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A model chain based methodology for quantitative planning of operating procedures
Computers and Chemical Engineering 23 (1999) 657 – 665
A model chain based methodology for quantitative planning of operating procedures Huasheng Li *, Mingliang Lu, Yuji Naka Process System Engineering Di6ision, Research Laboratory of Resources Utilisation, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226, Japan Received 11 February 1998; received in revised form 3 July 1998
Abstract To cope with the difficulties in planning operating procedures for the process with complicated operational constraints, a model chain based quantitative planning methodology is presented in this paper in which the whole planning problem is divided into two distinct but interrelated sub-problems: determination of operating path and synthesis of primitive operations. A two tier framework corresponding to those two sub-problems is used to describe the methodology in which the top-tier determines the operating path using optimisation methods, and the bottom-tier synthesises the primitive operations through a model based reasoning chain which is achieved based on the following findings: all the operational goals are accomplished by directly or indirectly adjusting the rele6ant flowrates and/or pressures through some primiti6e de6ices such as 6al6e, pump and compressor. The methodology is suitable for quantitative planning of operating procedures when operational constraints are more stringent. A case study is given to illustrate how the methodology is used in a case containing complex mixing constraints. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Operating path; Operating procedure; Process state; State transform
1. Introduction The increasing stringent safety, reliability and product quality requirements as well as environmental regulations to chemical industry require significantly improving the way of designing and operating the plants. The traditional plant design methodology which separates design from operation can not meet such requirements, and improving the operability of the designing plant has become one of the key issues in the area of process system engineering. Towards this, an operational design methodology (Naka, Lu & Takiyama, 1997), considering operational issues in the design stage, improves plant operability by generating, evaluating and modifying design alternatives containing both plant topology and operating procedures under various operational modes such as start-up, shut-down and emergency, etc. The planning of operating procedures is one of the key components in such an operational design methodology. * Corresponding author. Present address: Aigis System Inc., 270029, Rachel Terrace, Pine Brook, NJ 07058, USA.
The planning of operating procedures can be seen as searching for a set of sequential primitive operations such as open/close valves to transform system from initial state to final state through a series of intermediate states without violating operational constraints. For example, the planning of start-up procedures for a chemical process is to find out a set of primitive operations to bring system from pre-commissioning state to steady state (Fusillo & Powers, 1988; Foulkes, Walton, Andow & Galluzzo, 1988, Pradubsripetch, Lee, Adriani & Naka, 1996;). The recently representative progresses made in this field include: Fusillo and Powers (1987, 1988) introduced the concept of stationary state as intermediate goal and used a modified means/ends analysis and symbolic modelling technique in their operating procedure planning for which a constraint guided strategy is used to search for a feasible sequence of actions to drive the process from shutdown state to the production state. Lakshmanan and Stephanopoulos (1988a,b, 1990) developed a similar approach which was based on
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a hierarchical object-oriented modelling technique and emphasised on non-linear planning strategy deriving from constraint-posting philosophy to improve planning efficiency. Aelion and Powers (1991) developed a strategy for the retrofit synthesis of flowsheet structures and operating procedures. If no effective operating procedure can be generated, flowsheet structure modifications are proposed by the operating procedure planner. The common points among those methods include: (i) logic-based heuristic planning; (ii) feasible path based planning, and; (iii) model evaluation based qualitative planning. The differences among them are problem description, such as digraph and object oriented methods, and planning strategies, such as linear or nonlinear synthesis. When those methods are applied to process systems with more sophisticated and stringent constraints, they suffer from two main limitations: 1. Emphasising feasibility of operating path without considering plant performance such as cost and operating time. The feasible path oriented operating procedures may give poor results which are far from the optimal. 2. Underlining qualitative cause-effect models without characterising dynamic system behavior. Those methods are favoured for dealing with the constraints associated with qualitative ordering issues of actions, such as ‘A and B can not be mixed in the unit’, rather than the constraints requiring the quantitative planning of primitive operations, such as ‘A and B should be properly mixed to jump over explosive region of concentrations’. To improve this, a model chain based quantitative planning methodology consisting of two tiers: operating path determination (top tier) and primitive operation synthesis (bottom tier) is proposed in this paper which attempts to facilitate planning of operating procedures for chemical process with more stringent and/or quantitative operational requirements. The rest of the paper will first give an overview of the methodology and some related concepts, and then detail both of the two tiers in the following two sections. The reasoning models used in bottom tier are discussed by using mixer and valve examples. Finally, the methodology application in a chemical process with general and quantitative mixing constraints is used to demonstrate the advantages of the methodology.
should be used to select a better one from many alternatives. Besides, the conventional assumption– evaluation–modification loop based heuristic planing method for searching for a set of primitive operations to achieve each state on the operating path is undoubtedly far from optimal and efficient. The planning methodology proposed here divides the planning problem into operating path determination and primitive operation synthesis, which are respectively supported by a two-tier framework as shown in Fig. 1 (Li, Lu & Naka, 1997). In the top tier, the operating path is obtained by using an optimisation technique or by expert specifications depending on the complexity of operational constraints. In the bottom tier, the detailed primitive operations are synthesized to sequentially achieve each of the intermediate states (intermediate goals) on the operating path obtained from the top-tier till the final state (final goal). This is done by introducing a model chain based reasoning technique which is different from the heuristic planning strategy used in the conventional approaches. The advantages of the two-tier framework lies in that it makes it possible to obtain an optimal operating path from the top tier even if the operational constraints are much more complicated; and it also makes it much easier and efficient to synthesize detailed primitive actions from the bottom tier since the most of constraints are maintained in the top tier and only the preconditions of primitive operators are encountered in the bottom tier. To realize such a methodology requires the representation of state transform, the identification of operational goals, constraints classification and mapping between operational goals and primitive operations which are discussed below.
2.1. State transform and goal 6ariables The planning of operating procedures in a chemical plant involves the transformation of process states, and the representation of which has a significant impact on the planning program.
2. Methodology The planning of operating procedures involves specifying a feasible operating path linking the initial state to the goal state and consisting of a series of intermediate states without violating operational constraints. In most cases there are more than one feasible path existing for which more stringent performance criteria
Fig. 1. The framework of the planning methodology.
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The process state can be characterised by a state vector containing a set of process variables such as flowrates, temperatures, pressures, concentrations, etc. which are usually grouped around units. Although whole process variable values related to a certain unit provide a complete state description for the unit, it should be noticed that only a few of them play a key role in representing its operating path or state transform during which other state variables passively vary with those key variables following the domain laws. As each unit has a processing function towards its operational goals, such operational goals can sufficiently be described by a number of key process variables which are called as goal variables. For example. the outlet temperature is a goal variable of a heat exchanger; the goal variables for a mixer are component concentrations and liquid level in most cases. Therefore, the transform of the unit state driven by operation can be represented by the changes of goal variable values. Furthermore, the system state transform is the combination of the state transforms of the units forming the system. Interestingly, most of these goal variables are controlled variables in the control system configuration. Therefore, the goal variable identification shares some similarity of the controlled variable identification. However, since the current control system configuration mainly concentrates on normal state operation, some variables that play an important part in start up or shut down operations but not controlled variables can also be classified as goal variables. Similar to the setpoint of the controlled variable in the control configuration, we call each intermediate state a ‘setpoint’ of a goal variable. Therefore, all the intermediate states in the operating path of a goal variable from initial state to final state are called as a series of ‘setpoints’ of the goal variables. The transform of system state from one to another can actually be understood as the change over of the ‘setpoints’ for the goal variables, whereas other process state variables vary with goal variables following the domain laws such as mass and/or energy balances. Therefore, the determination of operating path is virtually to define a set of ‘setpoints’ for each of the goal variables which is done in the top-tier of the methodology framework.
2.2. Classification of constraints Fusillo and Powers (1987) classified operational constraints into five classes according to the factors concerned. They are: (i) preconditions for unit operations; (ii) requirements for reactions; (iii) production requirements; (iv) safety hazards and; (v) material of construction. To meet our two tier methodology requirement, we reorganise them into two types: action constraint and value constraint. The action constraints are used in the bottom tier as the preconditions for actions to
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qualitatively order primitive operations whereas the value constraints are used in the top tier to determine the operating path. Apparently, class (i) above belongs to action constraints, whereas the rest of four classes are value constraints. The action constraints are usually represented as: IF certain conditions are satisfied, THEN perform associated operation. A typical example is that IF the le6el of mixer reaches to its upper limit, THEN open the outlet 6al6e of the mixer, which can be used to activate the outlet valve operation of the mixer at the proper moment. It is worth mentioning that action constraints only facilitate in ordering the primitive operations, how to perform associated operations, such as valve opening and timing for above example, is guided by model based reasoning methods imbedded in the bottom tier. The value constraints, which can be represented as algebraic inequalites, equalites or even differential equations in some come cases, such as: Temperature ] 150, or x1 + x2 + · · ·+ xn = 1, etc. are used in the top tier for narrowing search space in determining operating path. It is necessary to mention that these value constraints may cover both goal and state variables. When the goal variables changed, other state variables are also changing, and the relationship between goal variables and other state variables is governed by domain law such as mass balance.
2.3. Mapping between goal and action The operation in chemical plant is implemented by carrying out a series of actions on special devices known as controllable devices including valves, pumps and compressors, which means the system state can and only be adjusted by these controllable devices. Analysing working mechanism of these controllable devices, we may find that only process variables that they can directly govern are flowrate and pressure known as manipulated variables. Therefore, all the operational goals can and only be accomplished by adjusting the manipulated variables (flowrate and/or pressure) through manipulating the three controllable devices. Therefore, we can conclude: 1. Only three controllable devices can be directly performed on by operators or control mechanisms in chemical plant which known as primitive operations. 2. Only two manipulated variables flowrates and pressures can be directly governed by primitive operations. 3. All of the operational states described in the values of goal variables of a system can be achieved by adjusting manipulated variables through primitive operations. For example, the requirement for component concentrations (goal variable) inside a mixer can be achieved
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by adjusting flowrates (manipulated variable) entering the mixer through manipulating the inlet valves; the specifications for reaction temperature and pressure (goal variables) can be realised by respectively adjusting the flowrate (manipulated variable) of cooling water entering the reactor jacket through manipulating the valve and the outlet pressure (manipulated variable) of a feeding pump through manipulating the pump, etc. Based on such a fact, it is possible to build the quantitative relationship between goal variables and the corresponding manipulated variables flowrate and/or pressure known as the goal-manipulated (G – M) model. There also exists a quantitative relationship between manipulated variables and associated primitive operations (or operating patterns) called the manipulated– primitive (M–P) model. Therefore, system states and primitive operations are bridged by both G – M and M – P models which form a reasoning chain: Goal variables [ (G – M model) × [ Manipulated variables [ (M –P model) [ Primitive operations By utilising this model based reasoning chain, we can, through the G– M model, map the operating paths of goal variables into the changing patterns of manipulated variables which are then, through the M–P model, converted into operating patterns of controllable devices which in fact are quantitative operating procedures. Both M–P and G – M models can be quantitatively described by a set of theoretical or empirical equations. For example, M–P models can mainly be described by flowrate–opening curve for the valve and pressure–rotative velocity curve for the pump or compressor, whereas G–M models are similar to the model of a process unit used for process simulation but with different calculating directions in most cases. An example on building the G–M and M – P models for a mixer unit and valve models can be found later in the section of bottom tier. Based on the above discussion, the following sections will provide more detailed representation of the methodology.
3. Top tier: operating path determination As mentioned previously, the operating path can be seen as a set of temporary ‘setpoints’ connecting initial and goal values corresponding to each goal variable. Therefore, determining the operating path is actually defining those temporary ‘setpoints’ for every goal variable. Such an operating path should meet all the value constraints so as to be feasible. Obviously, there are numerous feasible operating paths linking the certain
initial state and final state in the domain space among which there are three approaches capable of determining a better or even optimal one.
3.1. Comprehensi6e e6aluation approach This approach evaluates each of the feasible operating paths against some performance criteria which are usually classified into two classes of economy and operability, whereas operability can be further decomposed into controllability, flexibility, reliability, safety and so on. Based on the evaluation results, a better one among the existing operating paths can be determined. The advantage of this approach is that it strongly links the operating path with certain performance criteria together and the operating path obtained is certainly optimal among the operating paths evaluated based on a certain performance criterion. However, the significant difficulties in the use of this approach also exist, including, searching for as many feasible operating paths as possible for evaluation and building quantitative relationships between the operating path and the given evaluation criteria such as the reaction temperature and cost. Therefore, this approach can only be applied in cases where a limited number of feasible operating paths are candidates, and the qualitative evaluation results are accepted.
3.2. Optimization approach This approach uses optimization techniques such as nonlinear programming to directly search for an optimal operating path based on a simplified performance criterion: the shortest length of the feasible operating path linking the gi6en initial state and the final state. The shortest length of the feasible operating path also means the shortest operating time to transform the process state from the initial state to the final state, which is also proportional to the operational costs in most cases. Therefore, the operating path obtained, based on this simplified performance criteria, can be considered as optimal in the common sense. The simplified performance criteria can be described in the objective function and the value constraints mentioned earlier are directly used as constraints in the optimization algorithm. The operating path can be determined by solving the following nonlinear programming problem: n
Min % (xi − xi,goal)2
(1)
i=1
subject to: G(X, Y, U) ]0
(2)
H(X, Y, U) = 0
(3)
where n represents the number of goal variables, X the vector of goal variables, xi,goal a target value of goal
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Fig. 2. A mixing case process.
variable xi, Y the vector of manipulated variables, U the vector of other state variables, and G and H the inequality and equality constraints, respectively. For a mixing case process with a number of constraints avoiding the formation of dangerous mixtures as shown in Figs. 2 and 3, the operating path synthesis involves identifying goal variables, specifying both initial and goal states, defining constraints or/and performance criteria, and finally determining the operating path (intermediate ‘setpoints’), which are listed below: 1. goal variables: xi and L,
i= 1, 2, . . . ,n
2. initial and goal states: (x1, x2, . . . ,xn )(0) and (x1, x2, . . . ,xn )(E); L (0) and L (E); 3. objective function using performance criteria: n
2 (E) 2 Min % {(xi − x (E) )} i ) +(L −L i=1
4. value constraints: gj (x1, x2, . . . ,xn )]0,
j= 1, . . . ,m;
0 5L 5L (E), 0 5 xi 5 1,
i= 1, . . . ,n;
x1 +x2 + ···+xn =1. 5. Solve the above NLP problem formed by item 3 and 4 above. It is necessary to mention that before solving the above NLP problem, the constraints: gj (x1, x2, . . . , xn )] 0 describing the dangerous region
Fig. 3. Schematic of mixing constraint.
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should be properly multiplied geometrically for safety consideration. In solving the NLP problem, we are not only interested in the final optimum value but more interested in obtaining the iterative path from the initial state to the goal state. This is because the iterative path is actually our initial solution of the operating path. To make the operating path operable and reduce the number of corresponding primitive operations, this iterative path is further refined to several ‘setpoints’ as few as possible by merging a number of intermediate iterative points which is conducted through a refining program which consists of three steps: 1. linking the starting point to its next intermediate point and then checking whether the link line touches the constraint boundary; 2. if it does not, omitting this intermediate point and repeat step 1 above; 3. if it does, the last omitted point is a valid intermediate state which is chosen as new starting point and repeat step 1 till the goal state is reached. In such a way, a refined operating path consisting of valid intermediate states is finally obtained which is operable, safe, and has shorter operating time, and in most cases, lower operating cost. It should be mentioned that operating paths obtained by using different solution methods may be different depending on the searching mechanism of each solution method. The two guidelines can be used for selecting solution methods for a given optimization problem: 1. The optimal value of the objective function of the optimization problem should be zero so as to ensure that the operating path certainly reaches the final state from the initial state. 2. The number of intermediate states forming the operating path after refined from original iterative path should be as few as possible so as to ensure the operating path is operable in practice.
3.3. Heuristic approach The above approaches require detailed quantitative representation. Sometimes, qualitative approaches or graphical interactive approaches are more efficient in obtaining only feasible paths when constraints are not complicated. In such a case, the intermediate states of goal variables can directly be specified by human experts based on their knowledge and experience. Stationary state concept proposed by Fusillo and Powers (1987, 1988) can significantly facilitate this work. A stationary state is an intermediate state during the planning process which holds system for a period of time during which the system state does not change significantly until next action is taken. For example, the operation at total reflux of a distillation column is a stationary state. The stationary state should certainly be on the operating path the values of goal variables
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associated with which can directly be specified based on operational knowledge. This planning methodology supports the operating path specified by user as well which is known as heuristic approach. Once a path is obtained, it will be realized by planning a set of ordered primitive operations in the next section.
4. Bottom tier: primitive operation synthesis This tier synthesizes a set of primitive operations to achieve each ‘setpoint’ (intermediate state) till the final state on the operating paths of the goal variables. A model chain based planning technique is introduced here to achieve this which contains three steps: goal formulation, model based reasoning, and ordering and timing of primitive operation, as discussed below.
4.1. Goal formulation As mentioned earlier, each operating path contains a number of ‘setpoints’ of one or more goal variables. The first ‘setpoint’ is taken as the current goal which drives the planning of relevant primitive operations from the initial state to achieve it. Then, the current goal is shifted to the second ‘setpoint’ and the planning moves forward one step. In this way, the current goal moves from one ‘setpoint’ to another until the final goal in the path is reached. When considering the system wide problem, it is convenient to start planning from the goal variables at the feeding unit of the system and follow the stream direction.
4.2. Model based reasoning Once a current goal is formulated, a number of primitive operations are synthesized using a modelbased reasoning as described below: 1. Identify the associated controllable devices and check the action constraints bound up with the controllable devices, if the action constraints are met, turn to step 3 below, otherwise, continue. 2. Propagate unsatisfied action constraints to the relevant devices following the plant topology until such constraints are met. Once such a device is reached, go to step 1 above. 3. Activate a relevant G – M model and calculate the responsible manipulated variable values. 4. Perform the primitive operations of the current device based on M – P model to achieve the goal. 5. Formulate the next planning goal following the stream direction and repeat this procedure. Such a model-based reasoning can be seen as the planning chain: ‘Setpoints’ of goal variables [ G–M models [ Values of manipulated variables [ M–P
models [ Primitive operations. Notice that some goal variables are not directly, but indirectly controlled by manipulated variables through other state or goal variables, which is also covered by the G–M models. For example, the product quality (goal variable) from a fixed-bed reactor is usually controlled by inlet temperature (goal variable) of the reactor which is further controlled by fuel flowrate (manipulated variable) entering a furnace if the furnace is the upstream unit of the reactor. In such a case, the G–M model virtually represents the relationship between production quality and reactor inlet temperature as well as fuel flowrate.
4.3. Ordering and timing of primiti6e operation Any primitive operation in the operating procedures contains its sequence and timing. The sequence is ordered by action constraints bound up with each controllable device. For example, following two action constraints for mixer startup which are respectively imbedded in inlet and outlet valves of a mixer: IF the liquid le6el in the mixer is lower than bottom limit, THEN open the inlet 6al6e-1; IF the liquid le6el in the mixer is higher than top lim it, THEN open the outlet 6al6e-2. are used to order the relative sequence of the valve-1 and valve-2 based on the liquid level in the mixer. However, how to ‘open the inlet 6al6e-1 ’ or how to ‘open the outlet 6al6e-2 ’, that is valve’s opening and changing pattern, which is known as the timing of a operation, is determined by the dynamics specified in the G–M and M–P models mentioned above. It is clear that the G–M and M–P models in the bottom tier are the core of the synthesis of operating procedures the examples of which related to mixer and valve are given below.
5. Reasoning models A mixer is chosen to show its G–M model since its operation is often restricted by complicated constraints which prohibits the formation of a potentially dangerous or undesirable mixtures. Many former researchers focused on a specific type of mixing constraint, namely binary, qualitative mixing constraint, which implies that the components A and B should never be present at the same time in the same location within the chemical plant, that is, they are simply forbidden to come into contact with one another. However, a more general and often encountered quantitative constraint with prohibited concentration range shown in Fig. 3 is not yet dealt with which can be solved by using this two tier methodology.
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5.1. G–M model of mixer The G–M model describes the relationship between goal variables and responsible manipulated variables. However, it should be realized that G – M model of a process unit contains not only goal variables and corresponding manipulated variables, but also other necessary state variables. For example, the G – M model of a heat-exchanger calculates the cooling water flowrate (manipulated variable) based on the ‘setpoint’ of the outlet temperature of the hot stream (goal variable), its flowrate, the inlet temperatures on both sides and the relevant equipment parameters and physical properties. Different from traditional unit model solving, the G – M model utilizes the given output variables (goal variables) to specify some input variables (manipulated variables). Considering the mixing case process shown in Fig. 2, it is easy to see that the component concentrations and the liquid level inside the mixer are goal variables, the inlet and outlet flowrates are manipulated variables which are used to control the concentrations and level inside the mixer through associated valves. The G–M model for above mixing case process consists of following Eqs. (4) and (5), which are derived from the mass balance Eqs. (6) and (7) through discrete treatment. F (k) i =
x (k) Ar i (k − 1) F (k) n + L x (k) M n
x (k) i − 1) − 1) x (k −x (k n i x (k) n
(i= 1, 2, . . . , n) Ar (k − 1) (k − 1) (L (k)x (k) xn ) n −L M (k) Dt = (k) (k) (F (k) n −x n F n + 1)
(4)
(5)
ArL dxi =Fi − xi (F1 +F2 +· · · +Fn ) M dt (i =1, 2, . . . , n)
Ar dL = F1 + F2 +· · · +Fn −Fn + 1 M dt
(6)
Fig. 4. The flowsheet for case study.
filling period, for example) or by the G–M model corresponding to another downstream unit in which F (k) n + 1 is a manipulated variable. Given three aspects of information above, the flowrate of each inlet valve and corresponding maintaining time period for each state transform can be obtained through the G–M model and finally to bring the state to the goal state.
5.2. M–P model of 6al6e Once the flowrate of the valve is obtained through the G–M model, the corresponding valve opening can be calculated through the M–P model of the valve to achieve the flowrate. The M–P model of the valve describes the relationship between its flowrate and corresponding opening which can be obtained from valve performance curve that varies with valve type: (k) C (k) i = f(F i )
(i =1, 2, . . . , n+1)
(8)
Each valve opening obtained above is kept during the corresponding time period so as to maintain a certain flowrate to achieve a state transform. Finally, the operations containing valve opening and timing towards achieving certain goals under such generic and complicated mixing constraints are synthesized through the G–M model of mixer and the M–P model of the valve.
(7)
where superscript k refers to the series number of intermediate ‘setpoints’ or goal ‘setpoints’. The application of above G – M model requires three aspects of information: 1. The current value (referring to k −l) and next ‘setpoint’ (referring to k) of each goal variable. 2. The reference flowrate of a certain inlet valve F (k) n , which can be specified having several alternatives depending on different operational strategies one of which is to minimize operating time. In such a case, F (k) in Eq. (4) refers to the flowrate of valve n n corresponding to its maximum opening. 3. The outlet valve flowrate value F (k) n + 1 which is specified by an operator (it should be zero during the
6. Application of the methodology To illustrate the use of this methodology, this section introduces the synthesis of startup procedures for a subsystem of a plant in which emphasis is placed on the primitive operation planing on the system wide issues. Fig. 4 shows the flowsheet of a case based on the reaction section of a HDS process in which hydrogen (A) and sulphuret (B) as well as inert gas nitrogen are mixed through a tank-mixer and a pipemixer, respectively, and the output stream is heated to a certain temperature and the reaction takes place in a reactor, then the reactor output stream is cooled and the product is condensed and separated in a flash vessel.
H. Li et al. / Computers and Chemical Engineering 23 (1999) 657–665
664 Table 1 Goal variables and operating paths Goal variable
XA
XB
P1
T6
T8
L
P2
Initial value Intermediate value Intermediate value Goal value
0.2 0.4 0.5 0.55
0.0 0.2 0.3 0.35
1.0 1.2 1.6 1.8
25 70 +45°C/h 295
25
0.0
1.0
65
1.2
1.6
There is a dangerous mixing region: xA =(0.9 – 1.1)xB in the mixer and an operational constraint: dT6/dt 5 45°C/h for preheating catalyst in the reactor. Suppose that the initial status of all valves are closed, and goal variables are marked in Fig. 4, and their corresponding initial, intermediate and goal values are listed in Table 1. Starting from the goal variables related to the tankmixer, xA, xB and P1, the planner takes their first set of ‘setpoints’ as the first planning goal. Checking the action constraints bound up with V-1, V-2, V-3 and V4 respectively, finds the first three valves are ready to be operated and V4 requires goal variable P1 reaching its goal state ahead since its action constraint is IF P1 reaches its goal state, THEN opening 6al6e-4. The G–M models of the tank-mixer and the piper-mixer are activated to specify the flowrates F1, F2 and F3, and their corresponding operating time. The flowrates are further converted to the openings of three valves through M–P models associated with each valve. Finally, the primitive operations: adjusting V-1, V-2 and V-3 openings to 0.7, 0.2 and 0.5 for 15 min are proposed and executed. After the first set of ‘setpoints’ is achieved, the primitive operations respectively corresponding to the second, and then the goal ‘setpoints’ are synthesized and carried out in the same way. As soon as the final state of the mixer is reached, the primitive operation: adjusting V-4 opening to 0.6, is performed since its action constraint has been met at this time. Till now, the first planning goal has been achieved and T6 is chose as the second planning goal. Since the action constraint associated with V-5: IF V-4 is open, THEN opening V-5 has been satisfied, the primitive operation: adjusting V-5 opening to 0 3 for one hour, resulted in by the first ‘setpoint’ of T6 through G–M model of the furnace and further the M – P model of V-5, is synthesized, following that another set of actions for V-5 are synthesized and performed to achieve each of the ‘setpoints’ on its operating path till the final goal is reached. Meanwhile, the action constraint bound up with V-6: IF T6 exceeds 250 °C, THEN opening V-6, activates the G – M model of heat-exchanger at proper time and further the M–P model of V-6, and the action: adjusting V-6 opening to 0.7 for a hour is synthesized. In fact, the opening of V-6 varies with the increase of T6, here the planner only gives a discrete value for operability consideration.
Similarly, the opening of V-7 are synthesized through the G–M model of flash vessel and M–P model of V-7 and once the goal state of flash vessel is achieved, the action constraint of V-8 is met, therefore, V-8 is opened to maintain the level. Till now, the startup procedure for this case flowsheet has been synthesized. The patterns of valve operations are shown in Fig. 5 in which each color change indicates the variation of corresponding valve opening. It is obvious that the order of primitive operations is decided by action constraints bound up with controllable devices, whereas the timing is decided by the dynamic response of the associated models. To automate this methodology, a prototype system has been developed in C/C + +. The top tier defines operating path by user’s specification through GUI or NLP optimizer with additional refinement block. The bottom tier synthesizes primitive operations through a inference engine and a model library which currently contains G–M models for mixer including tank-mixer and pipe-mixer, splitter, heat exchanger, flash vessel, furnace, CSTR and PFR, etc. and M–P models for valve, variable speed pump and compressor. These two tiers are independent.
7. Conclusions To overcome the difficulties in planning operating procedures for the process with complicated operational constraints, a model chain based quantitative planning methodology is presented supported by two
Fig. 5. The operating pastern of valves.
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tiers. The top-tier determines the operating path using optimization methods with qualitative alternatives, and the bottom-tier synthesizes the primitive operations through a G–M and M – P model based reasoning chain. This is based on a discovery of the fact that all the operational goals are accomplished by directly or indirectly adjusting two basic manipulated variables: flowrate and pressure, through the manipulation of three controllable devices: valve, pump and compressor. Furthermore, two sets of models: G – M and M –P are abstracted to bridge the goal variable operating paths and the primitive operations. The G – M model maps the goal variable path into the manipulated variable patterns and the M – P extends such mapping to the primitive operations of controllable devices. Then a model chain based reasoning technique is presented which provides a procedure for each goal variable to go through the G–M model [ Manipulated variables [ M – P model [ Primitive operations chain. As the result, both the ordering and timing of the primitive operations can be obtained. The methodology has been successfully applied to plan the start up operating procedure of a case process with complex mixing constraints. The advantage of this methodology is efficient. The top-tier determines the operating paths of goal variables using either nonlinear programming or qualitative methods without concerning the detailed ordering and timing of primitive operations. Whereas the bottom-tier uses models and action constraints to order the primitive operations with timing for achieving the operating paths obtained from the top tier. The methodology is also generic, especially, the bottom tier can be used independently in different areas. This paper is a initial efforts toward the quantitative planning of the operating procedures in which only common issues involved are discussed and many other complex issues, such as nested states, recycle flowsheet and parallel sequences of the operating procedures, etc. remain to continue efforts.
Appendix A. Notation A Ci Fi
cross-sectional area of tank mixer opening of valve-i volume flowrate of i-th stream
.
L M P T t xi xi,goal r
liquid level molecular weight pressure temperature time goal variable goal value of goal variable fluid density
Superscript 0 k E
initial value intermediate value goal value
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References Aelion, V., & Powers, G. J. (1981). A unified strategy for the retrofit synthesis of flowsheet structures for attaining or improving operating procedures. Computer and Chemical Engineering, 5, 349– 360. Foulkes, N. R., Walton, M. J., Andow, P. K., & Galluzzo, M. (1988). Computer-aided synthesis of complex pump and valve operations. Computers and Chemical Engineering, 9/10, 1035 – 1045. Fusillo, R. H., & Powers, G. J. (1987). A synthesis method for chemical plant operating procedures. Computers and Chemical Engineering, 4, 369 – 382. Fusillo, R. H., & Powers, G. J. (1988). Operating procedure synthesis using local models and distributed goals. Computers and Chemical Engineering, 9/10, 1023 – 1034. Lakshmanan, R., & Stephanopoulos, G. (1988). Synthesis of operating procedures for complete chemical plants-I: hierarchical, structured modelling for nonlinear planning. Computers and Chemical Engineering, 9/10, 985 – 1002. Lakshmanan, R., & Stephanopoulos, G. (1988). Synthesis of operating procedures for complete chemical plants-II: a nonlinear planning methodology. Computers and Chemical Engineering, 9/10, 1003 – 1021. Lakshmanan, R., & Stephanopoulos, G. (1990). Synthesis of operating procedures for complete chemical plants-III: planning in the presence of qualitative, mixing constraints. Computers and Chemical Engineering, 3, 301 – 317. Li, H. S., Lu, M. L., & Naka, Y. (1997). A two-tier planning methodology for synthesis of operating procedures. Computers and Chemical Engineering, 21(Suppl.), S899 – S903. Naka, Y., Lu, M. L., & Takiyama, H. (1997). Operational design for start-up of chemical processes. Computers and Chemical Engineering, 9, 997 – 1007. Pradubsripetch, D., Lee, S., Adriani, A., & Naka, Y. (1996). Real time generation of operating procedures to support flexible startup operation. Computers and Chemical Engineering, 20 (Suppl. Part B), S1203 – S1208.
A model chain based methodology for quantitative planning of operating procedures Huasheng Li *, Mingliang Lu, Yuji Naka Process System Engineering Di6ision, Research Laboratory of Resources Utilisation, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226, Japan Received 11 February 1998; received in revised form 3 July 1998
Abstract To cope with the difficulties in planning operating procedures for the process with complicated operational constraints, a model chain based quantitative planning methodology is presented in this paper in which the whole planning problem is divided into two distinct but interrelated sub-problems: determination of operating path and synthesis of primitive operations. A two tier framework corresponding to those two sub-problems is used to describe the methodology in which the top-tier determines the operating path using optimisation methods, and the bottom-tier synthesises the primitive operations through a model based reasoning chain which is achieved based on the following findings: all the operational goals are accomplished by directly or indirectly adjusting the rele6ant flowrates and/or pressures through some primiti6e de6ices such as 6al6e, pump and compressor. The methodology is suitable for quantitative planning of operating procedures when operational constraints are more stringent. A case study is given to illustrate how the methodology is used in a case containing complex mixing constraints. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Operating path; Operating procedure; Process state; State transform
1. Introduction The increasing stringent safety, reliability and product quality requirements as well as environmental regulations to chemical industry require significantly improving the way of designing and operating the plants. The traditional plant design methodology which separates design from operation can not meet such requirements, and improving the operability of the designing plant has become one of the key issues in the area of process system engineering. Towards this, an operational design methodology (Naka, Lu & Takiyama, 1997), considering operational issues in the design stage, improves plant operability by generating, evaluating and modifying design alternatives containing both plant topology and operating procedures under various operational modes such as start-up, shut-down and emergency, etc. The planning of operating procedures is one of the key components in such an operational design methodology. * Corresponding author. Present address: Aigis System Inc., 270029, Rachel Terrace, Pine Brook, NJ 07058, USA.
The planning of operating procedures can be seen as searching for a set of sequential primitive operations such as open/close valves to transform system from initial state to final state through a series of intermediate states without violating operational constraints. For example, the planning of start-up procedures for a chemical process is to find out a set of primitive operations to bring system from pre-commissioning state to steady state (Fusillo & Powers, 1988; Foulkes, Walton, Andow & Galluzzo, 1988, Pradubsripetch, Lee, Adriani & Naka, 1996;). The recently representative progresses made in this field include: Fusillo and Powers (1987, 1988) introduced the concept of stationary state as intermediate goal and used a modified means/ends analysis and symbolic modelling technique in their operating procedure planning for which a constraint guided strategy is used to search for a feasible sequence of actions to drive the process from shutdown state to the production state. Lakshmanan and Stephanopoulos (1988a,b, 1990) developed a similar approach which was based on
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a hierarchical object-oriented modelling technique and emphasised on non-linear planning strategy deriving from constraint-posting philosophy to improve planning efficiency. Aelion and Powers (1991) developed a strategy for the retrofit synthesis of flowsheet structures and operating procedures. If no effective operating procedure can be generated, flowsheet structure modifications are proposed by the operating procedure planner. The common points among those methods include: (i) logic-based heuristic planning; (ii) feasible path based planning, and; (iii) model evaluation based qualitative planning. The differences among them are problem description, such as digraph and object oriented methods, and planning strategies, such as linear or nonlinear synthesis. When those methods are applied to process systems with more sophisticated and stringent constraints, they suffer from two main limitations: 1. Emphasising feasibility of operating path without considering plant performance such as cost and operating time. The feasible path oriented operating procedures may give poor results which are far from the optimal. 2. Underlining qualitative cause-effect models without characterising dynamic system behavior. Those methods are favoured for dealing with the constraints associated with qualitative ordering issues of actions, such as ‘A and B can not be mixed in the unit’, rather than the constraints requiring the quantitative planning of primitive operations, such as ‘A and B should be properly mixed to jump over explosive region of concentrations’. To improve this, a model chain based quantitative planning methodology consisting of two tiers: operating path determination (top tier) and primitive operation synthesis (bottom tier) is proposed in this paper which attempts to facilitate planning of operating procedures for chemical process with more stringent and/or quantitative operational requirements. The rest of the paper will first give an overview of the methodology and some related concepts, and then detail both of the two tiers in the following two sections. The reasoning models used in bottom tier are discussed by using mixer and valve examples. Finally, the methodology application in a chemical process with general and quantitative mixing constraints is used to demonstrate the advantages of the methodology.
should be used to select a better one from many alternatives. Besides, the conventional assumption– evaluation–modification loop based heuristic planing method for searching for a set of primitive operations to achieve each state on the operating path is undoubtedly far from optimal and efficient. The planning methodology proposed here divides the planning problem into operating path determination and primitive operation synthesis, which are respectively supported by a two-tier framework as shown in Fig. 1 (Li, Lu & Naka, 1997). In the top tier, the operating path is obtained by using an optimisation technique or by expert specifications depending on the complexity of operational constraints. In the bottom tier, the detailed primitive operations are synthesized to sequentially achieve each of the intermediate states (intermediate goals) on the operating path obtained from the top-tier till the final state (final goal). This is done by introducing a model chain based reasoning technique which is different from the heuristic planning strategy used in the conventional approaches. The advantages of the two-tier framework lies in that it makes it possible to obtain an optimal operating path from the top tier even if the operational constraints are much more complicated; and it also makes it much easier and efficient to synthesize detailed primitive actions from the bottom tier since the most of constraints are maintained in the top tier and only the preconditions of primitive operators are encountered in the bottom tier. To realize such a methodology requires the representation of state transform, the identification of operational goals, constraints classification and mapping between operational goals and primitive operations which are discussed below.
2.1. State transform and goal 6ariables The planning of operating procedures in a chemical plant involves the transformation of process states, and the representation of which has a significant impact on the planning program.
2. Methodology The planning of operating procedures involves specifying a feasible operating path linking the initial state to the goal state and consisting of a series of intermediate states without violating operational constraints. In most cases there are more than one feasible path existing for which more stringent performance criteria
Fig. 1. The framework of the planning methodology.
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The process state can be characterised by a state vector containing a set of process variables such as flowrates, temperatures, pressures, concentrations, etc. which are usually grouped around units. Although whole process variable values related to a certain unit provide a complete state description for the unit, it should be noticed that only a few of them play a key role in representing its operating path or state transform during which other state variables passively vary with those key variables following the domain laws. As each unit has a processing function towards its operational goals, such operational goals can sufficiently be described by a number of key process variables which are called as goal variables. For example. the outlet temperature is a goal variable of a heat exchanger; the goal variables for a mixer are component concentrations and liquid level in most cases. Therefore, the transform of the unit state driven by operation can be represented by the changes of goal variable values. Furthermore, the system state transform is the combination of the state transforms of the units forming the system. Interestingly, most of these goal variables are controlled variables in the control system configuration. Therefore, the goal variable identification shares some similarity of the controlled variable identification. However, since the current control system configuration mainly concentrates on normal state operation, some variables that play an important part in start up or shut down operations but not controlled variables can also be classified as goal variables. Similar to the setpoint of the controlled variable in the control configuration, we call each intermediate state a ‘setpoint’ of a goal variable. Therefore, all the intermediate states in the operating path of a goal variable from initial state to final state are called as a series of ‘setpoints’ of the goal variables. The transform of system state from one to another can actually be understood as the change over of the ‘setpoints’ for the goal variables, whereas other process state variables vary with goal variables following the domain laws such as mass and/or energy balances. Therefore, the determination of operating path is virtually to define a set of ‘setpoints’ for each of the goal variables which is done in the top-tier of the methodology framework.
2.2. Classification of constraints Fusillo and Powers (1987) classified operational constraints into five classes according to the factors concerned. They are: (i) preconditions for unit operations; (ii) requirements for reactions; (iii) production requirements; (iv) safety hazards and; (v) material of construction. To meet our two tier methodology requirement, we reorganise them into two types: action constraint and value constraint. The action constraints are used in the bottom tier as the preconditions for actions to
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qualitatively order primitive operations whereas the value constraints are used in the top tier to determine the operating path. Apparently, class (i) above belongs to action constraints, whereas the rest of four classes are value constraints. The action constraints are usually represented as: IF certain conditions are satisfied, THEN perform associated operation. A typical example is that IF the le6el of mixer reaches to its upper limit, THEN open the outlet 6al6e of the mixer, which can be used to activate the outlet valve operation of the mixer at the proper moment. It is worth mentioning that action constraints only facilitate in ordering the primitive operations, how to perform associated operations, such as valve opening and timing for above example, is guided by model based reasoning methods imbedded in the bottom tier. The value constraints, which can be represented as algebraic inequalites, equalites or even differential equations in some come cases, such as: Temperature ] 150, or x1 + x2 + · · ·+ xn = 1, etc. are used in the top tier for narrowing search space in determining operating path. It is necessary to mention that these value constraints may cover both goal and state variables. When the goal variables changed, other state variables are also changing, and the relationship between goal variables and other state variables is governed by domain law such as mass balance.
2.3. Mapping between goal and action The operation in chemical plant is implemented by carrying out a series of actions on special devices known as controllable devices including valves, pumps and compressors, which means the system state can and only be adjusted by these controllable devices. Analysing working mechanism of these controllable devices, we may find that only process variables that they can directly govern are flowrate and pressure known as manipulated variables. Therefore, all the operational goals can and only be accomplished by adjusting the manipulated variables (flowrate and/or pressure) through manipulating the three controllable devices. Therefore, we can conclude: 1. Only three controllable devices can be directly performed on by operators or control mechanisms in chemical plant which known as primitive operations. 2. Only two manipulated variables flowrates and pressures can be directly governed by primitive operations. 3. All of the operational states described in the values of goal variables of a system can be achieved by adjusting manipulated variables through primitive operations. For example, the requirement for component concentrations (goal variable) inside a mixer can be achieved
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by adjusting flowrates (manipulated variable) entering the mixer through manipulating the inlet valves; the specifications for reaction temperature and pressure (goal variables) can be realised by respectively adjusting the flowrate (manipulated variable) of cooling water entering the reactor jacket through manipulating the valve and the outlet pressure (manipulated variable) of a feeding pump through manipulating the pump, etc. Based on such a fact, it is possible to build the quantitative relationship between goal variables and the corresponding manipulated variables flowrate and/or pressure known as the goal-manipulated (G – M) model. There also exists a quantitative relationship between manipulated variables and associated primitive operations (or operating patterns) called the manipulated– primitive (M–P) model. Therefore, system states and primitive operations are bridged by both G – M and M – P models which form a reasoning chain: Goal variables [ (G – M model) × [ Manipulated variables [ (M –P model) [ Primitive operations By utilising this model based reasoning chain, we can, through the G– M model, map the operating paths of goal variables into the changing patterns of manipulated variables which are then, through the M–P model, converted into operating patterns of controllable devices which in fact are quantitative operating procedures. Both M–P and G – M models can be quantitatively described by a set of theoretical or empirical equations. For example, M–P models can mainly be described by flowrate–opening curve for the valve and pressure–rotative velocity curve for the pump or compressor, whereas G–M models are similar to the model of a process unit used for process simulation but with different calculating directions in most cases. An example on building the G–M and M – P models for a mixer unit and valve models can be found later in the section of bottom tier. Based on the above discussion, the following sections will provide more detailed representation of the methodology.
3. Top tier: operating path determination As mentioned previously, the operating path can be seen as a set of temporary ‘setpoints’ connecting initial and goal values corresponding to each goal variable. Therefore, determining the operating path is actually defining those temporary ‘setpoints’ for every goal variable. Such an operating path should meet all the value constraints so as to be feasible. Obviously, there are numerous feasible operating paths linking the certain
initial state and final state in the domain space among which there are three approaches capable of determining a better or even optimal one.
3.1. Comprehensi6e e6aluation approach This approach evaluates each of the feasible operating paths against some performance criteria which are usually classified into two classes of economy and operability, whereas operability can be further decomposed into controllability, flexibility, reliability, safety and so on. Based on the evaluation results, a better one among the existing operating paths can be determined. The advantage of this approach is that it strongly links the operating path with certain performance criteria together and the operating path obtained is certainly optimal among the operating paths evaluated based on a certain performance criterion. However, the significant difficulties in the use of this approach also exist, including, searching for as many feasible operating paths as possible for evaluation and building quantitative relationships between the operating path and the given evaluation criteria such as the reaction temperature and cost. Therefore, this approach can only be applied in cases where a limited number of feasible operating paths are candidates, and the qualitative evaluation results are accepted.
3.2. Optimization approach This approach uses optimization techniques such as nonlinear programming to directly search for an optimal operating path based on a simplified performance criterion: the shortest length of the feasible operating path linking the gi6en initial state and the final state. The shortest length of the feasible operating path also means the shortest operating time to transform the process state from the initial state to the final state, which is also proportional to the operational costs in most cases. Therefore, the operating path obtained, based on this simplified performance criteria, can be considered as optimal in the common sense. The simplified performance criteria can be described in the objective function and the value constraints mentioned earlier are directly used as constraints in the optimization algorithm. The operating path can be determined by solving the following nonlinear programming problem: n
Min % (xi − xi,goal)2
(1)
i=1
subject to: G(X, Y, U) ]0
(2)
H(X, Y, U) = 0
(3)
where n represents the number of goal variables, X the vector of goal variables, xi,goal a target value of goal
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Fig. 2. A mixing case process.
variable xi, Y the vector of manipulated variables, U the vector of other state variables, and G and H the inequality and equality constraints, respectively. For a mixing case process with a number of constraints avoiding the formation of dangerous mixtures as shown in Figs. 2 and 3, the operating path synthesis involves identifying goal variables, specifying both initial and goal states, defining constraints or/and performance criteria, and finally determining the operating path (intermediate ‘setpoints’), which are listed below: 1. goal variables: xi and L,
i= 1, 2, . . . ,n
2. initial and goal states: (x1, x2, . . . ,xn )(0) and (x1, x2, . . . ,xn )(E); L (0) and L (E); 3. objective function using performance criteria: n
2 (E) 2 Min % {(xi − x (E) )} i ) +(L −L i=1
4. value constraints: gj (x1, x2, . . . ,xn )]0,
j= 1, . . . ,m;
0 5L 5L (E), 0 5 xi 5 1,
i= 1, . . . ,n;
x1 +x2 + ···+xn =1. 5. Solve the above NLP problem formed by item 3 and 4 above. It is necessary to mention that before solving the above NLP problem, the constraints: gj (x1, x2, . . . , xn )] 0 describing the dangerous region
Fig. 3. Schematic of mixing constraint.
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should be properly multiplied geometrically for safety consideration. In solving the NLP problem, we are not only interested in the final optimum value but more interested in obtaining the iterative path from the initial state to the goal state. This is because the iterative path is actually our initial solution of the operating path. To make the operating path operable and reduce the number of corresponding primitive operations, this iterative path is further refined to several ‘setpoints’ as few as possible by merging a number of intermediate iterative points which is conducted through a refining program which consists of three steps: 1. linking the starting point to its next intermediate point and then checking whether the link line touches the constraint boundary; 2. if it does not, omitting this intermediate point and repeat step 1 above; 3. if it does, the last omitted point is a valid intermediate state which is chosen as new starting point and repeat step 1 till the goal state is reached. In such a way, a refined operating path consisting of valid intermediate states is finally obtained which is operable, safe, and has shorter operating time, and in most cases, lower operating cost. It should be mentioned that operating paths obtained by using different solution methods may be different depending on the searching mechanism of each solution method. The two guidelines can be used for selecting solution methods for a given optimization problem: 1. The optimal value of the objective function of the optimization problem should be zero so as to ensure that the operating path certainly reaches the final state from the initial state. 2. The number of intermediate states forming the operating path after refined from original iterative path should be as few as possible so as to ensure the operating path is operable in practice.
3.3. Heuristic approach The above approaches require detailed quantitative representation. Sometimes, qualitative approaches or graphical interactive approaches are more efficient in obtaining only feasible paths when constraints are not complicated. In such a case, the intermediate states of goal variables can directly be specified by human experts based on their knowledge and experience. Stationary state concept proposed by Fusillo and Powers (1987, 1988) can significantly facilitate this work. A stationary state is an intermediate state during the planning process which holds system for a period of time during which the system state does not change significantly until next action is taken. For example, the operation at total reflux of a distillation column is a stationary state. The stationary state should certainly be on the operating path the values of goal variables
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associated with which can directly be specified based on operational knowledge. This planning methodology supports the operating path specified by user as well which is known as heuristic approach. Once a path is obtained, it will be realized by planning a set of ordered primitive operations in the next section.
4. Bottom tier: primitive operation synthesis This tier synthesizes a set of primitive operations to achieve each ‘setpoint’ (intermediate state) till the final state on the operating paths of the goal variables. A model chain based planning technique is introduced here to achieve this which contains three steps: goal formulation, model based reasoning, and ordering and timing of primitive operation, as discussed below.
4.1. Goal formulation As mentioned earlier, each operating path contains a number of ‘setpoints’ of one or more goal variables. The first ‘setpoint’ is taken as the current goal which drives the planning of relevant primitive operations from the initial state to achieve it. Then, the current goal is shifted to the second ‘setpoint’ and the planning moves forward one step. In this way, the current goal moves from one ‘setpoint’ to another until the final goal in the path is reached. When considering the system wide problem, it is convenient to start planning from the goal variables at the feeding unit of the system and follow the stream direction.
4.2. Model based reasoning Once a current goal is formulated, a number of primitive operations are synthesized using a modelbased reasoning as described below: 1. Identify the associated controllable devices and check the action constraints bound up with the controllable devices, if the action constraints are met, turn to step 3 below, otherwise, continue. 2. Propagate unsatisfied action constraints to the relevant devices following the plant topology until such constraints are met. Once such a device is reached, go to step 1 above. 3. Activate a relevant G – M model and calculate the responsible manipulated variable values. 4. Perform the primitive operations of the current device based on M – P model to achieve the goal. 5. Formulate the next planning goal following the stream direction and repeat this procedure. Such a model-based reasoning can be seen as the planning chain: ‘Setpoints’ of goal variables [ G–M models [ Values of manipulated variables [ M–P
models [ Primitive operations. Notice that some goal variables are not directly, but indirectly controlled by manipulated variables through other state or goal variables, which is also covered by the G–M models. For example, the product quality (goal variable) from a fixed-bed reactor is usually controlled by inlet temperature (goal variable) of the reactor which is further controlled by fuel flowrate (manipulated variable) entering a furnace if the furnace is the upstream unit of the reactor. In such a case, the G–M model virtually represents the relationship between production quality and reactor inlet temperature as well as fuel flowrate.
4.3. Ordering and timing of primiti6e operation Any primitive operation in the operating procedures contains its sequence and timing. The sequence is ordered by action constraints bound up with each controllable device. For example, following two action constraints for mixer startup which are respectively imbedded in inlet and outlet valves of a mixer: IF the liquid le6el in the mixer is lower than bottom limit, THEN open the inlet 6al6e-1; IF the liquid le6el in the mixer is higher than top lim it, THEN open the outlet 6al6e-2. are used to order the relative sequence of the valve-1 and valve-2 based on the liquid level in the mixer. However, how to ‘open the inlet 6al6e-1 ’ or how to ‘open the outlet 6al6e-2 ’, that is valve’s opening and changing pattern, which is known as the timing of a operation, is determined by the dynamics specified in the G–M and M–P models mentioned above. It is clear that the G–M and M–P models in the bottom tier are the core of the synthesis of operating procedures the examples of which related to mixer and valve are given below.
5. Reasoning models A mixer is chosen to show its G–M model since its operation is often restricted by complicated constraints which prohibits the formation of a potentially dangerous or undesirable mixtures. Many former researchers focused on a specific type of mixing constraint, namely binary, qualitative mixing constraint, which implies that the components A and B should never be present at the same time in the same location within the chemical plant, that is, they are simply forbidden to come into contact with one another. However, a more general and often encountered quantitative constraint with prohibited concentration range shown in Fig. 3 is not yet dealt with which can be solved by using this two tier methodology.
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5.1. G–M model of mixer The G–M model describes the relationship between goal variables and responsible manipulated variables. However, it should be realized that G – M model of a process unit contains not only goal variables and corresponding manipulated variables, but also other necessary state variables. For example, the G – M model of a heat-exchanger calculates the cooling water flowrate (manipulated variable) based on the ‘setpoint’ of the outlet temperature of the hot stream (goal variable), its flowrate, the inlet temperatures on both sides and the relevant equipment parameters and physical properties. Different from traditional unit model solving, the G – M model utilizes the given output variables (goal variables) to specify some input variables (manipulated variables). Considering the mixing case process shown in Fig. 2, it is easy to see that the component concentrations and the liquid level inside the mixer are goal variables, the inlet and outlet flowrates are manipulated variables which are used to control the concentrations and level inside the mixer through associated valves. The G–M model for above mixing case process consists of following Eqs. (4) and (5), which are derived from the mass balance Eqs. (6) and (7) through discrete treatment. F (k) i =
x (k) Ar i (k − 1) F (k) n + L x (k) M n
x (k) i − 1) − 1) x (k −x (k n i x (k) n
(i= 1, 2, . . . , n) Ar (k − 1) (k − 1) (L (k)x (k) xn ) n −L M (k) Dt = (k) (k) (F (k) n −x n F n + 1)
(4)
(5)
ArL dxi =Fi − xi (F1 +F2 +· · · +Fn ) M dt (i =1, 2, . . . , n)
Ar dL = F1 + F2 +· · · +Fn −Fn + 1 M dt
(6)
Fig. 4. The flowsheet for case study.
filling period, for example) or by the G–M model corresponding to another downstream unit in which F (k) n + 1 is a manipulated variable. Given three aspects of information above, the flowrate of each inlet valve and corresponding maintaining time period for each state transform can be obtained through the G–M model and finally to bring the state to the goal state.
5.2. M–P model of 6al6e Once the flowrate of the valve is obtained through the G–M model, the corresponding valve opening can be calculated through the M–P model of the valve to achieve the flowrate. The M–P model of the valve describes the relationship between its flowrate and corresponding opening which can be obtained from valve performance curve that varies with valve type: (k) C (k) i = f(F i )
(i =1, 2, . . . , n+1)
(8)
Each valve opening obtained above is kept during the corresponding time period so as to maintain a certain flowrate to achieve a state transform. Finally, the operations containing valve opening and timing towards achieving certain goals under such generic and complicated mixing constraints are synthesized through the G–M model of mixer and the M–P model of the valve.
(7)
where superscript k refers to the series number of intermediate ‘setpoints’ or goal ‘setpoints’. The application of above G – M model requires three aspects of information: 1. The current value (referring to k −l) and next ‘setpoint’ (referring to k) of each goal variable. 2. The reference flowrate of a certain inlet valve F (k) n , which can be specified having several alternatives depending on different operational strategies one of which is to minimize operating time. In such a case, F (k) in Eq. (4) refers to the flowrate of valve n n corresponding to its maximum opening. 3. The outlet valve flowrate value F (k) n + 1 which is specified by an operator (it should be zero during the
6. Application of the methodology To illustrate the use of this methodology, this section introduces the synthesis of startup procedures for a subsystem of a plant in which emphasis is placed on the primitive operation planing on the system wide issues. Fig. 4 shows the flowsheet of a case based on the reaction section of a HDS process in which hydrogen (A) and sulphuret (B) as well as inert gas nitrogen are mixed through a tank-mixer and a pipemixer, respectively, and the output stream is heated to a certain temperature and the reaction takes place in a reactor, then the reactor output stream is cooled and the product is condensed and separated in a flash vessel.
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664 Table 1 Goal variables and operating paths Goal variable
XA
XB
P1
T6
T8
L
P2
Initial value Intermediate value Intermediate value Goal value
0.2 0.4 0.5 0.55
0.0 0.2 0.3 0.35
1.0 1.2 1.6 1.8
25 70 +45°C/h 295
25
0.0
1.0
65
1.2
1.6
There is a dangerous mixing region: xA =(0.9 – 1.1)xB in the mixer and an operational constraint: dT6/dt 5 45°C/h for preheating catalyst in the reactor. Suppose that the initial status of all valves are closed, and goal variables are marked in Fig. 4, and their corresponding initial, intermediate and goal values are listed in Table 1. Starting from the goal variables related to the tankmixer, xA, xB and P1, the planner takes their first set of ‘setpoints’ as the first planning goal. Checking the action constraints bound up with V-1, V-2, V-3 and V4 respectively, finds the first three valves are ready to be operated and V4 requires goal variable P1 reaching its goal state ahead since its action constraint is IF P1 reaches its goal state, THEN opening 6al6e-4. The G–M models of the tank-mixer and the piper-mixer are activated to specify the flowrates F1, F2 and F3, and their corresponding operating time. The flowrates are further converted to the openings of three valves through M–P models associated with each valve. Finally, the primitive operations: adjusting V-1, V-2 and V-3 openings to 0.7, 0.2 and 0.5 for 15 min are proposed and executed. After the first set of ‘setpoints’ is achieved, the primitive operations respectively corresponding to the second, and then the goal ‘setpoints’ are synthesized and carried out in the same way. As soon as the final state of the mixer is reached, the primitive operation: adjusting V-4 opening to 0.6, is performed since its action constraint has been met at this time. Till now, the first planning goal has been achieved and T6 is chose as the second planning goal. Since the action constraint associated with V-5: IF V-4 is open, THEN opening V-5 has been satisfied, the primitive operation: adjusting V-5 opening to 0 3 for one hour, resulted in by the first ‘setpoint’ of T6 through G–M model of the furnace and further the M – P model of V-5, is synthesized, following that another set of actions for V-5 are synthesized and performed to achieve each of the ‘setpoints’ on its operating path till the final goal is reached. Meanwhile, the action constraint bound up with V-6: IF T6 exceeds 250 °C, THEN opening V-6, activates the G – M model of heat-exchanger at proper time and further the M–P model of V-6, and the action: adjusting V-6 opening to 0.7 for a hour is synthesized. In fact, the opening of V-6 varies with the increase of T6, here the planner only gives a discrete value for operability consideration.
Similarly, the opening of V-7 are synthesized through the G–M model of flash vessel and M–P model of V-7 and once the goal state of flash vessel is achieved, the action constraint of V-8 is met, therefore, V-8 is opened to maintain the level. Till now, the startup procedure for this case flowsheet has been synthesized. The patterns of valve operations are shown in Fig. 5 in which each color change indicates the variation of corresponding valve opening. It is obvious that the order of primitive operations is decided by action constraints bound up with controllable devices, whereas the timing is decided by the dynamic response of the associated models. To automate this methodology, a prototype system has been developed in C/C + +. The top tier defines operating path by user’s specification through GUI or NLP optimizer with additional refinement block. The bottom tier synthesizes primitive operations through a inference engine and a model library which currently contains G–M models for mixer including tank-mixer and pipe-mixer, splitter, heat exchanger, flash vessel, furnace, CSTR and PFR, etc. and M–P models for valve, variable speed pump and compressor. These two tiers are independent.
7. Conclusions To overcome the difficulties in planning operating procedures for the process with complicated operational constraints, a model chain based quantitative planning methodology is presented supported by two
Fig. 5. The operating pastern of valves.
H. Li et al. / Computers and Chemical Engineering 23 (1999) 657–665
tiers. The top-tier determines the operating path using optimization methods with qualitative alternatives, and the bottom-tier synthesizes the primitive operations through a G–M and M – P model based reasoning chain. This is based on a discovery of the fact that all the operational goals are accomplished by directly or indirectly adjusting two basic manipulated variables: flowrate and pressure, through the manipulation of three controllable devices: valve, pump and compressor. Furthermore, two sets of models: G – M and M –P are abstracted to bridge the goal variable operating paths and the primitive operations. The G – M model maps the goal variable path into the manipulated variable patterns and the M – P extends such mapping to the primitive operations of controllable devices. Then a model chain based reasoning technique is presented which provides a procedure for each goal variable to go through the G–M model [ Manipulated variables [ M – P model [ Primitive operations chain. As the result, both the ordering and timing of the primitive operations can be obtained. The methodology has been successfully applied to plan the start up operating procedure of a case process with complex mixing constraints. The advantage of this methodology is efficient. The top-tier determines the operating paths of goal variables using either nonlinear programming or qualitative methods without concerning the detailed ordering and timing of primitive operations. Whereas the bottom-tier uses models and action constraints to order the primitive operations with timing for achieving the operating paths obtained from the top tier. The methodology is also generic, especially, the bottom tier can be used independently in different areas. This paper is a initial efforts toward the quantitative planning of the operating procedures in which only common issues involved are discussed and many other complex issues, such as nested states, recycle flowsheet and parallel sequences of the operating procedures, etc. remain to continue efforts.
Appendix A. Notation A Ci Fi
cross-sectional area of tank mixer opening of valve-i volume flowrate of i-th stream
.
L M P T t xi xi,goal r
liquid level molecular weight pressure temperature time goal variable goal value of goal variable fluid density
Superscript 0 k E
initial value intermediate value goal value
665
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