of the secondary cracks which are responsible for dilation and ultimately failure, and the existence of actual sliding cracks is not of critical importance. However, the pervasive network of grain boundaries in rock salt may behave similar to sliding cracks. The grain boundaries are known to be weaker than the salt

10"14

Final Measurement Made at Hydrostatic Stress State

10"15

10"16

&-" E

10.17

~J

t~

10-18

/ /

10"19 / 10"20

/

/

/

/

Initial Value Represents Maximum Upper Bound of Permeability

• • 10-21 0.00

I 0.05

TUA19 I Initial Value

m

i

0.10

0.15

Axial Strain Fig. 8. Permeability vs axial strain from triaxial test at 5.9 MPa confining pressure.

0.20

STORMONT and DAEMEN: 10 -16

i

GAS PERMEABILITY IN ROCK SALT

!

335

i

Final Measurements Made

10 -17

Y

I\

o

/'i/7

10"18 &--

g

/

o

10 -19 t~ ¢D

/

.E

/

/

/ /

41'

/

0.

/ / 10 .2o

/

r~

/

/

/

/

/

/

/ / / / /

10 -21

/

• • u •

// Inlllsl Values Represent Maximum / Upper Bound of Pet'mesblllty

TUA5 TUA9 TUA1S TUA16 TUA18 Initial Value

a •

10 "22 0.00

I

0.05

I

I

0.10

0.15

0.20

Axial Strain Fig. 9. Permeability vs axial strain from triaxial tests at 7.6 MPa confining pressure.

crystals themselves and have been shown to part or crack as a result of deformation. Fuenkajorn and Daemen [35] found that samples failed preferentially along grain boundaries during Brazilian tension tests as a result of the lower tensile strength of the grain boundaries compared to the crystals. The dilation during quasi-static compression testing or rock salt has been attributed in part to grain boundary sliding and opening [36]. Spiers et aL [19] and Hansen and Carter [37] directly observed grain boundary dilation on samples which had been subjected to quasistatic compression testing. In addition, during some creep tests on rock salt at low temperatures and stresses, grain boundary sliding and opening has been observed [38, 39]. Skrotzki and Haasen [40] reported that their creep samples first experience some grain boundary opening, and with continued straining develop intragranular cracks parallel to the axis of deformation. If the grain boundaries of rock salt act as frictional sliding cracks, sufficient connectivity may develop through a network of activated grain boundaries (cracked or opened) for the samples to become permeable. Thus, while the existence of sliding cracks may not be critical from a fracture mechanics viewpoint,

it may be fundamental when considering changes in hydraulic properties which result during microcrack initiation and growth. The principal question we seek to address with a simple microcrack model is: are the sliding and dilation of grain boundaries responsible for the development of permeability in rock salt, or is this a result of intragranular secondary tensile crack growth? The basis of the model of microcrack initiation and growth is briefly described below. The resistance to sliding along a microflaw T is given by: T = S +/~a,,

(5)

where S is the intrinsic shear strength of the microflaw, /a is the coefficient of sliding friction and a, is the normal stress across the microflaw. For the axisymmetric loading during triaxial tests, sliding on the microflaw is initiated or activated first on cracks oriented at an angle of 1/2 tan-'(l//~) with respect to the maximum principal stress. The criterion for sliding on the most favourable oriented crack is given by [41]: --

2S + a 3 [ x / ~ + 1) + 1el l) - s,]

(6)

336

STORMONT and DAEMEN: GAS PERMEABILITY IN ROCK SALT

The angles of cracks (/~) with respect to the maximum principal stress which slide at a particular stress are given by [42]:

~=~

+cos-'\~+~-;7~.-~j/J.

tan-'

The above microcrack model was applied to the loading histories of our samples to predict the stresses at which first sliding and then secondary cracking are initiated, and then the secondary crack length as loading continues. The coefficient of friction is taken as 0.7 [44], and the critical stress intensity factor is taken as 0 . 4 M P a / m v2 from the average value for rock salt reported by Atkinson [45]. The intrinsic shear strength of the frictional cracks is assumed to vary from 0 to 1.0 MPa. The initial sliding crack length is assumed to be 1 cm, the nominal grain dimension for our samples. The range of crack orientations which satisfy the sliding criterion and the crack initiation criterion are given in Fig. 13 from a triaxial test at 2.4 MPa confining pressure. These results reveal that if the microflaw is treated as a frictional surface, there will be a region of loading during which only sliding will occur. Continued loading will eventually become sufficient to induce secondary cracks. The "size" of the sliding range, as measured by the difference in axial stress for the sliding and secondary crack initiation criteria for the optimally oriented crack, is independent of confining pressure for this model. The model results in Fig. 13 also show that once the sliding criterion is met, a relatively wide range of crack angles become activated with little additional loading.

(7)

Secondary cracks are initiated when the tensile stresses induced by the overall compressive loading exceed the strength of the rock near the microflaw tip. The criterion for frictional sliding of Kachanov [31] developed from a fracture mechanics framework can be written as: 2klc K

f2 + 2S + ~3[x/~"+ 'V~L

=

+ l)

I) + ~]

(8)

-

where • is a constant, K~c is the mode [ critical stress intensity factor and L is the sliding crack length. The angles of the frictional cracks for which secondary cracks are initiated can be found from equation (7) with 2S replaced by 2K~c/X ( ~ 2 / n L ) + 2S for the criterion given by equation (8), Continued loading extends the length of the secondary cracks. The length of the secondary crack is found from the solution given by Steif [43].

10"16

. . . . . . .

,

.

.

.

.

.

.

.

.

,

.

.

.

.

.

.

.

.

,

e-...~...~

.

.

.

.

.

.

.

.

,

.

.

.

.

.

.

.

2.41 MPa

"----.-...,.,

10"17

oJ vE

>, 'R

=

10-18

.

MPa

0.

lO -19

. . . . . . . .

10 -20

I

A

. . . . . .

,I

. . . . . .

,,I

1

. . . . . .

. . . . . . .

1

10

1 O0

1000

10000

100000

Mean Elapsed Time (see) Fig. I0. Permeabilityvs time data from tests with 2.4 and 14.5MPa hydrostatic stress.

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

337

-0.03

/

I

/

/

P

",// /

-0.02

p,

E

-0.01

_= O :>

0.00

Inelastic Volume Strain Gas-Accessible Porosity 0.01

I

0.00

0.04

m

I

0.08

0.12

0.16

Axial Strain Fig. 1 I. Inelastic volume strain and gas-accessible porosity vs axial strain for test on a sample with a 4. i MPa confining pressure.

"I R e g i o n I

R e g i o n II

6

>-

5

g, .J

3

2

1

Increasing P o r o s i t y Fig. 12. Generalized permeability vs porosity respons¢ during triaxial compression tests on rock salt.

338

STORMONT and DAEMEN: GAS PERMEABILITYIN ROCK SALT

Table 2. Fitting of permeability-porositydata to general form of equation (3) Confining Exponentx Transition Transition pressure porosity permeability (MPa) RegionI RegionII (%) (mr) 2.4 4.73 0.98 l.ol 4 x 10-t~ 4.1 2.85 1.24 0.60 7 x 10-1° 5.9 1.32 0.38 0.42 2 x I0 -t7 7.6 1.08 (NA) (NA)

transition porosity, shown with solid circles in Fig. 14, the calculated secondary crack length at the transition porosity can be determined. These results suggest that the calculated lengths at the transition porosity may not be sufficient to result in an aligned flow network. We next incorporate a residual coefficient of friction in our secondary crack length calculations. Once sliding on the frictional crack has occurred and the secondary crack has been initiated, the coefficient of friction is assumed to drop to a residual value. Fuenkajorn and Daemen [35] found residual coefficients of friction to be 15-45% less than the peak or initial value from direct shear tests on bedded rock salt. We found that a residual coefficient of friction of about 40% of the original coefficient of friction results in a secondary crack length at the estimated transition porosity of between 0.5 and 0.75cm for the range of confining pressures used, perhaps sufficient to result in aligned flow network througout the sample. There are other possible reasons for the relatively short calculated secondary crack lengths. The critical stress intensity factor may be lower than the average value used in the model calculations. The range of critical stress intensity factors for rock salt given in Atkinson [45] includes values 50% less than the average value used for the model calculations. The model calculations ignore crack interaction effects, which may be important for a material such as rock salt which has a pervasive system of grain boundaries which intersect one another. Longer secondary cracks would be

Our experimental results reveal that most samples experience dilation and permeability increases in the calculated sliding region. At the stress state sufficient to just initiate a secondary tensile crack (i.e. at the end of the sliding-only region), all of the samples had begun to dilate and 8 of 10 had measurable permeability. As the secondary cracks grow under continued loading, they become increasingly involved in the flow network as they intersect other activated grain boundaries and secondary cracks. Eventually, they may grow and coalesce sufficiently so that nearly axial flow paths exist through the sample. Could the transition porosity observed in the experimental results be the point at which sufficient axial cracks develop and link? A reasonable estimate for the secondary crack length necessary to create an aligned flow network through the sample may be on the order of one-half to one grain boundary length (0.5-1.0 cm). The length of a secondary crack which grows from the optimally oriented sliding crack is calculated from the experimental data and is given in Fig. 14. From the stress at the estimated 20

i

I

15

10

Frictional Sliding Criterion

o

i

0

I 20

I

I 40

t

60

Angle Between Crack and Maximum Stress, ~ ( ° ) Fig. 13. Application of frictional sliding crack model using loading history of a sample tested at a 2.4 MPa confining pressure.

STORMONT and DAEMEN: GAS PERMEABILITY IN ROCK SALT 60

i

i

I

339

i

o"c = 7.59 MPa o c = 5.86 MPa

|f~¢=4"14MPa

= .41MPa

40

30

X

20

10

I •

0

0.000

I

0.001

!

0.002

I

0.003

Stress at Estimated Transition Porosity I

0.004

0.005

Secondary Crack Length (m) Fig. 14. Calculated secondary tensile crack length as a function of axial stress for tests at different confining pressures. Solid circles denote stress at estimated transition porosity.

predicted for grain boundaries longer than the average i cm length used in the calculations. Fluid pressure in the cracks would reduce the normal stress across both the frictional and secondary cracks, and longer secondary cracks would result. The shorter calculated secondary crack lengths at the transition porosity for the higher confining stresses suggest that these flow networks may include a considerable number of activated grain boundaries in order to be continuous from one end to the other. The permeabilities measured at the end of the deviatoric loading support this concept. For some tests at 4.1 and 7.6 MPa confining pressure, after the permeability is measured at the final (maximum) deviatoric load, and the samples are unloaded to hydrostatic conditions and permeability was measured again. The relative permeability increases upon removal of the deviatoric load are about a factor of 2 for tests at 4.1 MPa confining pressure and more than an order of magnitude for tests at 7.6 MPa. These results suggest that the samples deformed at the higher confining pressures have a substantial component of flow normal to the maximum stress. Because secondary cracks are strongly aligned in the direction of the maximum stress, some activated grain boundaries must be involved in the flow network and secondary axial cracks by themselves are not of the extent and/or RMMS

29i4--B

number to form a continuous network for flow through the samples. Our results suggest that the microcrack model is perhaps more applicable at lower confining pressures. This is not unexpected: frictional sliding and secondary cracking are brittle mechanisms, and ductile mechanisms become increasingly dominate for rock salt as the confining pressure is increased [36]. With sufficient confining pressure, the grain boundaries may more closely resemble plastic inclusions. Another factor which would influence the grain boundary behaviour as a function of the confining pressure is healing; we found the healing rate dramatically increases as the hydrostatic stress increases. Post-test observations. As a first effort at observing the microeracks which develop during quasi-static loading, some samples have been cut open and examined. Samples which have been examined included an as-received sample, a hydrostatically healed sample, a sample from a triaxial test at 2.4 MPa confining pressure deformed to 10% axial strain, a sample from a triaxial test at 4.1 MPa confining pressure deformed to 15%, and a sample from a triaxial test at 7.6MPa confining pressure deformed to 18% axial strain. To highlight visible cracks, a dye is applied to the cut surface.

3aO

S T O R M O N T and DAEMEN:

GAS P E R M E A B I L I T Y IN R-~X~K SALT

The hydrostatically healed sample provides a baseline or ambient appearance. Examination of this sample ( not shown), which had no measurable permeability under hydrostatic stress, reveals no discernable flow paths either along grain boundaries or through secondary tensile (intragranular) cracks. Thus, the sampling process itself (removal of hydrostatic stresses and sawing) does not introduce any visible pore structure. The as-received sample (not shown) is nearly indistinguishable from the hydrostatically healed sample, even though it had a permeability more than four orders of magnitude greater than a healed sample. Therefore, the flow paths responsible for the initial permeability of tile as-received samples are not visible with this technique. The lack of appreciable intragranular cracks in the as-received sample suggests that its permeability is a result of flow along the grain boundaries. Examination of the samples deformed under triaxial conditions reveals a pore structure. At the lowest confining pressure (2.4MPa), dye resides in both intragranular secondary cracks and grain boundaries (Fig. 15). The widths of some secondary cracks are exaggerated due to wedge-shaped chips which formed and fell out along cracks during sawing of the samples. The secondary cracks are strongly aligned parallel to the maximum principal stress (axial) direction. Many secondary cracks on the order of 1 cm long, and are often linked with other cracks to form much longer cracks. The secondary cracks are reasonably uniform throughout the sample, although there are a number of locations where the cracking may be localizing. Many grain boundaries with a wide range of orientations are also stained with dye. The presence of dye in these grain boundaries reveal that they must have dilated considerably because the (permeable) grain

boundaries of the as-received sample did not contain dye. With increasing confining pressure, less secondary cracks and fewer grain boundaries contain dye. The visible secondary cracks are shorter as the confining pressure is increased, At 4. l MPa confining pressure, the number and length of secondary cracks are less than those formed at 2.4 MPa, but still appear to be sufficient to form a continuous path through the sample. Fewer grain boundaries are stained with dye as well. At 7.6 MPa confining pressure, the secondary cracks are relatively short and well isolated from one another, and appear much tess likely to form a continuous network through the sample than the secondary cracks formed at lower confining pressures. Very few grain boundaries accepted dye even though some were probably the dominant flow paths in the sample, suggesting a 7.6 MPa confining pressure is sufficient to suppress their dilation. DISCUSSION

AND CONCLUSIONS

Applying a hydrostatic stress approximately equal to the virgin isotropic stress at the WlPP facility horizon (14.5 MPa) for 10 hr results in large, permanent changes in material properties of as-received samples: the gas permeability decreases from about 10 i'm: to immeasurably small values ( < 0 - ' ~ m : ) , the porosity decreases from an average of about 1 to 0.2% or less, and the compressibility approaches that of individual salt crystals. Collectively, these changes are referred to as healing, reflecting the fact that the hydrostatic stress returns the samples to a condition comparable to intact or undisturbed rock salt. Healing is a result of inelastic, largely non-recoverable reductions in the size and number of connected flow paths along grain boundaries.

Fig. 15. Photograph of a sliced and d}ed sample. This sample was axially strained 10'~,, at a confining pressure of 2.4 M P a

STORMONT and DAEMEN: GAS PERMEABILITY IN ROCK SALT The triaxial tests begin with hydrostatically healed samples. As they are deviatorically loaded, the samples experience a dramatic change in pore structure. For the complete range of confining pressures used (2.4-7.6 MPa), the rock salt samples strain harden and dilate. The dilation as measured by inelastic volume strain compares very well with the independent measurement of gas-accessible porosity, indicating that the developing pore structure is largely interconnected. At all but the greatest confining pressures used, the permeability increases rapidly until a transition porosity is reached, after which only modest increases are experienced. The limiting permeability decreases from about 10 -t4 to 2 x 10 -17 m 2 and the transition porosity decreases from about I to 0.4% as the confining pressure is increased from 2.4 to 5.9 MPa. At 7.6 MPa confining pressure, the permeability increases at a slower rate with respect to the gas-accessible porosity, and a limiting permeability is not evident. F r o m the experimental results and evaluation of the flow model and the microcrack model, we postulate a conceptual model for pore structure changes experienced by rock salt resulting from deformation during shortterm, deviatoric loading. The initial porosity in the samples develops due to sliding along grain boundaries. The lower the confining pressure, the easier it is for the sliding to be accompanied by dilation. At some point, enough cracks become activated so that a connected flow network develops. This network is relatively tortuous, and includes cracks of varying orientation with respect to the maximum stress direction. The lower the confining pressure, the more the cracks dilate under continued loading. During this stage of deformation, the permeability changes more at lower confining pressures. The deformation becomes increasingly plastic as the confining pressure is increased, perhaps such that little or no frictional sliding occurs along the grain boundaries at the greater confining pressures. With continued loading, secondary tensile cracks, induced by the frictional sliding of the grain boundaries, form in the direction of the maximum compression and the induced flow. At low confining pressures, sufficient secondary cracks develop so that they become the predominant flow paths. This point corresponds to a transition porosity, and further deformation of the samples results in only modest increases in permeability. The permeability beyond the transition porosity is strongly aligned in the direction of the maximum compression. The secondary cracks are longer and consequently permit greater flow the lower the confining pressure is. For the greater confining pressures, the secondary cracks may not be sufficient to form a continuous flow network and hence a transition porosity may not be reached. The microcracking which gives rise to the measurable gas permeability and porosity provides irrefutable evidence that rock salt experiences brittle deformation. Most models of rock salt behaviour only considers crystal plasticity as manifested by creep. While creep is indeed important, brittle deformation (damage) has very

341

important implications for both mechanical behaviour (e.g. reduced moduli) and transport properties (e.g. enhanced permeability). Whether treated separately or in a unified approach, the brittle component of deformation must be considered in formulating or interpreting predictive models for the response o f bedded rock salt to excavation. Accepted for publication 23 February 1992.

REFERENCES 1. Borns D. J. and Stormont J. C. The delineation of the disturbed rock zone surrounding excavations in salt. Proc. 30th U.S. Syrup. on Rock Mech., West Virginia University, pp. 353-360 (1989). 2. Guessos Z., Ladanyi B. and Gill D. E, Effect of sampling disturbance on laboratory determined properties of rock salt. Proc. 2rid Conf. on Mech. Behavior of Salt, Federal Institute for Geosciences and Natural Resources, pp. 137-158 (1988). 3. Sutherland H. J. and Cave S. P. Argon-gas permeability of New Mexico rock salt under hydrostatic compression. Int. J. Rock. Mech. Min. Sei. & Geomech. Abstr. 17, 281-288 (1980). 4. Peach C. J., Speirs C. J., Tankink A. J. and Zwart H. J. Fluid and ionic transport properties of deformed salt rock. Commission of the European Communities Report EUR10926, Luxembourg (1987). 5. Donath F. A., Holder J. T. and Fruth L. S. Coupled triaxial testing of rock salt specimens. Coupled Processes Associated with Nuclear Waste Repositories (C.-F. Tsang, Ed.), pp. 627-636. Academic Press, London (1987). 6. Lai, C.-S. Fluid flow through rock salt under various stress states. Ph.D. Thesis, Michigan State University, Ann Arbor (1971). 7. Brace W. F., Walsh J. B. and Frangos W. T. Permeability of granite under high pressure. J. Geophys. Res. 73, 2225-2236 (1968). 8. Wawersik W. R. and Stone C. M. A Characterization of pressure records in inelastic rock demonstrated by hydraulic fracturing measurements in salt. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 26, 613-627 (1989). 9. WawersikW. R. and Hannum D. W. Mechanical behavior of New Mexico rock salt in triaxial compression up to 200°C. J. Geophys. Res. 85, 891-900 (1980). 10. Mellegard K. D., Senseny P. E, and Hansen F. D. Strength and creep characteristics of 100-mm-diameterspecimens of salt from Avery Island, Louisiana. Report ONWI-250 Prepared by ReSpec, Inc., for Office of Nuclear Waste Isolation (1983). 11. Desai C. S. and Varadarajan A. A Constitutive model for quasistatic behavior of rock salt. J. Geophys. Res. 92, 11,445-11,456 (1987). 12. Scheidegger A. E. The Physics of Flow-Through Porous Media. University of Toronto Press (1974). 13. Walsh J. B. The effect of cracks on the compressibility of rock. J. Geophys. Res. 70, 381-389 (1965). 14. Gloyna E. F. and Reynolds T. D. Permeability measurements of rock salt. J. Geophys. Res. 66, 3913-3921 (1961). 15. Aufricht W. R. and Howard K. C. Salt characteristics as they affect the storage of hydrocarbons. J. Petrol. Technol. 13, 730-738 (1961). 16. Wawersik W. R. and Preece D. S. Creep testing of salt-procedures, problems and suggestions. Proc 1st Conf. on Mech. Behavior of Salt, The Pennsylvania State University, pp. 421-449 (1984).

17. Dusseault M. B., Mraz D., Unrau J. and Fordham C. Test procedures for salt rock. Proc. 26th U.S. Symp. on Rock Mech., Rapid City, SD, pp. 118-124 (1985). 18. Stormont J. C. Permeability changes in rock salt during deformation. Ph.D. Thesis, University of Arizona, Tucson (1990). 19. Spiers C. J., Urai J. L., Lister G. S., Boland J. N. and Zwart H. J. The influence of fluid-rock interaction on the theology of salt rock. Commission of the European Communities Report EURI0399, Luxembourg (1987). 20. Walsh J. B. Effect of pore pressure and confining pressure on fracture permeability. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 18, 429-435 (1981). 21. Ostensen R. W. Microcrack permeability in tight gas sands. Sac. Petrol. Engrs J. 26, 919-927 (1983).

342

STORMONT and DAEMEN:

GAS PERMEABILITY IN ROCK SALT

22. Jones F. O. and Owens W. W. A laboratory study of lowpermeability gas sands. J. Petrol. Techaol., 1631-1640 (1980). 23. Rose W. and Sampath K. Measurement of formation characteristics for Western Tight Sands-Quarterly Report, I January to 15 March, Institute of Gas Technology, Chicago (1981). 24. Paterson M. S. The equivalent channel model for permeability and resistivity in fluid-saturated rock--a re-appraisal. Mech. Mater. 2, 345-352 (1983). 25. Wyllie M. R. J. and Rose W. D. Some theoretical considerations related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data. Trans. Am. Inst. Mech. Engrs. 189, 105-1118 (1950). 26. Walsh J. B. and Brace W. F. The effect of pressure on porosity and transport properties of rock. J. Geophys. Res. 89, 9425-9431 (1984). 27. Katsube T. J. and Walsh J. B. Effective aperture for fluid flow in microcracks. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 24, 175-183 (1987). 28. Kessels W., FIentge I. and Kolditz H. DC geoelectric soundings to determine water Content in the salt mine ASSE (FRG). Geophys. Prospect. 33, 436-446 (1985). 29. Dullien F. A. L. Porous Media: Fluid Transport and Pore Structure. Academic Press, New York (1979). 30. Brace W. F., Paulding B. W. and Scholz C. Dilatancy in the fracture of crystalline rock. J. Geophys. Res. 71, 3939-3953 (1966). 31. Kachanov M. L. Microcrack model of rock inelasticity part I: frictional sliding on microcracks. Mech. Mater. 1, 29-41 (1982). 32. Horii H. and Nemat-Nasser S. Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J. Geophys. Res. 90, 3105-3125 (1985). 33. Olsson W. A. and Peng S. S. Microcrack nucleation in marble. Int. J. Rock Mech. Min. Sci & Geomech. Abstr. 13, 53-59 (1976).

34. Wong T.-F. Micromechanics of faultingin Westerly granite.Int.J. Rock Mech. Min. Sci. & Geomech. Abstr. 19, 49-64 (1982). 35. Fuenkajorn K. and Daemen J. J. K. Borehole closure in salt. Report NUREG/CR-5243 prepared by the University of Arizona for the US Nuclear Regulatory Commission (1988). 36. Carter N. L. and Hansen F. D. Creep of rocksalt. Tectonophysics 92, 275-333 (1983). 37. Hansen F. D. and Carter N. L. Creep of rock salt at elevated temperature. Proc. 21st U.S. Syrup. on Rock Mech., University of Missouri, pp. 217-226 (1980). 38. Blum W. and FIeischmann C. On the deformation-mechanism map of rock salt.Proc. 2rid Conf. Mech. Behavior of Salt, Federal Institute for Geosciences and Natural Resources, pp. 7-22 (1988). 39. Wawersik W. R. Alternatives to a power-law creep model for rock salt at temperatures below 16°C. Proc. 2nd Conf. on Mech. Behavior of Salt, Federal Institute for Geosciences and Natural Resources, pp. 103-128 (1988). 40. Skrotzki W. and Haasen W. The role of cross slip in the steady state creep of salt.Proc. 2ridConf. Mech. Behavior of Salt, Federal Institutefor Geosciences and Natural Resources, pp. 69-82 (1988). 41. Jaeger J. C. and Cook N. G. W. Fundamentals of Rock Mechanics. Third Edition, Chapman & Hail, London (1979). 42. Brady B. T. A statistical theory of brittle fracture for rock material, part l--brittle failure under homogeneous axisymmetric states of stress. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr. 6, 21-42 (1969). 43. Steif P. S. Crack extension under compressive loading. Engng Fract. Mech. 20, 463-473 (1984). 44. Bowden F. P. and Tabor D. Friction and Lubrication. Revised Reprint, Methuen, London (1967). 45. Atkinson B. K. Ed. Fracture Mechanics of Rock. Academic Press, London (1987).