xploratory studies at 100,000 p.s.i. and up to 1000" F. been restricted to batch studies because satisfactory pumps are not available ( 7 , 2, 4, 7). To overcome this problem, a pumping assembly has been developed and built. It does not require packing, does not contaminate the reactant feeds with hydraulic fluid, neither does it leak. This pumping assembly has been used in a new benchscale flow unit, which operates from 0 to 100,000 p.s.i. and from 70 to 1000" F. Equally important, available reactors for these pressures are cumbersome and difficult to assemble. The thick walls must be heated slowly to prevent excessive thermal stresses; such stresses plus internal pressure may rupture the reactor (5). The flow unit described here heats the reaction zone quickly, maintains the proper temperature and pressure, provides efficient contact between reactants and catalyst, closely controls the time that reactants are exposed to catalyst, and permits easy recover). of products.
E have
A PUMPING ASSEMBLY FOR
100,oo T h i s scheme can be used to study coiztinuous veaetions at extreme PYessures
Extreme-Pressure Pumping Assembly
The extreme-pressure pumping assembly is shown below (Figure 1). The Ruska pump meters hydraulic fluid at a predetermined rate into the low-pressure chamber of the intensifier ( 7 ) . In turn, hydraulic fluid from the high-pressure chamber of the intensifier pressures the void surrounding the bellows in the delivery chamber. One stroke of the intensifier piston equals about 39 ml. of hydraulic fluid at the discharge pressure of the intensifier. The bellows acts as a diaphragm between the hydraulic fluid and the liquid
Figure 7. The pumping assembly and exploded biew of the bellows. T h e assembly consists of a Ruska single-stroke positive displacement 40
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
W . J . C E R V E N Y
pump, an intens$er, and a delivery chamber or pressure vessel Lontaining a lead bellow attached internally to its top closure
feed and hence prevents contamination. As the pressure of the hydraulic fluid in the delivery chamber exceeds that within the bellows, the bellows is squeezed and liquid feed is forced from it and discharged from the pumping assembly. Auxiliary components are : a Sprague air-operated hydraulic pump, a manual hydraulic pump, a liquid-feed Ruska pump containing a Magne-Dash dasher assembly in its discharge cylinder, a spring-loaded check valve, and an intensifier piston-level indicator, The Sprague pump pressures the intensifier rapidly and the hydraulic pump returns the intensifier piston to its retracted position. The liquid-feed Ruska pump mixes gaseous and liquid feeds and pumps the feed into the bellows of the delivery chamber to 15,000 p.s.i.-a convenient operating pressure. T h e spring-loaded check valve provides protection against a differential pressure of 25 p.s.i. in the bellows; 25 p s i . was chosen because pressures slightly in excess of this pressure tend to shorten the life of the lead bellows. Finally, the piston-level indicator shows the position and travel of the intensifier piston by measuring the height of a n oil layer resting on the low-pressure piston. Similarly, it indicates the discharge rate of the pumping assembly. The bellows (below) is a lead tube 7/*-inch in outside diameter and 6 ' / 2 inches long made from '/sd-inch thick lead sheet. The tube seam is soldered with soft solder. Then the tube is soldered to two end connections. One connection adapts the bellows to the closure through a copper-gasket seal; the other seals the opposite end and
provides a n opening for cleaning. Sixty per cent of the volume of the bellows can be used without ruining it. T h e delivery chamber closure, a Bridgman-type (I), has a special packing wrench for safely removing the bellows from the separator. Flats on the packing wrench and connection hold the bellows firmly. Rotating the closure disconnects the bellows.
Figure 2. The Bow unii and exfiloded view of the reactor coupling. Liquid feed flows from the pum$ assembly through a tube reactor,
which is heated by a furnace. Products are depressured to atmospheric pressure through throttle valves into a calibrated glass receiver
Application of Pumping Assembly
T h e extreme-pressure pumping assembly is especially valuable for discharging exact amounts of a contaminantfree liquid feed at 100,000 p.s.i. or higher. Many applications exist. T h e following describes one. Figure 2 shows use of the pumping assembly in a unit similar to conventional liquid-flow units. T o measure and control flow effectively at 100,000 p.s.i., the pump and manually controlled throttle valves are used. Essentially, the pump acts as a feed reservoir and is maintained slightly above the operating pressure. Then the throttle valves control the flow of reactants and product through the unit. That is, the Ruska pump that pressures the extreme-pressure pumping assembly is set to obtain the desired liquid feed rate from the delivery chamber. The operating pressures are then maintained by adjusting the discharge rate of product. The reactor is a 20-inch length of tubing (9/16-inch in outside diameter and 3/16-inch inside diameter, type 316 stainless steel, nominal working pressure 60,000 p.s.i.). In three proof tests, this tubing failed at 100,800 f 800 p.s.i. and 1260 f 35" F. The reactor coupling is shown below (6). The tube
VOL. 5 5
NO. 7
JULY
1963
41
Thermodynamic Functions
Before we can correlate the thermodynamic properties of mixtures we must represent them algebraically. We have selected a function (Equation 1 ) first suggested by Guggenheim (7) and later popularized by Scatchard (73),Redlich (7 I),and Barker (2). The excess property, F(RE,,'P etc.), is expressed as a power series in the mole fraction of the second (or first) component and the coefficients, y.(h,, u,,, etc.), are determined by a least squares procedure. I
F = x(1 - x)
y.(l "-0
- 2%)"
is.approximately that of a skewed parabola; in other cases (such as S-shaped curves), it has no virtue, and one may as well use Equation 1. There are many advantages in fitting experimental data to Equations 1 or 2. Appropriate statistical rules can be applied in eliminating spurious values. Although uncertainties in Y may vary over the range of x and will differ with worker and experimental method, proper weighting allows all available data for a given
(1)
The behavior 01 the first three terms in this widely used equation is shown in Rowlinson's book, "Liquids and Liquid Mixtures" (12). When F ur. x is sharply skewed, the series of Equation 1 converges only slowly and is rather inefficient. This suggested a modification which proved useful in minimizing the number of parameters needed to fit a set of data. We introduce a pre-selected skewing constant B, where - 1 < B < 1:
" I
-101
I
I
a
I
0.0
B is not evaluated by least squares and, once selected, is used for all properties and all temperatures for a given system in order to keep the various functions easily differentiable. It is for this reason that we do not use a general power series in the denominator. The behavior of the first four terms in this skewed function is shown in Figure 1 ( B = 0.6). Equation 2 can serve the purpose of introducing other functional forms, such as the volume fraction form prcferred by Hildebrand and coworkers (8)or the van Laar equation used extensively by chemical engineers. For an excess function in the simple volume fraction form:
are volume fractions and PI and YZ where q1 and are the molar volumes of the two pure liquids. It is then easy to rewrite this expression in the form:
+
XIX2
+
(4)
- d ( P 1 - YZ)/(Yl Ydl in which it is okvious that B = -(VI - PZ)/(?I Yz), I1
(XI
+
+
vo = 2 k Y 1 ~ 2 / ( f 7 1 Pz),andyl = y~ = . . . = 0. A reasonably good choice for B can he made hy selecting that value which causes the maximum in the first
term of the series to occur at the same mole fraction as t h e maximum in an appropriate property (for example, the heat of mixing). If we define this mole fraction as xm.. this leads to an equation for B: (5)
It will normally suffice to round B offto an even tenth except, ofcourse, for extremeskewness ( B > 0.9). Equation 2 is useful only when the shape of the excess function 44
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
I
I
I
0.5
I
I'
I
1.0
and n = 0, I , 2, 3
property of a system to be used in determining y. We have assumed x to be the independent variable and assigned all uncertainty to the p values, but altrrnate programs are possible. Calculdional Sequences
Our ultimate goal is to develop a general program which will accept all the thermodynamic data available for a particular system (vapor pressures, solubility data, heats of mixing) together with appropriate weighting factors, perform a statistical analysis and synthesis, and yield values of g. in Equation 1 or 2 for the excess free energy, their temperature and pressure derivatives, and standard deviations for all of these. CH08A. The obvious place to begin is to fit directlymeasured excess properties PE, etc.) by the method of least squares, obtaining parameters (k, un, etc.) which can later be correlated with values of g. and their derivatives. The matrix inversion method of least squaring is used. Outvut includes coefficients y., calculated values of 9,
(nE,
limiting values of the slopes
(3, rz3 , -
and ' and standard deviations for all of these. The use of CHOBA to process thermodynamic data for alcohol and fluorocarbon systems studied in our laboratories isdlustrated in recent publications (7, 74, 75). Further details and copies of the Fortran source program are available from the authors. CH08B. This program takes total vapor pressureliquid composition data and determines the best least = 0
