Consequently, the bottoms composition (x) has to be controlled by manipulating the energy balance of the column by throttling the boil-up rate (V = Q). The relationship between separation (S) and the ratio of boil-up to feed (V/F), can be expressed as , where a and b are functions of the relative volatility, the number of trays, the feed composition and the minimum V/F. The boil-up rate (V) can be calculated by the following equation , where [V/F] is the desired boil-up to feed ratio.
The dynamic characteristics of the column (dead times and time constants) are compensated by the FY element identified as “dynamics” in Figure 3. If correctly tuned, it will guarantee that the feed-forward manipulations will arrive at the controlled variables (D and V) at the right time and in the right amounts. At the bottom of Figure 3, the characteristics of a number of dynamic compensators are described.
Two Products with Interaction
Interaction is unavoidable between the material and energy balances in a distillation
column. The severity of this interaction is a function of feed composition, product specification and the pairing of the selected manipulated and controlled variables.
Severe interaction is likely to occur when the composition controllers of both products are configured to manipulate the energy balance of the column. An example of such a case is when reflux flow (L) and steam flow (Q) are manipulated by the two product composition controllers. In such a case, the heat input is while the reflux rate is L = K1Q – K2F. Therefore, both product flow rates are dependent on energy balance terms.
In this configuration, if one composition controller is increasing the heat input to the reboiler, this action will force the other composition controller to increase reflux flow to withdraw that increased heat. Therefore, without decoupling, the two composition controllers “fight” each other, and severe interaction will occur.
In the decoupling equations given above for Q and L, the values of k1, k2 and K are determined by using the actual process values of [L/F], [V/F]min, and [V/F]. By implementing the decoupling equation L = K1Q – K2F, the tendency of a change in heat input at the bottom of the column, causing an upset in the composition at the other end, will be minimized (right of Figure 3), because the decoupling loop adjusts the reflux flow independently.
While the top composition loop is decoupled, the heat input is still coupled to reflux, because a change in reflux will still cause the bottom temperature controller to adjust steam flow. This type of half-decoupling, therefore, does not eliminate interaction completely, but is enough to reduce the interaction approximately twenty-fold.
The limitations of decoupling include that overrides can drive the loops to saturation when constraints are encountered. In some distillation columns, small measurement errors also can completely destroy the operation of such decoupling systems. Since the decoupler gain settings (k1, k2 and K) depend on the process gains, and because process gains change with variations in feed rate, product specifications and column characteristics, these systems require constant attention and retuning. Such adjustments are beyond the capability of the average plant operating personnel and require the availability of sophisticated column models.
The difficulties associated with decoupling justify the detailed evaluation of column behavior. As was discussed in the first article of this series, an important tool of such an evaluation is the calculation of the relative gains of the various configurations. One general rule worth remembering is that the composition controller for the component with the shorter residence time should adjust vapor flow, and the composition controller for the component with the longer residence time should adjust the liquid/vapor ratio.
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