Environ. Sci. Technol. 1992, 26, 478-484
Bidleman, T. F.; Billings, W. N.; Foreman, W. T. Enuiron. Sci. Technol. 1986,20, 1038-1043. Yamasaki, H.; Kuwata, K.; Miyamoto, H. Environ. Sci. Technol. 1982, 16, 189-194. Chiou, C. T.; Shoup, T. D. Environ. Sei. Technol. 1985,19, 1196-1200. Shah, J. J.; Kneip, T. J.;Daisey, J. M. J. Air Pollut. Control
ASSOC. 1985, 35, 541-544. Received for review June 18, 1991. Revised manuscript received August 26,1991. Accepted September 3,1991. This work was supported by a grant from the National Science Foundation. Contribution No. 909 of the Belle W. Baruch Institute.
Capillary-Flow Mechanism for Fugitive Emissions of Volatile Organics from Valves and Flanges: Model Development, Experimental Evidence, and Implications Sang J. Chol,+ Robert D. All, Mlchael R. Overcash, and Phooi K. Lim” Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905
Experimental and model results are presented to show that the so-called “nonleaker” emissions of volatile organics from valves and flanges probably proceed by a capillary mechanism. A capillary-flow model is formulated based on theoretical consideration and field data, and equations are derived which permit a test of the model under laboratory conditions. Model predictions are shown to be confirmed by an experimental study of emission from a valve. The results suggest some practical steps for reducing fugitive emissions of VOCs from valves and flanges: (1) the use of nonwetting and low surface energy packing and containment materials, (2) the use of a resilient, nonswelling or nonshrinking packing material, (3) the damping of vibrations and temperature or pressure cyclings, and (4) the application of a compressive stress just sufficient to produce small pore sizes in the packing but insufficient to harm the resiliency and life span of the packing.
I. Introduction The fugitive emissions of volatile organic compounds (VOCs) from flow-control devices-such as regular valves, pressure-relief and safety valves, flanges, containment vessels, drains, and pumps and compressors-is an important concern under the SARA Title I11 regulations (1-3). Plant data indicate that emission losses from the regular valves constitute the largest portion-possibly as high as 70%-of the total emission losses from all flowcontrol devices (3-5). Although the average emission loss from a valve is less than that from any other devices other than the flanges, the large number of valves in a process unit boosts their cumulative losses to the highest proportion. The usual approach to controlling fugitive emissions is to rely on a monitoring and maintenance (M & M) program to spot and repair or replace the leakers (3). The leaker emissions are generally the result of broken seal joints that have characteristic punctured openings larger than 100 pm and an emittant concentration higher than 10000 ppm. One or two such punctured openings are sufficient to turn a device into a leaker, but these can usually be spotted and fixed by an M & M program. Leaker emissions may be modeled as laminar or turbulent flows for liquid emittants and as sonic and subsonic compressible flows for gaseous emittants. Equations describing these flows are available (6). Emissions also occur from the so-called nonleakers, which are devices that nevertheless leak slowly and im‘On leave from Kyungpook National University, Korea. 478
Environ. Sci. Technol., Vol. 26, No. 3, 1992
perceptibly. These nonleaker emissions are somewhat harder to detect and fix because their emittant concentrations are often substantially lower than the 10000 ppm cutoff level that delineates them from the leaker emissions (3, 4). The nonleaker emissions proceed through small pores with characteristic dimensions of 1 pm or less. Precise data on nonleaker emissions are scarce, but their cumulative effect could be quite large if a significant number of the nonleakers do, in fact, leak continuously and imperceptibly. In the face of increasingly stringent emission standards that are being put in place ( l ) there , is a need to go beyond the M & M program and control the low-level emissions. In addition to lowering the overall emission, a control of the low-level emissions may also forestall the development of nonleakers into full-scale leakers. Unfortunately, the control of the low-level emissions is seriously hampered by a poor understanding of the fundamental emission mechanisms. A flow-through-pipe mechanism has often been presumed in the analyses of fugitive emissions (7,8), but, as will be shown shortly, it is often erroneous and misleading. In this paper, we present theoretical considerations and experimental data in support of a capillary-flow mechanism as the principal mechanism for the nonleaker emissions of VOCs from valves and flanges. By extension, the capillary-flow mechanism may also apply to the nonleaker emissions from other static devices. We formulate the capillary-flow mechanism in section II-A and show in section II-B that the mechanism explains some important trends of field data for which the flow-through-pipe model is inadequate. In section III-C, we present the results of experimental tests of the model under laboratory conditions. In section IV, we consider the implications of our findings with respect to emission control. Finally, in section V, we propose additional research to extend the present work to other static devices and to address some important issues which have not been treated in this study.
II. Theoretical Foundation of the Capillary-Flow Mechanism (A) Theortical Formulation and Justifications. We consider the steady-state emission of a VOC through the packing material of a valve and the gasket material of a pair of flanges. We assume that the emission proceeds through N parallel, nonconnecting paths that cut across the barrier material. Each of the N parallel paths is assumed to contain at least one pinch point which, for simplicity, will be modeled as a cylindrical or rectangular-slit pore. The pinch points are defined as narrow contrictions that limit the flow of the VOC. They are preceded and
0013-936X/92/0926-0478$03.00/0
0 1992 American Chemical Society
followed by pores of larger dimensions. Since a VOC may be broadly defined to encompass a volatile organic liquid and a condensable organic vapor, the transport through each of the N parallel paths may be thought to involve three sequential steps generally: (1) imbibition of liquid, (2) vaporization of the liquid at a liquid-vapor front, and (3) diffusion and discharge of the vapor to the atmosphere. The first two steps would be absent for a permanent gas or for a vapor above its critical temperature. They may be important for a condensable vapor if the condensation temperature or pressure is reached or if the pinch points are sufficiently small to induce capillary condensation (9). At steady state, the three steps occur at the same rate, which is determined by the slowest step. The rate of the second step is governed by heat transfer, which is likely to be fast relative to the other two steps. The involvement of the first step makes the fugitive emission rate higher than it otherwise would be. This may be seen in two ways: (1)the presence of a liquid front shortens the diffusion path of the vapor, and (2) the mass flow rate through a pinch point would be higher if the fluid moving through it were a liquid than if it were a vapor. The latter is expected because a liquid has a higher density and a higher surface-tension driving force than a vapor (see later). Consistent with this analysis, field data ( 4 ) show that, for the same flow-control device, the average emission rate is higher if the emitting fluid is a volatile liquid than if it were a permanent gas. Thus, the average leak rate for liquid-service flanges is 1.0 g h-l m-l after 1000 h of service and 2.0 g h-' m-l after 8000 h of service; the corresponding numbers for the gas-service flanges are 0.1 and 0.25 g h-l m-l. Similarly, according to the latest set of Synthetic Organic Chemical Manufacturing Industry (SOCMI) data supplied to the EPA (lo),the average emission factor for a light liquid valve is 2.91 g/h and for a gas valve is 1.51 glh. Moreover, statistical correlation analyses of the emission data (7,B) indicate that, contrary to the expectation based on a flow-through-pipe mechanism, the average emission rate of VOCs correlates poorly with the bulk-pressure driving force A P b , i.e., the pressure difference between the interior and exterior of a flow-control device. This unexpected finding provides strong, though indirect, evidence for a capillary-flow mechanism because in the capillaryflow mechanism surface tension, rather than bulk-pressure difference, is the principal driving force. Surface effects are important in the nonleaker emissions but are relatively unimportant in the leaker emissions because of the difference in pore sizes. The surface effects give rise to capillary flows for liquids and condensable vapors and Knudsen and surface diffusions for gases (see later). In the nonleaker emissions which are associated with small pores, the capillary flows and the surface and Knudsen diffusions dominate over the bulk-flow mechanisms that control the leaker emissions. Here the important parameters are not the bulk-flow parameters but rather the surface parameters and the pore structure, The capillary-pressure driving force aP, is given by AP, = (2a COS e)/z (1) where u is the surface tension of the liquid, 0 is the contact angle of the liquid with the solid surface (it is close to 0" for a wetting surface and 90' for a nonwetting surface), and 1 is equal to R for a cylindrical pore of radius R and 6 for a rectangular-slit pore with a slit separation of 6. It is seen that AP, increases monotonically with decreasing pore size. This means that a sufficiently small
1 can always be found at which AP,will greatly exceed APb For a liquid such as methylene chloride, which has a surface tension of 26.5 dyn/cm at 20 "C, a AP,on the order of 50 atm may be produced in a pore with a characteristic 1 of cm. A fib of this magnitude over the short distance of a pinch point is rare. Thus, the rate-limiting pinch point in the jth parallel path may be presumed to be filled by an imbibing organic liquid whose mass flow rate is given by mj =
~ p A P 3 R j 4-
T
-
8pLj
~
COS U
6 Rj4
4pLjRj* for a cylindrical pinch point pu cos e Wj6j3
pAFJcwjsj3 -
12pLj
6pLj6j* for a rectangular-slit pinch point (2)
where we have assumed a Poiseuille flow (6),p and p are the density and viscosity of the imbibiting liquid, Lj is the pore length, Rj is the pore radius if the pinch point is cylindrical, W jand aj are the slit dimensions if the pinch point has a rectangular-slit geometry, and superscript * denotes the pinch point with the liquid-vapor front. The justifications for using bulk properties in modeling a microporous process have been provided by Wingrave and co-workers ( l l ) who , studied the imbibition of liquid hydrocarbons through porous Vycor and found a good agreement between experimental data and model results based on bulk properties. Equation 2 may be cast into a more convenient form: pa cos e pu cos e 1 Ajrj = -(3) mj = 4K 411 Qj where A,. is the cross-sectional area of the pinch point, rj is the ratio of the characteristic pore dimension to the pore length
Rj2 rj
=-
for a cylindrical pinch point
26,Z =3Lj6,*
for a rectangular-slit pinch point
LjRj*
(4) and
aj is defined as
1 a,=-=-
'
Ajrj
LjRj* AjRj2 3Ljfij*
--
2Aj6j2
for a cylindrical pinch point for a rectangular-slit pinch point
(5) and may be considered as the resistance to flow in the jth path. If the j t h path contains more than one pinch point, the usual resistance-in-series formula applies, i.e.
a, = 1 = E - -1 Ajrj
n=l
Anrn
where the summation is over all the n . pinch points in series in the j t h path. It follows that the total emission rate from the N parallel, nonconnecting paths is given by
(7) Environ. Sci. Technol., Vol. 26, No. 3, 1992 479
If the density, surface tension, viscosity, and contact angle may be assumed uniform in all the pores, eq 7 may be simplified to p a cos 8 N mT = -- C A j r , = 4~ j = 1
p a COS
6'
N j=1
---r----T.---.--
N = 2.5
mT =
8w
flj
N
(r =
CAjrj = 1
c -- (9) N
j=1 flj
where d l and 82 are the respective contact angles of the imbibition liquid with the barrier material and with the containment wall. The summation term involving A T defines the dependence of the emission rate on tkh pore structurespecifically, the number of emission pathways (N), pore size and pore length, and their distributions. The pore structure is a function of the roughness of the seal surface, the depth of the barrier material, the compressive stress on the barrier material, and any physical or chemical interactions which the VOC may have with the barrier material. A rough seal surface will provide more emission pathways and will give a higher emission. A deep barrier material, on the other hand, will introduce more pinch points and will lower the emission. Thus, the lower emission rates of flanges relative to valves may be explained in this manner. A higher compressive stress will, within certain limits, give a smaller Ajrj and a lower emission rate. The expectation is, in fact, borne out by field experience. Interactions between VOC and the barrier material may lead to a volume change. Swelling will add to the compressive stress when the barrier material is confined to a fixed volume. This will tend to lower the emission unless the increased stress causes a material failure, such as a loss of resiliency and sealing capability. In the latter event, an increased emission will result, as in the case of a shrinkage. Equation 8 (or 9) indicates that the global emission rate is the sum of the emission losses from the N emission paths. The latter do not contribute evenly because the emission paths (and hence their flow resistances) are nonuniform. A knowledge of the distribution of the flow resistances (or, equivalently, a knowledge of the pore structure) is needed to compute the global emission rate from the equation. Unfortunately, such knowledge is seldom, if ever, available. The difficulty may be circumvented, however, by assuming an appropriate density distribution function of the flow resistance. For example, for a large N value (>lo5), one may reasonably consider the distribution of the flow resistance to be a continuous function of the flow resistance. It follows that eq 8 (and analogously for eq 9) may be cast into an integral form:
where f(Q) is the density distribution function of the flow resistance 9. A normal distribution function may, for 480
Plot A
p
---
Environ. Sci. Technol., Vol. 26, No. 3, 1992
20
40
60
80
= 0.75 CP
rk = 0.01 100
Ak* lo'6(d)
j= 1
8w
40 dyne/cm
p = 1.5 g/ml
0
pa(cos 1 9 + ~ cos 8,)
10'
0 = 20, dynelcm
(8)
Note that eq 8 implicitly assumes that the imbibition goes through the interior pores of the barrier material predominantly, as opposed to the boundary pores a t the interface of the barrier material and the containment wall. If the boundary pores are the dominant pathway, then the cos 8 term in eq 8 should be replaced by the average of two such terms (12), i.e. pcr(c0s 81 + cos e,)
*
for plot A
1
-
l _
4w
10
Figure 1. Model results showing the theoretical dependence of VOC emission on key parameters according to eq 8. Comparison is made relative to the reference plot A. Other plots are based on the same set of parameters, except for the parameter specified on each plot.
example, be assumed which is characterized by a mean flow resistance (8) and a variance s2
Thus, the effect of a nonuniform distribution of flow resistance may, in principal, be taken into account by means of a density distribution function such as eq 11or the like. In the following model analysis, however, we choose a monotonic distribution of flow resistance to simplify the analysis. Model results are generated from eq 8 by assuming some realistic parameter values. The results are shown in Figure 1. Although they do not necessarily represent any particular system, the model results nevertheless serve two useful purposes: (1) showing the functional dependence of emission on key parameters, and (2) defining the possible ranges of values that may be reasonably expected of the emission or of the parameters. Thus, it is seen that emission increases with the following factors: density and surface tension of the imbibing liquid, a wetting surface, number of emission pathways, and pore size of pinch point. On the other hand, emission decreases with the following factors: viscosity of the imbibing liquid, pore length of pinch point, reduction of pore sizes resulting from an increased compressive stress, and reduction of emission driving force by the substitution of a liquid with a vapor. As formulated, the capillary-flow mechanism applies only to liquid imbibition. However, the discovery of a surface flow (13-18) that is different from ordinary and Knudsen diffusions (see later) raises the intriguing possibility that the mechanism may also apply to gaseous imbibition. It is found that surface diffusion can occur in parallel with Knudsen diffusion and that, in common with the capillary-flow mechanism, it is independent of the bulk-pressure driving force (14). Even for helium, a gas that adsorbs weakly on surfaces, surface diffusion is found to contribute significantly to the overall diffusion when the temperature is sufficiently low (25). Extension of the capillary-flow mechanism to gaseous imbibition would require the assumption that the equivalent analogs of surface tension and conact angle exist for a vapor. Unfortunately, such a postulate is difficult to establish because, unlike the distinct boundary between a surface liquid layer and a bulk vapor in the case of a liquid, the boundary between a surface vapor layer and a bulk vapor
is ill-defined and hard to track. The scrambling effect of Brownian motions would tend to wash out any distinction there may be initially between the surface vapor layer and the bulk vapor. Nevertheless, extension of the capillaryflow mechanism to gaseous imbibition is logical because it explains surface diffusion and provides a symmetry for liquid and gaseous imbibitions. (B) Comparison with Flow-Through-Pipe and Knudsen Diffusion Mechanisms. It is instructive to compare the capillary-flow mechanism with two other mechanisms which play a role-though not necessarily a rate-limiting role-in the fugitive emissions of VOCs from valves and flanges, namely, the flow-through-pipe mechanism mentioned earlier and the Knudsen diffusion. Both differ from the capillary-flow mechanism in that they depend on the bulk-pressure difference as the driving force. Thus, according to the two mechanisms,the mass flow rate through N parallel paths consisting of cylindrical pinch points is given by Flow-through-pipe mechanism for a liquid or gas
where the summation is over all of the flow resistances in the N parallel paths and
LjRj*
fij=--
-
EL,Rj*7
AjRf n=l A,Rn where the summation is over all of the ni pinch points in the jth path. Knudsen mechanism for a gas
where the summation is over all of the N parallel paths, M is the molecular weight, Dk is the Knudsen diffusivity in the j t h path, and Lj L, -Rj3= En=l , R, where the summation is over all of the nj pinch points in the jth path. The relative importance of capillary and convective flows through a pinch point is given by the ratio of the driving forces @,/@b = (2a cos o)/(@b6) (16) For typical values of 2a cos 0 (>0.1 dyn/cm) and @b (
