Variables in Distillation

It was shown in Chapter 1 that to carry out a design calculation, the designer must specify values for a certain number of independent variables to define the problem completely and that the ease of calculation will often depend on the judicious choice of these design variables. 

In manual calculations, the designer can use intuition in selecting the design variables and, can define other variables as the calculation proceeds if it becomes clear that the problem is not sufficiently defined. When a problem is specified for a computer method, it is essential that the problem is completely and sufficiently defined. 

In Chapter 1 it was shown that the number of independent variables for any problem is equal to the difference between the total number of variables and the number of linking equations and other relationships. Examples of the application of this formal procedure for determining the number of independent variables in separation process calculations are given by Gilliland and Reed (1942) and Kwauk (1956). For a multistage, multicomponent column, there will be a set of material and enthalpy balance equations and equilibrium relationships for each stage (the MESH equations) and for the reboiler and condenser, for each component. 

To design the column, the designer must specify this number of variables completely to define the problem, but need not select the same variables. 

Typically, in a design situation, the problem will be to determine the number of stages required at a specified reflux ratio and column pressure, for a given feed, and with the product compositions specified in terms of two key components and one product flow rate. Counting the number of variables specified, it will be seen that the problem is completely defined  

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Modifying the CS3 structure by the addition of dual-composition control provides effective product quality control with essentially the same low variability in distillate flow rate. 

The typical response times for variables in distillation column control are as follows ... 

Typical ranges of process variables in distillate hydrotreating operations are ... 

Ratio and Multiplicative Feedforward Control. In many physical and chemical processes and portions thereof, it is important to maintain a desired ratio between certain input (independent) variables in order to control certain output (dependent) variables (1,3,6). For example, it is important to maintain the ratio of reactants in certain chemical reactors to control conversion and selectivity the ratio of energy input to material input in a distillation column to control separation the ratio of energy input to material flow in a process heater to control the outlet temperature the fuel—air ratio to ensure proper combustion in a furnace and the ratio of blending components in a blending process. Indeed, the value of maintaining the ratio of independent variables in order more easily to control an output variable occurs in virtually every class of unit operation. 

The high degree of sensitivity, selectivity, and efficiency of gas chromatography allows the elucidation of a complete profile of the volatile components of distilled spirits. The wide selection of chromatographic columns and techniques, such as gc-ms, gc-ftir, and gc-ms-ftir, has allowed the chemist to routinely identify and quantify individual constituents on a parts-per-biUion level. The two most critical variables in the analysis of volatile components of distilled spirits by gas chromatography are the selection of a suitable chromatographic column and of the most appropriate detector. 

While working in a plant, a troubleshooter read a pressure gauge daily for several weeks and only realized it was inaccurate when one day the blower was down. The gauge still read about normal operating pressure. Had this have been a distillation unit, it could have been more serious. In distillation service, pressure is a more important variable than in many other unit operations. Relative volatility is a function of pressure. Pressure, or more accurately delta-P, is the best indication of the tower hydraulics. 

At one time the requirement for phenol (melting point 41°C), eould be met by distillation of eoal tar and subsequent treatment of the middle oil with eaustic soda to extraet the phenols. Such tar acid distillation products, sometimes containing up to 20% o-cresol, are still used in resin manufacture but the bulk of phenol available today is obtained synthetically from benzene or other chemicals by such processes as the sulphonation process, the Raschig process and the cumene process. Synthetic phenol is a purer product and thus has the advantage of giving rise to less variability in the condensation reactions. 

Aromatic hydrocarbon resins. The polymerization procedure and variables in the reactions of the aromatic hydrocarbon resins are similar to those for the coumarone-indene resins. However, the Cg feedstreams used in the polymerization of the aromatic hydrocarbon resins do not contain significant amounts of phenols or pyridine bases, so they are submitted directly to fractional distillation. Distillation produced more byproducts than light coal-tar oils. The aromatic hydrocarbon resins obtained have softening points between liquid and 125°C and Gardner colour of 6 to 11. By changing distillation conditions, aromatic hydrocarbon resins with softening points between 65 and 170°C and Gardner colour of 5 to 10 can also be obtained. 

Shinskey (1984) has shown that there are 120 ways of connecting the five main parts of measured and controlled variables, in single loops. A variety of control schemes has been devised for distillation column control. Some typical schemes are shown in Figures 5.22a, b, c, d, e (see pp. 234, 235) ancillary control loops and instruments are not shown. 

S Entropy (kJ-K-1, kJkg-1-K-1, kJkmol-1-K-1), or number of streams in a heat exchanger network (-), or reactor selectivity (-), or reboil ratio for distillation (-), or selectivity of a reaction (-), or slack variable in optimization (units depend on application), or solvent flowrate (kg s-1, kmol-s-1), or stripping factor in absorption (-)... 

A third strategy can be carried out when the problem has many constraints and many variables. We assume that some variables are fixed and let the remainder of the variables represent degrees of freedom (independent variables) in the optimization procedure. For example, the optimum pressure of a distillation column might occur at the minimum pressure (as limited by condenser cooling). 

If we listed all the variables in this system and subtracted all the equations describing it and all the parameters that are fixed (all feeds), we would find that the degrees of freedom would be equal to the number of sidestreams plus two. Thus if we have no sidestreams, there are only two degrees of freedom in this multicomponent system. This is the same number that we found in the simple binary colunrn. T q)ically we would want to control the amount of heavy key impurity in the distillate and the amount of light key impurity in the... 

For example, in distillation simulations the distillate and bottoms composition should be called XD(J) and XB(J) in the program. The tray compositions should be called X(NJ), where IV is the tray number starting from the bottom and J is the component number. Many computer scientists put all the compositions into one variable X(NJ) and index it so that the distillate is X(1J), the top tray is X(2J), etc. This gives a more compact program but makes it much more difficult to understand the code. 

Thirty years ago these computed variables were calculated using pneumatic devices. Today they are much more easily done in the digital control computer. Much more complex types of computed variables can now be calculated. Several variables of a process can be measured and all the other variables can be calculated from a rigorous model of the process. For example, the nearness to flooding in distillation columns can be calculated from heat input, feed flow rate, and... 

There are usually many more state variables that manipulated variables. In a distillation column there are typically over 100 state variables N = 100), while there are only 5 manipulated variables (it = S). There is only one load disturbance shown in Eq. (15.54) for simplicity. If there were more than one, the effects of each could be determined individually. 

Toxicology. Epidemiological evidence suggests that workers intimately exposed to the products of combustion or distillation of bituminous coal are at increased risk of cancer at many sites, including lungs, kidney, and skin. The chemical composition and particle size distribution of coal tar pitch volatiles (CTPV) from different sources are significant variables in determining toxicity. ... 

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