Optimal air pollution control strategies: a case study

Ecolugical Modelling, 64 ( 1992) 221-239 Elscvier Science Publishers B.V., Amsierdam

Optimal

airpollutio9

221

control

stí-ategies:

a case study

G. Finzi and G. Guariso Center for Enrironmemal

Computer Scìence (CIRITA), Departnzent P~litecrtico di Milam. ~Wano, Italy

af E!ectrouics,

ABSTRACT

Finzi, G. and Guariso, G., 1992. Optimal Modelhg, 64: 221-239.

air pollution

controi

strategies;

a case study.

Ecol.

Air pollution can be controlled at a iegional leve1 in several different ways, s;rch as emission standards, taxes. permits, etc. The European Community decided to set standards on cnvironmental quaiity, namely on the distribution of pollutant concentrations measurcd at ground leve]. This paper deals with the problem of evaluating the trade-offs between such ambient standards and pollution abaicment costs. For this purpose, a two-objective linear program is formulated and solved for a 300 km? region in northern Italy, using a simulation model to evaluate the effects of each poIlution source. The software developed forms the basis of a more complete decision support system for this type of complex probfem. Its structure and components are describcd in detail.

1. INTRODUCTION

Air quality managemenr studies have become more and more interesting for the scientific community dwing the last 20 years due to the stwrgthening of the interactions between energy resources demand, pollution contrci polities and the related social costs. Decision makers involved in air quality con:ointed out that, although the methodology and the package have genera1 applicability, in the foliowing a particular pollutant (S021 wil1 be taken into cunsideration. This is due to the availability of data in the area? where SO, was the _mGn pollution problem. Consequently, the choice amon g different emission abatement technologies was restricted to the following (sec, for instanqe, Amman and Kornai, 1987): use of low sulfur fuels;

OPTIMAL

-

-

AIR

POLLLJTIC~N

CONTROL

Sl-RATEGIES

223

combustion modification (i.e. desulfurization during the combustion process) with a mean reduction of 50% in sulfur emissions; flue gas desulfurization by a wet Zmestone scrubbing process with a remova! efficiency of 90%; regenerative process, an advanced technology which achieves an efficiency of 98%.

2. PROBLEM

FC?RMULATION

The problem outlincd above can bc formally stated as a deterministic mtllti-objective mathematica1 programming problem with the objectives of minimizing the overall energy production costs of a set of plants and maximizing a suitable indicator of environmental quality of the atmosphere in the region. The decision variables of such a problem are the quantities, qi,i, of the various fuels, k, used by each plant, i, in the area, measured, for instance, in tonnes per unit time. Since normally there are only a few treatment alternatives for each type of pohutant, different treatments have also been consi&red as different fuel options, k. For instance, a HSF (high sulfur fuel) with an original sulfur emission concentration of 3% may be treated with a flue gas technology allowing a sulfur reduction of 90%. Ht can then 3s consider,zd as a different fuel with thr same heating power, aq emission .vith 0.3% sulfer content, and a tost equal to the original purchase tost of MSF plus the tost of the desulfurization process. Bbviously, not al1 the piants can use al1 the available treatment technologies, since their application may be limited to particular industrial processes or by suitable dimensions of the plant. For instance, a Iarge power plant with three or four heater-stack groups can have several different treatment alternatives for each of them, while a smal1 production unit may only be able to switch to a less polluting fucl ivithout any specific treatment.

The tost objective min(costs)

= min z tq,L) i=

funct:nn C

is intuitively

formulated

as

ckclik

f k uk’,

where qik is the quantity of fuel k used by plant i in a given time interval; ck is the unit tost of fuel k; 1 is the total number of sources considered in the region; and K, is the set of energy oytions avaitable for source i.

G. FINZi

224

AND

G. GUARKO

The tost ck includes, as already mentioned, the treatment of effluents. Their quantitative evaluation requires estimates of the costs of different air cleaning technologies. The costs of X3, removal processes used in the case study presented later have been developed by Bocola (19871, Baterman et al. (1986) and Amman and Kornai (1987). Estimates of abatement costs for other pollutants are presented, for instance, in the proceedings of the ENCLAIR C on f erence (ENEA, 1986). However, as recent events have clearly demonstrated, al1 economie evaluations of fuel costs may be subject to wide ffuctuations and a planner may be interested in testing the robustness of a proposed energy prodwction/air quality scenario with fuel costs very different from the present ones (considering, for instance, their long-term trends). This must be explicitly considered when designing a software package to support encrgy planning activities.

‘Fhe environmental objective can be represented by the minimization of the ground leve1 concentrations of the pollutant under examlnation, as suggested by the directives of the European Community. More precisely, EEC legislation for various pollutants (Directives NOS. 80/779, 84,/360 and 85/203) takes into consideration the yearly statistical distribution of the daily mean values at some receptor sites as a significant indicator of air quality. The Xtalian law for sulfur dioxide, in particular, prescribes two restrictions: one on the 50th percentiie, representative of the mean prevailing conditions, and the second on the 98th percentile, representative of the most critical episodes with low occurrence probability. The mean daily SB, concentration must Se lower than 80 pg/m” for at least 50% of the days of the year and lower than 250 pg/‘m” for at least 98% of the days. Both these thresholds and their probabilities of occurrence constitute the air pollution indicator and may thus be regarded as independent objectives of a genera1 energy production plan. Wowever, to adhere tc, the current legislation and to simplify the solution of the problem in the following example, oniy the median threshold, T’, has been cc3nsidered as a variable, while the ratio between the 5Uth and the 98th pe-centile values has been fixed according to law (i.e. VSO/250). The air quality objective may thus be formulated as mintair

pollution)

= min T’

at each point of with e set of constraints specifymg that thc concentration the measurement network is less than or equal to T’ 50% of the time and less than or equal to T” (= 250/80T’) 98% of the time.

OPTIMAL

AIR

POLLUTlON

The fornrulation

CONTROL

STRATEGIES

proposed

abuve implies that, for each pollution

225

sensor

gj( - ,..) is a function relatlng the pollutant concentration at the j-ih sensor to the cmissions ei of the considered sources. These emissions may easily be computed, once the quantities, qik, of fuePs used and their specific pollution emissions, sk, are known, as

where

$

-

where J is the total number of measurement points in the area, 6j is the background pollulion, i.e. that present independent of the sources considered in the planning problem, and LY’and LY”are the percentages of time (namely, 50 and 98% in our case) for which the thresholds T’ and ‘F” must not be exceeded. Two slmplifications must be applied to constraints (3) to solve the problem in real cases, where the number of decision variables can easily exceed a hundred. The first concerns the form of the function gj( *), which is assumed to be a linear function of the emission of each plant, as commonly suggested in the literature (Atkinsons and kewis, 1974, 1975; Krupnick et al., $983). This means that constraints (3) can be rewritten in the forrn

where *he so-called “transfer coefficients” aij are random variables depending un the meteorological condition WZ.The probability distribution of such conditions is usually expressed in discrete terms through the joint frequency distribution of atrnospheric stability classes, wind speed and direction classes, and thermal inversion elevation classes. The rationale behind fosmulation (4) is that the pollutant conceratration at each measure-

C. FINZI AND G. GUARISU

226

poiui (i.e.

ment

weighted

the variable sum of the emissions

constrained

by law) is interpreted

as a

The weights ajj depend upon the meteorological situation HZ, which is in turn a random variable. The physical dimensions of the aii are units of concentration/units of emission and their evaïuation wil1 be dealt with in Section 2.4. Formulation (4) requires that the effect of the different sources is simply additive, that is it implies that chemical reactions of the pollutant are negligible and that the pollutant itself is sufficiently stabIe. FOP sulfur dioxide and particulate matter, for instance, this assumption is usuahy wel1 satisfied. For other pollutants, such as NOX, it must be regarded with some caution, because the phenomenon of dispersion is much more complex. Nevertheless, the recent literature presents interesting apphcations of NO, dispersion models (e.g., Simpson et al., 1990) which could fit the preceding assumption. The second simplifkation introduced refers to the transformation of the probabiiistic constraints into deterministic ones. This can be accomplished in an exact way by adopting a mixed integer programming formulation (Fronza and Melli, 1983; Guariso and Lancini, 1989), but this has Enacceptable solution times in practica1 cases. Consequently, one is forced to look for a suboptimum solution by deciding in advance which meteorological conditions have to be taken into account. This can be accomplished on the basis of the following considerations. For a given meteorological situation HI, constraints (4b) are certainly satisfied if (4a) are satisfied (remember that 7’” > T’j; thus the situation PE may be considered only once, for (4a) or (4b). The total probabilities of occurrence must be ti’ and ti” and the probability rm of the occurrence of situation %n is provided by meteorological data. Thus, one must choose a first set of M, metesrological conditions such that

and write the retative

C

aij(m

i=l

~

T” -

bj

air quality constraints j=

l,...,J

mi?= l,...,M,

in the farm

~PTIMAL

AIR

P~LLUTI~N

CONTROL

and a secowd additional

227

SI-RATEGIES

set of (M2 - M,) situations

such that

M2 c

71;,),d’-d

m=M,+Z

with the relative air quality constraints in the form (6) with m = M, + 1 , . . . , M2, ad substituting T” for 7”. Provided that constraints (5) and (7) are satisfied, one must choose the least criticat meteorological conditions from the pollution viewpoint for inclusion i;l the problem. For instance, if emissions are mainly from high stacks, g;ne could first select streng wind or stable atmospheric conditions and then add situations with weaker wind and increased instability up to the required probability sf occurrence M”. The inclusion of constraints referring ts very rare, but dangerous, episodes would mean the adoption of control strategies more restrictive than those required by law, and hence more expensive than optimal ones, The clevesness of the analyst and his/her knowledge of the particular sïte are essential to determine which meteorologieal conditions must be disy-zgarded to find a good suboptimal solution. When all the constraints are expressed in the form (61, rhey have the additïonal advantage of allowing a preliminary check of whieh of them is dominated bye others, i.e. not influencing the optimaj solution. T’he elimination of such constraints can strongly reduce the computational complexity, and thus the solution time, of the simplex method used to solve the resulting linear programming problem (sec Seetion 2.4). 2.4 Evahalion

of the transfer

cueffìcimts

The last problem to examine is how ts compute the transfer coefficient a,,(m) for every particular meteorological condition m. A suitable model must be used to simulate the diffusion of the pollutant in the atmosphere., on the basis of the stabihty class, the wind direction and speed, and the thermal inversion classes as wel1 as al1 the characteristics of the emissions (gas temperature and speed, stack elevation in the case of point sources ar area in the case of distributed sources such as domestic heating, etc.). For instance, any of the available Gaussian models can be used for this purpose, since the specific form of the air quality constraints adopted above is independent of the simulation model used. Once the pollutant concentration, Cij, produced at Iocation j by emission ei has been evaluated, the transfer eoefficient aij is simply computed as a,j = Cii/e,. If the diffusion model is hnear in the emissions, such as for al1 the Gaussian models proposed by EPA (15X36), the transfer coefficient

G. FI.NZI AND

223

C. GWARISO

enclosed in the model; if it is and non-hnear, the ~zij may simply be considered as linear approximations thus they are more precise if the emissions used fox their evaluation are close to those produced by the final solution of the problem. Some iterations of the overall procedure may be required to attain this result. Tt is interesting to note that this kind of technique has been proposed (e.g., Gorelick, 1883) in an apparently quite different domain, underground water management, which presents similar modelling difficulties (for instance, the presehce of scveral pollution sources in a three-dimensional field). already cag%.~~~s ail the reilevant Hnformation

The last set of constraints to Dr included in the problem is that requiring that the production of each sCrurce meets its reskective dzmand Dj (energy demanded per unit time). AsLuming that pk represents the heating power (energy per unit weight) of the kth fuel and that Di takes into account the Tfficiency cif the plant, these constraints can be written as IC g,q,,, 2 Di kEKi

ì = IJ

(81

Only one of these constraints wil1 hold for those sourees that may werk in a cooperztive way. Fur instance, large power stations having more than one heater.stack group have to be assigned an aggregate demand. Wris demand may ba representative of the actual werking condition of the plant and, in this case, it can be evaluated trom past fuel consumption, or it may be possi& to forecast future demands, for instance by means of a statistical trend anafysis.

The final two-objective mathematica1 !hat emission e, = x sp,‘~~~1): kEKi T’

program

to be solved is (remember

OPTWvIAL ALR POLLVTLON

CONTROL

229

STRATEGIES

(12)

gik

2

0

k=

l,...,Ki

ì=

(15)

l,.*.,I

where al1 the decision variablts are no>r-negative since they represent fuel consumptions. Once the transfer coefficilents have been evaluated through M, simulations of the polhrtion dispersion model, the problem reduces to a simple two-objective linear program? for which efficient solutions can be computed using, for instance, the corstraint method and a linear program solver. The results of an accurate implementation in a northern Italian regi+xr are discussed in Section 4. 3. A SOFTWARE DECISIONS

PACKAGiZ FOR SWPPORTING

ENERGY

PRODUCTION

As already noted, severai variables in the above problem may not be precisely known in practice: fuel and treatmeat costs, energy demands, and meteorological conditions are surely parameters for which every decision maker would like to have some sensitivity analysis. Fur this reason, the most signitïcant result of this study is perhaps a software package allowing an interactive analysis of different economie and physical scenarios. The package, called ARIA, the Italian acronym for “air pollution reduction alternatives”, resembles, quite closely the classica1 structure of a decisfon support system (Guariso and Werthner, 1989) with a data base, a model base and some modules decdicated to communication with the user. Ht has been implemenced using programs written in the Fortran, Pascal and C languages, coordinated by a main C program. It has been used on a 386 FC, where the complete study of a new area, from data input to the determination of aar efficient energy production plan, requires from 1 to 6 h of computation, depending upon rhe number of plants and the accuracy of the description of the meteorology. The main modules of the package are: (1) plant data base (2) area definition

230

G

FINZI

AND

G. GUARISO

(3) meteorology definition (4) simulation and optimization model base (5) presentation and analysis of the results. 3.1 T’e plant duta buse The economie and physical data necessary for a complete study are numerous and complex; this is why they have been structured in a hierarchical data base, specifically designed to serve as the unique input data module. Tt offers al1 the traditional tools of a data base (storage, retrieval, deletion, correction, listing, etc., of the data relative to a very large number of plants). Stack heights and positions, gas flow, temperature and velocity, fuels used, working period and total energy produced are examples of the mformation stored for each plant. Startlng from these data, the module also computcs and stores the fuel and treatment costs, using standard values and formulae proposed in the literature or more precise information for the case under study supplied by the user. A specific option allows for a distinction ttr De made between the fuel andfor treatment technologie5 aiready used 2 y the plant and those which the user deeides to analyse in an energy plan. A centralized data base shows efficient access of the information by al1 the other modules and frees the use from thr necessitv of sge.cifjGng the data necessary for a model in a rigid format every time. The plant data base can in fact store data for a Sarge area and can be used as an When independent tool for normal surveying und archiving activities. developing a specific energy plan, the required data referring to the plants in the region unCur study wil1 automatically be retrieved and used by oth:r modules.

This module simply implements graphical access to the data basc. The user in fact decides the region to be studied by giving its extreme coordinates, checking on the screen whsre the plants are located and assigning the monitoring statioir to be considered. The gra&mic preseiatation shows immediate feedback to the user, who can easily reshage the area when he/she is not satisfied with the previous choice. In the same module the legal constraints of the problem, namely the pollution thresholld kalues (7’ and 7”‘) and their limit probability of occurrence Ia and a”), are also entered.

231

3.3 The meteorology defiinitionmodule

This is a separate program which selects the meteorological situations to be included in the optimization problem on the basis of an objective criterion chosen by the user. The choice made in this module is obviously critical, because a very detailed description of the meteorology corresponds to a large number of simulations of pollutant diffusion and to a high complexity of the optimization problem. At present, the options available are very few. For instance, one may choose the situations with the highest probability of occurrencc up to the probability LX”.This criterion is cumpletely site-independent and guarantees the minimum number of conhighly straints and thus the highest execution speed, but may provide suboptimal solutions. Another option available is the choice of the situations with the highest stability and the highest wind speed within each stability class. This criterion provided better results in the application described in Section 4 below. A single meteorological situation may also be selected to understand the impact of a specific scenario on the final energy plan. The user may easily add other options (i.e. other programs) implementing different criteria which are more adequate for a specific study. The input to this module are normally the tables of the joint frequency function of atmosphcric stability, wind direction and speed, and thermal inversion classes in a standard format (such as that provided bv the Italian Air Force Meteorological Service). 3.4 Simuìatiunand optimization modeE base The model base constitutes the core of the system and contains both the air gollution simulatiom and the tost minimizatiou models. A modified version of the Gaussian diffusion model (Cirillo et ar., 1986) and a linear programming algorithm form tne basic elements of the model base. However, the software is conceived in such a way that the user can insert in the package his/her own models in a very simple and straightforward way. A specific model management module allows the insertion of new user-supphed modeis into the base, their retrieval, deletion OF modification of their description. The user may decide how the model should be referred t:o in the menus and insert/edit a few lines of explanation uf the model scope and performance. In this way, the only computer-related information zhat is required for adding a new mode? to the package is the name of the executable program which implements it. PB user-supplied routine for modifying the data format is necessary if the new model does not comply with the standard input/output of those already present in the package.

G. FINZI

232 0

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9

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AN13 G. GUARISO 21

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1%

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-l-_ 23

Fig. 1, Sulphur dioxide concentralions (pg/m”) in the 24 X 12 km region of Piacenza-Castel San Giovanni (northern Italy). T’he vah*es are plotted from the results compllted for eight sensors for a median threshold value of 160.

This option may be vergr useful particularly when adding new simulation modeIs taking into accou~$ the characteristics of the examined sites irough terrain, coastal sites, urban areas, etc.) and the different mathematica1 formulations (Gaussian, puffs, particlcs, etc.). A simiaar option als0 exists for optimization algorithms, but the ger,zrality and reliability of the method already available suggest thut a large expansion of the base in this field is qui te unliI