Environmental integrated production planning for the ammonia synthesis

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

ELSEVIER

European Journal of Operational Research 97 (1997) 327-336

Environmental integrated production planning for the ammonia synthesis T. Penkuhn *, Th. Spengler, H. Piichert, O. Rentz French-German lnstitute ¢br Environmental Research (DFIU), University of Karlsruhe, Hertzstr. 16, D-76187 Karlsruhe, Germany

Abstract The efficient operation of existing plants in the process industries requires an adjustment of the technical parameters with respect to changing economic or environmental constraints. In this work a model is presented that enlarges the well known linear optimisation models for joint production planning problems, that are typical for the process industries, by integrating byproducts and residues as well as emission taxes. With respect to the technical implications of a real world process the model is based on thermodynamic equilibria calculations and therefore formulated as a nonlinear optimisation model. The model is implemented with the help of the process simulation system ASPEN PLUS and applied as an example to a real world ammonia synthesis plant. Keywords: Environment; Nonlinear programming; Production; Process simulation; Ammonia synthesis

1. Introduction The German Waste Recycling and Control Act requires companies to avoid emissions and by-products rather than to use them. Thus, the management of the by-product flows requires more and more process integrated measures for emission prevention which cannot be achieved with standard end-of-pipe measures. In the process industries, the avoidance of production wastes and residues has a long tradition, because many of them can be used economically as chemical by-products. However, the efficient operation of existing plants requires an adjustment of the technical parameters with respect to changing economic or environmental constraints. From a theoretic point of view, chemical processes have to be regarded as joint production processes with variable production coefficients and variable product qualities. Furthermore, most of them are multiple cyclic processes. The operative adaptation of the mass- and energy flows of a chemical process therefore requires an integrated assessment. By-product and thus environmental integrated production planning can be supported by decision support tools based on linear a n d / o r nonlinear programming approaches. In this case study, an environmental integrated operative planning model (OPM) is developed and applied to the A M V ammonia synthesis as a large

* Corresponding author. 0377-2217/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0377-2217(96)00201-9

328

T. Penkuhn et a l . / European Journal of Operational Research 97 (1997) 327-336 gas

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.

.

.

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.

ammoniaconverter

1

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Fig. 1. Flowsheet of the ammoniasynthesis. scale process. In order to reflect the technical and physical implications of the real world process, residues and by-products are integrated into the model and input/output relations are deduced from the nonlinear thermodynamic equations.

2. Problem definition Ammonia is important as a raw material for the synthesis of fertilizers. It is produced worldwide on a very large scale with capacities extending to 120 million tonnes. Fig. 1 represents a flowsheet for the ammonia synthesis, as it has been realised by ICI Inc. at Lambton Works, Canada. The synthesis gas feed is produced by the AMV process, a sophisticated steam reforming process that converts the natural gas feed into synthesis gas for ammonia. The design of the process permits an unusual low synthesis pressure of only 85 bar, instead of 200 bar of the standard process, which helps to economise on much of the energy necessary for gas compression. The circulating gas from the ammonia synthesis loop is mixed with the dried and cleaned synthesis gas and fed to a circulator. After heating, the gas is passed to the ammonia converter where ammonia is produced, following the well known exothermic Haber-Bosch-reaction: 3H 2 + N 2 ~ 2NH 3. The hot gas leaving the ammonia converter is cooled by further heat integration with high pressure boiler feed water and the feed gas to the converter. Ammonia is separated from the partially cooled gas using mechanical refrigeration. Inerts like argon and excess nitrogen from the ammonia synthesis loop are removed by purging from the circulator outlet and treating the purge by a hydrogen recovery unit. The recovered hydrogen is recycled back to the circulator inlet (Livingstone and Pinto, 1982). The joint products are thus the fuel gas, the superheated steam and the used cooling water. The main environmental problems of the process are the emissions that result from the combustion of the fuel gas, the consumption of cooling water and electrical energy for the two compressors and the refrigeration cycle. The environmental impact of the latter results from the combustion processes in the power plants as CO 2, SO x and NO x emissions. 140 -~" t 2 0 100 o

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0,03 Purge rate

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T. Penkuhn et al./ European Journal of Operational Research 97 (1997) 327-336

329

90

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200

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.........

300

400

500 "

-6?0-- o~ ~00

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Fig. 3. Ammoniaequilibrium concentrationsas a function of T and p (Winnackerand Ki~chler, 1982). The development of an environmental integrated process model demands an accurate representation of the technical implications of the process. Due to the high complexity of the process in question, the mass and energy balances that are to be influenced by the planning model have to be formulated carefully. In reality, the operation curves of unit operations, like reactors or absorbers, are highly nonlinear. Similarly, the prices as a function of product compositions, for example, are mostly nonlinear. The following two figures illustrate the principal technical sources of nonlinearities. Fig. 2 shows the recycle flow in the ammonia loop as a function of the purge rate. The important nonlinearity is a result of the change in the reaction equilibria in the ammonia converters with varying inlet concentrations. The ammonia equilibrium concentrations as a function of the temperature and the pressure are represented in Fig. 3. It can be seen that the ammonia yield is improved with higher pressures and lower temperatures. A linearisation of the transfer functions in Figs. 2 and 3 would lead to an over- or underestimation of operating points of up to 50% as a function of the linearisation point. This signifies an important loss of information about the process. For optimisation, this would result either in a solution that is not feasible in reality or in a suboptimal solution, because the feasible region is not exactly known. The objective of this case study is the development and application of an environmental integrated approach for planning in joint production of the ammonia synthesis. Due to the important energy conversion rates and the integrated process structure the potential for energy and by-product optimisation is relatively high.

3. Model formulation

Usually, linear programming approaches are used for the optimal program planning in joint production. The maximisation of the operating margin of the process is generally used in the objective function, which helps to avoid the problem of imputed cost. A survey and an extension of state of the art approaches has been made by Fandel (1988). These existing approaches only reflect the physical and technical implications of the above mentioned process in a qualified sense. First of all, the linearity assumption is in reality only valid for very special cases, because many unit operations in the process industries are based on chemical or phase equilibria, which are strongly nonlinear in the case of parameter variations as will be shown in the next paragraph. Secondly, a (stepwise) linearisation that is possible for few parameters, becomes impossible in practice, if large processes are to be planned. Thirdly, the optimisation potential of the process can be exploited only partially, if the solution area is more or less roughly approximated. The parameter optimisation of chemical processes has thus to be formulated as a constrained nonlinear optimisation problem (NLP).

T. Penkuhn et a l . / European Journal of Operational Research 97 (1997) 327-336

330

The following notation will be used for the mathematical formulation o f the model:

Indices: i = 1 ..... I Chemical components j=l ..... J Chemical reactions Material flows s = l .... , S u=l ..... U Unit operations of the process Thermodynamical phases 9 = 1 ..... V Inlet and outlet streams sc ~ {in,out} Decision variables: P Material flow o f chemical component i in a stream s of a product P from a unit musi, o u t , s = 1, ..., M operation u [kg • h - t ] E musi, o u t , s = M - t - 1 . . . . . N Material flow of chemical component i in a stream s of gaseous emissions E from a unit operation u [kg • h - l ] G musi, out, s = N + 1 . . . . . 0 Material flow of chemical component i in a stream s of used utilities G from a unit operation u [kg • h - l] A musi, out, s = 0 q - 1 . . . . . P Material flow o f chemical component i in a stream s of production waste A from a unit operation u [kg • h - l] R musi. in, S = P + 1..... Q Material flow of chemical component i in a stream s of resource R to a unit operation u [kg • h - l ] or [W] B musi,in, S = Q + 1 . . . . . R Material flow of chemical component i in a stream s of utility B to unit operation u [kg • h - l ] Parameters: Internal process flow o f component i in stream s from or to unit operation u m u s i ' I, S = R + l ..... S pes,S= l ..... M Unit prices for a stream s of product P [DM • k g - J ] aes, s = M + l .... , N Emission tax rates for a stream s of emission E [DM • k g - l ] k 0, s = Q + 1 ..... R Unit costs for recycling or disposal of a stream s of used utilities G [DM • k g - J ] k~A, s = O + l ..... P Unit costs for disposal of a stream s of production waste A [DM • k g - l ] Unit costs for a stream s of resource R [DM • k g - l ] or [DM • W - i ] k~, s = P + 1 ..... Q Unit prices for a stream s of utility B [DM • k g - ~] k~, s = N + 1 ..... 0 Temperature, reference temperature [K] r, ro Molar flow of a chemical component i from or to a unit operation u [kmol • h - l ] l'l ui, Molar weight of chemical component i [kg] Mi Stoechiometric coefficient of chemical component i in a reaction j in a unit Piuij operation u Rate of a reaction j in a unit operation u [kmol • m - 3 . h - t ] ruj Volume of a unit operation u with reaction [m 3] vR~ Chemical potential o f chemical component i in a unit operation u [kJ • m o l - J ] tXui Energy flow (by heat conduction) from or to a unit operation u [W] Qr. Thermal capacity of a chemical component i in a unit operation u [kJ • k g - l . K - ~] Cpui Energy flow (due to phase change) from or to a unit operation u [W] Qe,, Reaction enthalpy j in a unit operation u [J • m o l - l ] AHR .j Energy flow (due to conversion o f m e c h a n i c a l / e l e c t r i c a l energy) from or to a unit H~,~ operation u [W] A = (au.,).=

l..U" .with a.u,= u' = 1, ~ U

1, 0,

if a r c ( u , u') exists otherwise

Adjacency matrix.

T. Penkuhn et al. / European Journal o f Operational Research 97 (1997) 327-336

331

The general operative production planning model (OPM) can now be formulated as follows: For the operative production planning of the AMV-process, the objective function (1) has been formulated in terms of profit/operating margin, where only direct costs were considered, since fix costs are not relevant for short term decision making. Thus, the inlet and outlet streams of the process related to unit costs or prices are considered as decision variables. Furthermore, the chemical composition of the streams is considered which makes it possible to integrate quality relations into the model. The integration of the costs for recycling or diposal of emissions and wastes into the objective function represents an enlargement of the well known operative margin objective function and ensures an environmental integrated optimisation. U

M

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1

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Constraints (3) represent the molar balances of the different unit operations of the process in question. The first two terms represent the molar flows of the inlet and outlet streams that have been calculated from the mass flows in Eq. (2). The third term refers to the conversion of chemical components in chemical reactions. mui, nui, ~

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(3)

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Constraints (4) represent the enthalpy balances of the different unit operations of the process in question. The first two terms represent the enthalpy of the inlet and outlet streams of the unit operation (heat convection). At the same time, it is necessary to consider the integral for the thermal capacity over the temperature range, because the thermal capacity is a function of the temperature. The other terms in Eq. (4) represent the enthalpy terms due to chemical reaction, heat conduction, phase change and the conversion of electrical or mechanical energy. S

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Constraints (5) represent the chemical equilibrium of the chemical reactions, for example, in the ammonia reactor. A chemical reaction j is in equilibrium, if the sum of the chemical potentials of the participating chemical components multiplied with the corresponding stoechiometric coefficients equals zero. /

E

= 0

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(5)

i=1

Constraints (6), (7) and (8) represent the conditions for phase equilibrium in a unit operation. This very general formulation means that two phases are in an equilibrium, if the temperature, the pressure and the chemical potential of the components in the two phases are equal. T,q-T,q,=0,

Vu,q,q',

Puq--Puq,=O, Vu,q,q', I..Luiq -- ~Zuiq, = O, V U , i, q, q'.

(6) (7) (8)

332

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In constraint (9) the mole flow of chemical components leaving a unit operation is set equal to the mole flow of the same components entering another unit operation. This equation applies only if the stream exists. The necessary information is given by the adjacency matrix A which represents the topology of the flowsheet. nui, in--lIu'i,out=O

VU,U

(9)

t,

where a,,,, = 1 A u ~ u ' ,

Vi.

Eqs. (10), (11) and (12) limit the feasible region due to market restrictions, emission control acts and landfill capacities. 1

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--

i=1

out. max - -

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s .= M. + 1,

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(10)

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,

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(11)

P.

(12)

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1 i=l

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1 m uE si,

i=1 E

m u s i , o u t ->- 0 ,

i=1

1

E

E

1 A musi.out.ma x

--

E

O,

...,

i=1

Moreover, all decision variables are restricted by upper and lower bounds, for technical reasons, e.g., pipes or heat exchangers that support only a maximal or require a minimal material flow. Additional technical parameters can consist of all kinds of process parameters such as temperatures, pressures, heat fows, process internal mass flows, etc., and combinations of these. The relationship between the technical parameters and the decision variables is expressed in the mass and energy balances. For example, for the separation of the purge stream the technical parameter is the quotient of one of the output streams and the input stream. For the separation of the product ammonia, the technical parameter is the temperature which influences the separation efficiency as the energy and mass balances are coupled thermodynamically. These technical parameters are also restricted by upper and lower bounds, e.g., because of the maximal pressure of a pipe or the minimal temperature in a reactor.

4. Solution procedure and implementation The operative planning model was implemented on a PC, using a process simulation package. It consists of an optimisation module linked with a thermodynamic process model. For the development of the process model, a commercially available flowsheeting program, ASPEN PLUS, has been used (AspenTech, 1988). Flowsheeting programs are mathematical tools for the steady-state simulation of complex chemical plants. They offer subroutines for unit operations like reactors or columns, data banks for the physical properties of the components and mathematical algorithms for the iterative convergence of recycle loops. With the help of a flowsheeting program, the developing time of a process model, like the ammonia synthesis, can be reduced drastically to the order of months and, furthermore, process evaluations like case studies, sensitivity analysis or process optimisation become possible (Biegler, 1989). The optimisation module consists of a sequential quadratic programming algorithm (SQP) that is linked with the ASPEN PLUS process simulator (Biegler and Cuthrell, 1985). Today, the SQP algorithm is considered as the state of the art algorithm for nonlinear programming (Edgar and Himmelblau, 1989). The idea of the link is shown in Fig. 4. The link has been described by Kisala et al., (1987) and follows ideas of Powell and Biegler (Biegler and Cuthrell, 1985). Basically, it is a standard SQP that uses the BFGS update for the approximation to the Hessian of the objective function Lagrangian. The line search step size is found by using a penalty function described in

T. Penkuhn et al./ European Journal of Operational Research 97 (1997) 327-336

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N

333

,/.{ b,o=,so.,j\

L

new set of variables

P

Optimization

I ~

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Flowsheeting Program Aspen Plus

i

/

. Stop

--

Fig. 4. Flowsheetoptimisation(Kisala et al., 1987).

(Kisala et al., 1987). The main advantage of the implementation of the optimiser into the flowsheeting program is that the equality constraint functions resulting from the unit operations do not have to be known explicitly. This means that in every iteration the value of the equality constraint functions is calculated, by solving the complete energy and mass balance of the flowsheet in the simulator. The necessary gradient information, which is not explicitly available, has to be calculated by perturbation of the design and tear variables. This is an important feature, as the mathematical formulation of the equality constraint functions; i.e., the mass and energy balances of the unit operations, usually becomes one of the most difficult steps in process optimisation (Penkuhn et al., 1995). For the ammonia synthesis, the flowsheet model has been developed with 25 unit operations and I0 components which leads to an optimisation model with 250 mass balances, 25 enthalpy balances, 300 equations for the phase equilibria and further equations for the reaction equilibria and the flowsheet topology. In the objective function, 45 decision variables are considered. In the following, a few details on the process model are given briefly. The ammonia converters are simulated with the RGIBBS model from the ASPEN PLUS library. RGIBBS is a reactor model that calculates the thermodynamic equilibrium of the reactions by Gibbs energy minimisation. The thermodynamic property model used for this flowsheet is the Redlich-Kwong-Soave equation of state (AspenTech, 1988). Internal recycle loops, as for example the main ammonia loop, are calculated iteratively. The development time for the techno-economical optimisation model of the AMV ammonia synthesis was about 3 to 4 months of programming work. The model runs on a 60 MHz Pentium PC and the solution time for one optimisation problem is about 40-60 minutes.

5. Results and interpretation As shown above, an environmental integrated planning approach can be ensured by integrating the joint product flows into the objective function. The main environmental impact of the ammonia synthesis is the very important natural gas consumption of about 29 GJ per tonne of product. This leads to significant CO 2 and NO~ emissions from the plant. In the first step, it will be shown that an isolated maximisation of the ammonia production does not lead to an economic optimum because energy costs and joint product flows are neglected. Similar investigations on a different plant have been published by Kontopoulos (Kontopoulos et al., 1994). In Table 1 the following objective functions are compared: Base Case OF1 OF2 OF3 OF4

Actual situation of the plant with 100% load and without optimisation Ammonia sales income OF4 minus steam sales income minus water and electricity costs OF4 minus fuel sales income Complete objective function including all utilities and joint products.

334

T. Penkuhn et aL / European Journal of Operational Research 97 (1997) 327-336

Table 1 Influence o f the choice of the objective function Decision v a r i a b l e / t e c h n i c a l p a r a m e t e r

B a s e - c a s e (actual situation)

OF1 /1%

O F 2 "4%

Objective function N H 3 (product) C o m p r e s s o r duty Refrigeration d u t y Fuel production Steam production P u r g e rate Synthesis pressure

3 373 D M / h 45.3 t / h 9.85 M W 19.2 M W 11.8 t / h 43.1 t / h 0.068 [ - ] 82.5 b a r

- 5.27 0.08 7.8 7.8 - 0.44 - 4.3 - 2.9 7.6

- 6.31 0.01 6.5 7.2 0.02 - 5.2 2.9 6.9

OF3 /1%

-

1.15 0.06 1.3 1.5 0.34 0.5 4.4 1.2

O F 4 '4% J 1.33 0.01 - 3.8 -2.4 - 0.06 - 0.8 2.9 - 3.6

x '4% denotes the divergence b e t w e e n the optimal solution for the different objective functions and the result for the base case without optimisation; i.e,, without adjusting the process p a r a m e t e r s and variables.

As the operating margin of the ammonia synthesis depends, of course, on the model assumptions, it is more convenient to argue in the following in terms of relative improvement of the base case operating margin. The base case shows the actual situation of the plant for a 100% load without any optimisation. The first objective function OF1 includes only the ammonia product flow. This planning situation can thus be interpreted as a situation, where no internalisation of external effects exists at all. In this case, even the resources are free of costs. The comparison between the optimal result of OF1 and the base case shows that the optimal operation parameters for this planning situation would be suboptimal for the actual internalisation degree that is represented in the base case. Consequently, companies confronted with new emission or resource taxes, have to adjust the production parameters. The optimal operation of a plant can be ensured by integrating all relevant heat and mass flows into the objective function. In the same way, OF2 and OF3 represent planning situations where resources and byproduct flows are to be considered only partially. As for OF1, the process parameters that have been adjusted with regard to the planning situation represented in OF2 and OF3 would lead to a loss of operative margin of up to 6%, if new environmental acts were passed. In OF4, all resources and byproducts are considered with their actual price or tax rate and thus an improvement of approximately 1.3% compared to the base case was found. A variation of the demand is one of the most important operative planning problems in practice. This problem is in particular important for the referenced ammonia plant in Canada because the demand for fertilizers, the main end product of ammonia, declines in the winter season. The ICI Inc. has to manage loads Table 2 Optimisation results: Operative a d j u s t m e n t o f the process p a r a m e t e r s due to a d e m a n d decline Decision v a r i a b l e / technical parameters

B a s e - c a s e ( 1 0 0 % load)

7 0 % load ,4% i

80% load ,4%

9 0 % load ,4%

100% load ,4%

110% load /1%

Objective function N H 3 (product) NH 3 (by-product) Compressor duty Refrigeration duty Fuel production Steam production Cooling water P u r g e rate Synthesis pressure

3 373 D M / h 45.3 t / h 0.97 t / h 9.85 M W 19.2 M W 11.8 t / h 43.1 t / h 647 t / h 0.068 [ - ] 82.5 b a r

4.20 - 1.2 51.9 - 25.9 - 0.5 0.9 - 1.7 - 13.0 10.3 - 22.9

3.58 -0.5 16.9 - 23.8 1.2 0.7 - 1.5 - 9.9 4.4 - 21.2

2.29 1.4 55.8 - 21 - 0.7 1 - 2 - 6.4 - 11.8 - 18.9

1.33 -0.34 16.5 - 3.8 - 2.4 - 0.06 - 0.8 - 0.5 2.9 - 3.6

1.48 0.28 -6.4 7.8 - 4 - 0.6 0.3 1.0 4.4 7.6

] A% denotes the d i v e r g e n c e between the optimal solution and the results without optimisation; i.e., without adjusting the process parameters a n d variables for different d e m a n d levels.

T. Penkuhn et al./ European Journal of Operational Research 97 (1997) 327-336

335

2 ~4~ 2 '~21)

c

? 481 2 460

>

g

2 44(}

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2 ~6~ 2 q40 2 12¢~ 2 ~{}{

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'

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~

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from 70 to 110% for the AMV process. For this case study, we have examined the adaptability of the process parameters with respect to the demand situation. The main results are given in Table 2. As can be seen, it is possible to improve the operative margin to up to 4% compared to an operation of the process without adjusting the technical parameters. For a plant capacity of 100 tonnes per year, this leads to savings of up to approximately 815.000 DM per year. Further, Table 2 shows that the ammonia production is almost constant. The improvement of the operating margin is thus mainly due to a decrease in energy comsumption. These energy savings lead to an important emission reduction, not only in the ammonia plant, where for example less fuel has to be burnt, but also in the energy production sector, as less electricity is needed for the compressor and the refrigeration. Moreover, the cooling water consumption can be reduced in most cases. The least important improvement was found for a load of 100%, which is not astonishing, as the plant had been designed for this load. For the 70% load case, a sensitivity analysis was conducted to evaluate the influence of the two most important technical parameters, pressure and purge rate on the contour of the objective function. The small steps in Fig. 5 result from the fact that only a limited number of parameter combinations could be calculated with respect to the computing time, which was about 10 hours for the plot, because every single point means a complete calculation of the process flowsheet. It can be seen that the influence of the two technical parameters leads to a nonlinear contour of the objective function curve. First of all, this sensitivity analysis illustrates the nonlinearities in the constraints of the operative planning model. The variation of the two parameters crucially influences the reaction equilibria in the ammonia reactor, which consequently influences the mass and energy balances in every other unit operation of the process. The arrow marks the improvement of the objective function value achieved by the SQP optimisation. It also shows the necessary variation of the two technical parameters to achieve the optimum. A very interesting area of the plot in Fig. 5 exists for high pressures and high purge rates. For these parameter values the operating margin drops to zero because the parameter combinations are not technically feasible. This clearly shows one major advantage of this new method: the loss of information due to (stepwise) linearisation of the flowsheet equations (i.e., the mass and energy balances) can be avoided. Therefore the optimisation results provide good technical solutions, even if the algorithm stops at local optima due to nonconvexities.

336

T. Penkuhn et al./ EuropeanJournal of Operational Research 97 (1997) 327-336

6. Conclusions

In this case study an environmental integrated operative production planning system (OPM) for the AMV ammonia process has been developed. Instead of the usual linear approaches, a nonlinear model has been set up with respect to the nonlinearities in the thermodynamic process equations. In order to facilitate the formulation of the process specific equations, the mass and energy balances, a commercially available process simulation tool has been used. This reduces the implementation time for the planning model to months. The results show that it is possible to improve the operating margin of the AMV ammonia process with the proposed operative planning model. The optimisation potential for the base case is certainly not very important, as the process was optimised when the plant was set up. On the other hand, the use of a mathematical optimisation becomes more important when the technical, economic or legislative environment changes. In this case, e.g., for a 70% load, an improvement of the operative margin of approximately 4% or 815.000 DM per year was found as opposed to an operation of the process without parameter adjustment. This is an important contribution as the expenditures for the implementation of the OPM are far less important and no investment is necessary. The accuracy of the results is much higher than the results from conventional LP models. It has been shown in this case study that linear approximations of the transfer functions of the AMV process can lead to over- or underestimations of operating points of up to 50%. By the application of the OPM, the thermodynamic implications of real world chemical processes are reflected in the model without any loss of information due to linearisation. This leads to technically feasible solutions. The use of a commercial process simulator for the development of the process model that implicitly provides optimisation constraints leads to an significant facilitation, when adapting the OPM to other processes. In many cases the engineering plant model used for process development may be easily adapted for production planning purposes.

References AspenTech Inc. (eds)(1988), Aspen Plus Users Guide, Cambridge, Massachusetts. Biegler, L.T. and Cuthrell, J.E. (1985), Improved infeasible path optimization for sequential modular simulators, Computers Chemical Engineering, 9, 257. Biegler, L.T. (1989), Chemical process simulation, Chemical Engineering Progress, 50-61. Edgar, T.F. and Himmelblau, D.M., 1989. Optimization of Chemical Processes, McGraw-Hill. Fandel, G. (1988), Optimal Planning in Joint Production, In: G. Fandel, H. Dyckhoff and J. Reese (eds), Essays on Production Theory and Planning, Springer-Verlag, Berlin, New York, p. 130-148 Kontopoulos, A.J., Kalitventzeff, B., Rennotte, J. and Bovens, J.L. (1994), Can existing software handle industrial optimization problems? Optimization of Kemira's (B) ammonia synthesis loop, Computers Chemical Engineering, 18, S 165-169. Kisala, T.P., Trevino-Lozano, R.A., Boston, J.F. and Britt, H.I. (1987), Sequential modular and simultaneous modular strategies for process flowsheet optimization, Computers Chemical Engineering 11(6), 567-579. Livingstone, J.G. and Pinto, A. (1982), New ammonia process reduces costs, In: AICHE Ammonia Safety Symposium, Paper 123f, Los Angeles, California. Penkuhn, T., Piichert, H., Spengler Th. and Rentz, O. (1995), Planning models for the integrated byproduct management in the iron and steel industry, Proceedings of the R'95 Recovery, Recycling, Re-integration, Geneva. Winnacker and Kiichler (1982), Chemische Technologie, 2, 4th edn., Carl Hanser Verlag, M~nchen (in German).