Unfortunately, some engineers ignore Dalton’s Law when dealing with saturated air.
Vacuum equipment suppliers frequently receive inquiries for systems to handle wet (“saturated”) loads. These typically are in evaporation, crystallization, drying, degassifying, and, occasionally, distillation processes. Problems sometimes arise, however, because incorrect specifications are given — specifications that contradict Dalton’s Law.
Perhaps you recall Dalton’s Law of Partial Pressures from undergraduate chemical engineering. It simply states that the total pressure of a mixture of gases equals the sum of the gases. For wet air, it translates to:
P1 = Pv + Pa (1)
where P1 is the total pressure, and Pv and Pa are the partial pressures of water vapor and air, respectively, all in absolute pressure units.
We know P1, and can find Pv by looking on a vapor pressure chart for water vapor. The difference can be considered Pa.
Taking this into account, we can translate Eq. 1 into a load:
Â Lv = [Pv/(P1 Pv)] x (2)
(MWv/MWa) x La
where Lv and La are the lb/h of water vapor and air, and MWv and MWa are their molecular weights (18 and 29, respectively). Note that in order for this equation to make any physical sense, P1 must exceed Pv.
This relationship is presented in a graphical form in the latest edition of “Standards for Steam Jet Ejectors”  from the Heat Exchange Institute (HEI).
It can be seen from Eq. 2 that as Pv approaches P1, one ends up taking the reciprocal of a smaller and smaller number. This means the system has to be designed to handle increasingly larger amounts of water vapor, implying an increasingly larger vacuum system. For example, at 150 mm Hg abs and 90 Â°F. 1 lb of air will be saturated with 0.196 lb of water vapor, but, at 150 mm Hg abs and 135 Â°F, 1 lb of air will be saturated with 4.331 lb of water vapor.
Figure 1. Properties of saturated water vapor.
A Recurring Problem: In all too may instances, vacuum equipment manufacturers are being forwarded inquiries in which Pv (based on the inlet temperature) exceeds P1.
For instance, specifying 10 lb/h of air saturated with water vapor at 5 mm Hg abs and 100 Â°F is not meaningful. P1 = 5 mm Hg abs. Pv at 100 F = 49.1 mm Hg abs. So, P1 ,>
With a limited-capacity vacuum system, the process probably will never reach 5 mm Hg abs. It will “stabilize” at some absolute pressure above this point. This might be as high as 50 mm Hg abs, depending upon how the vacuum system is designed.
Consider a recent inquiry that called for a vacuum system to handle 25 lb/h of air saturated with water vapor at 50 mm Hg abs and 110 Â°F, coming from an existing shell-and tube precondenser. At 110 Â°F, Pv = 66.0 mm Hg abs. What would happen in reality is that none of the water vapor going to the precondenser would condense. The condenser simply would be nothing but a very expensive piece of stainless steel pipe. The customer was asked to respecify the suction pressure to the vacuum system at 67 mm Hg abs (or higher), so that P1 > Pv.
Carefully Check Conditions Of Service: In specifying a vacuum system, the purchaser should be absolutely certain that the conditions of service (COS) given are correct. Inaccurate information can lead to a problem of misapplication that could — in worst-case circumstances — haunt both the user and the manufacturer’s service department for the entire working life of the system.
Consider a recent inquiry for a vacuum system. COS were quoted as 4 in. Hg abs and 125 Â°F. Something, however, didn’t ring quite true. After persistent questioning by the manufacturer’s application engineer, it was discovered that the operating condition was 117 Â°F, not 125 Â°F. Now eight degrees doesn’t seem like a big difference — but, to a vacuum system, it can be! Designing for the incorrect higher temperature would cause excessive evaporation. Condensation would not occur. Temperature would rise to near boiling, and a slug of cold water passing through the system could flash to steam. Even in the best-case scenario, the system would never operate well.
In case of doubt, recheck your COS!
Assuring Optimum Operation: A dry air load can, of course, be at any temperature at all. But if a saturated air load is specified, total system pressure must be greater than vapor pressure based on load temperature for the system to make sense. (No, you won’t be arrested if you break Dalton’s Law — but you may pay a penalty in terms of a grossly oversized vacuum system, or, more likely, an undersized system incapable of bringing the process to the desired vacuum.) Better yet, specify the exact flow rate of water vapor that the vacuum system has to handle.
In practice, the process or system in question usually can be amended slightly to provide a more favorable suction pressure or temperature. Typically, the partial pressure of the vapor can be lowered or the design suction pressure raised. If these remedies aren’t feasible, be sure that your specification details all the water vapor/condensable vapors evolved by the process that will go to the vacuum system — and let the manufacturer take its best shot at working out a solution. Sometimes, a reasonably priced booster ejector may be suggested to solve the problem.
1. “Standards for Steam Jet Ejectors,” 4th Ed., p. 76, Heat Exchanger Institute, Cleveland (1988).
Author: S.W. CROLL, III is president of Croll Reynolds Co., Inc., a leading supplier of steam-jet-ejector systems. He has been with the firm since 1984. He is a graduate of Skidmore College, Yale University, and New York Law School.