Metallurgical Process Design - American Chemical

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Ind. Eng. Chem. Res. 2002, 41, 3797-3805

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Metallurgical Process DesignsA Tribute to Douglas’ Conceptual Design Approach Andreas A. Linninger* Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607

This case study illuminates a practical design problem for cleaner metallurgical manufacturing. The task consists of assessing the feasibility of a novel low-waste process capable of eliminating unwanted, hazardous waste streams in stainless steel production. The novel flowsheet evolves gradually as prescribed by the decision hierarchy of Douglas (Douglas, J. M. AIChE J. 1985, 31, 353-362). Successively refined economic potential estimators discriminate inferior options and discard process configurations with marginal economic performance early in the design cycle. The complex liquid metal reaction network is optimized via a multiphase total Gibbs free energy model. A bilevel mathematical program for the simultaneous optimization of economic performance at equilibrium within specified operational bounds is presented. The article uses the case study to elucidate methodological aspects in systematic decision making for metallurgical process synthesis. Examples for the beneficial use of mathematical modeling and nonlinear programming within a systematic design framework for a novel metallurgical process are offered. Introduction In process engineering, creative R&D efforts generate a continuous stream of new potentially marketable process ideas. Only a few inventions promise sufficiently large economic incentives to justify full-scale process development. It is evident that assessing the feasibility of many new process concepts is a crucial activity for innovative engineering businesses. To address this vital design challenge, Douglas developed a hierarchical process synthesis methodology for expeditious and systematic flowsheet generation.1-2 Although perfected for continuous petrochemical processes, this work confirms the merit of Douglas’ conceptual design procedure for a batch metallurgical synthesis task. Its background is introduced next. Conventional stainless steel manufacturing leads to unavoidable waste streams containing heavy metal oxides (see Figure 1). In today’s practice, these slags are still deposited as waste in landfills.3-4 Slag dumping is expensive and/or restricted when it contains certain heavy metals. From the environmental and economic points of view, it would be desirable to eliminate these wastes, thus avoiding the need for their disposal. One alternative to waste dumping consists of removal of hazardous contaminants from the slag. After cleaning and proper adjustment of their compositions, treated slags can even serve as a precursor to a commercial construction material. Hence, a new “low-waste process”, whose real identity is deliberately concealed for confidentiality reasons, should address the following goals: removal of toxic metallic species from the slag; transformation of slag into a building material, thus eliminating the need for landfill; and recovery of valuable metals for recycling to the stainless steel process. In this article, we evolve an entirely new metallurgical process and its corresponding flowsheet and assess its economic performance using a modified version of Douglas’ approach. Sections 1 and 2 investigate funda* To whom correspondence should be addressed. Tel.: (312) 996-2581. Fax: (312) 996-0808. E-mail: [email protected].

Figure 1. Material streams in conventional stainless steel manufacturing Table 1. Stages of Hierarchical Decision Making for Process Design (Douglas1) name

design activities

level 1 batch vs continuous level 2 level 3 level 4 level 5 level 6

plant capacity, raw material flows, and product specifications; principal reaction routes and process options input-output process streams, their phases and composition EP ) net balance of material values recycle reaction-separation system: reaction structure and phase equilibrium, Gibbs free energy minimization f optimal material charge detailed separations design: recycle streams, gas separations cleaning for solid removal and treatment of air pollutants heat energy and power integration of entire integration manufacturing site, pinch analysis process open process options, alternatives and alternatives variations, detailed kinetics and transport limitations

mental process options and preliminary information. The complex metallurgical reaction network is optimized using a thermostatic approach in section 3. We demonstrate the formulation of the equilibrium problem and selection of optimal key design variables via a bilevel mathematical program that ensures optimal economic, thermodynamic, and operational targets. Section 4 outlines the completion of the conceptual design of the new process. The article closes by drawing conclusions from this work for metallurgical process design. Level 1. Preliminary Information Table 1 depicts Douglas’ decision hierarchy adopted for this case study. The first phase concerns the gather-

10.1021/ie0107901 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/23/2002

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Figure 2. Conceptual objectives of a low-waste process.

ing of preliminary information on the primary chemical reaction routes and available process options. The reaction chemistry of liquid metal mixtures has several distinctive features, including (i) large numbers of reaction pathways between reduction and oxidation of metallic species and their oxides (ii) and highly nonideal phase behavior. Strong repulsive forces between liquid mixtures of metals and their oxides lead to almost perfect separation between the alloy and the ionic phase, i.e., steel and slag. Proper slag conditioning for low viscosity and density furthers the separability between metals and slags.5 This clean phase separation is essential in steel manufacturing routes in which deliberate formation of an oxide phase helps remove unavoidable impurities from the high-quality steel product. The natural separation between metal and slag also benefits our new process technology. A typical conventional stainless steel plant produces 800 000 tons of steel per year. This plant also discharges 200 000-250 000 tons of slags and dusts per year (see Figure 1). The formation of slags in the stainless process itself cannot be circumvented because of the high quality demand on stainless steels. A new secondary process should tackle the need for landfill of waste loads for economic and ecological reasons, as depicted in Figure 2. Hence, the main objective of the new process aims at eliminating heavy-metal-contaminated slags from the life cycle of stainless steels by their transformation into a useful building material. Demanding an available operability of approximately 6000 h/year, we arrive at an hourly production rate above 40 tons/h. This rather small expected capacity puts the new process in the batch category. We will therefore consider a single plant similar in size and operation to a small electric arc furnace used in mini-mills.6 The physical properties of slags impede selective physical separation of unwanted oxides by extraction. Slags build strong networks of large polymerized ions, predominantly silicate ions, as well as corresponding cations and anions from manganese oxide, iron oxide, manganese, and phosphorus. Because of the strong linkage of the slag matrix, extraction or other physical purification of the heavy metal oxides is impractical. This peculiarity of metallurgical processes impacts the separation process design in the later phases. It will lead us to designing a reactor-separator for the desired chemical reactions with simultaneous phase separation between metal bath and slag. A promising process option displaces unwanted oxides via chemical reactions. A reduction reaction exchanges the unwanted metal oxide complex (MxOy) with the oxide of a suitable reduction agent (RzOy) as specified

Figure 3. Schematic Richardson diagram showing oxidation potentials of important metals and their oxides.

in eq 1. Because of the phase separation between the liquid metal and its oxide, enclosures are used to distinguish between the metallic [ ] and oxidic ( ) phases.

(MxOy) + z[R] S x[M] + (RzOy)

(1)

where M represents the metals Fe, Mn, Si, Al, Ti, V, ...; R represents a reduction agent, ...; and x, y, and z are stoichiometric coefficients. The reduction agent R is typically a metal of lower oxygen potential than metal M. Typical key metals involved in most metallurgical processes include iron (Fe), silicon (Si), manganese (Mn), and aluminum (Al). In addition, we often find precious metals such as Ti, Ni, V, and Cr. Their corresponding oxides form highly nonideal liquid solutions, e.g., Al2O3, SiO2, FeO, V2O5, etc. The choices for suitable reaction agents R for a given metal M can be studied with the help of the Richardson diagram.3 It is depicted schematically in Figure 3 and explains the stability of metals and their oxides as a function of temperature. Metals with low oxidation potentials can reduce oxides located higher in the Richardson diagram. Lower oxidation potentials indicate more stable oxides. Hence, silicon can reduce the oxides of iron. Aluminum (Al) can, in turn, reduce silicon oxide. The strongest reduction agents are calcium (Ca) and magnesium (Mg). The preliminary analysis of the oxidation potentials points toward an opportunity for hazardous oxide elimination by chemical reactions of the type given in eq 1. In addition, the reduction reaction will release the corresponding elemental metal trapped in the harmful oxides. In effect, this reaction route also recycles valuable metallic alloys that would otherwise end up wasted in landfills. A critical advantage of this route further lies in the inexpensive and potentially total separation between the slag and the recycled metals, i.e., treated

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Figure 4. Input-output structure of the low-waste process. Table 2. Partial List of Cost Basis for a Low-Waste Process group product benefits reduction agents additives electricity

stream name slag benefit recovered iron recovered Ni carbon metal1 metal2 lime dolomite quartz energy cost energy efficiency

stream label

unit price ($/ton)

S1 P2 P2 R1 R2 R3 A1 A2 A3

60 115 8.000 100 540 1540 60 60 15 $4/MBU η ) 0.8

waste stream and raw material recycle. Hence, we shall pursue the process design task for the low-waste process based on the replacement reactions given above. Level 2. The Input-Output Analysis The central decisions in the input-output (I/O) analysis aim at identification of all chemical compounds and their categorization into input and output streams. The principal input to the low-waste process is the primary “waste” slag from steel manufacturing, S1 (see Figure 4). The process requires a metallic phase to start each batch (M1) to allow for a sufficiently large phase exchange area. The desired chemical reactions are engaged by adding a suitable reduction agent R. Additives (A) are needed to induce the desired phase separation between slag and metals and to meet the desired product compositions. When done properly, slag and metallic phase will perfectly desegregate already in the reactor-separator furnace without the need for additional separator units. Hence, the new low-waste furnace will have two product streams: chemically altered slag (P1) and recovered metals (P2). The principal product leaves the process as “clean” slag (P1). The byproduct gathers the recycled metals (P2). An off-gas stream (O) collects the gaseous byproducts composed predominately of the “oxides” of carbon and hydrogen, e.g., CO, CO2, and H2O. Off-gas rich in CO or H2 is highly reactive, offering the possibility of recycle to the reactor. Alternatively, it could be purged. In the absence of quantitative criteria to justify either choice now, we opt for the process option without gas recycle. The recycle configuration of reactive synthesis gas rich in CO and H2 is recorded as a possible process alternative. Economics of the I/O Structure. Douglas recommends repeated estimation of the economic potential (EP) for the novel process. This first EP estimate accounts for product value minus raw material cost, as raw materials typically make up 35-80% of the process’ manufacturing cost.2 Conducting this first input-output analysis using cost data for the processing streams given in Table 2, it becomes clear that all process alternatives based on pure elemental reduction agents such as precious metals (R2 and R3) are not economically viable.

This conclusion can be explained by the high cost of such agents compared to the rather inexpensive products. This early result of the I/O analysis triggered an obligatory search for alternative, cheaper reduction agents! The need for better reduction agents resulting from the I/O analysis points back to the Richardson diagram introduced in Figure 3. It also displays the oxidation potential of carbon, shown as a straight line with negative slope representing the equilibrium of elemental carbon and its oxide CO according to the equilibrium reaction

[C] + 2O2 S 2CO

(2)

For direct reduction with carbon, a strong increase in reactive strength can be observed at high temperatures. At temperatures above 1600 °C, carbon reacts with the undesired heavy metal oxides identified by a gray band in Figure 3. Hence, carbon could serve as an inexpensive reactant capable of reducing even very stable oxides. We conclude that direct reduction of undesired hazardous oxides with carbon is feasible above 1600 °C. As a consequence, the candidate list of reaction agents was augmented with carbon sources such as coal or coke, leading to a redesigned input-output structure. Reevaluating the EP for carbon-based chemistry exposes strong economic incentives, thus allowing the advancement of the process into the next stage. Level 3. The Recycle StructuresThe Reactor Separator Furnace The recycle structure analysis investigates the feasibility of chemical reactions and examines the reaction mechanisms in detail. It also determines the number and operating ranges of the required reactors, as well as the need for internal recycle streams and subsequent separations. For the low-waste process, a reaction temperature high enough for effective heavy metal reduction, but below the melting temperature of reactor linings, can be established. A suitable operation window opens between 1600 and 1900 °C, with reduction reactions taking place in the liquid phase. These considerations lead to a single lined furnace-type reactor. This furnace also separates the oxides (P1) from the recyclable alloys (P2). The key decisions for controlling both the optimal reaction and phase separation are tied to the choice of reactants. An overview of recycle structure decisions specific to metallurgical processes is presented in Table 3. Hence, the following key questions need to be addressed for the reactor-separator design: (1) What is the ideal mixture of reduction agents and additives capable of triggering the desired reactions? (2) Which charge mixture ensures phase separation within the reactor-separator, as product purification via peripheral physical separators is impractical? The clean phase separation of slag and metal that can be achieved in liquid metal reactors avoids the need for further product purification steps. The off-gases, however, are often loaded with dusts. Proper gas cleaning is mandated for environmental reasons.6 Hence, the recycle structure of the low-waste process foresees a gas cleaning system with dust recycle. Two possible recycle structures are depicted in Figure 5. Unfortunately, there are no reliable heuristics to answer the convoluted recycle structure questions for new metallurgical processes.7-8 Hence, we shall develop

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Table 3. Decision Hierarchy and Guidelines for Metallurgical Process Design size phases of product product delivery product quality improvement necessary byproducts

raw materials metal sources reduction agents additives

oxidation potentials number and operation of reactors recycle streams raw materials

Level 1. Preliminary Information batch or continuous tapping solid: reduction by roasting process (e.g. MIDREX), reduction furnace cascade liquid: blast furnace, coal gasification (COREX), electric arc process, plasma furnace gas: vapor decomposition, precipitation after evaporation delivered in solid form (roast sinter), as alloy (solid, liquid) or oxide (slag, ceramic) secondary metallurgy (yes/no), deploy sequence of reactors off-gas? when reactions produce CO, CO2, H2, H2O slag? removal of impurities dusts? unavoidable solid elutriation when using powdered charges/large amount of coal wastewater? follows from the need to scrub NOx, SOx, or halogenated compounds natural ores, scrap (recycled metals), recycled dust gaseous: carbon monoxide, hydrogen (synthesis gas) solid: carbon (coal, coke, anthracite), metallic (Al, Si, Mn) CaO (dolomite, lime), Al/Al2O3 (bauxite), quartz (SiO2) slags (conditioning of products) Level 2. Input-Output Structure Decisions sequence of oxides to reduce, sequence of metals to refine Is a reactor cascade needed (e.g., roasting)? reduction in the liquid phase (indirect with CO/H2; direct with elemental carbon, coal) Is refinement of carbon or impurities needed (e.g., desulfurization, de-hosphorization)? Compare to product specs Recycle or purge metallic charge (sump)? Should synthesis gas be recycled? If CO/H2 > 90%; otherwise, consider CO2 removal Should postcombustion of off-gas be used? If CO/H2 content is too low for reduction Should oxygen supply be purified (air vs pure O2)? Function of reactor temperature Can air/gas supply to burners be preheated? Note as process optimization option Can solid charge (ore, coal, metals,...) be preheated?

Level 3. Recycle Structure Decisions Is (partial) solid-phase reduction needed? Make use of recycled/reused off-gas stream Use operating conditions of a cascade? Function of the equilibrium concentrations Phase separation in liquid reaction? Which additives are necessary to ascertain the desired phase split/desired product purity? Do Gibbs free energy analysis Is solid recycle of dust (cyclone) needed? What are the energy requirements for the reactor? heating: gas burners, solid coal dust burners, off-gas burners, recycled off-gas (postcombustion) cooling: cooling panels in the freeboard, if the off-gas temperature is excessive for off-gas duct Which reactant has the highest impact on economic potential? Can it be replaced? Level 4. Separation Design Is product quality adjustment necessary? Do secondary metallurgy, e.g., laddle furnace Is solid gas cyclon needed? Economic reasons if 5-10% of solid streams are leaving Does the off-gas need chemical cleanup of gaseous contaminants (NOx, SOx, halogens)? Use acid/basic wash solution in scrubber Particulate removal? Use bag filter or E-filter Remove fine dust alongside air pollutants? Consider aerosol-based cleaning process, e.g., AIRFINE Are emissions clean? Send to flare Can off-gas be reused for heating purposes? Send to gas burners after filtration

Figure 5. Alternative recycle structures for the low-waste process.

a quantitative mathematical framework to conduct the recycle structure analysis of metallurgical processes,

relying on readily available computers and mathematical software. Subsection 3.1 discusses equilibrium models suitable for metallurgical reactor-separator design. The economics that can be achieved with optimal material charges are analyzed in subsection 3.2. 3.1. Equilibrium Thermodynamics of Metallurgical Reaction Networks. A challenge in metallurgical reaction networks rests in the large number of possible chemical reaction pathways coupled to the nonideal multiphase solution behavior. The formation and disappearance of crystalline phases compound the difficulty of the problem. An important conclusion for metallurgical reaction network design is the coupling of equilibrium reaction pathways and the phase stability problem.9 The law of mass action relies on equilibrium constants. Hence, it requires explicit enumeration of all prevailing reactions and stable phases, a piece of knowledge typically not available in the conceptual design phase.10 A far more robust model suitable for conceptual process design can be derived by means of the total Gibbs free energy of a system. Reactive phase equilibrium using Gibbs free energy minimization can resolve problems encountered with

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the law of mass action. It is an exercise in applied thermodynamics to prove that the mass action law expresses but a special case of the optimality conditions for ∆G minimization assuming known reaction pathways and stable phases.10 However, reaction models based on equilibrium constants offer no criteria for checking the validity of the underlying assumptions. In contrast to the law of mass action, minimization of the total Gibbs free energy requires no a-priori wisdom of the reaction pathways or of the distribution of species into the oxide and metallic phases, and it can also accommodate criteria for phase stability.11-12 The compact Gibbs free energy formulation entitled problem A in 3-5 represents equilibrium thermodynamics for a wide range of the process parameters. Its only limitation lies in species or atoms unaccounted for in the formulation (Ic, Ip) and the inherited shortcomings of the solution models deployed for each phase (aki ). In particular, the equilibrium composition of the product streams (nki ) can be computed by solving problem A for any specification of the input streams, e.g., slag, metal charge, reduction agents, and additives (bj). Once again, we follow Douglas’ arguments that economics dictate the best combination of charge materials, as discussed in the next subsection. Problem A

min G ) k

ni

nki (g0i + RT ln aki ) ∑ ∑nki µki ) k∈I ∑∑ k∈I i∈I i∈I

(3)

∑∑ k∈I i∈I

) bj j ) 1, ..., NE

(4)

nki g 0

(5)

p

P

c

p

ckij

nki

Gibbs free energy minimizationsthe subordinate objectivesensures chemical equilibrium among the product streams, i.e., metallic bath, slag, and off-gas. The activities for the complex solutions rely on the experimental data fitted to models of the regular solution theory and atom interaction parameters.4,15-17 A detailed discussion of the solution thermodynamics of metallic solutions is beyond the scope of this article but can be found in the Appendix and elsewhere.18 Hence, ∆G minimization rigorously captures all possible reactions among all compounds and the equilibrium distribution of species into the multiple nonideal phases, i.e., liquid metal, liquid oxides, gas, and pure precipitated solids. The constraints safeguard the product specifications and/or desired operational limitations. In the low-waste process, they are needed to enforce the exact target composition of the desired building material and proper slag basicity, as well as to delineate lower and upper bounds for the furnace temperatures. Additional constraints accommodate complementary operational requirements such as prescribed ratios among raw material blends; addition of flux to ensure low viscosity; and density of the slag and safety related constraints, e.g., avoidance of explosions triggered by vigorous reactions. Problem B

max EP ) vbmS1 + nki ,fki

vifki - vecQ ∑ ∑vinki - k∈R ∑∑ i∈I

k∈P i∈Ic

c

s.t.

c

3.2. Economics of the Reactor-Separator Furnace. The reactive equilibrium of the reactor-separator can be controlled by different choices of reactants appearing on the right-hand side of the constraints in eq 4. It was established above that the costs of reduction agents and additives impact the overall cost most significantly. Hence, the analysis of the recycle structure EP entails sensitivity studies for different charge policies because of the dominance of raw material cost. In principle, the sensitivity functions can be obtained by repeated evaluations of problem A. However, the large number of different types of reactants, the complex coupling between reactions, and the possibility of introducing unwanted phases call for a more efficient mathematical procedure. Fortunately, mathematical programming embedded within the decision framework offers yet another elegant modeling opportunity. Problem B, given in 6-10, expresses the maximum EP that can be attained for any equilibrium reactor-separator. It constitutes a bilevel nonlinear optimization problem.13,14 The economic potential, its principal objective, accounts for (i) benefits for avoiding slag deposition at landfill, S1, and (ii) the recovery value of the recycled metals (P2) and the value of the cement byproduct (P1). The EP diminishes with the cost for (iii) reduction agents and additives and (iv) energy. The program can choose the optimal feed blend of reduction agents and additives (fki ) to give maximum economic performance for the desired product specification. In addition, the reaction temperature (T) and pressure (P) can be treated as either open design variables or as adjustable parameters.

s.t.

min

equilibrium amounts

ckij nki ) bj ∑ ∑ k∈I i∈I p

(6)

c

G(nki ,P,T) ∀ j ) 1, ..., NE

(7) (8)

c

φ(nki ) e 0

(9)

ψ(nki ) e 0

(10)

Solution Approach. The bilevel problem B is a highly nonlinear mathematical program that cannot be solved directly. It is transformed into a single-level problem by replacing the thermodynamic equilibrium subproblem with its analytical optimality conditions.19 The introduction of appropriate Kuhn-Tucker (KT) multipliers for the second-stage objective (i.e., Gibbs free energy minimization) circumvents the double optimization. The resulting single-level nonlinear program, entitled problem C in 11-15, augmented with the Lagrangian multipliers λj can be solved numerically with commercial optimization software. Problem C

max EP ) vbmS1 +

nki ,fki ,λj

vinki - ∑ ∑vifki - vecQ ∑ ∑ k∈Pi∈I k∈Ri∈I c

∑ ∑ ckij ) 0 i∈I k∈I

s.t. (g0i + RT ln aki ) - λj

c

ckij nki ) bj ∑ ∑ k∈I i∈I p

(11)

c

(12)

p

∀ j ) 1, ..., NE

(13)

c

φ(nki ) e 0

(14)

ψ(nki ) e 0

(15)

3.3. Results of the Optimal Reaction-Separation Network. The bilevel optimization constitutes a com-

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Figure 6. Composition chart for optimal charge (the legend is kept schematic for proprietary reasons).

Figure 7. Cost distribution for optimal charge.

pact mathematical model for the process performance as a function of key design variables, i.e., different material charges, temperatures, and pressures. An analysis of the solutions obtained by the mathematical program rendered the optimal material charges for two distinct operational modes: (i) carbon-based reduction and (ii) metal-based reduction. Figure 6 shows the composition chart for optimal carbon-based process. It illustrates the fate of each species in terms of its amount normalized to 1 ton of reference slag input (S1). With a suitable amount of metallic charge M1 and a small quantity of reduction agent R1, 900 kg of product P1 can be attained in accordance with the specifications. The main product P1 is essentially a cement with a SiO2-Al2O3-CaOMgO matrix. The byproduct P2 amounts to approximately 150 kg/ton containing the recovered heavy metals. The expected off-gas is comparably small. The additives lime and dolomite are necessary to meet the basicity requirements. It should be noted that the specifications for the building material could not be met with the original set of additives. Hence, additional resource streams supplying the needed compounds were incorporated into the process’ input-output list. Figure 7 breaks down the cost contributions corresponding to raw material and product values. The true value of the economic potential cost was camouflaged by the use of virtual monetary units, rather than dollars per ton, for proprietary reasons. The computations also revealed that liquid iron oxide (FeO) had to be eliminated from the slag prior to the chemical removal of unwanted heavy metal oxides. This effort requires more reduction agent than anticipated

Figure 8. Economic potential for different reactor temperatures.

for heavy metal reactions only. The reason rests in the higher oxygen potential of FeO as seen in the Richardson diagram (see Figure 3). Because carbon is the cheapest reduction agent, pure economics would dictate reduction with carbon only. Reduction agents such as Ca, Mg, Si, and Al are chosen only to meet the product quality constraints because of their higher costs. In the final process design, these strong reaction agents might be needed to expedite reaction kinetics. Another avenue toward satisfying the product specifications lies in mixing in more additives. In each of the computations, process economics prescribe the minimal amount of additives, as their addition costs money. Influence of Reaction Temperature. Higher reaction temperatures increase the reduction potential, thus favoring the replacement of unwanted oxides. On the other hand, higher temperatures diminish the lifetime of the furnace lining, thus inflating the capital cost. Figure 8 depicts the cost performance resulting from these conflicting influences and points toward an effective reaction temperature range. Even though it is tempting to read the “optimum” reaction temperature from the graph, this would be premature. The results so far are rigorous in the mathematical sense, but they have to be considered approximate by virtue of the simplified modeling assumptions. The two-level problem formulation introduced in problems B and C render optimum results by a simultaneous consideration of process economics, equilibrium reactions, and constraints imposed on the desired product. The compact problem representation permits sensitivity analysis for different scenarios with little extra effort. A typical result is shown in Figure 9, which illustrates the minimum carbon requirement for maximum profit at different temperatures. The simple equilibrium model alone would require a tedious trial-anderror procedure. In light of the innumerable possibilities for varying the operation of the reaction network and design constraints, techniques based on simple graphical heuristics, spreadsheets, or hand calculations appear completely inadequate for the task. 4. Finalizing the Conceptual Process Design 4.1. Level 4. The Detailed Separation Structure. A particular characteristic of metallurgical processes stems from the impracticality of physical product purification, as explained in section 2 of this paper. Hence, the principal mode of attaining the desired product specification employs chemical reactions. In case the

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Figure 9. Sensitivity of carbon requirement to temperature.

clearly beyond the scope of this paper. The interested reader is referred to work in the open literature.20,21 Level 6 investigates process alternatives such as the process alternative with gas recycle. The detailed flowsheet and its refined economics gradually emerge. Further detailed results have to be omitted for proprietary reasons. The knowledge of the extent of economic incentive for this enterprise provides valuable insights into decisions and planning for further investment. The swiftness and low engineering effort required to conduct such a feasibility study underscore the strength of Douglas’ systematic approach for process synthesis. The preliminary results rooted in equilibrium thermodynamics warrant the advancement of the process to the pilot-plant stage. A crucial point in the subsequent phases will concern reaction kinetics and transport limitations. This ongoing research must involve further experimental trials alongside refined dynamic process modeling. Conclusions and Significance

Figure 10. Separation structure of the low-waste process.

principal reactor-separator does not yet satisfy the final purity specifications, further adjustments can be realized via secondary reaction metallurgy. Examples for product quality correction in subsequent metallurgical processes include desulfurization and dephosphorization in laddle furnaces, as well as high-quality application in vacuum and plasma furnaces. In the low-waste process, however, the product specifications can be met in a single reactor-separator, rendering further separators unnecessary. Solid particulates elutriated from the furnace with the off-gas stream constitute an exception. Their treatment is dictated by environmental legislation. Because the amount of solid lost does not significantly affect the economics of this plant, it will not be discussed further in this article. Options for the selection of a gas cleaning system, which slightly inflates the capital cost of the new process technology, are given in Table 3. Table 3 also provides guidelines for decision making specific to metallurgical process design. As a consequence, the separation structure analysis (level 4) adds a gas cleaning system and contributes estimates for the required capital charges (see Figure 10). 4.2. Level 5 and Higher. For the low-waste process, energy integration (level 5) has a minor importance because of the marginal contribution of the energy cost, as can be inferred from Figure 7. The low demand for energy is due to the almost-balanced overall reaction enthalpy of the metallurgical reaction network and the introduction of the slag (S1) and metal (M1) in the liquid state. In some cases, the chemical energy of the off-gas (O) needs to be exploited to improve the overall cost efficiency of the process. In that situation, energy integration couples the process to the energy demands of the entire manufacturing site. Total power and energy integration of the entire manufacturing process is

Classical metallurgical process design tends to emphasize the technical feasibility of operations. Traditional design strategies rely on generalized metallurgical thermodynamic relations such as those described in the Richardson3 or the Rist4,5 diagram. Design heuristics based on the thermodynamics alone offer little insight into the economics of a specific process. The costeffective design of reaction-separation networks was shown to be a strong function of the material choice charged to the process. A bilevel mathematical program considering process economic, thermodynamic, and operational constraints simultaneously addressed the lack of design guidelines for such a complex reactionseparation problem. Thus, the economic performance of the central reactor-separator furnace, its operating parameters, and material charge were determined optimally for an array of operational constraints. Difficulties in handling the multitude of unknown reaction pathways in heterogeneous metallurgical reactionseparation networks were effectively overcome via a total Gibbs free energy model embedded in the economic master problem. The bilevel program presented here is suitable for design problems involving large numbers of economical and ecological targets. Its use in conjunction with a systematic metallurgical process design framework is first reported here to the best of the author’s knowledge. Systematic decision making combined with powerful ∆G minimization offers a fast and more accurate conceptual design procedure. The approach presented here challenges current industrial practice, which relies on repeated performance calculations with flowsheet simulators or custom-built spreadsheet modules. In that mode, it is difficult to arrive at optimal charge mixtures that also satisfy all quality constraints with a reasonable number of computations. The lack of adequate models for standard unit operations of metallurgical reactors further weakens that popular design routine. The clear role of economics in driving the innovative search for new process options is a key feature in Douglas’ approach that is lacking in other design philosophies. Although expert developers and engineers have invented ingenious designs in the past, new business constraints such as consideration of uncertain raw material prices and shorter development cycles

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favor systematic procedures complemented with mathematical models. A case study confirmed the effectiveness of the proposed decision framework for a novel low-waste process. The gradual evolution of the entirely novel metallurgical process route followed the hierarchical design methodology developed by Douglas. The lack of design heuristics for complex metallurgical reaction networks was overcome via a simultaneous optimization of economics and Gibbs free energy. The example also demonstrates the validity of the fundamental decomposition principle proposed by Douglas for applications in metallurgical processes. Dedication This article is dedicated to Professor James Douglas, who shared fun and experience in process design with so many engineers and whose textbook raised our senior design courses from chaos to an exciting teaching and learning experience. Nomenclature

energy Gibbs free energy of mixing, and RT ln γi ) gexcess i is the excess Gibbs free energy of mixing. The use of empirical data available in the literature within a Gibbs free energy minimization requires the thermodynamic relations in eqs A2-A4. The derivation departs from a Taylor expansion of the activity coefficient around infinite dilution of a compound (Xi) in a bulk solvent, typically iron. At constant temperature and pressure, the expansion around the infinite-dilution coefficients (γ0i ) accounts for the influence of other species j on the activity coefficient of compound i (i.e., ∂ ln γi/∂Xj). In a first-order approach, higher-order terms O(X2) are neglected. Hence, eq A3 introduces the firstorder interaction coefficients ji. The coefficients ji measure the impact of a solute j on the activity coeffient of a solute i in an infinitely dilute solution in iron. Typcially, components i and j are elemental metals dissolved in a concentrated liquid iron mixture, e.g., liquid steel or pig iron. Values for the interaction parameters can be found in the open literature.9,16,17

RT ln γi ) RT ln γ0i |T,P,X1f1 + n

Roman Symbols aki ) activity of compound i in phase k bj ) atoms of type j entering with the feed streams cki ) stoichiometric coefficient of atom j of compound i in phase k EP ) economic potential fki ) feed of species i in stream k g0i ) standard specific Gibbs free energy of compound i mS1 ) mass of slag mixture S1 nki ) amount of compound i in phase k NE ) number of atoms in the system P ) reaction pressure Q ) net energy requirement T ) reaction temperature

(

RT ∑ j)2

|

∂ ln γi ∂Xj

)

Xj + O(X2) (A2) T,P,X1f1

Alternatively n

ln γi ) ln γ0i +

jiXj + O(X2) ∑ j)2

(A3)

where

ji ) RT

|

∂ ln γi ∂Xj

(A4)

T,P,X1f1

Greek Symbols vi ) price of compound i νb ) benefit for avoiding landfill νec ) energy price µki ) chemical potential of compound i in phase k λj ) Lagrangian multiplier for atom balance constraint j φ, ψ ) vector function for operational and additional constraints Index Sets R ) {M1, S1, A, R} ) index set of feed material stream (input) P ) {P1, P2} ) index set of products P1 and P2 (output) Ic ) {Fe, FeO, ...} ) index set of species in the system Ip ) index set of distinct phases in the system

Appendix. Excess Gibbs Free Energy Nonideal solution effects in liquid metallic solutions can be quantified via excess Gibbs free energy models. The chemical potential of a compound in solution can be written as follows

µi(T) ) g0i (T) + RT ln ai ) g0i (T) + RT ln xi + RT ln γi (A1) where g0i (T) is the Gibbs free energy of the pure species solution is the ideal at standard pressure, RT ln xi ) gideal i

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Received for review September 24, 2001 Revised manuscript received February 5, 2002 Accepted February 6, 2002 IE0107901