Feed Flow Rate Disturbances

Luyben (1993a) provided valuable insights into the characteristics of recycle systems and their design, control, and economics, and illustrated the challenges caused by the feedback interactions in such systems, within a multi-loop linear control framework. Also, in the context of steady-state operation, it was shown (Luyben 1994) that the steady-state recycle flow rate is very sensitive to disturbances in feed flow rate and feed composition and that, when certain control configurations are used, the recycle flow rate increases considerably facing feed flow rate disturbances. This behavior was termed the snowball effect. ... 

Figure 5 Flow rate control in case of feed flow rate disturbance rejection. Left controlled outputs. Right manipulated inputs.

The unmeasured feed concentration disturbance rejection posed more difficulties (Fig. 7). On the opposite, the measured feed flow rate disturbance is rejected without dynamic effects (Fig. 8) as the manipulated inputs are algebraically and linearly related to the disturbance value. Even if ratio control is globally less efficient that flow rate control, the capacity of ratio control to reject feed flow rate disturbances is attractive in some particular cases such as the pharmaceutical or the fine chemistry where the production is carried out by batches. Thus the set point remains constant because it is associated to the batch recipe resulting in a given final product concentration, and the main disturbance comes from the feed flow rate that can be modified by the pump operation or the operator. 

Let us return to the stirred tank heater (Example 4.4). If the feed flow rate (disturbance) is not expected to vary significantly, the volume of the liquid in the tank will remain almost constant. In this case dV/dt = A dh/dt = 0 and we can neglect the total mass balance and the associated state variable h. The mathematical model of interest for control purposes is given by the total energy balance alone [eq. (4.5b)], with temperature the only state variable. 

If we change the design feed flow rate, all the column internal and external flow rates and heat-exchanger duties simply scale directly with the feed flow rate. In addition, the resulting temperature and compositions profiles are exactly the same at any flow rate. This occurs because the column pressure and tray pressure drops are specified in the design program and do not change with flow rates. Therefore, in theory, any conttol structure that incorporates any flow ratio (refiux-to-feed, refiux-to-distillate, etc.) will drive the column to the desired product compositions (at steady state) for feed flow rate disturbances. 

If there are only small changes in one of the ratios, a single-end control structure with this ratio fixed may provide effective disturbance rejection in the face of both feed composition and feed flow rate disturbances. 

The results shown in Figure 7.44 show fairly large transient disturbances in both temperature and compositions for feed flow rate disturbances. The change in feed flow rate enters the column and must impact the control tray temperature before any corrective action in reboiler heat input occurs. 

Dynamic Performance. The three control structures are simulated in Aspen Dynamics, controllers are tuned, and feed flow rate disturbances are imposed on the system. At time equal to 0.2 h, the feed flow rate is increased from 100 to 120 lb mol/h. At time equal to 4 h, the feed is dropped to 80 lb mol/h. Finally, at time equal to 7 h, the feed is increased to 120 lb mol/h. These very large disturbances are handled with different degrees of effectiveness by the three control structures. 

Figure 8.18b shows the changes in other key variables. The solid lines are for feed flow rate disturbances. The dashed lines are for feed-composition disturbances. Notice that the CCxB composition-controller changes the set point temperature for the feed-composition disturbances, shifting it lower than the design 128 °F for higher propane compositions in the feed and higher for the lower propane compositions in the feed. Likewise, the RR is... 

Figure 8.42 (a) 20% feed flow rate disturbances, (b) Feed-composition disturbances. 

Figure 11.53 (a) Feed flow rate disturbances of both crudes, (b) Increasing Crude 1 and decreasing Crude 2. 

Figure 12.22 (a) 20% feed flow rate disturbances for divided-wall column, (b) 20% feed flow rate disturbances with QrIF ratio control, (c) 20% feed flow rate disturbances with QrIF ratio and RIF control. 

Figure 12.27 Comparison of DW and conventional feed flow rate disturbances.

The responses of the system to the feed flow rate disturbances are shown in Figure 18.20. The column pressure drop is controlled at 0.5 bar during the period at the high feed flow rates. But the temperature controller output signal OP TC (bottom left graph) does not windup. 

Figures 20.13 and 20.14 compare the performance of the MPC and multiloop control systems for a +1% set-point change in X at r = 0, followed by two feed flow rate disturbances a +30% increase at r = 50 min and a return to the original value at r = 100 min. The input and output variables are displayed as deviation variables. The numerical values of the integral of the absolute error (lAE) performance index (Chapter 12) are included for each output.

Example 1.4. For the heat exchanger shown in Fig. 1.4, the load disturbances are oil feed flow rate F and oil inlet temperature Tq. The steam flow rate f, is the manipulated variable. The controlled variable is the oil exit temperature T. 

Example 1.5. For a binary distillation column (see Fig. 1.6), load disturbance variables might include feed flow rate and feed composition. Reflux, steam, cooling water, distillate, and bottoms flow rates might be the manipulated variables. Controlled variables might be distillate product composition, bottoms product composition, column pressure, base liquid level, and reflux drum liquid level. The uncontrolled variables would include the compositions and temperatures on aU the trays. Note that one physical stream may be considered to contain many variables ... 

Constant holdup and perfect mixing are assumed in the cooling (acket Disturbances in inlet feed flow rate F(> and feed concentration C o tire step clmnges at time equal zero. 

Figures 5.4 through 5.6 give results for disturbances in feed composition and feed flow rate. Note that in Fig. 5.5 the controller gain has been decreased to 2.5 and a larger feed composition disturbance has been made. The response is quite oscillatory. We will discuss the tuning of temperature controllers in this type of system in much more detail later in this book.

If the only disturbances were feed flow rate changes, we could simply ratio the reflux flow rate to the feed rate and control the composition of only one end of the column (or even one temperature in the column). However, changes in feed composition may require changes in reflux and vapor boilup for the same feed flow rate. 

Let us choose a feedforward control system that holds both reactor temperature T and reactor concentration Cj conslant at their steadystate values, f and. The feed flow rate F and the jacket temperature Tj are the manipulated variables. Disturbances are feed concentration C o and feed temperature 7. ... 

Controlled variables include product compositions (x,y), column temperatures, column pressure, and the levels in the tower and accumulator. Manipulated variables include reflux flow (L), coolant flow (QT), heating medium flow (Qb or V), and product flows (D,B) and the ratios L/D or V/B. Load and disturbance variables include feed flow rate (F), feed composition (2), steam header pressure, feed enthalpy, environmental conditions (e.g., rain, barometric pressure, and ambient temperature), and coolant temperature. These five single loops can theoretically be configured in 120 different combinations, and selecting the right one is a prerequisite to stability and efficiency. 

Notice that, according to the developments above, a change in the inlet impurity fraction is a disturbance that strongly impacts the slow dynamics of the process. This is apparent in the simulation scenarios presented in Figures 4.12-4.14 and 4.18-4.20 the time required to reach steady state after an increase in j/io is clearly longer than the response time for an increase in the feed flow rate F() (Figures 4.9-4.11 and 4.15 4.17). 

Figures 7.9 and 7.10 show the evolution of the compositions and temperatures on representative column stages for a small step change in the feed flow rate. According to our theory, this disturbance influences the slow material-balance dynamics and has very little impact on the fast energy dynamics of the column. Indeed, while there are significant (albeit slow) changes in the stage compositions,...

The model predictive control used includes all features of Quadratic Dynamic Matrix Control [19], furthermore it is able to take into account soft output constraints as a non linear optimization. The programs are written in C++ with Fortran libraries. The manipulated inputs (shown in cm Vs) calculated by predictive control are imposed to the full nonlinear model of the SMB. The control simulations were made to study the tracking of both purities and the influence of disturbances of feed flow rate or feed composition. Only partial results are shown. 

In this work, the influences of two different sets of manipulated inputs have been compared in the case of linear model predictive control of a simulated moving bed. The first one consisting in direct manipulation of flow rates of the SMB showed a very satisfactory behavior for set point tracking and feed disturbance rejection. The second one consists in manipulating the flow rates ratios over each SMB section. At the identification stage, this strategy proved to be more delicate as the step responses displayed important dynamic differences of the responses. However, when the disturbance concerns the feed flow rate, a better behavior is obtained whereas a feed concentration disturbance is more badly rejected. 

The monitoring uses formulas that take into account feed flow rates, targets calculated by the optimization layer of multivariable control, controlled variables upper and lower limits and other parameters. The economic benefits are based on the degrees of freedom and the active constraints at the steady state predicted by the linear model embedded in the controller. In order to improve the current monitoring, parameters dealing with process variability will be incorporated in the formulas. By doing this, it will be also possible to quantify external disturbances that affect the performance of the advanced control systems and identify regulatory control problems. 

As in most processes, a distillation column and other separation processes must be maintained at operating conditions that result in products meeting certain specifications. To achieve this objective on a continuous basis the process is equipped with an automatic control system. Various disturbances can occur during the operation of the process, such as variations in ambient conditions or in the feed flow rate or composition. This can move the process away from design steady-state conditions, causing the products to be off-specification. The automatic controller counters the disturbances by adjusting the operating conditions such as to maintain the process variables at acceptable values. 

The operation of the heater is disturbed by external factors such as changes in the feed flow rate and temperature (F, and 7 ,). If nothing changed, then after attaining T - Ts and V = Vs, we could leave the system alone without any supervision and control. It is clear, though, that this cannot be true since T, and F, are subject to frequent changes. Consequently, some form of control action is needed to alleviate the... 

Specification of the Disturbances. Two are the main disturbances for the binary distillation column the feed flow rate Fj and the feed composition Cf. Their values are specified by the external world (e.g., a reactor whose effluent stream is the feed to the distillation column). Although the equations specifying Ff and c/ are not known to us, they do exist and remove two degrees of freedom, leaving four for additional specifications. 

Furthermore, assuming that from all possible disturbances only the feed compositions cA, and cA2 are expected to change significantly whereas the feed flow rates F, and F2 and feed temperatures Tt and T2 are expected to remain almost the same, we can omit from the mathematical model the total mass and energy balances and from the set of state variables volume V and temperature T2. Thus the simplified model is given only by the balance on component A [eq. (4.13a)]. 

Consider a change in the inlet concentration (load) or the desired effluent concentration (set point). Loop 1 will compensate for these changes by manipulating the feed flow rate. However, this change in the feed rate also disturbs the reactor temperature away from the... 

The feed flow rate F, and feed temperature T, are the main two disturbances for the stirred tank heater and they are both specified by the external world (e.g., the unit that precedes the tank heater). Although the equations that specify F, and T, may not be known to us, nevertheless they exist and remove two degrees of freedom. Thus we have 4-2 = 2 remaining degrees of freedom. 

Four manipulated variables are also available distillate flow rate (D), reflux rate (R), steam flow rate (S), and bottoms flow rate (B). The basic disturbances are feed flow rate and composition, and the cooling water temperature in the overhead condenser. Table 25.4 shows all possible control-loop configurations for the benzene distillation column. Let us now screen these alternatives and select the best. 

It is interesting to note that the variation of level is sensitive. Thus, an increase in feed temperature makes decrease the level at longer time. The outlet liquid flow rises slightly, although a decrease was expected because of a vaporisation effect. By increasing the feed flow, the level decrease is stopped and the opposite effect takes place. The accumulation is reversed again when the feed flow rate is reduced. In conclusion, the influence of disturbances on the outlet streams is damped by the level variation. This effect is of great importance in practice, when the insertion of a tank is often used to cut disturbances both in flow and concentrations. 

Finally, the results of controllability analysis are checked by closed loop dynamic simulation. Figure 12.19 displays the time variation of the distillate and bottom purity as fraction from the full scale for a disturbance of 40 kg/h (20%) in the feed flow rate. Both controllers are of Pl-type with c=l and reset time of 20 minutes. It may be observed that both disturbances are rejected conveniently, despite a very large disturbance. Controlling the purity of distillate is easier than of the bottoms, which confirms the controllability analysis. 

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