Binary feed mixtures

The assumption of equilibrium has two effects. First, the details of the flow and/or concentrations within the stage are not of interest. Second, streams L and V (exiting 

Total mass balance Component mass balance Equilibrium relationship  

Therefore, a fourth relationship is needed. Typically, the ratio L/V can be set. Now, expressions for yi and Xi can be derived in terms of the mass balances and equilibrium relationship (see if you can derive these) 

As stated above, the analysis of a separation process uses mass balances in conjunction with some specific relation(s) which describe the separation process. For an equilibrium-stage process, this specific relation is the equilibrium relationship that describes the concentration of a component in each phase with respect to each other exiting the stage. Note that the equations can be solved for a single stage once the equilibrium relationship is known. It does not have to be a linear one. 

The subscripts on x and y refer to the stage from which they exit. The quantities xo and yjv+i are inlet concentrations to the sequence of equilibrium stages. The flowrates L and V are assumed constant. This last assumption is useful for developing a basic understanding but is not a general requirement. 

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Robinson (1969) considered the following example problem. A binary feed mixture with an initial amount of charge, B0 = 100 kmol and composition xB0 = <0.50, 0.50> molefraction, having constant relative volatility of 2.0 was to be processed in a batch distillation column with 8 theoretical stages. The aim was to produce 40 kmol of distillate product (D) with composition (xd) of 0.5 molefraction for component 1 in minimum time (tF) using optimal reflux ratio (/ ). 

The example problems are taken from Tran and Mujtaba (1997) and Mujtaba (1999) and only binary feed mixtures are considered in all three examples. 

Referring to the generic separation schematic (Figure 3.28), assume that it represents a single stage of an equilibrium-based process for the separation of a binary feed mixture. 

For a binary feed mixture of gases A and B at feed partial pressures of Pf j, and p j, and permeate partial pressures of and pgp respectively, the permeation rates per unit membrane area of the two species are, respectively... 

According to equation (10.1.4), the thermodynamic minimum energy requirement per gmol of an ideal binary feed mixture of styrene (i — 2) and ethylbenzene (i = 1) yielding pure products is given by... 

With reference to Fig. 6.11, assume that this binary feed mixture enters the column as saturated vapor on the fourth plate. Ideally, the liquid on the plate above the feed inlet (point L5) has the same composition as the feed, but is at a lower temperature since the latter is at the bubble-point temperature rather than at the dew-point temperature. Within the column, vapor flows upward through the liquid layer on each plate, while the liquid flows across each plate and down to the next plate by means of a downcomer. The vapor transfers heat to the liquid on each plate as it bubbles through the liquid. This heat transfer results in the evaporation of a small amount of the more volatile component from the liquid layer and correspondingly in the condensation of a small amount of the less volatile component in the vapor. Thus, the vapor becomes richer in nitrogen as the vapor comes in contact with the liquid layer and the liquid layer becomes richer in oxygen as the liquid contacts the vapor and flows downward from plate to plate. This is illustrated in Fig. 6.12, which shows the ideal temperature-composition of the vapor and liquid above and below the feed entry. As the saturated liquid moves down the column, its composition moves to the left along the bubble-point curve (points L4, L3,... 

A general sketch of the inlet-outlet boundary conditions which will be defined for the carbon dioxide capture process, according to the previous analysis, is presented on Figure 2.1. The membrane process simulation framework will be presented in the next paragraph, based on a binary feed mixture in a first step, as explained above. 

It is desired to separate a binary mixture by simple distillation. If the feed mixture has a composition of 0.5 mole fraction, calculate the fraction which it is necessary to vaporise in order to obtain ... 

It is desired to separate a binary mixture by simple distillation. If the feed mixture has a composition... 

This illustrative example is taken from the recent work on interaction of design and control by Luyben and Floudas (1994a) and considers the design of a binary distillation column which separates a saturated liquid feed mixture into distillate and bottoms products of specified purity. The objectives are the determination of the number of trays, reflux ratio, flow rates, and compositions in the distillation column that minimize the total annual cost. Figure (1.1) shows a superstructure for the binary distillation column. 

A series of multielectrode sensors were developed based on Drosophila mutant AChE immobilised via photocrosslinking onto screen-printed carbon electrodes [8]. Four different mutant and wild-type AChE were evaluated for their sensitivity to the organophosphate paraoxon and the carbamate pesticide carbofuran. The response of the electrodes in thiocholine before and following a 15-min exposure to solutions of the pesticides was compared. The data was then processed using a feed-forward neural network generated with NEMO 1.15.02 as previously described [8,9]. Networks with the smallest errors were selected and further refined. This approach together with varying the AChE led to the construction of a sensor with capability to analyse the binary pesticide mixtures. 

The separation efficiency for a given membrane with a particular binary gas mixture will be dependent mainly upon three factors gas composition, the pressure ratio between feed and permeate gas, and the sepration factor for the two components. A higher separation factor gives a more selective membrane, resulting in a greater separation efficiency. This parameter is a function of the membrane material and is determined by the individual gas permeation rates. 

Pervaporation is a membrane separation process where the liquid feed mixture is in contact with the membrane in the upstream under atmospheric pressure and permeate is removed from the downstream as vapor by vacuum or a swept inert gas. Most of the research efforts of the pervaporation have concentrated on the separation of alcohol-water system [1-20] but the separation of acetic acid-water mixtures has received relatively little attention [21-34]. Acetic acid is an important basic chemical in the industry ranking among the top 20 organic intermediates. Because of the small differences in the volatility s of water and acetic acid in dilute aqueous solutions, azeotropic distillation is used instead of normal binary distillation so that the process is an energy intensive process. From this point of view, the pervaporation separation of acetic acid-water mixtures can be one of the alternate processes for saving energy. 

Figure 9.19 Fraction of benzene in permeate as a function of feed mixture composition for pervaporation at the reflux temperature of a binary benzene/cyclohexane mixture. A 20-qm-thick crosslinked blend membrane of cellulose acetate and polystyrene phosphate) was used [54]. Reprinted with permission from I. Cabasso, Organic Liquid Mixtures Separation by Selective Polymer Membranes, Ind. Eng. Chem. Prod. Res. Dev. 22, 313. Copyright 1983 American Chemical Society...

The liquid feed, at temperature T0 and pressure P0, and mole fraction z, enters the system. It is elevated to a higher pressure and temperature by a pump and heat exchanger, both requiring input of energy. The binary liquid mixture, now at TF and PF, proceeds to a valve, which reduces the pressure... 

Table 5.6 presents the results of a set of 5 maximum profit problems considered by Kerkhof and Vissers (1978). Each problem has different column configuration (i.e. different number of plates, N), handles different feed mixture (characterised by different relative volatility, a)y has different distillate product quality (xq), has different cost values (i.e. Pr, C0) and different set up times (ts). The initial charge, B0 = 100 kmol, V= 60 kmol/hr, t,= 1 hr, and Cf= 150 /hr. All cases deal with binary mixtures of different initial composition, xB0. 

For single separation duty, Mujtaba and Macchietto (1993) proposed a method, based on extensions of the techniques of Mujtaba (1989) and Mujtaba and Macchietto (1988, 1989, 1991, 1992), to determine the optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main-cuts and off-cuts. A two level dynamic optimisation formulation was presented so as to maximise a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation task and the optimal reflux ratio profiles during each production period. The outer level optimisation maximises the profit function by... 

The operation sequence for a single batch, shown in Figure 6.10, produces 2 main-cuts (PI and P2), 5 off-cuts and a final bottom product (P5). Specifications for products P3 and P4 could not be achieved directly because of the high purity requirement, low amount of component 3 and 4 in the feed mixture and the proximity of their boiling points with other components. Therefore, low purity off-cuts 2-5 (essentially binary or a ternary mixtures) are produced, collected in separate storage vessels and reprocessed when the amount of in each vessel reaches the full... 

Mujtaba (1999) considered the conventional configuration of BED processes for the separation of binary close boiling and azeotropic mixtures. Dynamic optimisation technique was used for quantitative assessment of the effectiveness of BED processes. Two distinct solvent feeding modes were considered and their implications on the optimisation problem formulation, solution and on the performance of BED processes were discussed. A general Multiperiod Dynamic Optimisation (MDO) problem formulation was presented to obtain optimal separation of all the components in the feed mixture and the recovery of solvent while maximising the overall profitability of the operation. 

Today s market is customer oriented. To satisfy customer demands all products must be produced on-specification. This means that all the components (or at least the desired component) must be recovered at given specifications. For binary mixtures Mujtaba (1999) assumes that both the components in the feed mixture are recovered at specified purities. Also the author assumes that the solvent recovered has the same composition as the original solvent fed to the column (see Figure... 

When a distillate product of specified purity is produced using a number of passes in a continuous column, the operation is defined as MPSSS operation. The number of distillate products depends on the number of components in the original mixture. This type of operation is used mainly to improve the recovery of a particular species in the feed mixture (see example section for further explanation). This type of operation can be applied to both binary and multicomponent mixtures. 

Even in the first publications concerning the copolymerization theory [11, 12] their authors noticed a certain similarity between the processes of copolymerization and distillation of binary liquid mixtures since both of them are described by the same Lord Rayleigh s equations. The origin of the term azeotropic copolymerization comes just from this similarity, when the copolymer composition coincides with monomer feed composition and does not drift with conversion. Many years later the formal similarity in the mathematical description of copolymerization and distillation processes was used again in [13], the authors of which, for the first time, classified the processes of terpolymerization from the viewpoint of their dynamics. The principles on which such a classification for any monomer number m is based are presented in Sect. 5, where there is also demonstrated how these principles can be used for the copolymerization when m = 3 and m = 4. 

The parameters a = l/rij5 the number of which equals m(m — IX are reciprocal reactivity ratios (2.8) of binary copolymers. Markov chain theory allows one, without any trouble, to calculate at any m, all the necessary statistical characteristics of the copolymers, which are formed at given composition x of the monomer feed mixture. For instance, the instantaneous composition of the multicomponent copolymer is still determined by means of formulae (3.7) and (3.8), the sums which now contain m items. In the general case the problems of the calculation of the instantaneous values of sequence distribution and composition distribution of the Markov multicomponent copolymers were also solved [53, 6]. The availability of the simple algebraic expressions puts in question the expediency of the application of the Monte-Carlo method, which was used in the case of terpolymerization [85,99-103], for the calculations of the above statistical characteristics. Actually, the probability of any sequence MjMjWk. .. Mrl 4s of consecutive monomer units, selected randomly from a polymer chain is calculated by means of the elementary formula ... 

The values of vy and Xp may be obtained from an adiabatic flash for a single phase feed or from the constant relative volatility estimated with the converged compositions at the feed stage and feed quality. This procedure can be reformulated for multiple feeds and side products as well as different key components. A pinch point near the feed stage occurs for nearly all binary ideal mixtures. However, for nonideal multicomponent systems, the pinch point exists in rectifying and stripping sections. 

Since pentane and water exhibit immiscibility, we might consider decantation as the first step. If it worked, it would be an inexpensive one to carry out. But a rigorous three-phase equilibrium calculation predicts that, in the presence of acetone and methanol, the small water fraction in the feed does not form a second liquid phase so we reject this idea. The calculation also reveals that the feed mixture is almost at the azeotropic composition for the pentane/methanol binary pair. 

The high boiling reactant is fed as feed 1 and the low boiling reactant as feed 2. Between the two feeds, there is the reaction zone. As a special application, feed 1 can serve as an extractive agent, e.g. in the case of the production of methyl acetate, acetic acid serves as an entrainer for the binary azeotropic mixture methanol and methylacetate. The ensemble is then a reactive extractive distillation column. 

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