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Short-term scheduling and recipe optimization of blending processes Klaus Glismann, Gu¨nter Gruhn * Department of Process and Plant Engineering, Technical Uni6ersity Hamburg-Harburg, Schwarzenbergstrasse 95, D-21071 Hamburg, Germany Received 10 May 2000; accepted 5 January 2001

Abstract The main objective of this paper is to develop an integrated approach to coordinate short-term scheduling of multi-product blending facilities with nonlinear recipe optimization. The proposed strategy is based on a hierarchical concept consisting of three business levels: Long-range planning, short-term scheduling and process control. Long-range planning is accomplished by solving a large-scale nonlinear recipe optimization problem (multi-blend problem). Resulting blending recipes and production volumes are provided as goals for the scheduling level. The scheduling problem is formulated as a mixed-integer linear program derived from a resource-task network representation. The scheduling model permits recipe changeovers in order to utilize an additional degree of freedom for optimization. By interpreting the solution of the scheduling problem, new constraints can be imposed on the previous multi-blend problem. Thus bottlenecks arising during scheduling are considered already on the topmost long-range planning level. Based on the outlined approach a commercial software system has been designed to optimize the operation of in-line blending and batch blending processes. The application of the strategy and software is demonstrated by a detailed case study. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Blending; Short-term scheduling; Recipe optimization; Mixed integer linear programming

Nomenclature Bk,i,l g−,g+ NB NCn NI NP NR NT VCm,n VPn VPn,i V. Pn,i w Cm Wk,i wPn

batch size, resp. throughput of blender k during interval i with task l negative/positive deviation from a goal, g− ] 0, g+ ] 0 number of blenders number of components for product n number of time intervals number of products number of recipes minimum running time of a recipe in terms of intervals volume of component m for product n volume of product n volume of product n in interval i goal volume of product n in interval i cost of component m availability of a blender k during time interval i, binary variable price of product n

* Corresponding author. Tel.: + 49-40-428783241; fax: + 49-40-428782992. E-mail address: [email protected] (G. Gruhn). 0098-1354/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 8 - 1 3 5 4 ( 0 1 ) 0 0 6 4 3 - 3

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1. Introduction This paper presents a strategy to coordinate shortterm scheduling of industrial blending processes with nonlinear recipe optimization. The focus is on blending processes but the strategy is also applicable to other multi-product processes having typical criterions of blending processes. Blending processes themselves can be characterized by the following key features: Blending stocks of widely different properties are supplied continuously or in batches. They are sent to intermediate tanks. Properties and volume flow raterates of the components usually vary over time. The different components are blended according to recipes in an in-line blender or in a batch tank. The blends are stored in tanks and/or are delivered directly. The recipes must guarantee an on-spec product with minimum give-away. Product property limits are often restricted by law. Similar products can be blended by applying different recipes. A common field for blending processes is the production of gasoline and gas oil in refineries. Nevertheless, blending applications can also be found in several variations throughout all branches of process industry. Today’s widespread approach for the scheduling of such processes is to use intuitive graphical user interfaces combined with discrete-event simulators (Bodington, 1996). Heuristics related to operating policies can be incorporated to speed exploration of alternate policies. However, each scenario still has to be constructed and rated manually. Mathematical programming techniques for shortterm scheduling of multi-product plants have been extensively studied in the past years (Reklaitis, 1995), but not much is reported about the application of these techniques to the short-term scheduling of blending processes. Even though the process has a simple structure and therefore should be well suited for creating an appropriate optimization model. The scheduling of crude oil can be named as a related application that is mentioned in the literature (Shah, 1996; Lee, Pinto,

Fig. 1. Hierarchical management levels.

Grossmann & Park, 1996). An approach based on a mathematical model offers a user-friendly treatment of the underlying scheduling problem: User-defined constraints and objectives can be included in a straightforward way. Thus, in this paper a strategy based on a combined nonlinear programming (NLP) and mixed-integer linear programming (MILP) formulation is developed. Planning the operation of blending processes covers proper coordination of feedstock and products with market requirements and economics. However, shortterm scheduling of blending processes is more complicated than scheduling of most other processes because of the option to blend a product in many different ways: Consideration of recipe optimization and shortterm scheduling within an integrated approach becomes necessary. In order to avoid arising nonlinearities in scheduling, an iterative scheduling strategy is developed so that the problem can still be modeled favorably as a MILP based on a resource-task network (RTN) representation (Pantelides, 1994). Nonlinear recipe optimization is carried out separately within long-range planning but can be integrated into the overall strategy.

2. Basic planning and scheduling approach Within each company of process industry three hierarchical business areas can be identified (Polke, 1994): planning, scheduling, and control (Fig. 1). Planning and operating of blending processes can be understood according to these levels. This hierarchical model can be described by the following features: Detailing and reliability of information increases from top to bottom. The longest planning horizon can be found at the top. The horizon shortens rapidly, when moving down towards the process control level. Complex planning and scheduling tasks are broken into simpler ones that are solved within each level. Results of each level are forwarded to the attached levels (in both directions). The developed strategy is built up according to this hierarchical view. A long-range plan for blending processes usually covers a horizon of about one month. Therein roughly scheduled customer demands are balanced with the available blending component volumes. State of the art models are multi-period models that consider multiple blends simultaneously (multi-blend optimization) (Rigby, Lasdon & Waren, 1995). They embody a nonlinear recipe optimization problem. During the optimization run the running times of each operation mode for all upstream facilities (e.g. the reformer) can also be determined.

K. Glismann, G. Gruhn / Computers and Chemical Engineering 25 (2001) 627–634

Fig. 2. Short-term scheduling strategies.

At this level, a large-scale NLP has to be set up and solved. The usual objective is maximum profit given by the sum of sold products minus the value of spent feedstock: NP

NC

n

max % wPn ·VPn − % wCm ·VCn,m . n=1

(1)

m=1

The free variables are, the component volumes related to each product and each period, the running times of each possible operation mode for the upstream facilities. Constraints arise from the blending process structure (flowsheet, tank, and blender data, etc.), the forecast on the component production defined by each operation mode for the upstream facilities, the product delivery-dates, the nonlinear and linear blending models, and the planning periods, given by product demands and specific planning priorities. The obtained solution is transferred to the short-term scheduling level: the calculated product quantities are the goal quantities that have to be met applying the optimized recipes. At this short-term level, specific attention is paid to the delivery-dates and the allocation of the blenders. The planning horizon is shortened to one week. The main scheduling priorities are (in the given order): 1. to obtain a feasible schedule satisfying all product demands, 2. to meet the goals set by the long-range planning, and 3. to optimize the operation of all blending facilities itself (e.g. to minimize product and recipe changeovers).

629

An appropriate MILP formulation derived from a RTN process representation can be developed in order to fulfill the named goals. The most important feature of this model is that alternate recipes for each product and period can be provided. A recipe changeover becomes a free variable for optimization. So, which one of the alternative recipes is preferred in a particular situation results from the optimization run. The mathematical model will be described in detail within the next chapter. After processing the scheduling problem deviations from the goals can occur because of the following reasons: The more precisely considered delivery-dates in scheduling require an earlier production, because within long-range planning product demands were defined for periods and not for precise deliverydates. The necessary number of changeover operations can not be determined within long-range planning. No equipment item can be assigned to different operations at the same time anymore. Simultaneous allocation of equipment can not be excluded within long-range planning. In long-range planning, material is balanced according to the defined periods. A violation of given tank limits inside a period can not be determined until scheduling is done. When one of the given goals can not be met within scheduling actions according to three different strategies are available: (a) The resulting feasible schedule is accepted in spite of the deviations. The closest approximation to all given goals can be guaranteed mathematically. (b)Within scheduling a modified problem is constructed in order to shift deviations between goals. This can be accomplished by applying different weights to each single goal. (c) Finally a strategy coordinating short-term scheduling with long-range planning can be applied. The scheduling level can be left and a modified multiblend problem can be solved utilizing knowledge of the bottleneck in scheduling. The new goals for scheduling are more likely to be met. This strategy leads to an integrated optimization of planning and scheduling. Selection between the given strategies depends mainly on the current situation and the given scheduling priorities. Fig. 2 illustrates all alternatives explained above. After passing the scheduling level, a schedule which can be visualized graphically as a Gantt-chart is recovered. Set-points for the process control level can be derived from it. The blending process itself is carried out within this operative level. The received operating instructions are transformed into control strategies for the process control system. Advanced control of all blenders, respectively blend tanks, adjusts their opera-

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630

tion to the given set-points taking into account the current situation that can differ from the assumed.

(NT − 1)Wk,i + 1 0 (NT − 1)Wk,i +

i‘ + 2 + NT

%

Wk,i

i‘ = i + 3

Ö i =1,2,···,(NI − NT + 1), Wk,i + 1 0 Wk,i

3. Scheduling model The scheduling model is based on a RTN representation. Fig. 3 shows an example of a simple in-line blending process with 1 blender, 2 products and 3 components. The mathematical model can by characterized by the following key features: Time is modeled according to a uniform discretization. Tasks can be given a temporary validity in order to adjust scheduling to the periods of long-range planning. The maximum count of a resource is 1. Resources with similar characteristics are treated as different resources. This assumption simplifies resource balances. To formulate a mathematical model for optimization requires a deliberate consideration of how time can be modeled. For semi-continuously operated blending processes the duration of each single blending operation is not known a priori. The same is true for batch blending processes with variable batch sizes. However, a continuous-time problem formulation is not appropriate since a nonlinear mixed-integer program would result from modeling the continuously refilled blending component tanks. The application of a model based on uniform discretization of time is less crucial because the most significant simplification can be lessened: previous fixing of the duration for an individual blending operation is necessary but by subdividing a blending order into several smaller tasks corresponding to the discretization of time, blending becomes more flexible. In order to avoid unreasonable short running times of a recipe and too many recipe changeovers constraints can be added to enforce a minimum running time for particular recipes on a blender k, Eqs. (2) – (4).

(3)

Ö i {i i] NI − NT + 1}

(4)

Forced recipe changeovers due to the periods defined within long-range planning are not restrained by these constraints. Additionally, the technique of goal programming is applied in order to minimize changes in throughput of all blenders between intervals. The objective function (minimization) is extended by the term given in Eq. (5). NB NI − 1 NR

% % % (g¯+ + g¯− ), k,i,l k,i,l

(5)

k=1 i=1 l=1

g¯+and g¯−are the positive and negative deviations from a given goal, defined by Eq. (6) 0= (Bk,i,l − Bk,i + 1,l )+ g¯+ − g¯− k,i,l k,i,l Ö k= 1,2,···,NB;

i =1,2,···,NI,

l= 1,2,···,NR.

(6)

By making use of a RTN representation, it is possible to define a different product recipe for each period defined in long-range planning. This is achieved by providing different tasks at different points of time. This temporary validity contributes to the operating strategy of running the blending process optimally as initially planned. Even better fulfillment of the targets of a long-range plan can be accomplished by providing alternative recipes for each product and period. Calculation of these alternative recipes is carried out in the multi-blend optimization on the long-range planning level. But it is not possible to calculate additional recipes in advance since the planning model is incapable of taking scheduling tasks into account. So these recipes are added to the second scheduling problem after deviations occurred in the first problem following the proposed coordination strategy.

4. Case study

NT

(NT −1)·Wk,1 0 % Wk,i, i=2

Fig. 3. RTN of a typical blending process.

(2)

In this section, an example is presented to illustrate the application of the short-term scheduling model together with the proposed strategy to coordinate scheduling with recipe optimization. The blending process example is defined by 2 operation modes of the upstream facilities, 3 products, stored in 3 tanks, 9 components, 6 are stored in intermediate tanks, 3 must be processed immediately, 2 in-line blenders capable of blending all 3 products. The process structure is given by the RTN graph shown in Fig. 4. Table 1 details all tank data regarding components and products. Components 7, 8, and 9 do not have any storage tanks.

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Fig. 4. RTN graph of the blending process.

Upstream facilities can be operated in 2 different modes, leading to the component volume flow rates listed in Table 2. The flow rates are assumed different according to the 2 periods given by long-range planning.Maximum throughput of all blenders is 90 m3/h. Table 3 sums up product demands and tank volume goals given by long-range planning for an overall future

period of 7 days. Data is defined for two distinct points of time: The end of the second day and the end of the seventh day. For fulfillment of the 9 product property values 8 different recipes are available: for each period and product one different recipe is provided. Product C can only be blended during operation mode 2 because

K. Glismann, G. Gruhn / Computers and Chemical Engineering 25 (2001) 627–634

632 Table 1 Tank data

Minimum volume (m3)

Material Component Component Component Component Component Component

1 2 3 4 5 6

Product A Product B Product C

Maximum volume (m3)

280 402 40 403 403 404

2808 4021.3 408 4036.8 4030.6 4045.4

314.7 3848.1 64 3373.7 2638.6 682.5

2927 3465 117.9

29276.4 34652 4036.5

13520.2 7192 1102.9

component 7 is needed which is available only during this mode. To guarantee immediate consumption of component 8 and 9 product A must be blended simultaneously with product C, utilizing a second recipe for product A. The RTN graph is formulated as a MILP as explained in the last section. Product demands are modeled by constraints and must be fulfilled entirely to obtain a feasible solution. Eighty four time intervals of equal duration (2 h) are defined. Product changeovers from A to B or from A to C (and vice versa) are possible but require 6 h. The same is true for switching between operation modes. Changeovers from product B to C and from C to B do not require extra time. The objective is to minimize absolute deviations from the given tank volume goals. A second term is supplied in order to minimize changes in throughput of all blenders between intervals (Eq. (5)), the weight w is set to 0.001, Eq. (7). The goals are defined by Eq. (8) and Eq. (6). NP

NI

(7)

k=1 i=1 l=1

0= (V. Pn,i − VPn,i )+g+ −g− n,i n,i Ö n=1,2,···,NP;

explained by looking at the recipe for product A within the second period (day 3–7). The consumption of component 3 at maximum blender throughput is higher than the production of the upstream facilities for this component. Together with the very low storage capacity of component 3 a bottleneck arises, blender throughput is reduced to a value that corresponds to the refilling stream. The calculations of long-range planning are based on the overall quantity of component 3 that is available throughout a period. Now, scheduling reveals that this component must be con-

Table 2 Blending stock production Material

Volume flow rate (m3/h)

Operation mode

Mode 1

Period

No. 1

No. 2

No. 1

No. 2

2.2 17.5 11.5 37 0 68.5 0 0 0

2.3 13.4 15 36 0 70 0 0 0

2.2 17.5 11.5 37 0 0 37 14 25

2.3 13.4 15 36 0 0 40 13 23

Mode 2

NB NI − 1 NR

min % % (g+ +g− ) +w· % % % (g¯+ +g¯− ), n,i n,i k,i,l k,i,l n = 1i = 1

Initial volume (m3)

i=1,2,···,NI.

(8)

The final problem consists of 10 952 equations and 10 415 variables. 1854 variables are binary ones. XPRESS-MP Release 11 (Dash Associates Limited, 1999) is used to solve the MILP. After 73 348 CPU seconds, an objective value of 3418.94 is obtained and the solver is stopped. The best bound is 3415.23. The resulting schedule and the tank volume development of all products are shown in Figs. 5 and 6. Fig. 7 details the tank volume development of all components. All product demands can be satisfied. In spite of utilizing all available degrees of freedom in optimization product A shows a deficit of 2012.9 m3 after the second day and of 855.1 m3 after the seventh day. In addition product C shows a deficit of 507.7 m3 after the seventh day. During the whole scheduling horizon product A is not blended with maximum throughput. This can be

Component Component Component Component Component Component Component Component Component

1 2 3 4 5 6 7 8 9

Table 3 Product demands and tank volume goals given by long-range planning Material

Demand (m3)

Tank volume (m3)

Date

T1

T2

T1

T2

Product A Product B Product C

2927 5144 370

7290 8220 450

15871.7 3465 948.9

14368.6 6077.7 1027.9

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Fig. 5. Schedule of all blenders, first problem (naming of recipes: A1P2 recipe 1 for product A, period 2).

sumed with a constant level to take the low storage capacity into account. Tank limits must be met at each point of time in scheduling. The original long-range planning problem is modified according to this knowledge: The maximum volume fraction of component 3 within product A in period 2 is lowered from 100% to 16.67%. This bound enforces that at maximum throughput of a single blender the consumption of component 3 exactly equals the refilling rate. The new recipe after carrying out the multi-blend optimization meets this new upper bound. The recipe is added to the scheduling problem and can be chosen as alternative to the old recipe. The second scheduling problem is solved and the optimizer is stopped after 77 979 CPU seconds. The objective value is 2123.24, the best bound is 2053.2. All product deficits after the second day stay unchanged. But the deficit of product A reduces to 39.3 m3 after the seventh day. The deficit of product C after the seventh day changes to a surplus of 119.6 m3.

Deviations in the given goals of long-range planning can be transferred to the recipe optimization problem according to the presented strategy: The NLP is modified based on an analysis of the solution resulting from the scheduling problem. So bottlenecks that can not be foreseen in long-range planning can be included. The altered NLP is solved and new goals are obtained that are more likely to be met within scheduling. The proposed planning and scheduling approach has been implemented into a commercial system for the overall optimization of blending processes. A high efficiency and sufficient ease of use could be proved by solving several problems of industrial magnitude.

5. Summary and discussion This paper has presented a strategy to coordinate short-term scheduling of blending processes with nonlinear recipe optimization. The recipe optimization problem is treated as a NLP and its results, the recipes and tank goals, are forwarded to the scheduling problem. The scheduling problem is formulated as a MILP based on a RTN representation. The scheduling model is capable of switching between alternative recipes during optimization, can take recipes into account that are defined to the long-range planning periods, and uses a combined strategy consisting of additional constraints and a special objective that avoids unreasonable short running times of recipes and that minimizes recipe changeovers.

Fig. 6. Tank volumes of all product tanks.

Fig. 7. Tank volume of all component tanks.

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References Bodington, C. E. (1996). Planning, scheduling and control integration in the process industries. New York: McGraw-Hill Chapter 6. Dash Associates Limited, (1999) Warwickshire, UK: XPRESS-MP Release 11. Lee, H., Pinto, J. M., Grossmann, I. E., & Park, S. (1996). Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial Engineering Chemical Research, 35, 1630–1641. Pantelides, C.C. (1994). Unified frameworks for optimal process planning and scheduling. In Proceedings of the second interna-

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tional conference on foundations of computer, CACHE Publications, pp. 253– 274. Polke, M. (Hrsg.) (1994). Prozeßleittechnik, 2. Auflage, Oldenbourg Verlag, Mu¨nchen, Wien. Reklaitis, G.V. (1995). Scheduling approaches for the batch process industries, Working Paper No. CIPAC 95-9, School of Chemical Engineering, Purdue University, West Lafayette. Rigby, B., Lasdon, L. S., & Waren, A. D. (1995). The evolution of texaco’s blending systems: from OMEGA to StarBlend. Interfaces, 25 (5), 64 – 83. Shah, N. (1996). Mathematical programming techniques for crude oil scheduling. Computers Chemical Engineering, 20 (Suppl.), S1227– S1232.

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