Accumulation self-regulating

We say that the inventory is self-regulating. Similarly, the plantwide control can fix the flow rate of reactant at the plant inlet. When the reactant accumulates, the consumption rate increases until it balances the feed rate. This strategy is based on a self-regulation property. The second strategy is based on feedback control of the inventory. This consists of measuring the component inventory and implementing a feedback control loop, as in Fig. 4.2(b). Thus, the increase or decrease of the reactant inventory is compensated by less or more reactant being added into the process. 

The first inequality characterizes recycle systems with reactant inventory control based on self-regulation. It occurs because the separation section does not allow the reactant to leave the process. Consequently, for given reactant feed flow rate F0, large reactor volume V or fast kinetics k are necessary to consume the whole amount of reactant fed into the process, thus avoiding reactant accumulation. The above variables are grouped in the Damkohler number, which must exceed a critical value. Note that the factor z3 accounts for the degradation of the reactor s performance due to impure reactant recycle, while the factor (zo — z4) accounts for the reactant leaving the plant with the product stream. 

If a process settles at a new steady state after an input change, the process is referred to as self-regulating. Levels in tanks, accumulators, and reboilers, and many pressure systems, behave as integrating processes. Consider the level in a tank for which both the flow in and the flow out are set independently. Initially, the flow out, is equal to the flow in, and the level is constant. Figure 15.8 shows the level as a function of time for a step change in the flow out at time equal to 10 s. Note that the level in the tank begins to decrease at a constant rate. This is an example of a non-self-regulating process, since the process does not move to a new steady state. 

The control of the accumulation can occur by self-regulation, or by manipulating process flows and operating conditions of units. 

In a similar manner, the accumulation term can be driven to zero in gas-phase operations by means of controlled self-regulation that makes use of a pressure controller. Chemical reactions can also act as self-regulating when the accumulated component is a reactant, or if this is involved in an equilibrium reaction. When the accumulated component is a product, there is no mean to limit its inventory, except to manipulate an exit stream, or to cancel its generation. The above procedure is intuitive, and may be used for small-scale problems. However, it does not indicate how to solve systematically this problem, and how to include design elements in analysis. 

With two-compartment cells the cathodic efficiency also represents the total current efficiency of the process. In the three-compartment cells, the current efficiency for sulfuric acid production (anodic efficiency) must also be taken into consideration. The overall current efficiency of electrolysis is represented by the lower of the two efficiencies. If, for example, the anodic efficiency is lower than the cathodic, acidity builds up in the sodium sulfate compartment during operation so that the cathodic current efficiency progressively decreases when it reaches the same value as the anodic, stationary process conditions are maintained. Therefore, the process is provided with a self-regulating mechanism. Alternatively, if the accumulation of acidity in the sodium sulfate compartment cannot be allowed, then a portion of the caustic soda produced can be fed into the sodium sulfate loop. The quantity of caustic soda available for use outside the electrolysis plant again represents the overall current efficiency, which still remains a function of the anodic efficiency. The anodic and cathodic current efficiencies can be made independent when the control of acidity in the sodium sulfate compartment is performed by means of sodium carbonate addition. 

Step 6. Fix a flow rate in every recycle loop and control vapor and liquid inventories (vessel pressures and levels). Process unit inventories, such as liquid holdups and vessel pressures (measures of vapor holdups), are relatively easy to control. While vessel holdups are usually non-self-regulating (Guideline 1), the dynamic performance of their controllers is less important. In fact, level controllers are usually detuned to allow the vessel accumulations to dampen disturbances in the same way that shock absorbers cushion... 

Self-regulation is feasible if there are sufficient reactions to adjust the consumption rate of each reactant such no accumulation occurs. This condition is expressed by Eq. (15). 

The first step is to determine which variables have some form of self-regulation. A variable is self-regulating when an accumulation or process condition returns to a new steady state value without an external intervention. This should be a value within the operating region, without exceeding capacity limits. Some examples of self-regulation are ... 

Only assumptions that relate to the inputs and outputs are relevant at the level of the environmental diagram. Assumptions with respect to self-regulating accumulations can be made later during the development of the behavioral model. Often this cannot be avoided, since the contribution of different terms has to be evaluated. 

Every incoming flow that has not been determined externally, should be controlled, except when the flow is established as a resirlt of self-regulation of the adjustable mass- or energy accumulation. 

---