Constraint processing

Process constraints often reduce the number of options that can be considered. Examples of constraints of this type are as follows ... 

A key feature of MFC is that future process behavior is predicted using a dynamic model and available measurements. The controller outputs are calculated so as to minimize the difference between the predicted process response and the desired response. At each sampling instant, the control calculations are repeated and the predictions updated based on current measurements. In typical industrial applications, the set point and target values for the MFC calculations are updated using on-hne optimization based on a steady-state model of the process. Constraints on the controlled and manipulated variables can be routinely included in both the MFC and optimization calculations. The extensive MFC literature includes survey articles (Garcia, Frett, and Morari, Automatica, 25, 335, 1989 Richalet, Automatica, 29, 1251, 1993) and books (Frett and Garcia, Fundamental Process Control, Butterworths, Stoneham, Massachusetts, 1988 Soeterboek, Predictive Control—A Unified Approach, Frentice Hall, Englewood Cliffs, New Jersey, 1991). 

With respect to their response, the discussion should emphasize why these are important anci why they adjust certain control settings. Among the deviations on which analysts should focus the discussion are the high and low alarm settings. Some alarms will require rapid response. Alarms may give insight into equipment-operation boundaries as well as process constraints. 

Material Balance Constraint There are two types of constraints for the unit. These are the process constraints and the equipment constraints. In each of these, there are equahty constraints such as material balances and inequality constraints sucti as temperature limits. Analysts must understand the process and equipment constraints as part of the preparation for the unit analysis. 

Other Process Constraints Typical of these constraints are composition requirements, process temperature limits, desired recoveries, and yields. These are frequently the focus of operators. Violation of these constraints and an inability to set operating conditions that meet these constraints are frequently the motivation for the unit analysis. 

Equipment Constraints These are the physical constraints for individual pieces of eqiiipment within a unit. Examples of these are flooding and weeping limits in distillation towers, specific pump curves, neat exchanger areas and configurations, and reactor volume limits. Equipment constraints may be imposed when the operation of two pieces of equipment within the unit work together to maintain safety, efficiency, or quahty. An example of this is the temperature constraint imposed on reactors beyond which heat removal is less than heat generation, leading to the potential of a runaway. While this temperature could be interpreted as a process constraint, it is due to the equipment limitations that the temperature is set. 

Constraints Limitations Typically, the plant performance is assumed to be subject to process constraints. 

Spreadsheet Analysis Once validation is complete, prescreening the measurements using the process constraints as the comparison statistic is particularly usenil. This is the first step in the global test discussed in the rectification section. Also, an initial adjustment in component flows will provide the initial point for reconciliation. Therefore, the goals of this prescreening are to ... 

Unfortunately, the actual plant operation is unknown. Therefore, the actual value of each of the measurements is unknown. The purpose of reconciliation is to adjust the measurements so that they close the process constraints. The imphcit hypothesis is that the resultant adjusted measurements better represent the ac tual unit operation than do the actual measurements. 

On the source-sink mapping diagram, sources are represented by shaded circles and sinks are represented by hollow circles. Typically, process constraints limit the range of pollutant composition and load that each sink can accept. ITie intersection of these two bands provides a zone of acceptable conqKisition and load for recycle. If a source (e.g., source a) lies within this zone, it can be directly recycled to tiie sink (e.g., sink S). Moreover, sources b and c can be mixed using the lever-arm principle to create a mixed stream that can be recycled to sink S. 

The scope of the previously addressed CE case study is now altered to allow for stream segregation, mixing, and recycle within the ethyl chloride plant. There are five sinks the reactor (u = 1), the first scrubber (u = 2), the second scrubber (u = 3), the mixing tank (u = 4) and the biotreatment facility for effluent treatment (m = 5). There are six sources of CE-laden aqueous streams (in = 1-6). There is the potential for segregating two liquid sources (lu = 2, 4). The following process constraints should be considered ... 

Many physical and process constraints limit the cycle time, where cycle time was defined as the time to the maximum exotherm temperature. The obvious solution was to wind and heat the mold as fast and as hot as possible and to use the polymer formulation that cures most rapidly. Process constraints resulted in a maximum wind time of 3.8 minutes where wind time was defined as the time to wind the part plus the delay before the press. Process experiments revealed that inferior parts were produced if the part gelled before being pressed. Early gelation plus the 3.8 minute wind time constrained the maximum mold temperature. The last constraint was based upon reaction wave polymerization theory where part stress during the cure is minimized if the reaction waves are symmetric or in this case intersect in the center of the part (8). The epoxide to amine formulation was based upon satisfying physical properties constraints. This formulation was an molar equivalent amine to epoxide (A/E) ratio of 1.05. 

The total stream and individual component flows do not normally need to be shown to a high precision on the process flow-sheet at most one decimal place is all that is usually justified by the accuracy of the flow-sheet calculations, and is sufficient. The flows should, however, balance to within the precision shown. If a stream or component flow is so small that it is less than the precision used for the larger flows, it can be shown to a greater number of places, if its accuracy justifies this and the information is required. Imprecise small flows are best shown as TRACE . If the composition of a trace component is specified as a process constraint, as, say, for an effluent stream or product quality specification, it can be shown in parts per million, ppm. 

In general, the equations will be non-linear, as the split-fractions coefficients (a s) will be functions of the inlet flows, as well as the unit function. However, many of the coefficients will be fixed by the process constraints, and the remainder can usually be taken as independent of the inlet flows (A s) as a first approximation. 

Table 4.3 shows the feed of each component and the total flow to each unit. The composition of any other stream of interest can be calculated from these values and the split-fraction coefficients. The compositions and flows should be checked for compliance with the process constraints, the split-fraction values adjusted, and the calculation repeated, as necessary, until a satisfactory fit is obtained. Some of the constraints to check in this example are discussed below. 

A distillation column divides the feed stream components between the top and bottom streams, and any side streams. The product compositions are often known they may be specified, or fixed by process constraints, such as product specifications, effluent limits or an azeotropic composition. For a particular stream, 5 , the split-fraction coefficient is given by ... 

Those that may exceed equipment or process constraints. 

For a first pass through the design, it is usually adequate, if process constraints permit, to set distillation pressure to as low a pressure above ambient as allows cooling water or air-cooling to be used in the condenser. If a total condenser is to be used, and a liquid top product taken, the pressure should be fixed such that ... 

If process constraints restrict the maximum temperature of the distillation, then vacuum operation must be used in order to reduce the boiling temperature of the material to below a value at which product decomposition occurs. This tends to be the case when distilling high molar mass material. 

So far the discussion on water minimization has restricted consideration to identify opportunities for water reuse. Maximizing water reuse minimizes both fresh water consumption and wastewater generation. However, the process constraints for inlet concentrations, outlet concentrations and flowrates have so far been fixed. Often there is freedom to change the conditions within the operation. Typical process changes that might be contemplated include ... 

Constraint (2.2) is the material balance around a particular unit j. It implies that the sum of the masses for all the input states used at time point p -1 should be equal to the sum of the masses for all the output states produced at time point p. Constraint (2.3) states that the amount of state s stored at the first time point, is the difference between the amount stored before the beginning of the process and that being utilised at the first time point. Constraint (2.4) only applies to the feed, since it is the state that is only used in the process. Constraint (2.5) only applies to intermediates, since they are both produced and used in the process. Constraints (2.6) and (2.7) only apply to products and byproducts, since they are the only states that have to be taken out of the process as shown by the terms d(s, p). 

Constraints (2.13) and (2.14) imply that state. v can only be used in a particular unit, at any time point, after all the previous states have been processed. Constraint (2.13) is only relevant in situations where more than one task can be conducted in one unit, otherwise it is redundant in the presence of constraints (2.14) and (2.15). Constraint (2.15) stipulates that a state can only be processed at a particular time point p in a particular unit j after it has been produced from another unit /. In case of a recycle, j is the same as /. It is worthy of note that constraints (2.14) and... 

Constraint (3.8) reduces the search space by ensuring that the time at which a state s can be processed in unit j at time point p is at least after the sum of the durations of all previous tasks that have taken place in the unit. Constraint (3.9) ensures that the processing of state Sin into unit j can only take place after the previous batch has been processed. Constraint (3.10) stipulates that state sin can only be processed in unit j after it has been produced from unit j, where units j and / are consecutive stages in the recipe. 

Due to the nature of the process constraints have to be derived that capture the essence of time. The first of these considered deal with the scheduling of the tasks in a unit. 

Thirdly, the inlet and outlet concentrations were specified such that one was fixed directly and the other determined by mass balance using flowrate and mass load. However, a number of variations are possible in the way that the process constraints on quantity (or flowrate) present themselves. For instance, it could happen that there is no direct specification of the water quantity (or flow) in a particular stream, as long as the contaminant load and the outlet concentration are observed. Furthermore, the vessel probably has minimum and maximum levels for effective operation. In that case the water quantity falls away as an equality constraints, to become an inequality constraints, thereby changing the nature of the optimization problem. 

The decisions should be taken in an optimal fashion subject to the plant topology and the processing constraints with the objective to maximize the profit, given as the difference of revenues for products and costs for the production. The demands are specified by their amounts and their due dates, where the revenues decrease with increasing lateness of the demand satisfaction. The production costs consist of fixed costs for each batch and for the start-up- and shut-down-procedures of the finishing lines, and variable costs for the product inventory. 

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