Lean stream

The flow directions in a PSA process are fixed by the composition of the stream. The most common configuration is for adsorption to take place up-flow. AH gases with compositions rich in adsorbate are introduced into the adsorption inlet end, and so effluent streams from the inlet end are rich in adsorbate. Similarly, adsorbate-lean streams to be used for purging or repressurizing must flow into the product end. 

As has been previously mentioned, the minimum TAC can be identified by iteratively varying e. Since the inlet and outlet compositions of the rich stream as well as the inlet composition of the MSA are fixed, one can vary e at the rich end of the exchanger (and consequently the outlet composition of the lean stream) to minimize the TAC of the system. In order to demonstrate this opdmization procedure, let us first select a value of e at the rich end of the exchanger equal to 1.5 X 10 and evaluate the system size and cost for this value. 

The candidate lean streams can be classified into Nsp process MSAs and Nse external MSAs (where Nsp + Nse — Ns). The process MSAs already exist on plant site and can be used for the removal of the undesirable species at a very low cost (virtually free). The flowrate of each process MSA that can be used for mass exchange is bounded by its availability in the plant, i.e.,... 

Next, a global representation of all process lean streams is developed as a lean composite stream. First, we establish Ns/> lean composition scales (one for each process MSA) that are in one-to-one coirespondence with the rich scale according to the method outlined in Section 3.5. Next, the mass of pollutant that can be gained by each process MSA is plotted vei us the composition scale of that MSA. Hence, each i xx ess MSA is represented as an arrow extending between supply and target compositions (see Fig. 3.5 for a two-MSA example). Ihe vertical distance between the arrow head and tail is given by... 

As can be seen from Fig, 3.7, the pinch decomposes the synthesis problem into two regions a rich end and a lean end. The rich end comprises all streams or parts of streams richer than the pinch composition. Similarly, the lean end includes all the streams or parts of streams leaner than the pinch composition. Above the pinch, exchange between the rich and the lean process streams takes place. External MSAs are not required. Using an external MSA above the pinch will incur a penalty of eliminating an equivalent amount of process lean streams from service. On the other hand, below the pinch, both the process and the external lean streams should be used. Furthermore, Fig. 3.7 indicates that if any mass is transferred across the pinch, the composite lean stream will move upward and, consequently, external MSAs in excess of the minimum requirement will be used. Therefore, to minimize the cost of external MSAs, mass should not be transferred across the pinch. It is worth pointing out that these observations are valid only for the class of MEN problems covered in this chapter. When the assumptions employed in this chapter are relaxed, more general conclusions can be made. For instance, it will be shown later that the pinch analysis can still be undertaken even when there are no process MSAs in the plant. The pinch characteristics will be generalized in Chapters Five and Six. 

Table 3.2 Data of Process Lean Streams for the Benzene Removal Example ...

Three MSAs can be used to remove the solvent from the gaseous emission. The equilibrium data for the transfer of the organic solvent to the yth lean stream is given by y - mjXj, where the values of my are given in Table 4.2. Throughout this problem, a minimum allowable composition difference, Sy, of 0.001 (kg organic solvent)/(kg MSA) is to be used. The data for the MSAs are given in Table 1. 

Having determined the individual loads of all process streams for all composition intervals, one can also obtain the collective loads of the waste and the lean streams. The coUective load of the waste streams within the itth interval is calculated by summing up the individual loads of the waste streams that pass through that interval, i.e. 

Similarly, the collective load of the lean streams within the tfa interval is evaluated as follows ... 

As has been mentioned earlier, the CID generates a number Ni , of composition intervals. Within each interval, it is thermodynamically as well as technically feasible to transfer a certain mass of the key pollutant from a waste stream to a lean stream. Furthermore, it is feasible to pass mass from a waste stream in an interval to any lean stream in a lower interval. Hence, for the J th composition interval, one can write the following component material balance for the key pollutant ... 

Having determined f/MOC> wc should then proceed to match the pairs of waste and lean streams. In the sequel, it will be shown that matching has to start from the pinch and must satisfy a number of feasibility criteria. 

Conversely, immediately below the pinch, each lean stream has to be brought to its pinch composition. At this composition, any lean stream can only operate against a waste stream at its pinch composition or higher. Since a MOC design does not permit the transfer of mass across the pinch, each lean stream immediately below the pinch will require the existence of at least one waste stream (or branch) at the pinch composition. 

On the other hand, since the flowrate of each MSA is mfltnown, exact capacities of MSAs cannot be evaluated. Instead, one can create a TEL per unit mass of the MSAs for the lean streams. In this table, the exchangeable load per unit mass of the MSA is determined as follows ... 

The dephenolization problem was described in Section 3.2. The data for the waste and the lean streams are summarized by Tables 6.1 and 6.2. 

Capacity of lean streams per unit mass of MSA (kg phenol/kg MSA) ... 

Having identified the values of all the flowrates of lean streams as well as the pinch location, we can now minimize the number of mass exchangers for a MOC solution. As has been previously mentioned, when a pinch point exists, the synthesis problem can be decomposed into two subnetworks, one above the pinch and one below the... 

Material balance for each lean stream around composition intervals ... 

Given a number Nr of waste (rich) streams and a number Ns of lean streams (physical and reactive MSAs), it is desired to synthesize a cost-effective network of physical and/or reactive mass exchangers which can preferentially transfer a certain undesirable species. A, from the waste streams to the MSAs whereby it may be reacted into other species. Given also are the flowrate of each waste stream, G/, its supply (inlet) composition, yf, and target (outlet) composition, yj, where i = 1,2,..., Nr. In addition, the supply and target compositions, Xj and x j, are given for each MSA, where j = 1,2, Ns. TTie flowrate of any lean stream, Ly, is unknown but is bounded by a given maximum available flowrate of that stream, i.e.. 

A process lean stream and an external MSA are considered for removing H2S. The process lean stream, S1, is a caustic soda solution which can be used as a solvent for the reactive separation of H2S. An added bonus for using the process MSA is the conversion of a portion of the absorbed H2S into Na2S, which is needed for white-liquor makeup. In other words, H2S pollutant is converted into a valuable chemical which is needed in the process. The external MSA, S2, is a polym ic adsorbent. The data for the candidate MSAs are given in Table 8.2. The equilibrium... 

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