H-x diagram

The graphical technique most frequently used in distillation is the x-y or McCabe-Thiele diagram (1). The H-x, or Ponchon-Savarit diagram (2,3), is herder to visualize and cannot be readily extended to multicomponent distillation. Due to their limited application, H-x diagrams were excluded from this book, and are discussed elsewhere (4-6). 

Using an H-x diagram to adjust Eqs, (2,9) and (2,10) for latent heat effects. This approach also converts each component balance line into a curve, but the curve is constructed using an H-x diagram instead of a computer simulation. Further details are described by Fisher (10),... 

Using an H-x diagram to derive pseudo molecular weights and pseudo latent heats of vaporization for the components. These pseudo properties are then applied to construct an x-y diagram. This method is described in detail by Robinson and Gilliland (6),... 

Enthalpy-concentration charts are particularly useful for two-component systems in which vapor and liquid phases are in equilibrium. The Gibbs phase rule (Equation 6.2-1) specifies that such a system has (2 -I- 2 - 2) = 2 degrees of freedom. If as before we fix the system pressure, then specifying only one more intensive variable—the system temperature, or the mass or mole fraction of either component in either phase—fixes the values of all other intensive variables in both phases. An H-x diagram for the ammonia-water system at 1 atm is shown in Figure 8.5-2. 

Each point on the saturated liquid curve is associated with a point on the saturated vapor curve at equilibrium with it. The equilibrium vapor and liquid compositions may be obtained from Y-X or Y-X diagrams. Saturated vapor and liquid points on the H-X diagram at equilibrium with each other are joined by straight lines called tie lines. The single-stage graphical representation described in Section 5.3.1 is an illustration of a tie line. If, for instance, X is known, L can be determined as a point on the saturated liquid curve with composition coordinate X. Point V must lie on the other end of the tie line on the saturated vapor curve. Point F can then be determined either from information on the relative rates of feed, liquid, and vapor or from its composition or enthalpy. 

The H-X diagram may be constructed on the basis of either experimental data or computations using any of the prediction methods such as equations of state (Chapter 1). 

Binary distillation columns are solved on the H X diagram by graphically imple-... 

FIGURE 5.13 Modeling condensers on the H X diagram (a) partial condenser, (b) total condenser. 

The versatility of the H-X method is also demonstrated in the analysis of the performance of multiple-feed and multiple-product columns. The basic approach is unchanged relate the passing vapor and liquid streams at the point of interest in the column by performing an energy balance, then implement the relationship graphically on the H-X diagram. 

The binary model, conveniently represented on the Y-X or H-X diagrams, demonstrates the effect on column performance of the reflux ratio, product rate, number of trays, feed location, and thermal conditions. In the cases that follow in this section, the feed is assumed of fixed flow rate and composition. The effect of column pressure, which influences column performance through its effect on the equilibrium curve, is not considered here and is held constant. 

H-X diagram. Given a fixed distillate rate, a higher reflux ratio implies larger vapor... 

Using the H-X diagram, if the feed tray is not fixed, its optimum location can be determined as discussed in Section 5.3.3. 

The H-X diagram technique for determining the number of stages and optimum feed location for a specified separation was described in Section 5.3.3. It was implied that the reflux ratio was also specified since the condenser and reboiler duties were given. If the number of stages is specified, but the condenser and reboiler duties are allowed to vary, it becomes necessary to repeat the above procedure with different pivot points (corresponding to different condenser and reboiler duties) until the number of stages is matched. 

Using the H-X Diagram. Fnthalpy and phase equilibrium data for the methanol (l)/water (2) mixture are given below ... 

Construct the Y-X and H-X diagrams for this binary. What assumptions are necessary for generating the enthalpy diagram from the given data alone ... 

A binary stream at the rate of 1000 kmol/h containing 35% mole of component 1 (the lighter component) is to be separated in a distillation column to produce 95% component 1 in the distillate and 90% component 2 in the bottoms. The column will have a partial reboiler and a partial condenser, and will operate at 1 atm. It is proposed to utilize an existing hot process stream in the plant as a heat source for the reboiler, which limits the reboiler duty to 58 x 10 kJ/h. Using either the Y-X diagram or the H-X diagram, determine the number of theoretical trays required, the optimum feed location, the product rates, and the condenser duty. Assume feed thermal conditions that result in a saturated liquid at the feed tray pressure. Use thermodynamic data from Problem 6.1. 

Two alternative schemes are proposed (1) Mix the feed streams and send the mixture to a single point in the column and (2) Feed each stream separately to different trays in the column. For each option calculate the required number of trays, the optimum teed locations, and the condenser and reboiler duties. Use either the Y-X or H-X diagram methods. 

Equation (10-4) is the three-point form of a straight line and is shown in a one-phase field on an H-x diagram in Fig. 10.1. 

Moller, J.T. and O. Hansen, Computer-drawn H-X diagram and design of closed-cycle dryers, Proc. Eng., 53,84-86,1972. 

In Fignre 14.37 the h-x diagram for an open-cycle drying process is presented. The actual state of the atmospheric air is represented by 0. Supposing that the mass flow rate of the air is m, heat flux into the air is the tanperature increase of the air can be calculated ... 

The direction of the operation of such a dryer is, principally, the same as that written before. Representing the process in an h-x diagram, some differences arose from the facts that the stack is partially irradiated by the absorber and the airflow contacts a differing area of the absorber surface before entering the stack. To elaborate the direction strategy of solar dryers operating by recirculation, experiments are recommended. 

The heat effects accompanying a crystallization operation may be determined by making heat balances over the system, although many calculations may be necessary, involving knowledge of specific heat capacities, heats of crystallization, heats of dilution, heats of vaporization, and so on. Much of the calculation burden can be eased, however, by the use of a graphical technique in which enthalpy data, solubilities and phase equilibria are represented on an enthalpy-composition H x) diagram, sometimes known as a Merkel chart. 

The use of the FF x diagram for the analysis of chemical engineering unit operations such as distillation, evaporation and refrigeration processes, is now quite common, and the procedures are well described in textbooks, e.g. Coulson and Richardson (1991), McCabe, Smith and Harriott (1985). These charts are less frequently applied to crystallization processes, however, because not many H x diagrams are available. 

Figure 4.8. An adiabatic mixing process represented on an H-x diagram...

---