Single-Stage Batch Equilibrium

This process is generally used when a small amount of a fluid, the solution, is to be treated, such as in the case of pharmaceuticals. The adsorbent and the solution are mixed thoroughly in a container until equilibrium is reached between the phases. 

If the solution volume, assumed fixed, is 5 m and the adsorbent mass, also constant, is M kg, then by adsorbate material balance the amount of adsorbate leaving the solution equals what is adsorbed  

Activated granular carbon is used to treat water contaminated with phenol. The granular carbon is mixed with the water at 25°C and stirred thoroughly until equilibrium is reached. The equilibrium at 25°C can be represented by the Freundlich isotherm, 

In one such operation 1 nc of water containing 0.3 kg/m phenol was treated with 1.5 kg activated carbon wilh no residual contaminants. Determine the final phenol concentration in the water and in the adsorbent. 

Equation 19.9 is solved with the Freundlich equation to determine and q. For the given values. Equation 19.9 is written as 

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The Rayleigh model was developed for a single stage batch distillation-where a liquid mixture is charged in a still and a vapour is produced by heating the liquid. At any time, the vapour on top of the liquid is in equilibrium with the liquid left in the still. The vapour is removed as soon as it is produced but no part of the vapour is returned as reflux to the still after condensation. 

Contrary to single stage batch distillation, the product concentration Xg, is not in equilibrium state with the bottom concentration Xg. Besides the phase equilibrimn, the relationship between product and vessel concentrations (Xg, and Xg) depends on the niunber of stages as well as on the reflux ratio colunm Two... 

Single-stage, batch or continuous separation steps in multiphase systems can only lead to near-complete separations when the partition (or distribution) coefficients of the components over the various phases are sufficiently different. Because of the common structural similarity of main products and contaminants, this is usually not the case. The key parameter is the so-called separation factor S (Fig. 3). Assuming thermodynamic equilibrium between outlet flows of a single equilibrium stage, the separation factor S relates performance to the ratio of auxiliary flow (V) and feed flow (L) and the distribution coefficient of the... 

Ordinarily it would be assumed that in the experiments equilibrium had not been obtained and that the stage efficiency was" low. Examination of their experimental procedure indicates that such low stage efficiencies would be highly unlikely, and indeed the same phenomena have been observed with other oil-solvent systems (82, 141, 147). The difficulty can be laid to the fact that the system is not composed of simply three components, and the distribution of a particular component will depend upon the amount and kind of others that are in the extract (90). The equilibria therefore change with the extent of extraction, and data based on single-stage batches cannot directly be applied to multistage extraction. 

The simplest example of batch distillation is a single stage, differential distillation, starting with a still pot, initially full, heated at a constant rate. In this process the vapour formed on boiling the liquid is removed at once from the system. Since this vapour is richer in the more volatile component than the liquid, it follows that the liquid remaining becomes steadily weaker in this component, with the result that the composition of the product progressively alters. Thus, whilst the vapour formed over a short period is in equilibrium with the liquid, the total vapour formed is not in equilibrium with the residual liquid. At the end of the process the liquid which has not been vaporised is removed as the bottom product. The analysis of this process was first proposed by Rayleigh(24). 

In general, with a sufficiently large equilibrium constant (distribution ratio) and a rapid rate of attainment of equilibrium, quantitative transfer from one phase to another can be made in a single stage. For such highly favorable systems, batch liquid-liquid extractions can be used in which one phase is equilibrated with several successive fresh portions of a second phase. Such batch separations are most effective when one component remains quantitatively in one phase while another distributes itself between the two phases. 

The batch contactor is limited to use with reactions that go to completion in a single stage or in relatively few stages. Difficulties may also arise with batch contactors if resin regeneration requires a greater number of equilibrium stages than the service portion of the cycle. 

Flash vaporization is a single-stage operation wherein a liquid mixture is partially vaporized, the vapor is allowed to come to equilibrium with the residual liquid, and the resulting vapor and liquid phases are separated and removed from the apparatus. It may be batch or continuous. 

The simplest case of batch distillation corresponds to use of the apparatus shown in Fig. 9.1. There is no reflux at any instant, vapor leaving the still pot with composition yo is assumed to be in equilibrium with the liquid in the still, and yn = Xp. Thus, there is only a single stage. The following nomenclature is used assuming that all compositions refer to a particular species in the multicomponent mixture. 

Single contact. This involves the use of a single stage, where solution to be separated and extracting solvent are contacted once and extract and raffinate phases separated. Operation may be batch wise or continuous. The distillation analog is flash vaporization or equilibrium distillation. 

Flash Units. In simulators, the term flash refers to the module that performs a single-stage vapor-liquid equilibrium calculation. Material, energy, and phase equilibrium equations are solved for a variety of input parameter specifications. In order to specify completely the condition of the two output streams (liquid and vapor), two parameters must be input. Many combinations are possible—for exanple, temperature and pressure, temperature and heat load, or pressure and mole ratio of vapor to liquid in exit streams. Often, the flash module is a combination of two pieces of physical equipment, that is, a phase separator and a heat exchanger. These should appear as separate equipment on the PFD. Note that a flash unit can also be specified for batch operation, in which case the unit can serve as a surge or storage vessel. 

The leached solids must be separated from the extract by settling and decantation or by external filters, centrifuges, or thickeners, all of which are treated elsewhere in Sec. 18. The difficulty of solids-extract separation and the fact that a batch stirred tank provides only a single equilibrium stage are its major disadvantages. 

With a single equilibrium stage and no reflux, the separation power in differential distillation is obviously limited. It is the equivalent of a batch flash operation. Consequently, practical applications would include the separation of wide-boiling mixtures, with low expectations on the purity of the products. 

The batch system is basically inefficient since the establishment of a single equilibrium will give incomplete removal of the solute in the feed solution. When the affinity of the resin for this solute is very high, it is possible diat the removal is sufficiently complete in one stage. The batch process has the advantage over fixed bed processes that solutions containing suspended solids may be treated. In these cases, the resin particles, loaded with the adsorbate and rinsed from the suspended solids, may be placed in a column for recovery of the adsorbate and for regeneration. 

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