Vapor-Liquid Contacting in Descending Cocurrent Flow Robert C. Shufelt, Charles C. Peiffer, and Robert H. McCorrnick* Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
An experimental single-stage equilibrium ynit was designed and tested to investigate descending cocurrent contacting of vapor and liquid streams in tubular contactors for possible adaptation in industrial multitubular tray columns. The unit consisted of a tubular contactor mounted vertically between an inlet receiver and a vapor-liquid separator, a reboiler to produce the vapor, and a condenser. Glass construction was used wherever possible to permit visual observation of the hydraulic behavior in the unit. Single tubular contactors 0.511 in. i.d. with lengths of 12, 15, and 18 in. were utilized and a multitubular arrangement of six 15-in. long parallel tubes 0.305 in. i.d. For all the tubular contactors investigated, the efficiency was at a minimum at a throughput of approximately 5000 g h r - ’ cm-2 of cross-sectional contacting area. This minimum plate efficiency varied from 64 to 73% depending on tube diameter and length. It then increased, and appeared to approach an asymptotic value of approximately 85% as the throughput was increased to approximately 16,000 g hr-’ cm-*.
Introduction The physical separation and/or purification of liquid and gaseous mixtures by distillation and gas absorption techniques is one of the most important processes used in the chemical industry today. Important factors that are considered in the design of contacton or trays for use in continuous industrial columns include plate efficiency, pressure drop, liquid dumping, weeping, flooding, the range of stable operation, .liquid entrainment, hydraulic and concentration gradients, and the ease of construction and maintenance. Most attempts to design better contacting devices have been based on countercurrent flow patterns because of the simplicity of construction and the effectiveness of such contacting on the separation. Each design has its own operating characteristics and has both advantages and disadvantages. For any given design, the maximum throughput for gas and liquid flow is limited by the physical properties of these two phases. By employing cocurrent descending flow with a suitable means for separating the two phases as they exit from the contacting device, it should be possible to operate a t rates higher than can be attained in cocurrent ascending flow, or in countercurrent contacting of the phases. In most cases the main disadvantage in cocurrent flow of the phases during the contacting period is the approach to a zero driving force as 100% efficiency, or complete equilibrium, is reached. For the case of countercurrent flow, the driving force rarely approaches zero. Despite this disadvantage in cocurrent flow, considerable work has been done to investigate this method of gas-liquid contacting. In many of these studies, one-stage units were employed since it is difficult to design multistage equipment with cocurrent contacting on each stage and an overall countercurrent flow of the phases. However, several such studies have been made in multistage units utilizing cocurrent contacting on individual stages. Angelino, et al. (1963), employed upward cocurrent contacting using a watersteam system over a wide range of capacity. Malyusov (1967), using an ethanol-water system, found that efficiencies were high and entrainment moderate in a column employing ascending cocurrent contacting. Peiffer, et al. (1971), reported efficiencies approaching 100% for the hydrocarbon system of cyclohexane-n-heptane using a 6-in. long, 0.25-in. i.d. packed annular contactor in a fourstage unit with ascending cocbrrent flow on each stage
and an overall countercurrent flow pattern. This latter investigation led to the design of a 20-stage unit utilizing the same type of flow pattern (Peiffer, et al., 1972). The main purpose of the present work was to design an experimental single-stage equilibrium unit and then use it to study the effectiveness of descending cocurrent vaporliquid contacting in small diameter, vertical tubes. It was reasoned .that by utilizing a downward flow in the contactor, the force of gravity on the liquid would decrease the pressure drop losses since much of the pressure loss in ascending flow is due to the energy required to lift the liquid through the contactor.
Flow Pattern The flow patterns of the vapor and liquid streams in the unit can be easily followed by referring to the schematic diagram in Figure 1. Vapor from the reboiler enters the top of the inlet receiver, where it is mixed with liquid reflux. Both phases then descend through the vertical contacting section and are disengaged in the vapor-liquid separator. The vapor then flows to the condenser, after which it is returned to the inlet receiver as liquid reflux. The liquid from the separator is pumped to the reboiler for recycling. For equilibrium operation of a single plate at total reflux, the liquid entering should have the same composition as-the vapor leaving it, and the liquid leaving should have the same composition as the vapor entering it. The unit was designed for operating at total reflux to meet the above conditions. Because of cocurrent flow of gas and liquid phases the maximum possible separation is fixed as equivalent to one theoretical plate. Therefore, the plate efficiency of the unit can be calculated from the analysis of the vapor a d liquid phases in either the inlet or outlet receivers. Plate efficiency is then defined as the per cent of this maximum possible separation reached on a single plate. For this work the vapor and liquid phases from the outlet receiver were used according to the following equation
The single-stage unit, shown schematically in Figure 1, consists basically of a vertical, small diameter, tube as the contacting section, an inlet receiver, an outlet receiver or vapor-liquid separator, a reboiler, a condenser, and the Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 2,1974
165
Thermocouples
contacting
SBCtiOO
7 1 1
i
the operating level of 1 in. For each run a time period of 1.5-2 hr of steady operation was allowed prior to sampling. To ensure that steady-state conditions prevailed, a duplicate set of readings and samples were taken after an additional 0.5 hr. Prior to sampling, an adequate purge of liquid was removed from the lines. Each sample was cooled and stoppered to prevent vaporization. Analysis of each sample was made from refractive index measurements using a four-place refractometer at 20". For the range of compositions covered, 40-60 mol % cyclohexane, a deviation of 0.0002 in refractive index corresponds t o a difference of 0.5-0.6 mol 70 or a deviation of 0.05 plates.
c Nitrogen
Deflector
4 steam O u t l e t
Figure 1. Schematic of single-stage equilibrium unit to study descending cocurrent contacting of vapor and liquid phases.
necessary auxiliary piping for transport and sampling of the phases, and for measuring pressure drop losses in the unit. The inlet receiver and vapor-liquid separator consist of a 6-in. length of 4-in. i.d. Pyrex pipe, two 0.25-in. thick steel plates, and Teflon-covered gaskets. The steel plates of both receivers were fitted with connectims for the vapor and liquid lines, the contacting section, sampling lines, pressure taps, and thermocouples. Similar construction was used for the reboiler which is a horizontal 12-in. length of Pyrex pipe. For most industrial distillation columns the contacting trays operate with the entering streams a t the equilibrium bubble or dew points. To operate similarly for this unit a vertical, jacketed, cold-finger type condenser was designed to provide reflux a t its bubble point. The vapor entering the condenser contacts the liquid leaving and thereby maintains the reflux at its bubble point. In this way, mass transfer efficiencies were not significantly influenced by heat transfer mechanics in the contactor. A constant temperature box of tempered hardboard lined with glass wool enclosed the contacting section and the inlet and outlet receivers. A glass front was used to permit visual observation while the unit was in operation. The box was heated electrically and the temperature was maintained constant by forced circulation of the air. The temperatures were measured by the use of thermocouples and the pressure drops by water-filled manometers. Taps to remove samples for the analysis were constructed of stainless steel tubing with cooling water jackets. Operation The tests were made with the cyclohexane-n-heptane system. Experimental vapor-liquid equilibrium data for this system have been previously reported by Myers (1957), and Sieg (1950), and calculated values have been reported by Black (1959). Myers' data were used in this work. To begin operation of the unit the box temperature and the liquid reflux rate from the condenser were set at the desired level. The pump to return liquid to the reboiler was started when the liquid level in the separator reached 166
Ind. Eng. Chern., Process Des. Develop., Vol. 13,No. 2, 1974
Discussion of Results Preliminary investigations using small diameter tubes up to 1-in. i.d., packed with Metex screen, resulted in efficiencies approaching 95%. The pressure drop losses over 12-in. lengths of these packed contactors approached 10 in. of water, which would be considered prohibitive in most industrial applications. Thus, these preliminary investigations included tests only at throughputs of up to 7000 g hr-1 cm-2 when operating at 10 in. of water pressure drop. The plate efficiency increased from 70 to 95% as the throughput was increased from 2000 to 7000 g hr-1 cm-2. After comparing these results with those obtained for the ascending cocurrent contactor investigated by Peiffer, et al. (1971), it was decided to investigate unpacked contactors of 0.511 in. i.d. with varying lengths of 12, 15, and 18 in. Although a decrease in plate efficiency was to be expected for these contactors, it was felt that some efficiency could be sacrificed for the significantly lower pressure drops. The data for these studies are presented in Table I and plotted in Figure 2 and show the relationship between plate efficiency and throughput for this single-stage unit. An interesting observation of these investigations, and one that is of importance in establishing the optimum conditions necessary for maximum efficiency, is that a distinct minimum occurs in the efficiency-throughput relationships. Visual observations of the vapor-liquid mixing action, made at all rates studied, seem to help explain this phenomenon. Beginning at the lowest investigated throughput of approximately 2000 hr-1 cm-2, the mixing of vapor and liquid phases appeared to be minimal. The liquid flowed as a film along the walls of the contactor, while the vapor flowing through the center appeared to contact only the surface of the liquid film. A change in this mixing action was not observed until a throughput of 5000-6000 g hr-1 cm-2 was reached. At throughputs lower than this range of values the relationship shows a constant decrease in efficiency as the throughput is increased, which may be explained by a decrease in the residence contact time between phases. The contacting time could be the controlling factor in the degree of mass transfer since it and the amount of mixing are usually two major factors involved in the transfer of mass in operations of this type. As the minimum in the plate efficiency curve was reached, a change occurred in the appearance of the liquid film, observed by shining a light beam on the glass contactor. At the lower flow rates the liquid film appeared as a clear, colorless liquid on the walls of the contactor, with very little disturbance, such as rippling. At throughputs between 5000 and 7000 g hr-1 cm-2, flashes of light began to appear in the liquid film, which may have resulted from reflections of light from a rippled surface or from small droplets being detached from the liquid film and entrained in the vapor stream. As the throughput was fur-
Table I. Efficiency, Throughput, and Pressure Drop Data for Unpacked Tubular Contactors Using a Cyclohexane-+Heptane Test System Cyclohexane concn leaving contactor, mol %
Run no.
__
~
Liquid
Vapor
Pressure
drop,
Plate Throughefficiency,~ put, water % ghr-lcrn+ in. of
Contactor: 1.d. 0.0511 in.; Length 12 in. 1 2 3 4 5 6 7 8
48.2 47.9 48.2 48.2 47.9 47.1 46.2 45.6
56.5 64.9 56.3 57.0 56.0 56.0 56.0 55.8
0.9 0.3 0.1 0.05 0.55 1.6 2.9 4.3
66.6 64.9 64.5 70.6 64.9 71.3 78.6 81.3
8,358 5,672 3,784 1,883 7,293 10,316 13,157 15,888
ID
a
0 A
0511 0511
I
I
a 601
' 2000
I
I
1
LENGTH
12 15
8385 185 I
I
4000 6000 8000 io000 12000 14000 16000 THROUGHPUT - GMSIHOURKM~
Figure 2. Effects of length and diameter on efficiency-throughput
relationship for unpacked tubular contactors.
Contactor: 1.d. 0.511 in.; Length 15 in. 9 10 11 12 13 14 15 16
45.9 45.6 45.6 45.6 45.6 45.6 45.6 46.5
17 18 19 20 21 22 23 24 25 26 27
47.9 47.9 47.9 47.7 47.9 48.5 48.5 47.9 48.5 48.5 49.1
56.3 56.3 56.0 55.5 55.0 54.2 54.2 55.8
4.6 5.7 3.1 1.4 0.8 0.3 0.1 0.05
83 . O 85.4 83.4 79.3 75.3 68.9 68.9 74.1
14,930 16,214 12,546 9,225 7,679 6,182 3,637 1,985
Contactor: 1.d. 0.511 in.; Length 18 in. 58.3 58.3 57.8 56.5 56.5 58.0 59.0 58.5 58.0 57.8 58.3
2.7 1.9 1.0 0.4 0.2 0.1 4.1 6.0 0.6 0.5 0.1
83.3 83.3 79.2 71 . O 69 . O 76.4 85.0 85.3 76.4 74.4 73.7
11,309 9,758 7,914 6,187 4,447 2,243 13,636 16,016 7,146 6,544 2,962
Contactor (six tubes in parallel) 1.d. 0.305 in.; Length 15 in. 28 29 30 31 32 33 34 a
45.3 42.0 42.6 42.0 42.6 42.9 41.2
56.0 52.9 52.9 51.6 51.6 52.7 52.1
1.6 2.7 0.8 0.4 0.2 0.1 4.5
85.8 87.6 82.7 76.8 71.9 78.3 87.8
8,330 10,434 6,776 5,429 4,435 2,746 13,112
Defined in eq 1 in text of paper.
ther increased the flashes of light became more prevalent, and at 8000-10,000 g hr-1 cm-2 the liquid film began to appear white in color. At still higher throughputs it became impossible to see into the contactor. When throughputs exceeded 10,000 g hr-l cm-2, the liquid and vapor were discharged from the contactor into the vapor-liquid disengaging section as a spray. It was difficult to determine whether this spray was prevalent throughout the contactor or whether it occurred only as the vapor expanded through the liquid film as it entered the vapor-. liquid separator. An increase in length of the contacting zone resulted in a proportionate increase in plate efficiency. For example, the minimum efficiency, increased from 64 to 70% as the tube length was increased from 12 to 18 in. It also appears from Figure 2 that the efficiency asymptotically approaches a constant value a t the higher throughputs. A further increase in throughputs may result in a decrease in efficiency because of a reduced contact time. Pressure drops for the 0.511-in. i.d. contactors ranged from 0.05 to 4.3 in. of water for the 12-in. tube at throughputs from 1885 to 15,765 g hr-1 cm-2, respectively. The pressure drop increased with increased contactor length to
a maximum of 6 in. of water for the W i n . tube at 16,000 g hr-1 cm-2. On the basis of the throughput and pressure drop characteristics, for the 0.511 in. i.d. single-tube contactors, a multitubular arrangement was preliminarily investigated. Such a design would be necessary if descending cocurrent phase flow contacting is to be adapted to industrial applications. Otherwise, throughputs comparable to, or greater than, those attained in present tray designs would not be possible. Provision for equal distribution of the vapor and liquid phases in each contacting tube would be necessary in the design. A contactor utilizing six parallel contactors was made of 0.25-in. copper water pipe (0.305 in. i d . ) 15 in. long. This number and dimensions of tubes were selected to permit adaptation to the existing equipment. The results of these tests are included in Table I and plotted in Figure 2, and indicate higher plate efficiencies than those for the single, larger diameter tube. Although visual observations could not be made of the mixing within the tubes, the vaporliquid action as the mixture exited into the disengaging section appeared similar to that for the single-tube contact ors . The design of gas-liquid contacting devices, such as presented in this work, depends on the ease and accuracy of predicting the efficiency, or the approach to true equilibrium, that can be obtained. The data presented here have been correlated by using the length to diameter ratio multiplied by the superficial vapor velocity in the open contacting tube. However, other variables such as liquid and vapor physical properties, and relative volatility, as well as molecular diffusivities and interfacial area for mass transfer will influence the overall model for predicting plate efficiency. Therefore, to develop an improved correlation or mathematical model, it will be necessary to direct future studies at obtaining data similar to those presented here, but on vapor-liquid systems exhibiting differences in the properties previously mentioned. In conclusion, the present results show that descending cocurrent contacting of liquid and vapor phases can be made efficient and has potential use for industrially designed equipment, especially for applications for which high throughputs and low pressure drops are important design factors. Acknowledgment The authors are grateful to the Diamond Shamrock Co. for the fellowship grant provided for this project. Nomenclature X A , X B = liquid composition of cyclohexane and n-hepInd. Eng. Chem., Process Des. Develop., Vol. 13, No. 2,1974
167
tane, respectively l’b YB = vapor composition of cyclohexane and n-heptane, respectively (YAB = volatility of cyclohexane relative to n-heptane as reported in literature 7 = efficiency, or fractional part of a theoretical stage
Black, lnd. Eng. Chem., 51, 211 (1959). Malb’usov, V. A., lnt. Chem. Eng., 7 , 2 6 4 (1967). Myers, H. S . . Petrol. Refiner, 3, 175 (1957). Peiffer. C. C., McCormick. R. H., Fenske, M. R.. lnd. Eng. Chem., Process Des. Develop., 10,380 ( 1 9 7 1 ) . Peiffer, C. C., Metcalfe, R. S., Kopko, R. J., McCormick R. H., lnd. Eng. Chem., Process Des. Develop., 1 1 , 525 (1972). Sieg, L.. Chem. lng. Tech., 22, 322 (1950).
Literature Cited Received for review August 17, 1973 Accepted D e c e m b e r 11,1973
Angelino, G. C., Brigoli, B.. Silvestri, M.. Energ. Nucl. (Milan). 10, 85
(1963).
Feedback Direct Digital Control Algorithms for a Class of Distributed-Parameter Systems Rajakkannu Mutharasan*’ and Donald R. Coughanowr’ Department of Chemical Engineering, Drexel University, Philadelphia, Pennsylvania 19 104
A novel method to design a digital control algorithm for a class of hyperbolic distributed-parameter systems is developed. Simulations of the control system containing such an algorithm are presented for a flow-forced isothermal tubular reactor, a flow-forced heat exchanger, and a wall temperature-forced exchanger. Simulations show that the proposed algorithm has very good transient response. The algorithm is easily implemented in a practical situation and requires only approximate values of the process parameters. A modified version of the algorithm containing a tuning parameter is shown to improve transient response and the performance index characterized by the integral of error-squared, when modeling errors are present. Applications of the method to several other systems are outlined and discussed.
I. Introduction and Previous Literature Several published papers on the control of distributedparameter systems have been based on first approximating the distributed model by a discretized model, and then designing a control system utilizing the well-established theory for lumped-parameter systems. Such an approach is natural from an engineering point of view; however, it does not provide deep insight into the dynamic behavior and can obscure certain dynamic features of the process as evidenced by Stermole and Larson (1963), Penrod and Crandall (1966), and Paraskos and McAvoy (1970). The main emphasis of most of the investigations to date has been on the synthesis of a control law, which will transport a system from one state to another in an optimal fashion, with respect to a quadratic performance index (for example, Koppel and Shih, 1968; Koppel, e t al., 1968; Ball and Hewitt, 1973; Lim and Fang, 1972; Wang, 1964). Also, a few authors have worked with an error-squared performance index (Hahn, et al., 1971; Seinfeld, et al., 1968a, 1970; Baldwin, et al., 1970; Vermeychuk and Lapidus, 1973). A feature of a distributedparameter control problem with an error-squared performance index is that it leads to singular control problems. Seinfeld and Ladipus (196813) considered the optimal control of the wall temperature-forced heat exchanger, with an error-squared performance index.
’
Address all correspondence to this author at the Department of Chemical Engineering, University of Toronto, Toronto M5S 1A4, Canada * On sabbatical leave at Swiss Federal Institute of Technology, Zurich. Switzerland
168
Ind. Eng. Chern.,
Process Des. Develop., Vol. 13, No. 2, 1 9 7 4
Vermeychuk and Lapidus (1973) presented a method for suboptimal feedback control of hyperbolic and parabolic systems. Their technique is based on successive instantaneous minimization of the performance functional kernel. Application of such a technique to a flow-forced reactor system leads to a multi-level bang-bang type of control (or “table-look-up” algorithm) in a feedback configuration. The algorithm of Vermeychuk and Lapidus (1973) is flexible enough to have potential for practical use; however, it should be tested for parameter variations and modeling errors; also, study of its applicability when sampling of the controlled variable is done infrequently would be of great practical use. Paraskos and McAvoy (1970) studied feedforward-feedback computer control of a flow-forced exchanger. They derived their feedforward algorithm using finite difference formulation of the dynamic equation. Feedback proportional-integral control action was added to offset steadystate errors arising from modeling errors. Transient behavior of their algorithm when implemented on an experimental setup proved to be far superior to conventional Ziegler-Nichols settings. Kamman and Koppel (1966) and Stermole and Larson (1963) have reported experimental data on the dynamics of a flow-forced exchanger to step changes in flow rate. Stermole and Larson (1963) and Penrod and Crandall (1966) have reported experimental frequency response of flow-forced heat exchangers. Kamman and Koppel (1966) considered eq 1 as the model and found it to fit the experimental data better than the linearized equation, which was presented by Koppel(l962).
