ROCK

PERMEABILITY

UNDER

UNEVEN

COMPRESSION

A. V. M i k h a l y u k

Provlsion for reliable circulation of an intermediate working fluid in a system of cavities in the enclosing rock mass is one of the elements of shaflless mining technology. Such fluids can be acid solutions (leaching of lean ores, hydraulic acid hewing), cold (tappLng of geothermal energy) or hot water (underground melting of sulfur, elevation of fluidRy of viscous petroleums and bRamens), and other Iiquids and gases which are either integral elements of the technology or its products (industrLal and municipal waste). The large scale of modern mLnlng necessitates substantLal quantRies of working fluLds be used in the geotechnical process and a hLgh rock permeability whose natural level generally does not ensure the necessary productivity of the mining systems. In view of the development of shaRless mlnLng technology, m u c h attention is being paid to the techniques of directed rock preparatLon for minLng tn order to faLse the rock permeability to the desLred level. In general, rock permeability can be raised artLficially by creating a network of macrocracks. However, Ln usual techniques of impact on a rock mass, spatial growth of macrocracks is limited: in underground explosions the rupture zone does not spread beyond 18-20 radii of the charge; the length of the perforatLon channels in gun and ctunulatLve perforation does not exceed several scores of centimeters; in hydraulic fracmrLng the cracks extend by scores of meters, but they are rare. Therefore, the study of the conditions wh Lch permit elevation of rock permeabLILty to the limiting level (to the macrofracturing state) deserves special attention. Such condttLons can be created by uneven spatial compression of the rocks when theLr Lntergranular cavities grow LrreversLbly due to dllatatLonal loosening [1-4]. For instance, it was shown in [5] that rock permeability can be raised by uneven compression by an order or more; two- to fourfold increase (includLng 35-40% Lrreversible increase) of permeabLIity was recorded in [6-8]. The experiments were performed with a limited number of rocks in an uneven stressed state varying in the course of the experiment. This dLd not permit necessary generalLzations. To establish the general features of correlation between dilatational rock Loosening on uneven compression and the varlatLon of rock permeabLlity in a constant stressed state, experiments were performed according to a scheme not basically different from that described in [6], but instead, of a gas (argou), the movement of a liquid (kerosene) was studLed Ln the sample. The flow dingram of the experiments is shown in Fig. 1. The test sample i with a height h = 73-76 m m and a diameter d = 40 nun was put in the chamber 2 simLlar to the one described in [3]. The inlet of the saturating solution 3 was at the base of thLs chamber. At the top and bottom the sample had hLghly permeable pads 4 which facilitated creatLon of a plane filtratLon flow Ln the sample. For hydraulic insulation of the sample from the liquid (oLl)that developed a lateral stress, the padded sample was pat Ln a 0.2-mm-thLck beryllium bronze jacket. The axial stress was developed by a hydraulic press, and the lateral stress, by an NSVD-2500 high-pressure pumping unit; the saturating liquid was fed from the pressure acctunulator 6. The pressure of the compressing and saturating liquid and of the gas (nitrogen) in the accumulator was monitored by the manometers 6. The pressure dLfferenttal in the liquLd at the entry into and exit from the sample was Indicated by the differentLal manometer 7. The readings of the manometers were converted by the transducers 8 into electrLc signals recorded automaticaUy on an N-115 loop oscillograph. In view of the fact that steady ILquLd filtration does not starts instantaneously, but after a significant lapse of time (up to several hours), the experiments were performed under statLc stresses. Until the time when the sample attained mechanLcal equilibrLum under external Impact, the ILquid pressure in the sample pores was kept equal to the atmospheric pressure (the valve 9 of the saturating hydrosystem was closed). After completion of the deformation process registered by the clock-type indLcator i0, valve 9 was opened, and this produced in the sample a pressure differential, whLch was recorded by the differential manometer 7. The permeabL1ity of the sample was calculated by the equatLon [9]:

kp = Qh_~p[darcy],

(1)

Institute of Geophysics, Academy of Sciences of the Ukraininan SSR, Kiev, Translated from FizikoTekhnlcheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 24-29, March-April, 1983. Original artLcle sabmitted November 4, 1981.

0038-5581//83//1902 - 0115507.50 9 1984 Plenum Publishing Corporation

115

Fig. 1. Flow diagram of m e a s u r e m e n t of r o c k permeability under uneven compressLon. TABLE

1 m"

Rocks ,q

Medium-

Sra.~d sun.tone

Anhyddce $ilr~to~e Sulfur ore

2,39 2,90 2,58 2,36

9,0 2,0 5,4 4,3

3,68 4,55 3,26 2,43

0,13 8t2 2,74 0,30 0,i9 2,86 0,29 329 i,~O

7,6 t,l 4,0

tt,2--16,t 0,4--0,9

4,7--4,9 1,4--8,7

2,3

8,0

i6,5

ii,O I0,5

0,08--0,30

0,01~--0,04 0,(~--0,15 0,06--0,10

where Q is the volume liquid flow rate, cmS/sec; h, s a m p l e height, era; 7, cosffLcient of dynamLo v i s c o s i t y of the saturating liquid, cP; oJ, c r o s s - s e c t i o n a l a r e a of the sample, cm2; Ap, p r e s s u r e differential, k ~ / c m s. The quantltLes h and co depend on the sample size, and ~ is the certified c h a r a c t e r i s t i c of the saturating medium. F o r calculations by Eq. (1) Lt is essential to know the rate of liquid flow through the s a m p l e at a given Ap. This flow r a t e can be determined f r o m the nLtrogen expansLon in the p r e s s u r e a c c u m u l a t o r (the p e r m e a bilLty was m e a s u r e d a l t e r the c o m p r e s s e d gas attained thermodynamic equilibrium with the surrounding m e dium). Since the nLtrogen p r e s s u r e varLatLon in the a c c u m u l a t o r was small, the nitrogen t e m p e r a t u r e during the kerosene flow was practically constant. This m a k e s it possible to r e g a r d the uitrogen expansion p r o c e s s in the accumulator as isothermal. Then, based on the Boyle--Mariotte equation, the i n c r e a s e in the gas volume in the accumulator and hence also of the volume of k e r o s e n e flow will be

AV= Vx--Vo= Vo(~--t)

C~"~

(2)

where V 0 and P0 a r e the initial volume and p r e s s u r e of nitrogen at the Lnstant of openLng of the v a l v e 9; Vt and Pt are the volume and p r e s s u r e of nitrogen at the moment of the m e a s u r e m e n t s . If the s u c c e s s i v e m e a s u r e m e n t s were made after t seconds, then -T" "~ - ' / -

-- i

ictus/tool.

(3)

The p e r m i s s a b l e conditions for u s l ~ Darcyts l i n e a r filtration law for caloulatL~ r o c k p e r m e a b i l i t y w e r e checked by comparing the speed of the saturatLng liquid flow through the sample during the t e s t s with a c r i t i c a l speed Vcr which delimits the lamLnar and turbulent flow regLons. The vor value was determined by the MillLonsheh[kov and Shchelkachev equations [9] relyLng oa the r o c k p r o p e r t y data. Its values (in m / s e e ) a r e listed in T a b l e 1, along with the r e c o r d e d p r e s s u r e differential lap, Pa) and flow r a t e (Q, cm3/sec) data. Simple c a l c u lations show that under the experimental conditions the actual flltratLon r a t e was lower than the crLtLcal b y t h r e e o r d e r s . This indicated that the use of Eq. (1) f o r analyzing the experLmental data Ls justLfied. The r e l a t i v e e r r o r in permeabLlity determinatLoa was calculated by the procedure recommended in [10] and was 9 3.48%. The rock permeability experiments w e r e p e r f o r m e d under dilatational l o o s e n l ~ conditions with m o d e r ately strong m e d i u m - ~ r a i n e d sandstones, an~ydrites, sLltstoaes, and sulfur ores containL~ N 30% elemental sulfur. Brief information about the average mechenLoal and filtration p r o ~ r t L e s of t h e s e r o c k s in t h e i r natural

116

p-p,, tO8 Pa

p-q ,#i>,

I I I,0

2.,o

\

1,0

o,,

O,F

o

-l,o

-0,5

Fig. 2

o

3,0

1,5 3,o

0,5 @l~

o -1~o

2,0

'

-0,5

0

0~%

Fig. 3

Fig. 2. Dllatational deformation and variation of permeability in sandstone under uneven compression: ~ = 0.08 (1);0.12 (2); 0.2 (3); 0.5 (4). F i g . 3. DLlatational d e f o r m a t i o n a n d v a r i a t i o n of p e r m e a b i l i t y in a n h y d r i t e u n d e r u n e v e n c o m p r e s s i o n : ~: = 0 . 0 4 (1); 0.15 (2); 0.4 (3).

state is given in Table 1, where, In addLtLon to the designatLons known already, the following designatLons were adopted: density p, kg/mS; porosity n, %; velocity of elastic waves Vp, m/sec; Potsson's ratio v; ultimate strength in unaxlal compression q0, Pa; ~onng's modulus E, Pa; natural permeability l~p, darcy. In the experiments the axial pressure ql, lateral pressure q3, and pore pressure pp reached 2.5 9108, 8 9107, and 3" 107 Pa, respocttvely. The natural permeability of the samples was determined by the method described above, but the unstressed sample was placed in a rigid impervious holder. T h e experiments were performed at a constant nonnnlformRy of the stressed state, which is characterized by the coefficient ~ = q~/ql, where ql and a q are the m a x i m u m and m i n i m a m principal stresses. The ~ value varied from 0.04 to 0.5. The total mtmber of experiments was 22. In Figs. 2-5, where the volume deformation e is plotted against the effective average normal stress, equalIng the difference between its absolnte value p and the ~ r e pressure pp, the solid lines represent the volume rock deformation under uneven compression. The dashed lines represent the corresponding variation in the permeablilty of the samples (for generalization, the experimental permeability data are presented as a ratio of the carrent permeability kp to the InRial permeability l~p). A n analysis of the curves will show that the direction of the deformation process under uneven compression decisively affectsthe permeabliRy of the deformed rocks. If the rock deformation proceeds toward compaction, the rock permeability diminishes, this being faster the greater the volumetric rock compressibility. The Irreverslbillty of rock compaction is accompanied by irreversible diminntion of rock permeability. For instance, the permeability diminishes irreversibly by 51% in sandstones (Fig. 2, curve 4) at the irreversible dilatattonal deformation component 0 i = 0.75 910 -3 (0.83c~ of total porosity), by 25% in anhyctrites (Fig. 3, carve 3) upon Ixreversible compaction of 0.25-10 -3 (1.25c~ of total porosity), by 27% in siltstones (Fig. 5, curve 3) at 0 i = 0.15%, and by 40% in sulfur ores (Fig. 4, curve 3) at 8 i =

0.125% Where uneven stress facilitates dllatationalloosening, the rock permeability rises Ixrevers ibly to a considerable extent. In this case, ifthe deformation process suddenly proceeds toward loosening, the rock permeability rises with the start of deformation (Figs. 2, 3). If at the initialstage of the process a compaction region appears due to partial decrease of microfissuration [3],then the relative permeability also decreases initially. The m i n i m u m sample permeability generally coincides with the m a x i m u m compaction. But it is restored with the initiationof dtlatattonal loosening much faster than what Is expected from the deformation process. For instance, in sulfur ores and slltstones a permeability higher than the natural is observed at a dflatatlonal deformation 20-40% lower than the deformation on m a x i m u m compaction over the duration of the process; In this case, the test sample occurs in a state of compaction. A similar phenononon was observed in [6]. W h e n the resttltLngdliatationaldeformation in the sample under uneven compression reduces to zero (Figs. 4, 5), the sample permeability exceeds the natural value by 15-25%. Further loosening facilitates rapid rise In sample permeability. Despite the fact that in the experiments the m a x i m u m stress on the sample did not exceed 117

p--,O]), lO a Pa p-pp I0 r p,,

h

3,0 l,V

~.,0

0,5

0 -0,5

o,5 e,~

o

0,5 o

-I,o

Fig. 4

2~

~ I,o

-0,5

o

e,~;

Fig. 5

Fig. 4. Uneven compression of sulfur ore and permeability variation in the ore on compression at ~ = 0.1 (1); 0.2 (2); 0.5 (3). Fig. 5. Uneven compression and variation in permeability of stltstone: = 0.05 (i); 0.15 (2); 0.3 (3). (0.8-0.9)~0 with due regard for lateral and pore pressure, upon m a x i m u m loosening the permeability rose b y 3.1-3.7 times in sandstones, 2.42-2.9 times in s{Itstones, 2.4-3.8 times l, aahydrites, and 1.6-2.0 times in sulfur ores. For comparison, w e mention that upon m a x i m u m loosening the permeability rose by 2.54-2.9 times [6], whlch stands close to the data cited above. In sandstones the permeability was found to riae due to dtlatational loosening even after the s t a r t of the s t r e s s . As can be seen from c u r v e s 1, 2 in Fig. 2, the permeability was maximum at a dllatational deformation = - 0 . 7 ~ , which is 24.3-40.2% less than the deformation that corresponds to maximum loosening. In one experiment in [6] the maximum permeability of granites was noted at a dilatational deformation which Is 35.1% lower than the deformation on maximum loosening. F r o m a comparison of Figs. 2-5 in conjunotlon with [6] it can be concluded that the permeability rises a little a f ; e r the start of the s t r e s s in rocks with heightened c a p a c ity for dilatatlonal loosening. In weak, porous rocks the permeability falls immediately with the start of the w[thdrawal of s t r e s s . From an analysis of the c u r v e s in Figs. 2-5 t~ follows that under uneven c o m p r e s s i o n the rock p e r m e a bility depends oa both the type of the s t r e s s e d state and the magnitude of the s t r e s s . We will consider this dependence as a correlation between the relative variation in sample permeability per unit of the maximum effective average normal p r e s s u r e

kp//~

attained In the experiment and the coefficient of uneven s t r e s s i n g

(Fig. 6). Curve 1 is constructed for permeability values corresponding to the maximally attained average normal p r e s s u r e Pm, and curve 2, for irreversible kp values. As can be seen from Fig. 6, the points representing the experimental data for four types of rocks can be grouped satisfactorily around the respective c u r v e s . This makes it possible to propose, for predictive calculations, amathematlcal expression for the dependences being cons ldered, obtained by the l e a s t - s q u a r e s method: for sample permeability on maximum stressing kp = 7.42.t0-ek~ (p,, -- p~ exp (-- 7.795{;);

(4)

for irreversible sample permeability = 5,495.10-'k

(p. - pp),=p ( -

(s)

where Pm and pp are expressed in Pa. In comparing curves 1, 2 in Fig. 6, attention should be paid to the fact that the maximum permeability exceeds the irreversible permeability only in the vase of dllatattonal loosening (in Fig. 6 at ~ < 0.25-0.30). Where the volumetric r o c k deformation is oompacttonal, the sample permeability corresponding to the maximum s t r e s s is lower than the i r r e v e r s i b l e .

118

~P/k~. foS pa-1 p.,-epp "

o

0,2

0,4

Fig. 6. Correlation of the ma~dm~l (1) and i r r e v e r s i b l e (2) variation of the p e r meability with the quantity P m - Pp and the unevenness r of stressing. The foregoLng makes it possible to draw the following conclusions: Uneven stressed state and intense stressing decisively affect rock permeability variation in the deformation process due to dilatatLonalrock loosening. Dllatatiorml rock loosening makes it poss [bleto raise rock permeability severalfold Ln the prelimitLng state (untLlmacrofracturlng), the rise being irreversible to an appreciable extent. This can be used for developing devLces and techniques of directed rock-massif preparation for extraction of minerals by geotechnical techniques. LITERATURE 1. 2. 3. 4. 5. 6. 7. 8.

9. 10.

CITED

A.N. Stavrogin, "A study of ILmitLng states and deformatLon of rocks," Izv. Akad. Nauk SSSR, FLz. Zeml[, No. 12, 3 (1969). A.V. Fadeev, "Rock strength under uniaxLal and unis compressLon," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1969). A.V. MLkhalyuk, "Peculiarities of deformatLon and strength characteristics of rocks under uneven volumetrLc d y ~ m L c loads," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1979). A.V. MLld~alyuk, Rocks under Uneven DynamLc Loads [in Russian], Naukova Dumka, Klev (1980). A.N. Stavrogin and A. G. l>rotosenya, Rock Plasttclty [in RussLan], Nedra, Moscow (1979). M . D . Zoback and J. D. Byerlee, "Effect of microcrack dUatancy on the permeability of Westerly granite," J. Geophys. Res., 80~ No. 5 (1975). W . F . Brace and A. S. Orange, "Electrical resistivitychanges Ln saturated rocks during fracture and frictionslsliding," J. Geophys. Res., 7_33,No. 4 (1968). N.N. Pavlova, A. A. Fomin, and E. T. Davydov, "BeversLble and Lrreverstble changes in porosity and permeability of rocks at dtf.fereutvolumetric stressed states and temperatures," in: Physical Properties of Rocks and Minerals at High Pressures and Temperatures [in Russian], Mitsnlereba, Tbflisi (1974). V . M . Maksimov, V. D. Babushkin, N. N. VerLgin, et al., Handbook for Hydrogeologists [Ln Russian], Vol. I, 3rd roy. and enl. ed., Nedra, Leningrad (1979). V.N. Kobranova, B. I. Izvekov, S. L. PatsevLch, and M. D. Shvartsman, Sample-by-sample Determination of Petrophysical Characteristics [in Russian], Nedra, M o s c o w (1977).

119