Continuous adsorption pumping

Cryogenics 36 (1996) 119-121 0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 001 l-2275/96/$15.00 ELSEVIER

Continuous

adsorption

pumping

M. Yu. Liburg Laboratory of High Energy Physics, Joint Institute for Nuclear Research, Dubna Moscow region, RU-141980 Russia Received 20 June 1995 A new scheme for an adsorption pump is proposed. The vacuum pump is designed to operate with respect to a rigidly determined four-stroke closed cycle which consists of two isotherms and two isosteres. It is shown that routine information about the thermodynamic properties of the adsorbent is required for detailed calculation of the operating characteristics of the continuous adsorption pump (CAP). Some design peculiarities, such as a small difference in the temperatures of the adsorption and desorption processes, the adsorbent positioning and the method of adsorbent heating, together are expected to provide a pumping capacity for a CAP which is comparable to that of a Roots pump. Keywords: adsorption

pumping;

thermodynamics;

Adsorption pumping involves the technical use of the high adsorptivity of some materials such as activated charcoal, silica gel, etc. It is an attractive method for experimental situations where it is desirable to avoid the injurious effects of conventional pumps 2 4. Nevertheless, to date adsorption pumps have not been widely used in cryogenic set-ups because of the low capacity realized. The reason for this is as follows. A scheme of adsorption pumping-out suggests two different regimes: isothermal adsorption under a temperature Tl and an adsorbent regeneration stage under a temperature T2. In order to obtain a suitable efficiency of a pump, one attempts to enlarge the amount of gas adsorbed during the cycle by increasing both the total mass of adsorbent and the difference T2 - T,, moves which, together with the traditional method of adsorbent heating, increase the necessary time of the operating cycle. The aim of the present paper is to discuss another approach to the problem based on a new design idea. The approach will be formulated at a preliminary level, and then the scheme of an adsorption unit will be described. To generalize the description, a thermodynamic consideration is undertaken. Numerical examples will demonstrate that the obtained analytical expressions can be used as working formulae for calculating the parameters of a continuous adsorption pump (CAP).

Design

continuous

adsorption

pump

heated by the method, excluding the influence on the coolant so that there plete removal of the latter. Realization one to obtain fast-acting pumping-out

Adsorption

possibility of direct is no need for comof the CAP permits facilities.

unit

Let adsorbent 1 (Figure 1) be glued on an outer surface of a metallic vessel filled with coolant 2. A hermetic volume A is equipped with inlet 3 and outlet 4 valves. The electromagnetic field, excited inside A, has a maximum electrical component on the spot of adsorbent 1. The operating closed cycle (Figure 2) consists of two isotherms l-2, 3-4 and two isosteres 2-3,4-l. Point 1 characterizes the adsorbent state of lowest pressure and the least amount of adsorbed gas. If valve 4 is closed and 3 is opened, the gas comes from the evacuating volume, the state of the adsorbent being changed along the isotherm l-2. At point 2 the valve is closed and the electromagnetic field excited in A (Figure 1) heats the adsorbent. At the end of stroke 2-3 the adsorb-

concept

The CAP is suggested to operate with respect to a closed cycle which consists of two isotherms T, and T2 and two isosteres. The working region of each isotherm is that of a maximum slope, the difference T2 - T, being as small as possible. A relatively small amount of adsorbent can be

Figure 1

Schematic

Cryogenics

diagram

of adsorption

1996 Volume

unit

36, Number

2

119

Continuous

adsorption

pumping:

M. Yu. Liburg 78K

-

’

Numerical values of the partial derivatives of an adsorbent’s volume V(P,T) can be determined from the family of adsorption isotherms, the latter being general experimental information satisfactorily described by the theory. For W, one can write the following

\

10 -

7

En .

-

5

_

W,=Cj,=qmh+Qma

L

(4)

where a is the number of moles of the adsorbent per mass unit of adsorbent (see Figure 2). As can be shown, 4 = 0 for the isotherms presented in Figure 2. For the steady isothermal process 3-4 it is easy to obtain from Equation ( 1)

Tj

T - T, = ( W,, - q,malt,)llh I

Figure 2

I

I

0.1

1

Family of adsorption

I

I

10 100 PlPal

(5)

I

1

1000

and the same for l-2

isotherms

T- T, = (q,malt,)NA

ent is transferred to state 3, the point belonging to the other isotherm. During stroke 3-4 valve 4 is opened and the desorbed gas is evacuated by an outer pump. At point 4 the electromagnetic heating is off and both valves are closed, the state of the adsorbent being changed along 41. What is above termed a CAP is a combination of four units with different strokes carried out at the same time. The nitrogen adsorption isotherms for charcoal presented in Figure 2 are calculated on the basis of the appropriate theory confirmed by experimental data’.

(6)

where t, is the time of the stroke and q1 and q2 are calculated from Equation (3) for the corresponding isotherm. The equation for the 2-3 and 4-l strokes is nonlinear in the general case. But when q(T) is a continuous function inside the region under consideration, there is the opportunity to simplify the task. The approximate equation is given by p(mc + cz) + r)( AA + p) = W,, + T&l

(7)

where cr = ma(q,lT,

+ qzIT2)/2

Calculations and Let the adsorbent be spread homogeneously enough over surface 1 so that its mass per unit area m and the depth of layer E are assumed to be constant. The other parameters of the adsorbent such as heat conductivity h and specific heat capacity c are assumed to be known. The total heat flow W(t) changes the temperature T of the adsorbent and is partly transferred to the coolant at temperature T,; thence the heat balance equation is given by

Finally,

?‘mc + (T - T&I/l = W(t)

where 8 = (mc + a)/( A/I + /3) and To is the temperature the adsorbent at the beginning of the stroke.

(1)

where W(t) = W,, + W,, i.e. it consists of ted with the electromagnetic heating of the heat of adsorption, respectively. The specific heat of adsorption 4 is with the help of the Clapeyron-Clausius

two parts connecthe adsorbent and usually calculated equation

dP q = T(v”- v’) z where v” and v’ are the molar volumes occupied by molecules of the gas and adsorbed phases, respectively; derivative of pressure P with respect to the temperature being calculated along the phase equilibrium curve. In case under consideration, v” >> v’ and by changing variables Equation (2) is transformed to a formula further calculations given by

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1996 Volume

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the the T the the for

P = ma(qzlTz - qi/T& the solution of equation

W,, + TJll T=-p A/1 + p

(7) is expressed

as

(8)

( 1 - e-I”) + Toe-“e

Numerical

examples

For numerical following

calculations

the reference

of

data used are the

A, (W cm-’ K-‘)

0.03

4, (J mol-r ) 7 060

h, (W cm-’ K-‘)

0.28

q2 (J mol-‘)

c (J g-’ K-‘)

0.14

p (g cme3)

14 500 0.5

Two limiting quantities A, and A, are used to take into account the different qualities of heat contact between the adsorbent and coolant. According to this, the results of the numerical calculations are divided into two groups: the first eight lines of Table 1 present data obtained with h, and the lower eight are for data with h,. Inside every group, the four upper and four lower lines show the results obtained with m = 0.25 g cm-* and m = 0.5 g cmm2, respectively. The

Continuous Table 1

Calculated

Stroke

characteristics

YS,

of four adsorption

4

(J cm-? 10.1

0.58 3.27 0.58 1.49

14 14 14 14

l-2 2-3 3-4 4-l

2.33 13.1 2.33 5.98

56 56 56 56

l-2 2-3 3-4 4-l

0.06 0.35 0.06 0.16

1.5 1.5 1.5 1.5

l-2 2-3 3-4 4-l

0.25 1.4 0.25 0.64

6.0 6.0 6.0 6.0

20.7 20.1 41.3 10.1 20.7 20.1 41.3 _

specific heats of adsorption for two isotherms are determined by the above-mentioned method (where p is the bulk density of charcoal). The calculation procedure and results are now commented upon stroke by stroke. 1-2:

lsothermic

adsorption

From Equation (6) it is possible to estimate IV,, and then the knowledge of Q, = qma makes it possible to calculate t,. The inequality ts > 0 satisfies the condition of the steady process. The molar flow from the evacuation volume is shown in the seventh column, the total square of the adsorbent spread being assumed to be 100 cm*. The value of t, is taken as a constant for all the following strokes. 2-3:

M. Yu. Liburg

Wh

W,

(W cm-*)

(W cmm2)

AI (mm01 s-l)

0.72 -1.1 -1.48 0.26

0 2.76 3.52 0

10.2 0 -10.2 0

0.36 -0.55 -0.74 0.13

0 1.38 1.76 0

5.1 0 -5.1 0

6.72 -10.25 -13.8 2.48

0 25.8 32.8 0

95. 0 -95. 0

3.36 -5.12 -6.9 1.24

0 12.9 16.4 0

47.5 0 -47.5 0

the coolant and the thin layer of adsorbent (m = 0.25 g cm-*) is achieved, but this requires an electromagnetic wave generator with an average output power of -6 kW. The latter can be lowered if the thermal contact between the coolant and the adsorbent is changeable. One can easily see that when the contact is off during the 2-3 and 3-4 strokes, the necessary heater power is only equal to W, < W,,/2. The changeable thermal contact, of course, will complicate the adsorption unit, but such a complication will lead to a CAP with a very high pump capacity, with modest coolant consumption and heater power. The CAP designed for helium or other gases of interest in cryogenics will have the same pump capacity at the proper temperature and pressure2.

lsosteric transfer

The only purpose of this stroke is to overheat the adsorbent up to temperature T2. Substitution of T2, p, 0 and t, in Equation (8) affords the opportunity to calculate IV,,. 3-4:

pumping:

units

;,

l-2 2-3 3-4 4-l

adsorption

Isothermal

desorption

The feasibility of this stroke is connected with the capacity of the outer pump shown in the seventh column of Table I. W,, is calculated from Equation (5).

Conclusions The working parameters of the continuous adsorption pump (CAP) can be calculated on the basis of a family of adsorption isotherms. The pump capacity of the CAP proves to be comparable to that of a Roots pumps, which makes it possible to use the CAP in cryogenic set-ups. In particular, it is applicable to pumping out the vapour of cryogenic liquids in He evaporation and 3He/4He dilution refrigeratorG6.

4- 1: lsosteric transfer The corresponding substitutions in Equation (8) allow one to check that the final temperature of the adsorbent is approximately T,. The CAP, consisting of four identical adsorption units, will have a molar flow of the value shown in the seventh column, in the lines for the l-2 strokes. The outer pump has to provide a molar flow of the same value during the 3-4 strokes, but the necessary pumping speed becomes k times as low as in the case of the absence of a CAP. As one can judge from Figure 2, the compression factor k > 10. Increasing m or decreasing A apparently leads to increasing 13and, consequently, to lowering the pump capacity. Molar flow as large as 0.095 mol s-l can be reached when very good thermal contact (A = 0.28 W cm-i K-l) between

References Gregg, SJ. and Sing, K.S.W. Adsorbtim, .%&ace Area and Porosity Academic Press, London, UK (1967) Ch 4 Fruneau, M., Lacaze, A. and Weil, L. Helium-3 cryostat with adsorption pump Cryogenics (1967) 7 135-137 Lee, S.G. and Kwon, H.C. Compact 3He cryostat for use in thermometry Cryogenics (1993) 33 742-744 Lavrenchenko, G.K. and Zmitrochenko, J.V. Characteristics of refrigerator with adsorption pumping of liquid working agent at temperature lower 65 K Cryogenics (1994) 34 227-235 Borisov, N.S., Bunyatova, E.I., Lihurg, M.Yu., Matafonov, V.N. et al. Frozen spin polarised deutron target 60 cm3 in volume J Phys E: Sci Instrum (1988) 21 1179- 1182 Borisov, N.S., Kulikov, V.V., Neganov, A.B. and Usov, Yu.A. Powerful 3He/4He dilution refrigerator for frozen spin target Cryogenics (1993) 33 738-741

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