Distillation energy balance problem

Process Technology 2—Systems—study of common process systems found in the chemical process industry, including related scientific principles. Includes study of pump and compressor systems, heat exchangers and cooling tower systems, boilers and furnace systems, distillation systems, reaction systems, utility system, separation systems, plastics systems, instrument systems, water treatment, and extraction systems. Computer console operation is often included in systems training. Emphasizes scale-up from laboratory (glassware) bench to pilot unit. Describe unit operation concepts solve elementary chemical mass/energy balance problems interpret analytical data and apply distillation, reaction, and fluid flow principles. 

Try the following problem to sharpen your skills in working with material and energy balances. Crude oil is heated to 525° K and then charged at a rate of 0.06 m /hr to the flash zone of a pilot-scale distillation tower. The flash zone is maintained at an absolute temperature of 115 kPa. Calculate the percent vaporized and the amounts of the overhead and bottoms streams. Assume that the vapor and liquid are in equilibrium. 

The calculational base consists of equilibrium relations and material and energy balances. Equilibrium data for many binary systems are available as tabulations of x vs. y at constant temperature or pressure or in graphical form as on Figure 13.4. Often they can be extended to other pressures or temperatures or expressed in mathematical form as explained in Section 13.1. Sources of equilibrium data are listed in the references. Graphical calculation of distillation problems often is the most convenient... 

In the usual distillation problem, the operating pressure, the feed composition and thermal condition, and the desired product compositions are specified. Then the relations between the reflux rates and the number of trays above and below the feed can be found by solution of the material and energy balance equations together with a vapor-liquid equilibrium relation, which may be written in the general form... 

However, in batch distillation, the system is frequently very stiff, owing either to wide ranges in relative volatilities or large differences in tray and reboiler holdups. Therefore, if methods for non-stiff problems are applied to stiff problems (ODE models but having column holdup and/or energy balances), a very small integration step must be used to ensure that the solution remains stable (Meadow, 1963 Distefano, 1968 Boston et al., 1980 Holland and Liapis 1983, etc.). 

A comparison of the method proposed in this paper with other methods is difficult because there are few published solutions for nonideal distillation problems. We were unable to find a completely solved problem with all material and energy balances satisfied. We have demonstrated that the Jacobian matrix gives rapid convergence in the vicinity of the solution, and this method might serve as a basis to evaluate other methods. 

The material balance from Problem 3-6 and either ASPEN PLUS or CHEMCAD-III computer software is used to develop the energy balance around each piece of equipment in the ethylene separation section. For example, around distillation column, C-601, the computer program establishes the heat content 6f streams 533, 602, and 603 above a selected datum plane. The distillation calculation indicates the flow rates of the oveiiiead and bottoms streams. The reflux and reboil then indicate the flow rates of the streams that are returned to the column and permits evaluation of the condenser and reboiler duties. In kW " this pan be expressed as... 

Binary Distillation 379 Material and Energy Balances 380 Constant Molal Overflow 380 Basic Distillation Problem 382 Unequal Molal Heats of Vaporization 382 Material and Energy Balance Basis 382 Algebraic Method 382... 

A convenient way to represent enthalpy data for binary solutions is via an enthalpy-concentration diagram. Enthalpy-concentration diagrams (H-x) are plots of specific enthalpy versus concentration (usually weight or mole fraction) with temperature as a parameter. Figure 4.21 illustrates one such plot. If available, such charts are useful in making combined material and energy balances calculations in distillation, crystallization, and all sorts of mixing and separation problems. You will find a few examples of enthalpy-concentration charts in Appendix I. 

Take a mixture of two or more chemicals in a temperature regime where both have a significant vapor pressure. The composition of the mixture in the vapor is different from that in the liquid. By harnessing this difference, you can separate two chemicals, which is the basis of distillation. To calculate this phenomenon, though, you need to predict thermodynamic quantities such as fugacity, and then perform mass and energy balances over the system. This chapter explains how to predict the thermodynamic properties and then how to solve equations for a phase separation. While phase separation is only one part of the distillation process, it is the basis for the entire process. In this chapter you will learn to solve vapor-liquid equilibrium problems, and these principles are employed in calculations for distillation towers in Chapters 6 and 7. Vapor-liquid equilibria problems are expressed as algebraic equations, and the methods used are the same ones as introduced in Chapter 2. 

The calculation procedures [the 0 method, Kb method, and constant composition method] developed in Chap. 2 for conventional distillation columns are applied to complex distillation columns in Sec. 3-1. For solving problems involving systems of columns interconnected by recycle streams, a variation of the theta method, called the capital 0 method of convergence is presented in Secs. 3-2 and 3-3. For the case where the terminal flow rates are specified, the capital 0 method is used to pick a set of corrected component-flow rates which satisfy the component-material balances enclosing each column and the specified values of the terminal rates simultaneously. For the case where other specifications are made in lieu of the terminal rates, sets of corrected terminal rates which satisfy the material and energy balances enclosing each column as well as the equilibrium relationships of the terminal streams are found by use of the capital 0 method of convergence as described in Chap. 7. 

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