Equilibrium feed composition

In the highly nonlinear equilibrium situations characteristic of liquid separations, the use of priori initial estimates of phase compositions that are not very close to the true compositions of these phases can lead to divergence of iterative computations or to spurious convergence upon feed composition. 

For a given drum pressure and feed composition, the bubble- and dew-point temperatures bracket the temperature range of the equilibrium flash. At the bubble-point temperature, the total vapor pressure exerted by the mixture becomes equal to the confining drum pressure, and it follows that X = 1.0 in the bubble formed. Since yj = KjXi and since the x/s stiU equal the feed concentrations (denoted bv Zi s), calculation of the bubble-point temperature involves a trial-and-error search for the temperature which, at the specified pressure, makes X KjZi = 1.0. If instead the temperature is specified, one can find the bubble-point pressure that satisfies this relationship. 

Continuous Countercurrent Systems Most adsorption systems use fixed-bed adsorbers. However, if the fluid to be separated and that used for desorption can be countercurrently contacted by a moving bed of the adsorbent, there are significant efficiencies to be realized. Because the adsorbent leaves the adsorption section essentially in equilibrium with the feed composition, the inefficiency of the... 

The plate to plate type calculation is a fundamental procedure wherein the tower is assumed to be composed of theoretical equilibrium plates. The actual plates required are determined from the number of theoretical plates using a predicted overall tower efficiency. The starting point for a tower calculation is usually a specified feed composition, feed temperature, and tower operating pressure. The procedure involves defining the compositions and temperamres on each plate in the tower and subsequently the resultant compositions and temperatures of the product streams. The actual computations, which involve trial... 

Since the product materials are calculated in the number of moles that can be obtained at equilibrium under given conditions of temperamre, pressure, and feed composition, Equation 6-5 is modified to give... 

This paper surveys the field of methanation from fundamentals through commercial application. Thermodynamic data are used to predict the effects of temperature, pressure, number of equilibrium reaction stages, and feed composition on methane yield. Mechanisms and proposed kinetic equations are reviewed. These equations cannot prove any one mechanism however, they give insight on relative catalyst activity and rate-controlling steps. Derivation of kinetic equations from the temperature profile in an adiabatic flow system is illustrated. Various catalysts and their preparation are discussed. Nickel seems best nickel catalysts apparently have active sites with AF 3 kcal which accounts for observed poisoning by sulfur and steam. Carbon laydown is thermodynamically possible in a methanator, but it can be avoided kinetically by proper catalyst selection. Proposed commercial methanation systems are reviewed. 

In an equilibrium flash process a feed stream is separated into liquid and vapour streams at equilibrium. The composition of the streams will depend on the quantity of the feed vaporised (flashed). The equations used for equilibrium flash calculations are developed below and a typical calculation is shown in Example 11.1. 

While the H20/CO ratio is crucial for the performance of LT WGS, it was particularly interesting to study the activity of catalysts at stoichiometric ratio and at H20/CO ratio of 3 1. Both are lower than those used in the commercial LT WGS processing of the gas exiting HT WGS. This was done deliberately for two reasons. The first is that there was no C02 present in the feed. Hence, the H20/CO ratio could be lower because there was no need to compensate the C02 influence on equilibrium with higher H20 concentration (due to reverse WGS reaction). The second reason was the intention to study the behavior of LT WGS catalysts at relatively low inlet CO concentration (0.5 vol%) with respect to the usual inlet CO concentrations used in the industrial process (1.5 to 3 vol%). The feed composition used here was similar to that reported in Refs. [45,46], except that the CO concentration and the H20/C0 ratio were lower. 

Figure 7.7 Influence of the increasing molar ratio of water and carbon monoxide, and of the addition of 50% H2 to the feed gas mixture on the CO conversion in WGS reaction over Cu0 2Ce08O2 y, catalyst at different feed compositions with SV = 5000 hr1. The solid lines are model fits assuming first-order reversible kinetics. The dotted lines represent the equilibrium conversions for the specific feed compositions. (Reprinted from [51 ]. With permission from Elsevier.)...

The constraints on m1 and m4 are explicit. The lower limit of m, however, does not depend on the other flow rate ratios, whereas the upper limit of m4 is an explicit function of the flow rate ratios m2 and m3 and of the feed composition respectively [25]. The constraints on m2 and m3 are implicit (see Eq. 4), but they do not depend on m1 and m4. Therefore, they define a unique region of complete separation in the (m2, m3) plane, which is the triangle-shaped region abw in Fig. 4. The boundaries of this region can be calculated explicitly in terms of the adsorption equilibrium parameters and the feed composition as follows [25] ... 

When a specific feed composition is given, the constraints on m1 and m4 as well as the complete separation region in the (m2, m3) plane can be determined,since these depend only on the parameters of the adsorption equilibrium isotherms and the feed composition itself. Based on these values an operating point can be selected, i. e. a set of four values of = 1,..., 4 fulfilling the complete separation requirements. Since the flow rate ratios are dimensionless groups combining column volumes, flow rates and switching intervals, the constraints on the flow rate ratios are independent of the size and productivity of the SMB unit. 

Typically, adsorption isotherms are generated using a batch experiment at a fixed temperature and a fixed feed composition. These experiments include exposing a known amount of adsorbent to a known concentration of adsorbate at a constant temperature. Once equilibrium is established, the net adsorbate concentration in the liquid is measured. This process is repeated at multiple adsorbate concentrations and temperatures. A plot of adsorbate loading (g adsorbate/g adsorbent) versus adsorbate concentration reveals the adsorption isotherm with the shape of the isotherm determining the suitability of a particular adsorbent for a particular system [20]. 

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... 

To obtain the number of ideal stages in the contactor, one starts by plotting the point y +1 (which is the feed composition of the gas) on the operating line this defines x N. This corresponds to solving the material balance given by Eq. (24) to determine x N. Next, one draws a vertical line from the point (x N, y +1) to the equilibrium curve this defines y N. This corresponds to solving the equilibrium relationship to determine yfN. From the point... 

The operation is most easily understood by reference to the equivalent true countercurrent system (Fig. 15). If we consider a feed containing two species A and B, with A the more strongly adsorbed, and a desorbent C, then in order to obtain separation the net flow directions in each section must be as indicated. With the equilibrium isotherms and the feed composition and flow rate specified, this requirement in effect fixes all flow rates throughout the system as well as the adsorbent recirculation rate or switch time. From simple theoretical considerations it can be easily shown that the affinity of the adsorbent for the desorbent should be intermediate between that for the strongly and weakly adsorbed feed compounds (i.e., a c > 1 -0, bc < 1 -0). The heights of the individualized bed sections are then determined by the requirement that each section contain sufficient theoretical plates to achieve the required purity of raffinate and extract products. For a linear system the analysis is straightforward since simple expressions for the concentration profile are available in terms of the kinetic and equilibrium... 

Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the vapour enthalpies. The input data required to evaluate these thermodynamic properties were taken from Reid et al. (1977). Initialisation of the plate and condenser compositions (differential variables) was done using the fresh feed composition according to the policy described in section 4.1.1.(a). The simulation results are presented in Table 4.8. It shows that the product composition obtained by both ideal and nonideal phase equilibrium models are very close those obtained experimentally. However, the computation times for the two cases are considerably different. As can be seen from Table 4.8 about 67% time saving (compared to nonideal case) is possible when ideal equilibrium is used. 

The number of plates (defining the column configuration), feed, feed composition, column holdup, etc. for the problem are given in Table 4.9 (Chapter 4). The vapour-liquid equilibrium data and the kinetic data are taken from Simandl and Svrcek (1991) and Bogacki et al. (1989) respectively and are shown in Table 4.10 (Chapter 4). The vapour and liquid enthalpies are calculated using the data from Reid et al. (1977). As mentioned in Chapter 4, these data do not account for detailed VLE calculations and for any azeotropes formed. 

To determine minimum reflux, construct the q-line and identify its point of intersection with the equilibrium curve. Then draw a line from the product composition point on the 45° diagonal line to this intersection point, From Eq. (2,29), the slope of the line is RmiJ (/ min + 1), and the intercept of this line on they axis is XrJ(RmiT. + 1). Minimum reflux can be determined from either of these. If minimum reflux occurs at a tangent pinch, the minimum reflux is independent of the q-line and the feed composition, It can then be determined from the equilibrium curve alone (13). 

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