Process systems with purge streams

In what follows, we begin by introducing two examples of process systems with recycle and purge. First, we analyze the case of a reactor with gas effluent connected via a gas recycle stream to a condenser, and a purge stream used to remove the light impurity present in the feed. In the second case, the products of a liquid-phase reactor are separated by a distillation column. The bottoms of the column are recycled to the reactor, and the trace heavy impurity present in the feed stream is removed via a liquid purge stream. We show that, in both cases, the dynamics of the system is modeled by a system of stiff ODEs that can, potentially, exhibit a two-time-scale behavior. 

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It is evident that the above models (Equations (4.5) and (4.14)) have terms of 0(1) and O(e) and are in a singularly perturbed form. This suggests, potentially, a two-time-scale behavior for the process systems with recycle and purge streams that they describe. In the next section, we will develop a generic modeling framework for such systems that captures this feature and allows a more general analysis of their dynamic behavior. 

In practical applications, for economic and operational reasons, the flow rate of the purge stream is very small compared with the throughput of the process. Hence, we can assume that the ratio of the purge flow rate to the feed flow rate under steady-state conditions is very small, i.e., Ps/FotS = e 1. We will also consider that the mole fraction of the impurity in the feed (and, consequently, the rate at which the impurity enters the system) is very small, or yio = /3ie, where fa is an 0(1) quantity. 

Note that, from steady-state considerations, in order to remove an appreciable amount of impurity from the recycle loop via the purge stream (whose flow rate is small), the mole fraction of the impurity in the vapor phase in the condenser, 2/i, has to be 0(1). This implies that O(e) moles of impurity enter and leave the system through the feed and purge streams. Note also that our assumption concerning the mass-transfer properties of the component I implies that a negligible amount of impurity leaves the recycle loop through condensation, exiting the process with the liquid stream from the bottom of the condenser. 

Conversely, impurity levels should be controlled by varying the flow rate up of the purge stream. up is clearly the only manipulated input available in the model of the slow dynamics (4.35). The rate at which impurity is input to or generated in the process (as captured by the term (d/dx)gI0(x) x=T-i(()) cannot be set by a process operator and constitutes a (typically unmeasured) process disturbance that the control system must deal with. 

BPA is separated from byproducts in a proprietary solvent crystallization and recovery system (5) to produce the adduct of p,p BPA and phenol. Mother liquor from the purification system is distilled in the solvent recovery column (6) to recover dissolved solvent. The solvent-free mother liquor stream is recycled to the reaction system. A purge from the mother liquor is sent to the purge recovery system (7) along with the recovered process water to recover phenol. The recovered purified adduct is processed in a BPA finishing system (8) to remove phenol from product, and the resulting molten BPA is solidified in the prill tower (9) to produce product prills suitable for the merchant BPA market. 

Step 7. Ethane is an inert component that enters with the ethylene feed. It can be removed from the process only via the gas purge stream, so purge flow is used to control ethane composition. Carbon dioxide is an unwanted by-product that leaves in the C02 removal system. As long as the amount of carbon dioxide removed is proportional in some way to the C02 removal system feed, we can use this valve to control carbon dioxide composition. Oxygen inventory is accounted for via composition control with fresh oxygen feed. Inventory of ethylene can be controlled to maintain gas loop pressure, since ethylene composes the bulk of the gas recycle. 

Recycle is a common feature of chemical processes. Its most common use is to send unused raw materials emerging from a process unit back to the unit. Overall system balances are usually (but not always) convenient starting points for analyzing process with recycle. A purge stream is withdrawn from a process when a species enters in the process feed and is completely recycled. If this species were not removed in the purge, it would keep accumulating in the process system and eventually lead to shutdown. 

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