Material and Energy Balance Control

Often a goal of a control scheme for a distillation column is to maintain the quahty of the top product on specification while also maintaining the material balance. Material balance control and energy balance control are two control schemes that can achieve this. Different criteria can be considered for the selection of a control scheme. Since the performance of both control schemes has a large impact on the profitable operation of the distillation column, this choice is not trivial. 

The name material balance control was introduced by Shinkey (1984). The different control schemes that the author developed were based on the concept of relative gains (= power of control) of the different input-output combinations. Speed of control was only considered as a secondary factor. A simple explanation is given by Ryskamp (1980). Also Van der Grinten (1970) presented a nrrmber of common control schemes for distillation colnmns. The latter author used behavioral models in the eontrol scheme selection procedure. None of the mentioned references takes inverse responses into accoimt when X 0.5. In the case of the more traditional approach, the energy balanee eontrol, the reflux ratio and/or vapor flow is used to eontrol the top product qrrality, while the distillate and bottom flow are nsed to maintain the mass balanee. In the ease of the material balance control, one of the prodnct flows is used to control product qrrahty, while the other product flow maintains the material balance. 

The control schemes are developed for the case of dual composition control. Also other material and energy balance control schemes are possible. The main difference between the control schemes is that in the case of energy balance control the reflux and vapor flow affect the outpoint (distillate-bottom-ratio) as well as the fractionation, whereas in the case of material balance control outpoint and fractionation control are separated. Either the reflux ratio or the vapor flow is manipulated to control the fractionation. As can be seen, the developed control scheme of Fig. 34.5 is similar to the energy balance control scheme. 

One point of interest is the position of the quality measurement for the top product composition. In some cases this measurement is positioned in the distillate flow, another possibility is to position it between the top of the distillation column and the reflux drum. The latter situation offers several advairtages, such as faster detection of the top composition changes, easier gas chromatographic analysis since the flow at this location is aheady in the vapor phase and less interaction between top qnality and reflux drum level. Therefore only this situation will be considered as also shown in Fig. 34.6. 

Control of liquid accumulation in the coluiim is nsually done by controlling the levels of the reflux drum and bottom. The level in the reflux drum can be controlled by the leflnx flow (i ), in which case the control scheme is called material balance control, or the top prodnct draw-off D), in which case it is called energy balance control. To make the right selection for reflux drum level control, the following factors should be considered  

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Table 34.2. Advantages and disadvantages of material and energy balance control schemes.

In the equation-oriented approach, the executive organizes the equations and controls a general-purpose equation solver. The equations for material and energy balances may be grouped separately from those for the calculation of physical properties or phase equiHbria, or as ia the design of some simulators, the distinction between these groups of equations may disappear completely. 

Material and energy balances are based on the conservation law, Eq. (7-69). In the operation of liquid phase reactions at steady state, the input and output flow rates are constant so the holdup is fixed. The usual control of the discharge is on the liquid level in the tank. When the mixing is adequate, concentration and temperature are uniform, and the effluent has these same properties. The steady state material balance on a reacdant A is... 

Parameter Estimation Relational and physical models require adjustable parameters to match the predicted output (e.g., distillate composition, tower profiles, and reactor conversions) to the operating specifications (e.g., distillation material and energy balance) and the unit input, feed compositions, conditions, and flows. The physical-model adjustable parameters bear a loose tie to theory with the limitations discussed in previous sections. The relational models have no tie to theory or the internal equipment processes. The purpose of this interpretation procedure is to develop estimates for these parameters. It is these parameters hnked with the model that provide a mathematical representation of the unit that can be used in fault detection, control, and design. 

This chapter has presented time-domain solutions of unsteady material and energy balances. The more usual undergraduate treatment of dynamic systems is given in a course on control and relies heavily on Laplace transform techniques. One suitable reference is... 

Process simulators contain the model of the process and thus contain the bulk of the constraints in an optimization problem. The equality constraints ( hard constraints ) include all the mathematical relations that constitute the material and energy balances, the rate equations, the phase relations, the controls, connecting variables, and methods of computing the physical properties used in any of the relations in the model. The inequality constraints ( soft constraints ) include material flow limits maximum heat exchanger areas pressure, temperature, and concentration upper and lower bounds environmental stipulations vessel hold-ups safety constraints and so on. A module is a model of an individual element in a flowsheet (e.g., a reactor) that can be coded, analyzed, debugged, and interpreted by itself. Examine Figure 15.3a and b. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

A variety of control schemes are shown separately in Figures 3.14 and 3.15 for the lower and upper sections of fractionators. To some extent, these sections are controllable independently but not entirely so because the flows of mass and heat are interrelated by the conservation laws. In many of the schemes shown, the top reflux rate and the flow of HTM to the reboiler are on flow controls. These quantities are not arbitrary, of course, but are found by calculation from material and energy balances. Moreover, neither the data nor the calculation method are entirely exact, so that some adjustments of these flow rates must be made in the field until the best possible performance is obtained from the equipment. In modern large or especially sensitive operations, the fine tuning is done by computer. 

In an adiabatic operation, Q = 0, and as such there is no attempt to heat or cool the contents in the reactor. The temperature T in the reactor rises in an exothermic reaction and falls in an endothermic reaction. It is essential to control T so that it is neither too high nor too low. To assess the design of both the reactor and the heat exchanger required to control T, the material and energy balance equations must be used together with information on rate of reaction and rate of heat transfer because there is an interaction between T and XA. 

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. It has been found 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-to-vapor ratio, because severe interaction is likely to occur when the composition controllers of both products are configured to manipulate the energy balance of the column and thereby "fight" each other. 

A detailed model of the pilot-plant MVC was derived and validated against experimental data in a previous study (Barolo et al., 1998 and also see Chapter 4). The model consists of material and energy balances, vapour liquid equilibrium on trays (with Murphree tray efficiency to account for tray nonideal behaviour), liquid hydraulics based on the real tray geometry, reflux subcooling, heat losses, and control-law calculations based on volumetric flows. The model provides a very accurate representation of the real process behaviour, but is computationally expensive for direct use within an optimisation routine. Greaves et al. (2003) used this model as a substitute of the process. 

The reliability of the process measurements1 data is extremely important for good monitoring, control and optimization of chemical process. On-line rectification of a measurement error is possible be it a random error or a gross bias, if additional information is available. Such information is supplied by the extent to which the material and energy balances are satisfied by the recorded data. These balances are simple, involve parameters usually well known, and they should be satisfied independently of the measurements accuracy. 

The process configuration is based on complete process flow diagrams (PFD s) and material and energy balances that show the main recycle streams and control loops. 

Some simpler approaches to conversion control using material and energy balances on a train of CSTRs are described by Amrehn (1977). 

Process flowsheets embody the material and energy balances and include the sizes of major equipment of the plant. They include all vessels, such as reactors, separators, and drums special processing equipment heat exchangers pumps and so on. Numerical data include flow quantities, compositions, pressures, and temperatures. Major instrumentation essential for process control and the complete understanding of the flowsheet without reference to other... 

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