Plant-wide optimal waste management

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Computers and Chemical Engineering Supplement (1999) 567-570 © 1999 Elsevier Science Ltd. All rights rese....·ed PU: 50098-1354199/00079-4

Pergamon

Plant-wide Optimal Waste Management Andreas A. Linninger and Aninda Chakraborty Laboratory for Product and Process Design Department of Chemical Engineering, University of Illinois at Chicago e-mail: {linninge, achakrl}@uic.edu

Abstract

Synthesis of optimal waste treatment policies on a plant wide level is a formidable challenge due to (i) the knowledge necessary to do selection of treatment steps and (ii) the combinatorial complexity of the resulting problem space. This paper presents a hybrid methodology for an automatic synthesis of feasible alternatives, the superstructure generation, followed by rigorous combinatorial optimization. In step one, evaluation of waste properties against regulatory limits as well as a relaxed set of technology selection criteria gives rise to a tree of feasible treatment options. In step two, rigorous integer progranuning techniques expose optimal waste management policies with best trade-off between different levels of environmental, ecological and logistic constraints: Results of the application of the methodology onto a case study from the pharmaceutical industry are discussed. These figures demonstrate clearly the huge degree of flexibility that can be obtained by systematic waste management using computerized methods. Keywords

Decision-Making, synthesis, waste treatment, pollution prevention

Introduction Synthesis of optimal waste treatment policies requires knowledge on how to select technically feasible treatment technologies. For a given waste stream numerous alternatives may be available. With the inclusion of recycle and reuse options for pollution prevention, the problem space is even increased more. In this case physical separation techniques for material recovery must be considered alongside destructive treatment options. Traditionally, process optimization in engineering used to be concerned with finding the optimal process parameters for a given process flowsheet. The underlying base case flowsheet may have emerged from earlier research and development. Recently, conceptual design targeting towards finding the best structural alternatives before refining detailed operational parameters is gaining more attention, e.g. Grossman, 1996. Following this more innovative paradigm, a large number of structural alternatives corresponding to different choices of raw materials, auxiliary chemicals such as solvents as well as utilities, needs to be considered. Unfortunately, even small problems may host a huge space of design alternatives. This combinatorial aspect makes computer-aided methods attractive for the solution of such synthesis problems, e.g. Friedler et aI., 1994; Ali et aI., 1998. This paper will demonstrate a hybrid technology for the automatic computer-aided synthesis of plant-wide optimal waste treatment policies. We will show in section one, how rule-based inference can generate a

tree of all feasible treatment options. The resulting problem superstructure implicitly embeds all feasible treatment policies subject to the given selection criteria and availability of property data. It can be optimized rigorously. Optimal waste management allows plant managers to implement feasible pollution prevention efforts and/or reach desired levels of compliance at minimal cost.

1. Superstructure Generation The first stage aims at synthesizing all feasible treatment options for a set of wastes WjQ of known amount and composition. This problem requires (i) identification of the regulatory offences of all wastes, (ii) selection of feasible treatment options and (iii) possible expansion for the treatment of residuals from prior' treatment steps. A superstructure of feasible treatment steps for each waste stream can be generated by means of planning theory as described in the subsequent paragraphs. 1.1. Deducing feasible treatment options

The methodology for superstructure generation is derived form earlier work for the assessment of pharmaceutical wastes, e.g. Linninger and Stephanopoulos, 1996. A detailed desciption is beyond the scope of this discussion. Fig. I, top section, summarizes superstructure generation in formal logical

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Computers and Chemical Enginecr'ng Supplement (1999) 567-570

notation. The following comments are intended for the continuation of the main ideas. The reasoning mechanism involves three steps: (i) diagnosis (ii) preselection (iii) execution. The diagnosis step characterizes each waste WiO and detects possible regulatory offences. For each offence a specific treatment goal is generated. Preselection searches the treatment database T, which holds about 40 treatment options for destructive waste treatment and material recovery. A treatment, t, is a-treatmentoption for a waste, WiO, if it can satisfy at least one goal, g. In the Execution step, all treatment options found in steps two are "applied" on waste WiD. This simulation produces additional nodes WiJ that represent the residuals resulting from the treatment. These residual calculations rely on short-cut prediction methods using an operation-centered modeling paradigm as described in the BDK project, e.g. Linninger, et ai, 1994.

1.2. Representing the superstructure: After the completion of diagnosis, pre-selection, execution, each non-compliant residual is submitted to another reasoning cycle. Repeated application leads to a tree of all feasible treatment alternatives. The systems uses a State Task Network (STN) representation, e.g. Kondili et al., 1993, in which wastes wij stand for the nodes, while the treatments t constitute the arcs, see Fig. 2. An ordered sequence of options that treats a waste WiD and all its residuals to compliance is called a treatment path R. The set of all feasible treatment paths p for a given waste WiD is called a treatment tree. Two treatment paths are called disjunct, if they do not belong to the same tree. The superstructure S is the union of all treatment trees for all wastes W. A treatment policy IT in S is a set of disjunct treatment paths p with exactly one feasible path per waste. The

fvr all WvJc 51rc:mu

number of embedded policies is equal to the cardinality of the cross-product of all disjunct paths. 2. Optimal Waste Treatment Policy Management Although the superstructure generated in phase one contains all feasible treatment policies, it does not answer to plant-specific' constraints. In stage two of the proposed methodology, plant managers can find optimal waste management strategies using rigorous mathematical programming techniques. The options include (i) exploring different levels of utilization of plant-specific infrastructure and resources (ii) locating the best trade-off between conflicting economical and ecological objectives and (iii) finding the globaIly optimal waste treatment policy subject to a deliberate set of capacity, environmental and logistic constraints.

2.1. Problem Formulation; This subsection, we will describe how the logic of the superstructure in its STN encoding can be easily transformed into an equivalent mathematical description. Due to space limitations, we will focus the discussion on the description of four categories of constraints as weIl as their mathematical formulation. Logical Consistency. Binary design variables Xi are assigned to each treatment task t. Path consistency can be expressed using logical rules, which are equivalent to equality constraints involving the design variables Xi as described in Equation 2 of Fig. 3. The superstructure in the formulation of Fig. 3 captures all feasible policies without the need for explicit enumeration. Implicit formulations of treatment policies are absolutely required for maintaining tractability in large problem spaces. Capacity Constraints. In modem production plants, available treatment facilities are shared for numerous production lines. Frequently, limited

I SUPERSTRUCTURE GENERATION Diagnosis: Definition of Treatment Goals Ift'{e E w) "I 3p, rep "propmy(e» "

(, E

R)" ( ..iotutes (p.'»)) => Goa/(e);

Preselection: Deduction of Treatability IfI.w,e(/E T)" [!3/,p(1 EL)" (p" p,opmy(e» 1\

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1\

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" (satisfies (g,,))]=> treatmencoption (t,"1;

Execution: Prediction of residue composition 1!:i.e execute (I. w) V I. WI,eutm.ncoplion (I, w)

Nomenclature : c: Compound w: Waste IV: Set of Wastes p: Property r : Regulation R: Set of Regulations g: Goals

I: Limitation L.: Set oflimitation

rules Cor treatment t e : Effects &: Set of effectiveness rules for treatment1 T : Database of available

treatmentoptions

NEDVORKOPTIMIZATION • Constrained Integer Programming

Fig.I. Overview of the hybrid methodology for waste treatment synthesis

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Computers and Chern;'al Engineering Supplement (1999) S67-570

W21 . ---:,, _

•..,W'jl

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I

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Fig.2. Treatment plan of a liquid organic waste capacities and availability of these options may constrain further production expansion. Therefore it may be important to include these limitation for a plant wide optimum design. Using the design variables, capacity constraints can be expressed by simple summation over the particular treatment category, e.g. Equation 3 in Fig. 3. Environmental Constraints. Environmental constraints express limitation on emissions per unit time. Even though the superstructure only contains compliant terminal nodes, the total amount of emissions may be regulated by (i) governmental agencies on federal, local or municipal level or (ii) be subject to voluntary corporate environmental standards. Environmental constraints can be considered by adding the respective emissions in the leaves of the superstructure, e.g. Equation 4 and Equation 5 in Fig. 3.

Cost function. Cost estimation used in the proposed methodology reflects only variable cost associated with different treatment alternatives, i.e. operating and maintenance cost. Consideration of capital cost is straight forward, but is typically of lesser importance due to long payback periods and lifetime of waste treatment facilities. The following table lists the different cost models used in the proposed system: • Composition Dependent Costs (CDC) are function of the species in a treated mixture e.g. heating value for incineration; Evaporation, Scrubbing and Neutralization. • Composition Independent Cost (CIC) depend only on the quantity of the raw material, irrespective of their composition e.g. Wet Air Oxidation, Biological Treatment, Final Treatment such as Landfill and Waste-water Treatment. • Negligible costs (NC) in operations like ionexchange, leaching with water are neglected when compared to more expensive treatments like the Incineration. Typically cost correlations appear as the objective function in the optimization problem, e.g, Equation 1, in Fig. 3. 2.2. Solution ofthe optimal waste treatment problem: Mathematical expressions for the cost function, environmental emission and logical. constraints are automatically generated by the symbolic features of the proposed environment. The resulting mathematical problem is surprisingly simple. Since all non-Iinearities have been dealt with in the superstructure generation step: (i) physical, chemical, environmental property predictions, (ii) residue composition simulation, (iii) non-linear cost estimation; the final optimization problem is a linear integer program. In the form of Fig. 3, policy optimization can be more precisely qualified as a multi-bin knapsack problem. Although this formulation is still NP-hard, the elegant formulation of this proposal can solve waste treatment synthesis problems even for a large number wastes with commercial algorithms. For the case study described in Chakraborty, 1998; optimal solutions were found

w

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Unconstrained case

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Constrained case

Eqn.l

Path Constraint for all nodes

Eqn.2

Plant Capacity Constraint

Eqn.3

Environmental Constraint

Eqn.4

Environmental Constraint

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Fig.3. Superstructure Optimization

Computers and Chemical Engineering Supplement .-1999) 567-570

below 1 CPU second on a 300 MHz Pentium II PC using the CONOPT algorithm of GAMS [1996].

Waste

twI1'olicy

PoIIutioD

Treatment Policy

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PrevemioD

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3. Case Study. A case study of seven wastes from the first stage of a pharmaceutical manufacturing has been studied by Chakraborty and Linninger, 1998. Fig. 2 shows the tree for the first waste, which is an organic spent wash solution. The entire superstructure S has a cardinality of 35 individual treatments t, and plans involving only 2 - 9 alternative paths. Nevertheless, the superstructure embeds over 10,300 different treatment policies. Fig. 4 demonstrates the flexibility in resource consumption pertaining to different policies. For the same set of wastes W, incineration capacity varies by 70% between the highest and the lowest alternative. Table 1 summarize the cost associated with distinct pollution prevention efforts. It allows to quantify the relation of distinct waste management strategies and their respective cost and environmental impact. In this case study, a reduction of waste disposal at landfills of 50% leads to a cost increase of approximately 700,000 $/yr.

Cos' [Slyr]- .

-

Unconstrained (Base case)

-700.559

MOSI Expensive

410.516

No Wasle Water

-447.947

252.612

197,485

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'=0

700.560

50% Reduced Incineration Capacitv 50% Reduced LandfillCapacity

1.111.076

• Negativesign reflects benefitsfor reuse of raw materials •• PollutionPreventionCost = Total Cost of PolicyminusCOSI of Base case

Table 1. Total cost of different policies and associated relative cost for pollution prevention. selection, the methodology may lead to new approaches for automatic process flowsheet synthesis.

Acknowledgements The research was funded by the mc - CRB Grant S98. Provision of the GAMS language and the optimization codes from GAMS Development Corp. is gratefully acknowledged.

4. Conclusion:

References:

A hybrid methodology for the computer-aided synthesis and optimization of plant-wide optimal policies was presented. A superstructure containing all feasible treatment alternatives was generated through pruning of 'lhe search space by means of relaxed technology selection rules and application of nonlinear shortcut models for predicting of residue composition. The methodology leads to a linear integer programming formulation for finding the minimum cost waste treatment policy subject to environmental, logistic and path constraints. Through the separation of model-based superstructure generation from the structural constrained optimization problem, the combinatorial complexity of optimal waste management could be reduced and solved in reasonable computer effort in little CPU time. Although the presentation illustrated waste treatment

Ali, S; Linninger A.A. andG. Stephanopoulos,"Synthesis of Batch Processing Schemes as Synthesis of Operating Procedures: A Means-Ends Analysis and Non-Monotonic Planning Approach", Paper 216c, AICHE Annual Meeting, Miami, Fl, 1998 Chakraborty, A and AA. Linninger; "Computer-aided Synthesis of Waste Treatment Alternatives : A Case Study", Proceedings of the 21st Midwest Environmental ChemistryWorkshop,Ann Arbor, MI, Oct. 17 -18,1998. Friedler, F.; Varga, J.B., Fan L.T., Algorithmic Approach to Integration of Total Flowsheet Synthesis and Waste Minimization, in "Pollution Prevention via Process and Product Modifiations", AlChE Symposium Series, 90 (303), 1994. GAMS Release 2.25; A Users Guide; GAMS Development Corporation, 1996 Grossman, I.E.; Mixed-Integer Optimization Techniques for Algorithmic Process Synthesis, in "Advances in Chemical Engineering" (1. Anderson,Eds), Vol 23, AcademicPress, 1996. Kondili, E., C. C. Pantelides, and R. W. H. Sargent, "A general algorithm for short-term scheduling of batch operations", Compo Chern. Eng., 17,21,1993. Linninger, A A. and G. Stephanopoulos, "Computer-Aided Waste Management of Pharmaceutical Wastes", Paper 23a, AlChE Meeting, New Orleans,LA, 1996. Linninger, A. A.; S. A. Ali, E. Stephanopoulos, C. Han and G. Stephanopoulos, "Synthesis and Assessment of Batch Processes for Pollution Prevention", AIChE Symposium Series, 90 (303),46-53, 1994.

FigA. Extremal resource utilization of different treatment policies