THE PERMEABILITY SATURATION
AND NATURAL
OF C O A L
S. V. K u z n e t s o v , V. I. K o s t y u k o v ,
WATER
SEAMS R. I. K r i g m a n , a n d A . N. L e o n o v
UDC 532.546 : 622
To solve many of the filtration problems involved in the mining of coal seams, we need to know their permeability. In this article, using the Derezovka seam as an example, we show that in some cases [1, 2] the filtration volume of the pores of a gassy seam is filled with connate water, and the gas is present only in the sorbed state. Practical methods for determining the permeability of water-saturated coal seams have been suggested. They are based on the use of liquid flow curves recorded at constant pressure in a borehole, this pressure being higher than the sorption saturation pressure, or alternatively on pressure reduction curves, recorded after stabilization of flow at this pressure. The experimental sector was located in the east flank of the take of the No. 8 Gaev Colliery, in the K 3 Derezovka seam, outside the zone of influence of mining operations. The i m m e d i a t e floor and roof of the seam are sandy-clay shale of thicknesses 3.3 and 2.1 m, respectively. From a roadway driven in Zolotarka Kg seam, lying below the floor of this seam at a distance of 10.0 m, five boreholes of diameter 46 m m were driven into and fight through the Derezovka seam normal to the stratification. All the boreholes had measurement pockets, the length of which was equal to the same thickness h (1.35 ram). The dynamics of liquid and gas emission were measured by a system consisting of graduated cylinder, and connecting tubes. From the measurement pocket the water and and microvalve to the graduated cylinder, from which the gas and air-displaced water measuring device; after deducting the volume of water evolved in the given period, the determined from the GSB readings.
a gas-measuring device, a gas passed through a tube were fed to a GSB, gasflow rate of the gas was
The experimental procedure enabled us to assess from our data the natural permeability of the seam i n the experimental sector by different mutually monitored methods: from data of the change in flow and from the curves of pressure reduction in a borehole, closed after stabilization of flow. Using this procedure, after pressure stabilization in ali the boreholes (at 70-71 atm in our case), in one of the boreholes we measured the waterand gas flows at a pressure Pc (regulated by the rnicrovalve), with simultaneous monitoring of the change in pressure in the neighboring boreholes, and then recorded the pressure reduction curve. Figures 1-3 give the results of two experiments in borehole No. 1 at a pressure* Pc of 50 and 30 atm. The curves of pressure reduction at distances of 2 and 5 m from borehole No. 1 (Fig. 3) indicate the presence of a filtration current from the seam into the open borehole. Observation on gas emission in both experiments revealed that evolution of 1 crn 3 of water corresponded to emission of 0.3-0.4 cm 3 of gas. It should be noted that at a methane solubility coefficient a = 3.3" 10 -2 cm ~ and a pressure of ?0 atm, 1 cm 3 of connate water can contain 2.3 cm 3 of gas, i.e., a far greater amount than that emitted from the seam together with water. Similar results were obtained i n the experiment in borehole No. 5, performed at Pc = 30 atm. When the pressure in this borehole was brought to atmospheric, a two-phase current appeared, the characteristics of which are given in Table 1. * The sorption saturation pressure for this seam was about 30 atm. O. Yu. Shmidt Institute of Physics of the Earth, Academy of Sciences of the USSR, Moscow. Makeevka Scientific-Research Institute, Donetsk Region. Translated from Fiziko-Tekhnicheskie problemy Razrabotki poleznykh Iskopaemykh, No. 4, pp. 54-60, July-August, 1973. Original article submitted submitted October 10, 1972.
9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
396
q'cr~-/rnil
r
x
l x
X
X
X
X
IX
X
X
X X
\o 0
0
X
X
X
x
•
-
X
-<
XX
1
o 0
0
0
I oO ]
o
x
xX xx ~x_x x_.R__xx x__~
XXXX
X
o
l
i
o
10
t, h
20
Fig. 1. Results o f measurements o f f l o w rate of w a t e r : 1) at Pc = 50 a t m ; 2) at Pc = 30 arm.
"T"
P~
arm 60
50
,
X
P,,
I
arm
x
xx - X ~ X X~ J;~
7
f 64 2
40 .60
0
20
40
'
f4 h
O
fO
20
SO
t,h
Fig. 3. Curves of pressure reduction in boreholes Nos. 2 and 3 at different distances from N o . l : 1) 2 m at Pc -- 50 atrn; 2) 2 m at Pc = 30 arm; 3) 5 m at Pc = 30 arm.
Fig. 2. Experimental curves of pressure reduction in borehole No. 1 : 1) at Pc = 50 atrn; 2) at Pc = 30 atrn.
Thus the results of observations in the e x p e r i m e n t a l sector of the Derezovka seam at the No. 8 Gaev Colliery revealed that under specific conditions, when the filtration volurne of the pores is filled with water, a one-phase liquid current may be formed. This enables one to use the well-known piezoconductivity equation [3] for c a l c u lations involved in determination of the physical characteristics of a seam from the data of hydrodynamic investigations of boreholes. In the case of an axially symmetric liquid current the equation has the form
asp
I Op
r'-~ o + - 7 0-7 = T
1 ap
(1)
o--i"
399
TABLE 1 .~ . .. . . . . ~ l Flow s rate (q) . .IT i cm/rain i h
I
0,1I 18,0 0,7 1,13 1,~ 2,C 2,5 3,5 4,0 5,0
8,0 7,0 7,0 5,7 5,1 5,3 5,0 5,0 5,0 4,8
743 584 148 137 110 105 97 90 74 69 64
Fl~ rate (q)'l cruZ/rain [
Remarks
I[The t i m e
155 181 226 297 346 370 396 468
4,2 4,0 4,0 4,0 3,7 3,6 3,5 3,5
was ! 45 [reckoned from moment at 32 Ithe | [which the pres. 23 [sure in borehole 18 I No. 5 was brought 18 to atmospheric 17 I6 15
490
3,5
14
--
Here p is the pressure, r is a spatial coordinate, t is the time, • is the piezoconductivity coefficient, k
/1
(2)
+
where k is the p e r m e a b i l i t y of the seam, g is the viscosity of the liquid, m is the porosity, and El and ~ spectively, the moduli of elasticity of the liquid and the seam.
are, re-
The boundary conditions for filtration of a liquid into a borehole of radius r 0, where a constant pressure Pc is maintained, ensuring one-phase flow of the liquid, are written thus:
Pl,=,o =
Pit=0 = Po;
Pc;
pl,=o~ = P0.
(3)
The e x a c t solution of Eq. (1) for conditions (3) is represented as a series, or in terms of integrals of c y l i n d r i c a l functions. Thus the equation for the overall yield of a borehole operating at a constant face (bottom) pressure has the form [4] Q (t) ::: 2~r2oh ( P o -
k Q,
P,,) -~,
(x),
(4)
where 4 c~
Q* (~)
I .... e- u~x
=-= ~ 9 7~--'-7-~-2 du "-~ o .~ [j~ (u)-r- v0 (,,)
(5)
is the dimensionless overall yield, T is the dimensionless time, x__fi~ t . o , %
(6)
J0 and Y0 are zero-order Bessel functions of the first and second series, respectively, and u is an i n t e g r a t i o n v a r i a b l e . Krigman [5] obtained a simple approximate equation for dimensionless overall yield; it has the same asymptotic form as exact equation (5):
Q;
(~) -
398
,n(l+ # )
(7)
As shown by Krigman [5], the error in calculations using this equation, in comparison with that of c a l c u l a tions from the exact equation, performed by Van Everdingen and Hurst [4], for r values in the range 10-2-10 -z2 is less than 1.6%. Equation (7), which is a very good approximation for the integral function of dimensionless flow, can be used to solve the reverse problem: to determine the filtration properties of a seam from data of the change in the overall y i e l d of a borehole. By Eqs. (4), (6), and (7) we get k
.o~a (po - Pc) T
e
O (t) = ln(1 ~ For the two values tt and t 2 and their corresponding Q(q) and Q(t2), we get
In (I -r- a l/-~) = C, In (1 + b V~.)
(9)
where a -- V~.~.
b - - 1/~-7~. 2ro '
2to '
C
Q (tl) t2 Q(t2) t l "
(10)
Solving Eq. (9), we determine the piezoconductivity )r and then find the p e r m e a b i l i t y of the seam, k, from Eq. (8). At fairly high values of t, d e t e r m i n a t i o n of the required characteristic is simplified because the unit below the sign of the logarithm can be disregarded. From Eq. (8) we have
t
Q (t)
_
g
4 n h (Po - - Pc) k
(In a---LZ-i-In t). \
4ro2
]
(11)
Converting to c o m m o n logarithms, we get
Q (t)
h (pope) k
This gives a linear graph t / Q ( t ) vs log t. From the slope iQ of the linear sector which reaches the asymptote, we can readily determine the seam p e r m e a b i l i t y from the equation
iQ:=Lt(p0 -Pc) k - - d t l g t )
(13)
Hence k
0.183 - - h (Po - - Pe)iQ
(14)
Note that i f [Q(t)] = m 3, It] = h, [tl] = m, and [p] = atm, from Eq. (13) we readily see that [ k / g ] = m2/h 9 atm. Bearing in mind that the viscosity of water g = 1 cP, the seam p e r m e a b i l i t y k, expressed in millidarcy, is obtained by multiplying the value ( k / g ) ( m 2 / h 9 atm) by the conversion f a c t o r n =
-
103.10 ~ = 2.78- 10 ~. 3600
(15)
For mutual monitoring we used the method of determining the p e r m e a b i l i t y of a seam from the pressure reduction curve in a borehole, closed after a fairly prolonged period of operation under steady conditions at a pressure Pc. The e x p e r i m e n t a l data were processed by the method of Herner [6], which takes account of the period elapsing from the beginning of operation to abandonment of the borehole, i.e., the period of evolution of water
399
from the seam at a pressure Pc- According to this method, the increase in pressure in the borehole, p(t), for fairly high values of t is interpreted by the equation r'~
~1~4
p ( t ) = p o - - O . 1 8 3qo,ttl_T ~ . ~ . ~t [ '
i
where q0 is the steady yield of the borehole before closure; T and t are, respectively, the duration of influence of the borehole before and after abandonment. In the coordinates p(t) and log t / ( T + t), this dependence is represented by a straight line with a slope of
2 0
0,4
0,8
(16)
l.gt
Fig. 4. Overall flow of water from borehole No. i vs time, expressed as a graph of t/tQ(t) vs log t.
ip = 0 183qdx kit
'
(17)
arm from which the value of the permeability k is determined. By extrapolating the line until it meets the axis log t ~ T + 0 = 0, corresponding to t = *% we get the value of the steady pres-
70
sure P0.
pc =5 o
r •215
o
SO
i
J
J
•
•
3o-2
- I,~
- ~,o
0
-0,5
Let us calculate the permeability of the seam i n question from the field data. Figure 4 shows the experimental data obtained in both experiments on the variation of the overall flow of water, represented as a graph of t / Q (t)vs log t. It will be seen that for the first experiment the points are located fairly close to a straight line, the slope of which, iQ, is 2.13"10 3 h / m 3. Substituting this value into (14), we get
log?-~7 0,183 =0297. - - 1.35.(71.4 -- 50) 2.13- 10:'
k __
Fig. 5. Pressure reduction in borehole No, 1, plotted in the coordinates p ( t ) - l o g t / ( T + t).
10 -5 m e / h " atm
or k = 0.82" 10 -2 mdarcy.
From the measurements in the second experiment (at Pc = 30 atm) we get iQ = 1.30.103 h / m s. Hence from Eq. (14) we get k =
0.183 = 0.252.10-5 '1".35(71.4--30 ) 1 3 0 . 1 0 z
m2/h"
arm,
whence k = 2.78- 103. 0 . 2 5 2 . 1 0 -5 = 0.70, 10 -2 mdarcy. For the case when Pc was 50 atm, the calculations were performed from Eqs. (8) and (9). The value of the permeability was again 0.82-10 -2 mdarcy. To determine the permeability from the pressure restoration curves, in accordance with Eq. (16) the experimental data were again plotted as a graph of p(t) vs log t / ( T + t). The value of T in experiments 1 and 2 was, respectively, 26 and 39.6 h. It will be seen from Fig. 5 that the slopes of the linear sectors of the converted pressure restoration curves for the first and second experiments are, respectively, 7.8 and 13.0 attn. From Eq. (7), when ip = %8 atm, q0 = 2.5 cmS/min = 1.50- 10 -4 mS/h (see Fig. 1), we get k 0.183.1.50-10-4 ~---0.262.10 -5 m 2 P a ' a t m , 1x - 1.35-7,8 whence k = 2.78 -103 . 0.262 9 1 0 - 5 = 0 . 7 3 9 10 -2 rndarcy. Similarly, for the conditions of the second experiment, substituting into Eq. (17) ip = 13.0 arm and q0 = 3.5 cmS/ rain = 2.1" 10 -4 mS/h, we get k = 0.61.10 -2 mdarcy. In both cases, by extrapolating the straight lines in Fig. 5 we find that the seam pressure is 72 atm, which agrees satisfactorily with the experimental value P0 = 71.4 atm.
400
The permeabilities of the seam determined by different methods are fairly close. The results lead us to recommend these methods of determining natural permeability for gassy coal seams in which the filtration volume of the pores is filled with connate water. These methods can be used in cases when the measured amount of evolved gas does not exceed the maximally possible amount of dissolved gas at a borehole pressure greater than or equal to the sorption saturation pressure, which indicates that the entire filtration volume is filled with water and that.we are justified in regarding filtration as one-phase. To ascertain that this is actually the case, i n any d e t e r m i n a t i o n of coal-seam permeability the amount of water evolved must be determined.
LITERATURE CITED 1. 2. 3. 4. 5. 6.
S.V. Kuznetsov, in: Dynamics of a Cor~inuous Medium [in Russian], Vol. 6, Nauka, Novosibirsk(1969). S.V. Kuznetsov, Fiz.-Tekh. Probl. Razrabotki Polezn. Iskop., No. 4 (1971). V.N. Shchelkachev, Working Oil- and Water-Bearing Beds under Elastic Conditions [in Russian], Gostoptekhizdat, Moscow(1959). A.E. Van E'verdingenand W. Hurst, Journal of Petroleum Technology, _I, No. 2 (1949). R.N. Krigman, Izv. Vuzov. Gornyi Zhurnal, No. 8 (1970). C.R. Herner, "Pressure build-up in wells,= Third World Petroleum Congress, PrOc. Sec. 11 (1951).
401
