Sizing of vacuum relief valves for atmospheric distillation columns

Sizing of vacuum relief valves for atmospheric distillation columns Konstantine Glinos* and Ronald D. Myers Rohm and Haas Company, USA

Engineering

Division, PO Box 584, Bristol, PA 19007,

A distillation

column operating under pressurized conditions may not be designed for full vacuum. A vacuum relief valve on such a column must, therefore, be sized to prevent negative pressures in the shell under the worst case scenario, i.e. when the feed, bottoms, distillate and reboiler steam are cut off, but the condenser still operates. The valve can be sized considering that the inflowing air (or other gas) first accumulates in the condenser, which is the vacuum source, and blankets the heat exchange area stopping the condensation. A conservative estimate of the amount of air required to blanket the condenser is given by the condenser volume. The rate at which this inflow must occur can be found from a transient total energy balance around the column, as described below. This method has been applied for valve sizing in real columns and results in reasonable valve sizes. To the best of our knowledge, no other method for carrying out this calculation is avajlable in the open literature. (Keywords:

relief devices; valves; distillation

columns)

During an emergency shut-down of a distillation column, a conceivable situation can occur, where, while the distillate, feed, bottoms and reboiler steam are all shut off, the condenser still operates condensing overhead vapours. Reflux is returned to the column, since the reflux pumps will keep working as long as there is condensate accumulating in the reflux drum. Under this worst-case scenario, the pressure and temperature in the column will decrease as heat is subtracted from the system. Since any column can tolerate only a certain vacuum, the engineer must ensure that the pressure will not fall below this value under any circumstances. For this purpose, a vacuum relief (VR) valve is installed, which should be designed to open if the pressure in the column falls below a threshold value (usually slightly lower than 1 atm). Although installing such VR valves is common a sizing method with some practice in industry, engineering or scientific foundation does not seem to exist. In this paper, we propose an approach to size this kind of valve. The method has been applied to real problems and results in reasonable valve sizes. An alternative method, where the valve is sized for an air rate equal to the volumetric condensing rate (that corresponds to the heat removal at the condenser) at AP = [l atm] - [vacuum rating of column], has been

Received

5 November

166

VR f-

X : valve

1990

*Present address: Direction Centrale Technique-Process Engineering, SOLVAY & Cie, rue de Ransbeek 310, 1120 Brussels, Belgium 0950-4230/91/030166-04 @ 1991 Butterworth-Heinemann

found too conservative, resulting in valve sizes that may be larger than the diameter of the vapour line. The system we are dealing with is essentially a closed system, from which heat is continuously subtracted at a certain rate (see Figure 1). The main variable determining the valve size is the rate of

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Figure 1 Column schematic

shut off

Sizing

pressure drop. Note that if the pressure falls sufficiently slowly to allow for some action to be taken, the operator can try to shut off the flow of the cooling medium, or increase its temperature. The VR valve will open if all else fails. Method Any air that enters through the relief valve will flow in the direction of the condenser, which is the vacuum source. The air will decrease the heat transfer coefficient in the condenser tubes and eventually will form a blanket, preventing any further condensation from taking place. Therefore, it is reasonable to say that the maximum amount of air required equals the condenser volume. A methodology follows for estimating the time interval available for supplying this amount of air to the column.

of vacuum

(1)

mlU1

= -Qc(t2

-

tl)

(2)

where subscripts 2 and 1 denote the final and initial states of the system respectively. Since: U=h-Pv

(3)

where h is the mass enthalpy and v is the mass volume, we can finally write: *r = _ m(&

- hr) - V,g(p~ - Pr)

Q,

and R. D. Myers

hz - hl = C,(T,

-

T,) -

Ah”(wr - w,)

(5)

assuming that cP and the heat of vaporization Ah’ do not change substantially in the temperature range [T,, T,]. The difference wr - w1 represents the fraction of the total mass that was condensed, and w, and wz can be calculated from a mass balance as: V,

dt where U is the internal energy per mass unit, m is the total mass in the system, and Q, is the cooling duty. Note that Q, is not necessarily at its design value, but should be determined by rating the condenser with little or no fouling. If Q, is considered constant during the time interval we are examining, then integration of Equation (1) gives: m2Uz -

K. Glinos

valves:

the condenser, the reflux drum and the vapour and reflux lines. The total mass is m. Most of it will be liquid, which mainly consists of the liquid in the column bottom, the total tray holdup and the liquid in the reflux accumulator. All of these can be easily estimated. For single component systems, the pressure is related to temperature by Antoine’s equation, the starting and final temP = f(T). Therefore, peratures, T, and T,, can be calculated. If w denotes the fraction of the total mass that is liquid, the enthalpy difference is

Time interval available for vacuum relief

Neglecting the air inflow, the system we are dealing with is closed (no material in- or out-flows). The total energy balance is:

-d(mW -z-Q,

relief

(4)

V, is the total volume of the system and g is a units correction factor. If SI units are used, g = 1; if P is in psi and V, in ft3, g = 0.185114. Equation (4) gives an estimation of the time the system needs to reduce its pressure from P, to P2. It can be applied for both multicomponent and single component systems in a straightforward way, once the difference h2 - h, is evaluated. This is a simple calculation for single component systems, but somewhat more involved for multicomponent mixtures. Of course, all distillation systems are at least binaries, but some of them can be approximated as single component, such as the stripping of a solute-from a dilute aqueous solution. The vacuum relief valve will open at pressure P, (slightly less than atmospheric) and P, is the minimum pressure the column shell can tolerate. V, is the total volume of the system, which includes the column itself,

vg

m w=

(6)

0, - vg

where the mass volume of the liquid, vr, can be considered constant in (T,, T,), while the mass volume of the gas is: vg =

z(MW)RT

(7)

P

where z = 1 for pressures close to or below atmospheric (except for organic acids). This is all the information needed to calculate the enthalpy difference from Equation (5) and insert it in Equation (4) to get At. Alternatively, for components like water, the mass volumes and enthalpies of the vapour and liquid can be read directly from the steam tables. For multicomponent mixtures, the calculations are more complex, mainly because temperature and pressure are not directly related through Antoine’s equation. To simplify the solution, we have to estimate an average composition of the liquid in the system, which we will assume remains constant through the depressurization. For instance, consider the high purity separation of A (light) from B (heavy) with 750 lbs of liquid holdup at the bottom of the column, 250 lbs in the reflux drum and negligible tray holdup. Since the liquid at the bottom is mostly B and in the drum mostly A prior to the reboiler steam shut-off, the average liquid composition is 25% A. This average liquid composition can be used in the following equation, which approximately relates total pressure to temperature: P = 2

xiyip;

where Pf is the vapour pressure, given by Antoine’s equation, and yi the activity coefficient of component i. Since the pressure is known, Equation (8) ‘must be solved iteratively for temperature. The vapour fraction of component i may then be found from: Yi =

X,Y,PS P

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Process

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1991,

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167

Sizing

of vacuum

relief

valves:

K. Glinos

and R. D. Myers

These calculations can be made using any flash routine. Knowing the vapour and liquid compositions, pressure and temperature, it is easy to calculate the enthalpy difference to be used in Equation (4). Note that Equation (5) is only approximately correct for species that have similar heats of vaporization and specific heats. However, Equations (6) and (7) still apply, provided the weight-average molecular weight of the vapour is used in Equation (7), and the weight-average mass volume of the liquid in Equation (6). An additional consideration concerns the effect that the drainage of cold liquid from the upper trays down to the hotter column bottom will have on the column pressure. To illustrate this point, consider a column separating a binary mixture at the moment when the steam flow is shut off. The pressure differential in the column will be lost, and the liquid holdup of the trays will drain through the tray holes down to the bottom. Because this draining liquid has a lower temperature than the bottoms of the column, their mixing should cause a pressure upset. The magnitude of this pressure change will depend on the difference in the vapour pressures of the components, their heat capacities, the relative amount of tray holdup to the bottom holdup and the speed at which this phenomenon occurs. A simplified analysis showed that the total pressure in the column will always have the tendency to increase because of this effect. The magnitude of the increase can vary widely depending on the specific components involved. A pressure increase seems reasonable, since the sudden rise in the temperature of the volatile species will generate a sudden rise in its vapour pressure, which will be only partly negated by the drop in the vapour pressure of the heavy species. Therefore, taking this phenomenon into account in our calculations would result in a possible elongation of the time interval available for vacuum relief; neglecting it should lead to conservative results. There are two additional factors we may want to take into account to adjust the heat subtracted from the system, Q,. The first is the heat lost to the environment through the column shell, especially for columns poorly insulated. The second is the sensible heat contained in the reboiler tube walls, which will be gradually released after the steam is shut off. For example, if c, is the heat capacity of steel, W, the weight of the reboiler (empty) and T, the temperature of the steam (approximately the wall temperature), the total heat released by the reboiler is Wrc,(T, - T), where T is the final temperature. It is, however, difficult to evaluate what fraction of this heat will be released in the time interval At. Also note that the heat losses and the reboiler heat are of opposite sign and partially cancel out. Sizing and position of the VR valve The required inflow of air is given by

VC

(10)

4air = t

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with V, being the volume of the condenser. Equation (10) will give a conservative estimate of qair, because Q, was considered constant and having its maximum value in Equation (4). In reality, as soon as some air reaches the condenser, the heat transfer coefficient will be drastically reduced, which will cause a sharp decrease in Q, and an increase in At. Thus, it is not really necessary to fill the entire condenser volume, V,, with air before condensation slows down. If the air flow calculated from Equation (10) results in an unacceptably large valve size, there are two alternatives: (a) decrease the minimum vacuum pressure the column tolerates (if the column is not yet built), or (b) provide for a pressurized gas source (e.g. nitrogen) being connected to the relief valve, so that the valve will open at a pressure higher than atmospheric; this will result in increasing the time interval, At, available for vacuum relief. Note that the pressure difference for which the valve should be sized is not given by P, - P2, because the valve will open at P, (usually close to atmospheric), but the pressure in the column will only gradually reduce to P,. To clarify this point, consider the equation typically describing a valve: z

= K(P,

-

P)‘p

(11)

where dV is the volume of air flowing through the valve in the time interval dt, K is the constant of the valve, and P is the pressure in the column, which changes with time. If this change is roughly linear, we can write approximately: P=

pl+pt

Pl

-

p2

At

(12)

where At is given by Equation (4). Substituting Equation (12) into Equation (ll), integrating from [V = 0; t = 0] to [V = V,; t = At], and using Equation (lo), we finally obtain:

9air= KtZ(pI - p*)1”2

(13)

Therefore, the effective pressure difference for sizing the valve is only 4/9 (44%) of PI - Pz. The valve must be positioned as close as possible to the condenser to minimize the time needed for the inflowing gas to reach the vacuum source. It can, therefore, be placed on the vapour line, or on the condenser itself.

Example Assume we need to size a VR valve for an HCN stripper. The dimensions of the column, the number of trays and tray holdup, and the liquid level at the bottom are known. The condenser volume is 63 ft3 (cubic feet). The condenser duty is 11.5 MM Btu h-' , the operating pressure is 25 psig, and the shell is rated for -2 psig maximum vacuum. The HCN-water mixture is dilute,

Sizing

and, for our purposes, it can be considered as being pure water. From the column dimensions and the condenser volume we can estimate the total system volume to be V, = 1794 ft3. The volume of the liquid in the column is approximately equal to the sum of volumes of liquid at the bottom, on the trays and in the condenser system, and is found equal to V, = 436.3 ft3. The liquid specific volume at 39.7 psi is found from the steam tables to be o, = 0.01715 ft’ per lb, therefore, the total liquid mass is M, = 436.3/0.01715 = 25441 lb. The total vapour volume is V, = 1794 - 436.3 = 1357.7 ft3, and the vapour specific volume at 39.7 psi is V, = 10.5 ft3 per lb. the Hence, mg = 1357.7/10.5 = 129 lb. Therefore, total mass in the system is m = 25441 + 129 = 25570 lb. Since the valve will open at a pressure slightly less than atmospheric, and the final pressure should not be less than 12.7 psi, we will apply Equations (4), (5) and (6) for PI = 14.7 and P2 = 12.7 psi. From the steam

tables we find u1 = 0.01672 and ug = 26.83 ft’ per lb at 14.7 psi, and u1 = 0.01667 and ug = 30.59 ft3 per lb at 12.7 psi. Using these numbers in Equation (6) we get W, = 0.998007, and w2 = 0.998250. The water temperature at 14.7 psi is 212”F, and 204.9”F at 12.7 psi. The average heat of vaporization is 972.5 Btu per lb. Using now these numbers in Equation (5) we get h2 - hI = 7.336 Btu per lb. Finally, from Equation (4) we obtain the final result, At = 58 s. This means that we have 58 s available to pass 63 ft’ of air through the valve to the condenser. This corresponds to an average air flow rate of 1.09 ft3 s-l at a pressure differential of about 0.9 psi [0.44 x 2.0 psi, see Equation (13)], for which a relatively small size valve will suffice. Note that if the valve was sized to handle the volumetric condensing rate (according to an alternative method), the corresponding figure would be (Q,u,)/Ah’ = 90 ft3 s-l, which is excessive and would result in an unrealistic valve size.

of vacuum

relief

valves:

K. Glinos

and R. 0. Myers

Conclusion A method has been presented to size vacuum relief valves for atmospheric distillation columns. The method is approximate, but results in reasonable valve sizes when applied to actual problems.

Nomenclature CP

g Ah’ h

K In P P: Q 4su

R T I lJ V " W, w Xi Yn Z Yn

Subscripts 1

Specific heat capacity Specific heat capacity of reboiler steel Unit conversion factor in Equation (4) Heat of vaporization Specific enthalpy Valve constant Mass Total pressure Vapour pressure of component i Heat duty Inflow of air through valve International gas constant Temperature Time Specific internal energy Volume Specific volume Weight of reboiler Fraction of total mass that is liquid Liquid mole fraction of component i Vapour mole fraction of component i Compressibility factor Activity coefficient of component i

Conditions at the pressure at which vacuum relief valve opens Conditions at minimum allowable column pressure Condenser Gas Liquid Reboiler Steam Total

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