Systematic Procedure to Handle Critical Decisions ... - ACS Publications

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Ind. Eng. Chem. Res. 2007, 46, 5600-5613

Systematic Procedure to Handle Critical Decisions during the Conceptual Design of Activated Sludge Plants Xavier Flores,† Ignasi Rodrı´guez-Roda,* and Manel Poch‡ Laboratory of Chemical and EnVironmental Engineering, UniVersity of Girona, MontiliVi Campus s/n 17071 Girona, Spain

Laureano Jime´ nez§ Department of Chemical Engineering, UniVersity of Barcelona, Martı´ Franque` s 1, 08028 Barcelona, Spain

Rene´ Ban˜ ares-Alca´ ntara| Department of Engineering Science, Oxford UniVersity, Parks Road, OX1 3PJ, Oxford, United Kingdom

This paper presents a systematic procedure that assists the designer of activated sludge plants to make critical decisions during the decision making process. By critical decisions we mean those (i) with a great influence on the overall design process and (ii) involving a set of options that satisfy the design objectives to a similar degree. Decision making for critical decisions is especially difficult when several design objectives (e.g., environmental, legal, economic, and technical) must be taken into account, i.e., when the evaluation of the most promising options is a multicriteria problem. The systematic procedure consists of three steps: (1) preliminary multiobjective optimization, where the most promising options (those located close to optimum conditions) are compared based on the results of dynamic simulation, (2) identification of the strong and weak points of each option by means of classification trees and the subsequent extraction of rules for each option, and (3) evaluation of the tradeoff between the improvement of the criteria identified as weak points of the option and the loss of the overall process performance through the integrated application of dynamic simulation and qualitative knowledge extracted during the design process. The capabilities of this new procedure are demonstrated with a case study where the (bio)reactor of an organic carbon and nitrogen removal plant is redesigned to achieve simultaneous organic carbon, nitrogen, and phosphorus removal. The results demonstrate how the new procedure supports the systematic analysis of critical decisions for activated sludge plant design Introduction Design in (bio)chemical processes is performed during the implementation of new technologies, the specification of equipment dimensions and operating conditions, the creation of new facilities and the retrofit of existing processes. It normally involves several design tasks performed in sequence, from data gathering, process synthesis, and case base development to detailed design and optimization.1 The traditional design approach incorporates economic objectives, such as fixed capital investment, net present value (NPV), operating cost, and payback period. In accordance with this approach, Uerdingen et al.2 presented a systematic methodology for screening options to improve the economics of continuous chemical processes, while Rapoport et al.3 presented a strategy using heuristics for the generation of alternative options. Recently, however, process design and analysis has included other types of objectives such as environmental objectives, controllability and robustness. Furthermore, it should be noted that the importance of each of the objectives to the decision makers might vary over time, in part because of pressure that stakeholders exert. * To whom correspondence should be addressed. E-mail: ignasi@ lequia.udg.es. Telephone number: 34.972.418281. Fax number: 34.972. 418150. † E-mail: [email protected]. ‡ E-mail: [email protected]. § E-mail: [email protected]. | E-mail: [email protected].

During the past decade, pressure from the entire spectrum of stakeholders has increased considerably and has led to consideration of several types of objectives in process design efforts. Thus, Chen and Shonnard4 presented a systematic and hierarchical approach to incorporate environmental considerations into all the stages of chemical process design, Shinnar5 used a concurrent design methodology in which control considerations were an important part in all the design phases, and Luyben and Hendershot6 studied the dynamic disadvantages of the reduction in the amount of dangerous chemicals during inherently safe process design. Multicriteria decision analysis (MCDA) is a well-established method7,8 to aid or support decision makers faced with complex decisions that involve the consideration of several objectives. MCDA is a structured and iterative process that consists of several steps that can be grouped into two main phases, namely problem structuring and problem analysis. Problem structuring involves, among other activities, the identification of the stakeholders who are involved in the decision process, the definition of the issues (decision problems) to be solved, the identification of criteria to measure the degree of satisfaction of the proposed objectives, and the generation of possible options. During problem analysis, information is obtained about the potential consequences of the implementation of the proposed options and about the preferences of those stakeholders involved in the decision making process. Activated sludge plants can be considered to be a type of (bio)chemical process because they treat wastewater using

10.1021/ie061426a CCC: $37.00 © 2007 American Chemical Society Published on Web 07/12/2007

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5601

Figure 1. Overview of the proposed procedure.

microbial growth processes. However, their performance can be enhanced using methods such as the addition of chemicals to bring about the precipitation of wastewater pollutants. Traditional activated sludge process design relies exclusively on the use of heuristic knowledge and numerical correlationss i.e. rules-of-thumb focused on the evaluation of economically optimal process configurationssamong many other possible process alternatives. Once the configuration is selected, process performance can be evaluated by means of steady-state models of the process, but there is hardly ever a consideration of the dynamic operability and the control performance of the process under design. There is some preliminary work that has addressed the consideration of multiple criteria during the design of activated sludge plants.9 The conceptual design of such plants is especially difficult when several objectives (e.g., environmental, legal, economic, and technical) must be taken into account, i.e., when the evaluation of the competing options is a multicriteria problem, and when there is a large number of critical decisions that designers must consider. By critical decisions, we mean those with a great influence on the whole design process (i.e., influencing many other decisions and hence having a strong influence on process structure and operation) and with a set of possible solutions that result in a similar degree of satisfaction of the design objectives (the most promising options). As far as we know, there is a lack of methodologies to assist a designer dealing with the close interplay and apparent ambiguity that exists in the multicriteria evaluation of design options. In this paper, a new systematic procedure to address critical decisions during the design of activated sludge plants is presented. The evaluation procedure of the design options was described in a previous paper.10 This paper summarizes the

overall design procedure and covers in detail the problems of dealing with the critical decisions that arise during the conceptual design of activated sludge plants, optimizing the most promising options, identifying their strong and weak points, and, finally, evaluating the tradeoff between the improvement of the criteria identified as weak points of the option and the loss of the overall process performance. The usefulness of the complete procedure is demonstrated using a case study where an organic carbon and nitrogen removal plant is redesigned to achieve simultaneous organic carbon, nitrogen, and phosphorus removal. Methodology The proposed procedure follows an evolutionary approach that combines dynamic simulation, preliminary multiobjective optimization, and knowledge extraction to assist the designer during the selection of the best alternative in accordance with the design objectives and process performance. It comprises seven steps organized into two phases: (I) hierarchical generation and multicriteria eValuation of design options and (II) analysis of critical decisions. A flowchart that highlights the most important steps in the procedure is shown in Figure 1. The first phase of the procedure (steps 1-3, Figure 1) was described in detail in a previous paper.10 Phase I: Hierarchical Generation and Multicriteria Evaluation of Design Options. In the first phase (steps 1-3), the design options are evaluated combining the hierarchical decision process11,12 with multicriteria decision analysis (MCDA) techniques. Thus, the design problem is reduced to a set of (Z) issues [I ) {I1, .., IZ}] that follow a predefined order: reaction, separation, and recycling.

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In step 1, the collection and analysis of all the required information is addressed. The goal is to define the context within which the activated sludge plant is to be designed. Step 2 includes the definition of the design objectives [OBJ ) {OBJ1, .., OBJP}] and the evaluation criteria [X ) {X1, .., XW}] used to measure the degree of satisfaction of objectives. Weight factors [w ) {w1, .., wP}] are assigned to determine the relative P wk importance of the objectives and normalized to sum 1 [∑k)1 W ) ∑i)1 wi ) 1]. In step 3, there is a number of tasks: the identification of the issue to be solved Il (step 3.1); the generation of the base case solution options [A ) {A1, ..., Am}] (step 3.2); the selection of a subset of criteria [X ) {X1, ..., Xn}] defined for this issue (step 3.3); and the evaluation of the proposed options (step 3.4). This evaluation is approached as an MCDA and comprises quantification (step 3.4.1) and normalization (step 3.4.2) of the evaluation criteria and a weighted sum (step 3.4.3). All the criteria [X] are quantified by dynamic simulation. The quantification of an option Aj with respect to criterion Xi is indicated as xj,i. Thus, each option under evaluation can be formulated as a vector of scores and represented as an n-dimensional performance score profile [Aj ) (xj,i, ..., xj,n)]. Value functions [V(Xi)] map the score profiles of all options into a value V(xj,i) normalized from 0 to 1. The 0 and 1 values are associated with the worst (xi*) and the best (x/i ) situations respectively while a mathematical function is used to evaluate the intermediate effects. The collection of the best [x/ ) (x/1, ..., x/n)] and the worst [x* ) (x1*, ..., xn*)] scores for all criteria determine the best [V(x/) ) (V(x/1), ..., V(x/n)) ) 1] and the worst profiles [V(x*) ) (V(x1*), ..., V(xn*)) ) 0]. Finally, a weighted sum is created to obtain a unique value for each option (eq 1). The weighted sum is calculated by adding the product of each normalized criterion V(xj,i) multiplied by its corresponding weight (wi). The options are ranked according to the score obtained.

s(Aj) ) V(xj,1)‚w1 + ... + V(xj,i)‚wi + ... + V(xj,n)‚wn ) n

V(xj,i)‚wi ∑ i)1

(1)

It is important to mention that although we made use of this methodology (steps 1-3) to generate and evaluate the design options, other procedures could also be applied for the generation and evaluation of design options, e.g., those proposed by Uerdengen et al.13 and Hoffman et al.14 Phase II: Analysis of Critical Decisions. The focus of this paper is on the second phase of the procedure and comprises steps 4-6. This second phase is considered only for those issues that are found to be critical decisions. By critical decisions, we mean those with a great influence on the whole design process and with options that satisfy the design objectives to a similar degree. In step 4, a preliminary multiobjective optimization is carried out to compare two or more options when each is close to the optimum design conditions. Thus, we propose deferring a numerical optimization until we have selected the most promising options and we are certain that we will proceed with the final design, i.e., when we attain a sufficient amount of accuracy to be able to address the next issue in the sequence of decisions, thereby allowing a more unbiased comparison. Step 4 starts with the identification of those variables [V ) {Vj,1, ..., Vj,y}] for the most promising options identified previously (step 4.1). A variable Vf for a given option Aj is represented as Vj,f. In step 4.2, the behavior of the evaluation criteria [X] is

investigated by varying by a small percentage (≈(5-10%) the value of the variable being analyzed with respect to the initial design conditions (base case). Finally, in step 4.3, these variables are ranked hierarchically according to their impact (see eq 2) using the rank order parameter presented by Douglas et al.15 n

∂s(Aj) ∂Vj,f

∂( ∆Vj,f )

V(xj,i)‚wi) ∑ i)1 ∂Vj,f

∆Vj,f

(2)

The sensitivity of the process with respect to a variable Vf is calculated for each option Aj. ∂s(Aj)/∂Vj,f are the components of the objective function gradient, and ∆Vj,f is the scaling factor. The objective function (see eq 1) is maximized by following an evolutionary approach, i.e., by optimizing, one by one, the selected variables with respect to the design objectives and process performance. The use of local sensitivity values instead of global ones, e.g., see the work of Sobol,16 is justified on two counts: (1) we are interested in studying the sensitivity of a base case design rather than the overall sensitivity of the models used and (2) we want to avoid excessive computational time during the conceptual design stage. Thus, in our study, the calculated optimal solution does not have to coincide with the global optimum. In order to account for the different emphases that stakeholders place on various design objectives, a sensitivity analysis of their weights is performed in step 5. Thus, the designer is provided with useful information, such as under which conditions each of the alternatives becomes the preferred one, which alternative is the best choice for the widest range of situations, and the identification of each option’s strong and weak points. A design option Aj has a weak point (xj,i*) when due to a low score in one or more evaluation criteria it does not sufficiently satisfy a given objective (OBJk). Conversely, an option has a / strong point (xj,i ) when due to a good score in one or more evaluation criteria it satisfies a design objective. The identification of these points is carried out by combining sensitivity analysis and machine learning techniques. A sensitivity analysis of weights allows the study of the variation in the selected option when the relative importance of the design objectives within the region defined as feasible is changed. That is done by both recalculating the weighted sum and ranking the options each time (step 5.1). If a given option Aj needs a low weight value (wk) of the objective OBJk in order to be selected, the option does not sufficiently satisfy OBJk, i.e., it has a weak point. Next, all the data generated is processed in step 5.2 and qualitative knowledge is extracted by means of classification trees and rules.17 This set of rules represents the relationships between the design objectives and the selected option and facilitates the interpretation of the multidimensional response surfaces that are generated during analyses. The extracted set of rules simplifies the relationships between design objectives and the most promising options. Thus, within the limits of the feasible region, it is possible to identify both the strong and weak points for each option when the weight of a given objective requires low and high values, respectively. In step 6, there is an evaluation of the tradeoff between the improvement of the criteria identified as weak points of the option and the loss of the overall process performance. This evaluation is carried out combining dynamic simulation and qualitative knowledge. Qualitative knowledge is extracted in step 6.1 by classifying the effect of the analyzed variables, Vf, on the evaluation criteria, V(xj,i), into four different categories


Figure 2. Flow diagram of the activated sludge plant to be redesigned

according to their trends: directly proportional, indirectly proportional, constant, and nonmonotonic. Next, the knowledge is codified as IF-THEN rules (step 6.2) of the type “FOR decision II IF Vj,f increases, THEN V(xj,i) decreases”. These rules are linked to an inference engine in order to maintain a record of the design decisions [I] together with the design variables [V] and the behavior of the evaluation criteria [V(X)]. In step 6.3, the rule-based system automatically searches the knowledge base constructed during steps 6.1 and 6.2 to propose a set of actions [Ac ) (Ac1,1,1, ..., Acm,n,y)] aimed at improving the weak points of each option identified in step 5. At the same time, the system alerts the designer to any negative implications in the event of the weak points’ possible implementation. Next, this qualitative knowledge is combined with numerical models and the parameter rj,i,f is calculated (eq 3). This equation represents the rate of improvement in a weakly satisfied criterion xj,i* in terms of the change in the objective function s(Aj) when one of the decision variables Vj,f is modified.

rj,i,f )

| | | | ∂V(xj,i*) ∂Vj,f ∂s(Aj) ∂Vj,f

(3)

The higher the value of rj,i,f, the higher the improvement in criterion X with a minimum variation in the overall optimum. The parameter rj,i,f is also a useful tool for guiding the direction of the design of the process because it provides a look-ahead capability and uncovers any hidden limitations in the plant’s performance. Finally, in step 7, and based on the information generated during phases I and II, the designer can be more confident of selecting the best alternative from among the most promising options. The same procedure is applied to solve each new critical decision that arises until the design of the activated sludge plant is completed. Note that objectives are not fixed and can evolve through time, thus allowing a refinement of the initial design objectives as shown in Figure 1. Case Study The redesign of an activated sludge plant to achieve simultaneous carbon, nitrogen, and phosphorus removal is used to illustrate the capabilities of the proposed procedure. Each of the steps in the procedure, together with numerical details, is described and discussed in the following sections.

Steps 1 and 2: Initial Exploration State and Definition of Design Objectives and Criteria. The activated sludge plant to be redesigned is the COST simulation benchmark plant (see Figure 2), a standardized simulation and evaluation example that includes plant layout, simulation models, model parameters, and a detailed description of the disturbances to be applied during the testing and evaluation of criteria to check the relative effectiveness of control strategies in activated sludge plants.18 This plant has a modified Ludzack Ettinger configuration with five reactors in series. Tanks 1 (ANOX1) and 2 (ANOX2) are anoxic with a total volume of 2000 m3, while tanks 3 (AER1), 4 (AER2), and 5 (AER3) are aerobic with a total volume of 3999 m3. Tanks 5 and 1 are linked by internal recirculation. Finally, there is a secondary settling tank (with a volume of 6000 m3) and two proportional and integral (PI) control loops. The first loop controls the dissolved oxygen (DO) in the third aerobic tank (AER3) by the manipulation of the air flow rate (as KLa), and the second loop controls the nitrate level (NO) in the second anoxic tank (ANOX2) by manipulating the internal recycle flow rate (Qintr). In the aerobic section of the plant, the organic matter and ammonia (ammonia is the common form of nitrogen in influent wastewater) are oxidized to carbon dioxide and nitrate. In the anoxic section, the nitrate transported by the internal recirculation is reduced to nitrogen. This reduction requires an electron donor, which can be supplied in the form of influent wastewater organic matter, endogenous respiration, or an external carbon source. The average dry weather wastewater to be treated has a flow rate of 18 500 m3‚d-1 with an organic, nitrogen, and phosphorus load of 7031 kgCOD‚d-1 (chemical oxygen demand (COD)), 971 kgN‚d-1, and 231 kgP‚d-1, respectively, and is proposed by Gernaey and Jorgensen.19 The plant is designed to remove carbon and nitrogen, although denitrification efficiency is very low. Also, since it is located in a sensitive area, it has to remove phosphorus before the water is discharged into the environment. Finally, the redesign budget is restricted to an investment of 1.1 × 106 Euro and operating costs of 1.1 × 106 Euro‚y-1, but there is no limitation on land occupation. Table 1 shows the design objectives and the criteria used to measure their satisfaction.10 Different weight factors are assigned to each objective by the experts/designer according to their relative importance. As weight assessment is not a central issue of this paper, equal importance for the four design objectives is assumed in the case study, thus wp ) 0.25. Step 3: Decision Procedure. The decision procedure starts with the identification of the issues to be resolved. The

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Table 1. Design Objectives, Criteria, and Criteria Scales objective (OBJk) OBJ1: minimize environmental impact OBJ2: minimize economic cost OBJ3: maximize technical reliability

criterion (Xi)

references

X1: impact on water X2: construction costs X3: operating costs X4: robustness X5: flexibility X6: control performance X7: risk of separation problems

OBJ4: meet the European directive

X8: TIV (time in violation) COD X9: TIV BOD X10: TIV TSS X11: TIV TN X12: TIV TP

hierarchical decision process determines the direction of the design process by fixing the order of all the issues that arise during redesign, starting with the reaction section. Once all the issues related to the reactor section are resolved, the design continues with the separation and finally the recirculation sections. An MCDA that allows the simultaneous consideration of several objectives is used as an evaluation method throughout the decision procedure. Steps 3.1, 3.2, and 3.3: Identification of the Issues to be Resolved, Generation of the Options, and Selection of Criteria. The first issue (I1, I ) 1) in the reaction section is the reaction path for phosphorus removal. The removal of phosphorus from wastewater is possible in two different ways: via biological or chemical treatment. In biological phosphorus removal, excess P is incorporated into the cell biomass, which is then removed from the process as a result of sludge wasting. An anaerobic section (without oxygen and nitrates) is needed to promote anaerobic P release and to provide the phosphorus accumulating organisms (PAO) with a competitive advantage over other bacteria. Next, PAO organisms grow using intracellular storage products as a substrate during the anaerobic phase, with oxygen or nitrate as electron acceptors and consuming nitrogen and phosphorus as nutrients. In chemical phosphorus removal, the phosphorus in the influent wastewater is precipitated by the addition of a metal salt and subsequently removed from the mixed liquor with the waste sludge in the sedimentation tank.25 Three modifications to the original reactor (m ) 3) are considered in order to resolve this issue: (A1) biological phosphorus removal with a preliminary 2000 m3 anaerobic tank (with a hydraulic residence time of 2.6 h); (A2) chemical phosphorus precipitation with iron salts in the third aerobic reactor, with a constant dosage of 0.75 m3‚d-1; and (A3) a hybrid solution with partial biological phosphorus removal (using a 1500 m3 preliminary anaerobic tank) enhanced with chemical precipitation in the third aerobic reactor (constant dosage of 0.65 m3‚d-1). In turn, a set of 12 criteria (n ) 12) is selected (Table 1) to evaluate the options generated for the first issue (I1) in the hierarchy of decisions: X1 (impact on water), X2 (construction costs), X3 (operating costs), X4 (robustness), X5 (flexibility), X6 (control performance), X7 (risk of separation problems), and X8-X12 (time in violation). Step 3.4. Evaluation of the Options. Step 3.4.1. Criteria Quantification. In this step, criteria X1 and X3-X12 are quantified by dynamic simulation, while X2 is evaluated by cost estimations. Simulations are performed using the MatLab-

X7-1: foaming risk X7-2: bulking risk X7-3: rising risk

Flores et al.,10 Gernaey and Jorgensen19 US EPA20 Vanrolleghem and Gillot21 Vanrolleghem and Gillot21, Flores et al.22 Vanrolleghem and Gillot21, Flores et al.22 Stephanopoulos23 Comas et al.24 Comas et al.24 Comas et al.24 Copp18 Copp18 Copp18 Copp18 Copp18

Simulink environment. Reactors are modeled as a series of continuous stirred tank reactors. The International Water Association activated sludge model number 2d (IWA ASM2d) was chosen as the biological process model.26 The ASM2d has 19 state variables and describes (bio)chemical phosphorus removal with simultaneous nitrification and denitrification processes in activated sludge systems by means of a set of nonlinear differential equations. The double-exponential settling velocity function of Takaćs et al.,27 based on the solid flux concept, was selected as a fair representation of the settling process, using a 10 layer discretization. Default values at 15 °C for kinetic and stoichiometric parameters are used, except for phosphorus precipitation kinetics which are adjusted.28 The settling model parameters used are reported by Copp.18 Two automatic control loops are included in the plant: (1) a dissolved oxygen control (DO) in the third aerobic reactor manipulating the aeration transfer with a setpoint of 2 (-COD) g‚m-3 (Kp ) 500 m3‚d-1‚g(-COD)-1‚m-3, Ti ) 0.005 d) and (2) an internal recirculation flow control to ensure a nitrate concentration (NO) in the second anoxic reactor of 1 gN‚m-3 (Kp ) 15 000 m3‚d-1‚gN-1‚m-3, Ti ) 0.05 d). The DO sensor is assumed to be ideal, without delay or noise, unlike the NO sensor which has a time delay of 10 min, with white, normally distributed and zero mean noise (standard deviation of 0.1 g‚m-3). External recirculation, waste flow, and aeration flow in the first and second aerobic reactors are constant, and their respective values are 18 446, 385 m3‚d-1, and 240 d-1. The simulation procedure follows a steady-state simulation; this ensures a consistent initial point and eliminates the bias due to the selection of the initial conditions in the dynamic modeling results.18 Even though the length of the influent used to carry out the simulations is of 28 days, only the data generated during the last 7 days are used to quantify the criteria. MatLab-Simulink is used to calculate construction costs, which are estimated using the CAPDET model.20 Default parameters for unit costs (excavation, concrete walls, concrete slabs, handrails, etc.), equipment (5 hp vertical mixer), and construction labor rates are used for the cost estimations. It is important to emphasize that the results of the quantified criteria depend heavily on the model selection. When modeling activated sludge plants, there is a lack of agreement on the best model to apply to a given case. The representation of biomass decay,19 the modeling of phosphorus removal,19,26,29,32 and the oversimplification of the settling models (i.e., nonreactive in most cases, despite the fact that a significant amount of biomass is often stored at the bottom of the secondary clarifier)30 are issues still under discussion.

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5605 Table 2. Scores and Extreme Profiles for the Three Evaluated Options A1 xj,1 xj,2 xj,3

82.03 770520 909180

A2 80.88 0 1035900

A3 OBJ1 83.51 OBJ2 700000 1029500

x/i

xi*

100

Table 3. Normalized Criteria and Weighted Sum after the First Phase of the Procedure

0 %

0 1100000 Euro 900000 1100000 Euro‚y-1

xj,4 xj,5 xj,6 xj,7-1 xj,7-2 xj,7-3

14.70 10.26 0.78 0.00 61.46 31.10

18.91 15.16 0.78 0.00 28.72 74.41

OBJ3 14.34 11.76 1.52 0.00 66.52 48.66

20 20 0 0 0 0

0 0 1 100 100 100

(gN‚m-3)2‚d % % %

xj,8 xj,9 xj,10 xj,11 xj,12

0.00 0.00 0.00 90.18 29.32

0.00 0.00 0.00 100.00 0.00

OBJ4 0.00 0.00 0.00 66.37 25.45

0 0 0 0 0

100 100 100 100 100

% % % % %

Once the criteria are quantified, we obtain the score profile for each design option considered. The score profiles are presented in Table 2. It is important to mention that the construction cost for option A2 (adding chemical precipitation without modifying the layout) has been taken as nil. Even though this configuration requires the installation of one or more storage tanks, pumps, and a system of pipes, this cost is negligible when compared with the construction cost of an additional reactor. Also note that, in this case study, X7-1, X8, X9, and X10 have the same values, so they are not useful for discriminating between competing options. Steps 3.4.2 and 3.4.3: Criteria Normalization and Weighted Sum. To compare the effects of different variables on the design, it is necessary to normalize the results. Each criterion in the competing options is normalized between 0 and 1 by means of value functions V(Xi). Value functions award values of 0 and 1 to the worst and the best situations considered, while a mathematical function is proposed to evaluate intermediate effects. The extreme profiles (based on expert judgment) for the criteria used in this case study are summarized in Table 2. Next, a linear model is interpolated between these extreme values and is applied to calculate the intermediate effects (e.g., for criterion X1, the value function is the following: V1(X1) ) 0.01‚xj,1). Finally, a weighted sum (eq 1) is worked out in order to obtain a single value for all the options, which are then ranked according to the scores obtained, with the final decision resting with the process designer. The results of the criteria normalization and weighted sum are shown in Table 3. The results reported in Table 3 lead us to the following conclusion: in accordance with the design objectives, the recommended option is biological phosphorus removal (A1) with a score of 0.72; and the rejected options are A2 (chemical phosphorus precipitation with a score of 0.69) and A3 (hybrid system with a score of 0.62). It is important to note that the scores of the first and second options shown in Table 3 are so similar that in practice they can be considered equivalent. However, the configurations have completely different implications for the resulting plant structure and operation. In particular, if option A1 is selected, the next issue to be resolved would include a modification in the location of the anaerobic reactor, and the inclusion (or not) of an additional internal recycle.25 In contrast, if the selected option were to be A2, the next issues to be resolved would be related to the dosage point25 and the increase in the secondary settling area.25

V(xj,i)

A1

A2

A3

wi

V(xj,1) V(xj,2) V(xj,3) V(xj,4) V(xj,5) V(xj,6) V(xj,7-1) V(xj,7-2) V(xj,7-3) V(xj,8) V(xj,9) V(xj,10) V(xj,11) V(xj,12)

0.82 0.30 0.95 0.74 0.51 0.22 1 0.39 0.69 1 1 1 0.10 0.71 0.72

0.81 1.00 0.32 0.95 0.76 0.22 1 0.71 0.26 1 1 1 0 1 0.69

0.84 0.36 0.35 0.72 0.59 0 1 0.33 0.51 1 1 1 0.34 0.75 0.62

0.250 0.075 0.175 0.062 0.062 0.062 0.021 0.021 0.021 0.050 0.050 0.050 0.050 0.050 1

OBJ

units

OBJ1 OBJ2 OBJ3

OBJ4

n s(Aj) ) ∑i)1 V(xj,i)‚wi

Table 4. Sensitivity Analysis and Criteria Recalculation for Option A1 and Variable V1,1 -10% V1,1 x1,1 x1,2 x1,3

1800 81.43 741160 917030

-5% 1900 81.84 747250 911010

0 2000 OBJ1 82.03

+5% 2100 82.00

OBJ2 770520 859500 909180 911830

+10% 2200

units m3

81.76 % 869600 919160

Euro Euro‚y-1

x1,4 x1,5 x1,6 x1,7-1 x1,7-2 x1,7-3

15.75 11.75 0.88 0.00 59.52 43.01

15.14 11.05 0.82 0.00 60.12 38.99

OBJ3 14.70 10.26 0.78 0.00 61.46 31.10

14.42 9.34 0.75 0.00 62.95 20.83

14.20 8.04 0.74 0.00 65.18 17.26

(gN m3)2‚d % % %

x1,8 x1,9 x1,10 x1,11 x1,12

0.00 0.00 0.00 82.89 62.65

0.00 0.00 0.00 85.71 51.94

OBJ4 0.00 0.00 0.00 90.18 29.32

0.00 0.00 0.00 93.90 11.61

0.00 0.00 0.00 95.39 6.85

% % % % %

Thus, the first issue in the hierarchysthe reaction path for phosphorus removalsis considered a critical decision and requires a more detailed analysis to ensure selection of the best alternative among the most promising options proposed in this first phase. In the second phase of the procedure, the analysis of critical decisions is carried out. The overall analysis is developed to determine which should be the option selected to resolve the first issue: A1 (biological phosphorus removal) or A2 (chemical phosphorus removal). 4. Preliminary Multiobjective Optimization of the Most Promising Options. Step 4.1: Selection of the Design/ Operation Variables. For the first option (A1), five variables were selected: anaerobic volume (V1,1), waste flow (V1,2), external recirculation flow (V1,3), DO setpoint (V1,4), and NO setpoint (V1,5). For the second option (A2), the variables were the following: metal flow (V2,1), waste flow (V2,2), external recirculation flow (V2,3), DO setpoint (V2,4), and NO setpoint (V2,5). A sensitivity analysis was carried out for both options to determine the most sensitive parameters. Step 4.2: Sensitivity Analysis of the Design/Operation Variables. First, all the selected variables varied around the vicinity of their base values ((2.5%, (5%, (7.5%, and (10%). However, one sensitivity analysis (V1,1) is shown and discussed below. The first variable to analyze for option A1 (biological phosphorus removal) is the anaerobic volume (V1,1). As stated previously, this value varies from -10% (1800 m3) to +10% (2200 m3) around its base case value (2000 m3), simulating eight

5606


Figure 3. Variation of the evaluation criteria when the initial value of the anaerobic volume (V1,1) is decreased by -5% and -10%, respectively.

Figure 4. Variation of the evaluation criteria when the initial value of the anaerobic volume (V1,1) is increased by +5% and +10%, respectively.

additional scenarios, although only four are shown in Table 4. The representation of the percent of variation with respect to the initial value when it is decreased and increased is depicted in Figures 3 and 4, respectively. From the results generated in the previous analysis, we can conclude that if the volume increases, the construction costs (x1,2), bulking risk (x1,7-2), and TIV for TN (X1,11) also increase as shown in Figure 4. Criterion x1,2 increases with volume because a higher volume implies higher earthwork, concrete slab, and concrete wall costs. This volume enlargement implies a proliferation of PAOs, a subsequent increase in biomass and reduction in biochemical oxygen demand (BOD) in the reactor section, which in turn causes a reduction in the FtoM ratio and thus an increased risk of bulking. In addition, an anaerobic volume enlargement supposes a decrease in the plant’s nitrification capacity, which results in a lower production of nitrogen (nitrate) to be denitrified in the aerated reactors and a worse overall nitrogen removal efficiency (see Figure 5). This decrease in nitrification capacity is attributed to a major decay of autotrophic bacteria due to the additional anaerobic volume. Nevertheless, experimental observations31 suggest that the decay rate is electron acceptor dependent and thus different under anaerobic, anoxic, and aerobic conditions. As a result, a lower effluent ammonium concentration should be expected. This knowledge is included in more recent activated sludge models (e.g., ASM333) and in modifications of the original ASM2d model.19

Figure 5. Evolution of the total nitrogen concentration in the effluent for the different scenarios: option A1 analyzing variable V1,1 (anaerobic reactor volume).

On the other hand, this volume enlargement causes a reduction in the robustness (x1,4), flexibility (x1,5), control performance (x1,6), rising risk (x1,7-3), and TIV for TP (x1,12) criteria. Surprisingly, this fact implies a reduction in the ability of the plant to adapt to short-term variations, e.g., rain and storm events and nitrogen and phosphorus impacts, and long-term variations, e.g., step increase, of flow, nitrogen, and phosphorus, although one would expect the opposite. This is attributable as mentioned before to an increased autotrophic decay rate at bigger anaerobic volumes, provoking a worse overall nitrogen removal and a major variation in the effluent quality term used to quantify both robustness and flexibility.21,22 With respect to control performance, quantified by the integral square error (ISE),23 the nitrate control loop works better with a bigger anaerobic reactor because more organic matter is consumed in the anaerobic section for PAOs to form organic cell products and there is a lower variation in the BOD arriving in the anoxic section, thus facilitating the maintenance of the desired setpoint and making it easier for the controller to compensate for the situation. The decrease in nitrification capacity caused by the increase in volume of the anaerobic section causes a reduction in the nitrogen (nitrate) that is recycled from the last aerobic reactor to the sedimentation tank, resulting in a decrease in the rising risk. The nitrate in the secondary settler is sent to the first anaerobic reactor via the sludge recycle loop. The presence of lower nitrate concentrations in the anaerobic reactor results in a less pronounced inhibition of the P release, because the organic matter entering the plant is used preferentially for the buildup of cell internal products instead of using it for denitrification, improving the overall phosphorus removal (Figure 6). Criteria x1,1 and x1,3 have a maximum and a minimum value when the anaerobic volume is 2050 and 2000 m3, respectively (results not shown). For criterion x1,3, if the anaerobic volume is increased, there is a higher consumption of electricity due to pumping (PE) and mixing (ME), but if this volume is reduced, there is a higher consumption of electricity due to aeration energy (AE) and an increase in the fines to be paid for the pollutants discharged (EQ). Finally, with respect to criterion x1,1, if V1,1 is reduced by -10% or increased by +10%, there is a drop in phosphorus and nitrogen removal, respectively, and a consequent decrease in overall pollution removal efficiency. Finally, eq 2 is used to determine which variables have more impact on process performance: the higher the improvement in the multiobjective function, the more impact the variable has. These variables listed in decreasing order of impact are V1,2,

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5607 Table 5. Optimum Values for the Most Promising Options (A1 and A2)

Figure 6. Evolution of the total phosphorus concentration in the effluent for the different scenarios: option A1 analyzing variable V1,1 (anaerobic reactor volume).

Figure 7. Variation of the multiobjective function s(A1) during the sensitivity analyses carried out for the key variables.

V1,5, V1,1, V1,3, and V1,4 for option A1 and V2,1, V2,2, V2,5, V2,4, and V2,3 for option A2. The impact on process performance is calculated by a weighted sum using the same procedure described in phase I (see eq 1) with an improvement in the objective function of 0.89%, 0.60%, 0.29%, 0.15%, and 0.05% for the first option and 1.83%, 0.49%, 0.23%, 0.14%, and 0.10% for the second option, respectively. Figure 7 shows the sensitivity of the objective function for option A1 with respect to the selected variable. In the following step, the variables are optimized in the order of their impact. Step 4.3: Optimization of the Design/Operation Variables. As for the sensitivity analysis, the multiobjective function is a weighted sum (eq 1). The optimized values for each manipulated variable are found through a series of optimization runs in an interval of ((2.5%) until the optimum is reached. Table 5 is a comparison of the base case values with the optimized variables for the competing options. As the analysis of all the optimization parameters would require a lengthy discussion, only one variable for option A2 is presented and discussed below. Variable V2,4 (DO setpoint) is the chosen optimization parameter for option A2 after the fourth evolution with an accumulative improvement in the multiobjective function of +4.9%. The relative improvements for V2,1, V2,5, and V2,2 were +2.61%, +1.52%, and +0.7%, respectively, while there was no improvement for V2,3. Figure 8 presents the variation in

design/operation variable

initial value

best value

units

V1,2 V1,5 V1,1 V1,3 V1,4 V2,1 V2,5 V2,2 V2,3 V2,4

385 1 2000 18446 2 0.75 1 385 18446 2

298.38 0.4 2000 18446 2 0.6 0.53 308 18446 1.15

m3‚d-1 gN‚m-3 m3 m3‚d-1 g(-COD)‚m-3 m3‚d gN‚m-3 m3‚d-1 m3‚d-1 g(-COD)‚m-3

design objectives for option A2 for different values of the analyzed variable. As well, it can be seen how the DO setpoint in the reactor decreases from a value of 2 to 1.15 g(-COD)‚ m-3. A reduction in the DO setpoint implies an improvement in the objective function of +0.96% with respect to the previous evolution and a total optimization improvement of +5.71%. As expected from the sensitivity analysis, a reduction in the oxygen setpoint causes an overall reduction in operating costs (x2,3) due to aeration energy savings (AE), although pumping energy (PE) is increased (see the decrease in OBJ2 satisfaction in Figure 8). The increase in PE can be explained by the reduction of nitrate concentration in the last aerobic reactor, a consequence of reduced nitrification efficiency. This fact explains the negative effect on x2,1 (impact on water) where, as the DO setpoint increases, the quantity of oxygen that returns with both recirculation and recycling also increases, thereby inhibiting the denitrification process and increasing the risk of rising (see OBJ1, OBJ3, and OBJ4 in Figure 8). The simulation results show the existence of an interaction between the two control loops: the higher the nitrate concentration in the aerobic reactor, the lower the volume of mixed liquor that has to be pumped via the internal recirculation to maintain the nitrate setpoint. Also, it is important to mention the failure in plant disturbance rejection, directly correlated with the lowering of control performance. Thus, we can conclude that it is more desirable to adopt a setpoint of 1.15 g(-COD)‚m-3. The differences between the optimized configurations and the base case are summarized in Table 5. The objective function increases by +3.54% and +5.71%, respectively. For option A1, the most important contribution comes from variable V1,5 although during the sensitivity analysis it has a lower percentage difference than other variables within the evaluated limits. In contrast, option A2 shows a higher impact in the value function (+5.71%), mainly due to the optimization of metal flow (V2-1).

Figure 8. Optimization of the variable V2,4. Evolution of the different design objectives and the multiobjective function s(A2).

5608


Table 6. Score Profiles for the Most Promising Options Once Optimized A1

A2

units

OBJ1 xj,1

81.62

80.75

%

OBJ2 xj,2 xj,3

770520 899570

0 989020

Euro Euro‚y-1

OBJ3 xj,4 xj,5 xj,6 xj,7-1 xj,7-2 xj,7-3

14.74 9.65 0.24 28.13 77.98 71.28

xj,8 xj,9 xj,10 xj,11 xj,12

0.00 0.00 0.00 90.18 20.69

18.35 13.35 0.49 0.60 67.86 80.36

(gN‚m-3)2‚d % % %

OBJ4 0.00 0.00 0.00 100.00 2.83

% % % % %

The new score profiles for options A1 and A2 are summarized in Table 6 and can be compared with the originals in Table 2. 5. Characterization Analysis of the Most Promising Options. In this step, a sensitivity analysis with respect to the criteria weights is performed for the four design objectives. The purpose of this step is to enable understanding of the effect of the stakeholders’ preferences with regard to the design space. Thus, the designer is provided with information about the preferred design alternative for the widest range of situations and, at the same time, is informed about the strong and weak points of each option. Step 5.1: Weight Sensitivity Analysis. The weighted sum is recalculated varying the value of each weight within a feasible region defined as (0.10 as its initial value (with a 0.05 interval). Following this procedure, the options are ranked again. Step 5.2: Classification Tree Generation and Extraction of Rules. All the data generated in step 5.1 is processed, and a set of rules is extracted using classification trees.17 The classification tree predicts the value of a discrete dependent variable (in this case the selected option) based on the values of a set of independent variables (in this case the values of the evaluation weights, within the limits fixed previously). The classification tree is generated by the algorithm C4.517 using the WEKA software package. All the parameters for the tree induction were left at their default values. Figure 9 shows the representation of the classification tree generated. Thus, a set of 5 rules are extracted from a data set of 86 samples using 4 continuous variables (the weights w1, w2, w3, and w4) that predict if the selected options would be A1, A2, or A3. These rules properly classify 97.68% of the cases, which is a fairly good predictive capability. This set of rules and the correct/incorrect number of classified instances are summarized as follows.

Figure 9. Classification tree generated with the data matrix of the weight sensitivity analysis.

Figure 10. Breakdown of the operating costs (X3) for the three evaluated options.

R1: IF w2 ) 0.15 and w3 e 0.2, THEN the selected option would be A1 [3]. R2: IF w2 ) 0.15 and w3 > 0.2, THEN the selected option would be A2 [12/1]. R3: IF w2 > 0.15 and w3 e 0.3, THEN the selected option would be A1 [60]. R4: IF w2 > 0.15 and w3 > 0.3 and w4 e 0.2, THEN the selected option would be A1 [8]. R5: IF w2 > 0.15 and w3 > 0.3 and w4 > 0.2, THEN the selected option would be A2 [3/1]. As can be seen in R1, R3, and R4, A1 is the favored option for the widest range of situations. From rules R3 and R4, it can be seen that when OBJ2 is favored the selected option would be A1 despite its construction cost (see x1,2 in Table 6). Otherwise, when OBJ3 is prioritized as in R2 and R5, A2 would be the selected option. Moreover, from rule R5, A2 would be the selected option if w4 had a high value. Nevertheless, R4 and R5 show that A2 would be the selected option unless OBJ1 is prioritized because the sum of the objective weights is normalized to 1, i.e., if the value of w1 is high; the value of w4 has to be low, giving an advantage to option A1. These rules can be explained in terms of physical processes and their interaction. For example, option A1 has the lowest operating costs, as can be seen in the breakdown of the operating costs in Figure 10, because it does not require the purchase of chemical products. Option A2 presents the best technical characteristics and for this reason is selected when OBJ3 is favored (see rules R2 and R5). This is mainly due to its low sensitivity to both short and long term perturbations. Sensitivities (S) to different short term (robustness) and long term (flexibility) perturbations are summarized in Table 7, where it can be seen that A2 has the lowest values for most of them. This is because A1 is more sensitive to influent conditions with respect to the removal of N and P (influent BOD), and it is subjected to major variations in comparison to A2, where the removal of P is by precipitation. Moreover, this option favors the formation of floc organisms to the detriment of filamentous bacteria. This behavior can be attributed to a lower solids retention time (SRT) and a higher food to microorganism (FtoM) ratio for this configuration. On the other hand, A2 achieves a worse overall pollution removal efficiency compared to A1 as a result of the insufficient anoxic zone and the low biodegradable fraction in the influent organic matter. This inhibits the reduction of the

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5609 Table 7. Sensitivities to Perturbations (Si), Calculation of the Robustness (X4), and Flexibility (X5) Criteria22

S1 (rain event) S2 (storm event) S3 (nitrogen impact event) S4 (phosphorus impact event)

X4 )

1

x

A2

A3

0.073822 0.004264 0.000247 0.000003

0.01270 0.00658 0.00016 0.00002

14.70

18.91

14.34

4

∑S 4 1

2 i

i)1

S5 (step increase in flow) S6 (step increase in nitrogen) S7 (step increase in phosphorus)

X5 )

A1 0.001091 0.007160 0.000326 0.000003

1

10.26

x∑ 1

0.028347 0.003841 0.000053

0.013436 0.003211 0.000207 15.16

0.01894 0.00174 0.00099 11.76

3

3 i)1

Si2

nitrate produced in the aerobic section and, as a consequence, results in partial nitrogen removal. Nevertheless, a good performance in phosphorus removal (x2,12 in Table 6) compensates for the low denitrification rate (x2,11 in Table 6) because both pollutants have equal weights resulting in a better satisfaction of OBJ4. Thus, we conclude that option A1 has as weak points x1,4*, x1,5*, and x1,11*, giving a comparative advantage to A2 with respect to OBJ3 and OBJ4. This is due to the sensitivity of the efficiency of nitrogen and phosphorus removal to the influent organic matter content. In contrast, the weak points identified for A2 are x2,1* and x2,3*, resulting in a poorer satisfaction of OBJ1 and OBJ2 which, in turn, are attributable to the additional costs of the metal salt for phosphorus precipitation and the insufficient anoxic zone for nitrogen denitrification. 6. Evaluation of the Tradeoffs. The tradeoffs between the improvement of the criteria identified as “weak” and the loss of the overall process performance are calculated in this step. The information about the tradeoff is provided to the designer in two different ways: first, through the parameter rj,i,f that represents the ratio between the improvement of the targeted criterion and the loss in the objective function and, second, as qualitative information in the form of rules that enable the

identification of the causes of the degradation of the overall process performance. Step 6.1: Data Handling and Knowledge Extraction. A new sensitivity analysis at the optimum found in step 4 is carried out. The data generated during the new sensitivity analysis is processed to enable qualitative knowledge to be extracted. The objective of this step is to find, for each option, the correlations between the 5 analyzed variables and the 12 criteria used. Trends in the evaluation criteria are computed within (10% of the new base case value found in step 4.3. Finally, these trends are classified into four categories: directly proportional, indirectly proportional, constant, and nonmonotonic. Table 8 summarizes the correlations between the normalized criteria and the variables. Step 6.2: Knowledge Codification. The knowledge extracted from the data is codified in the form of IF-THEN rules. The set of rules [R ) (R1,1,1, ..., Rm,n,y)] constitutes a knowledge base containing the relationship between the variables that govern the overall process (y ) 5) and the 12 evaluation criteria (n ) 12) for each option considered (m ) 2). Finally, these rules are used as an input to an inference engine (in this case we use CLIPS). As an example, two rules extracted from the data in Table 8 are shown. R1,11,3: IF V1,3 (recirculation flow) increases, THEN TIV TN (x1,11) improVes. R2,3,1: IF V2,1 (metal flow) increases, THEN operation costs (x2,3) worsen. Step 6.3: Knowledge Extraction and Evaluation of the Tradeoffs. Finally, in step 6.3, dynamic simulation is integrated with qualitative knowledge to evaluate the tradeoff between the improvement of the weak points for a determined option identified in step 5 and the loss of the overall process performance. Thus, a set of actions that have the potential to improve the weak criteria for A1 (x1,4*, x1,5*, and x1,11*) and for A2 (x2,1* and x2,3*) are searched for automatically in the knowledge base built in steps 6.1 and 6.2 and summarized in Table 8. Next, the optimum sensitivity is calculated, i.e., the rate at which the multiobjective function changes with changes to one of the decision variables. Once the actions are proposed, the adverse effects resulting from the application of those actions are highlighted. To illustrate these ideas, we present an example run of the system. The alternatives under study are options A1 and A2, and some of the possible actions aimed at improving the satisfaction

Table 8. Relationship between Evaluation Criteria and Analyzed Variables variable

directly proportional

indirectly proportional

V1,1

V(x1,6), V(x1,12)

V1,2

V2,2

V(x1,4), V(x1,7-1), V(x1,7-3), V(x1,12) V(x1,1), V(x1,3), V(x1,4), V(x1,5), V(x1,11) V(x1,1), V(x1,4), V(x1,5), V(x1,6), V(x1,11), V(x1,1), V(x1,3), V(x1,5), V(x1,11) V(x2,1), V(x2,5), V(x2,7-1), V(x2,12) V(x2,7-1), V(x2,7-3), V(x2,12)

V2,3

V(x2,1), V(x2,3), V(x2,7-3)

V(x2,7-1), V(x2,7-2), V(x2,12)

V2,4

V(x2,4), V(x2,5), V(x2,6), V(x2,7-3), V(x2,12) V(x2,1), V(x2,7-3)

V(x2,1), V(x2,3), V(x2,7-1)

V1,3 V1,4 V1,5 V2,1

V2,5

V(x1,2), V(x1,4), V(x1,5), V(x1,7-1), V(x1,7-2), V(x1,11) V(x1,1), V(x1,3), V(x1,5), V(x1,6), V(x1,11) V(x1,7-1), V(x1,7-2), V(x1,12) V(x1,3), V(x1,7-1), V(x1,12) V(x1,4), V(x1,6), V(x1,12) V(x2,3), V(x2,6), V(x2,7-3), V(x2,1), V(x2,3), V(x2,6)

V(x2,3), V(x2,4), V(x2,5), V(x2,6), V(x2,12)

constant

nonmonotonic

V(x1,8), V(x1,9), V(x1,10)

V(x1,1), V(x1,3), V(x1,7-3)

V(x1,2), V(x1,8), V(x1,9), V(x1,10) V(x1,2), V(x1,8), V(x1,9), V(x1,10) V(x1,2), V(x1,7-2), V(x1,8), V(x1,9), V(x1,10) V(x1,2), V(x1,7-1), V(x1,7-2), V(x1,8), V(x1,9), V(x1,10) V(x2,2), V(x2,7-2), V(x2,8), V(x2,9), V(x2,10), V(x2,11), V(x2,2), V(x2,8), V(x2,9), V(x2,10), V(x2,11) V(x2,2), V(x2,8), V(x2,9), V(x2,10), V(x2,11) V(x2,2), V(x2,7-2), V(x2,8), V(x2,9), V(x2,10), V(x2,11) V(x2,2), V(x2,7-1), V(x2,7-2), V(x2,8), V(x2,9), V(x2,10), V(x2,11)

V(x1,7-2) V(x1,6), V(x1,7-3) V(x1,7-3) V(x1,7-3) V(x2,4) V(x2,4), V(x2,5), V(x2,7-2) V(x2,4), V(x2,5), V(x2,6)

5610


Figure 11. Tradeoffs between the multiobjective function s(A1) and the normalized value of criterion time in violation for TN x1,11.

of criteria x1,11 (TIV-TN) and x2,3 (operation costs) are presented and commented on below. The examples are partially edited to shorten the output. The answers given by the user are underlined in italics (e.g., Option A1, TIV-TN), and the text printed by the system is in courier font.

When the recirculation flow is increased, e.g., +10%, in option A1 and the proposed scenario is simulated, there is a decrease in the TIV for TN (-12.05%), i.e., a better satisfaction of the legal limits concerning total nitrogen. Nevertheless, this increase would suppose an increase in the total suspended solids in the biological reactor and a subsequent decrease in the FtoM ratio. This decrease would result in an increase in the foaming and bulking risks (+34.39% and +1.34%, respectively). Improved nitrogen removal efficiency implies a higher consumption of organic matter for denitrification with a subsequent restriction of phosphorus release and an overall decrease in phosphorus removal efficiency (there is an increase in the TIV for TP of +146.75%). All these adverse effects bring about a decrease in the overall process performance of -0.62%. The tradeoff between the normalized value of x1,11 and the multiobjective function s(A1) is shown graphically in Figure 11. As another example, take the case of option A2 where the action proposed is aimed at improving the satisfaction of OBJ2, i.e., reducing operating costs:

In this case, there is a dramatic increase in TIV for TP (from 2.83% to 66%) when metal flow is decreased in option A2. This is due to the fact that phosphorus removal in this plant is carried out by chemical precipitation. If the dosage of iron is reduced, the quantity of phosphorus that precipitates is also reduced thereby increasing the impact on water and reducing the overall pollution efficiency (-0.43%). It is important to note that the small reduction in operating costs (-0.09%) can be explained by the rise in effluent fines although the cost associated with the quantity of metal salt decreases. The variation in the normalized value of x2,3 and multiobjective function is shown in Figure 12. If the tradeoff between criteria improvement and loss in overall process performance is evaluated using eq 3 (see the values of r1,11 for Vj,3 and r2,3 for Vj,1 in Table 9), we can conclude from these examples that A1 could be improved with a smaller loss of overall performance. This can be observed in Figures 11 and 12 which show the change in the target criteria and the multiobjective function as a response to the variation

Figure 12. Tradeoffs between the multiobjective function s(A2) and the normalized value of criterion operation costs x2,3. Table 9. Parameter r (eq 3) for the Identified Weak Criteria of Each Option

Vj,1 Vj,2 Vj,3 Vj,4 Vj,5 Y (Σf)1 rj,i,f)/Y

r1,4

r1,5

r1,11

r2,2

r2,11

10.50 0.95 7.31 40.24 1.33 12.07

29.30 1.80 20.81 110.04 11.79 34.75

110.70 42.42 179.19 317.63 192.54 168.50

0.19 6.39 18.31 24.93 1.79 10.32

1.52 0.12 0.75 1.45 0.05 0.78


in internal recirculation and metal flow, respectively. Moreover, we reach the same conclusion if the parameter rj,i,f is calculated for the rest of the weak criteria identified in step 5 and all the actions proposed by the system: A1 undergoes a smaller variation in overall process performance while simultaneously improving all the criteria identified (automatically) as “weak”. Hence, this indicates that the objective function for option A1 is less sensitive than for option A2. The higher sensitivity of A2 is mainly due to the fact that high phosphorus removal, one of the plant’s strong points, is directly correlated with high operating costs. For this reason, there is a large penalty attached to the objective function when metal flow is decreased and there is a consequent reduction in the degree of satisfaction of OBJ1 and OBJ4 (see Figure 12). Furthermore, it is important to note the plant’s inability to remove nitrogen. Since nitrogen and phosphorus are equally weighted, the high score of x2,12 compensates for the lack of accomplishment of x2,11 in OBJ4. This fact can be corroborated from the rules extracted in step 6.2 and summarized in Table 8, given that there is no possible action to improve criterion x2,11, i.e., the effluent nitrogen concentration is always above the legal limit. The low improvement in criterion x2,1 is caused by further phosphorus removal rather than by an improvement in denitrification capacity. According to these results, improvement to criteria x2,11 would require consideration of additional issues (e.g., an additional carbon source, upgrading or adding an anoxic zone). However, this would increase the value of both x2,2 and x2,3 and worsen the satisfaction of OBJ2 (a weak point identified in step 5 for A2), as a tradeoff for the improvement of x2,11. Step 7: Selection of the Best Option. From all the information generated during the evaluation of the first issue of the reaction section, we conclude that the best alternative is biological phosphorus removal. This implies the construction of additional anaerobic volume, but it would also result in a reduction in operating costs, an improvement in both nitrogen and phosphorus removal, and a more balanced accomplishment of European Directive 91/271/ECC. In addition, even though both options have a similar value after optimization, the improvement in the weak points identified in step 5 for option A1 supposes a lower penalty (see Table 9) in the objective function compared to A2, with a major increase in the satisfaction of the criteria. Finally, it is important to mention that during the evaluation of the tradeoff between the improvement of the criteria identified as weak points of the option and the loss of the overall process performance, a “look ahead” step is being performed. As a result of this, the inability of option A2 to achieve good levels of phosphorus removal without reducing operating costs and removing nitrogen (due to inefficient denitrification) is identified, making it necessary to consider more issues in the reaction section to remediate this inherent design problem. The ability to predict undesirable process design directions has important implications during the selection of the best alternative. The design process would continue through evaluation of the remaining issues for the reaction section (e.g., location of the anaerobic reactors), separation section (e.g., increase of the settling area), and, finally, the recirculation section (e.g., additional anoxic anaerobic recycling). Conclusions This paper has addressed the problem of critical decisions that arise during the conceptual design of activated sludge plants

when several design objectives (e.g., environmental, legal, economic, and technical) must be taken into account. It has contributed to the solution of this problem by proposing a systematic three-step procedure to support the management of the close interplay between, and the apparent ambiguity emerging from, the multicriteria evaluation of competing design options. The preliminary multiobjective optimization allows comparisons to be made between two or more options when each is close to the optimum design conditions. Thus, we propose deferring a numerical optimization until we have selected the most promising options and we are certain that we will proceed with the final design, i.e., when we attain a sufficient amount of accuracy to be able to address the next issue in the sequence of decisions, thereby allowing a more unbiased comparison. The characterization of the options enables an understanding of the design space, so that the designer is aware of the weak and strong points of the most promising options. The classification tree and subsequent extraction of rules provides a clear overview of the performance of the competing options. Hence, this evaluation both supports the designer in interpreting the influence of the weights of the design objectives in the final decision and facilitates data analysis. At the same time, the set of rules shows the preferred option for the widest range of situations. The analysis of the tradeoff shows the rate at which overall process performance changes with variations in the design variables (parameter rj,i,f). At the same time, the system alerts the designer to any negative implications in the event of their possible implementation. All this information has important implications in the selection of design options and provides the designer with valuable information for the reuse of the knowledge generated during the sensitivity analyses. Hence, otherwise hidden limitations in plant performance could suggest future desirable (or undesirable) design directions during the plant’s retrofit or revamping. There are other advantages in the extraction and maintenance of a record of design knowledge. On the one hand, it is possible to reduce the cognitive load on the designer and enhance his/ her understanding thanks to the automatic identification of adverse effects in the event of the implementation of actions in respect of overall process performance. On the other hand, a wider scope of decision making is made possible by decreasing the number of iterations and enabling the concurrent manipulation of multiple criteria (more than a dozen in the case study presented). The methodology allows the geographical and temporal reuse of knowledge that would otherwise be tacit and of potential use to a single designer only. The procedure has been applied in activated sludge plants but could be adapted for other types of (bio)chemical process that environmental/ chemical engineers have to address. Acknowledgment The authors gratefully acknowledge financial support from the Spanish “Ministerio de Ciencia y Tecnologıá” (DPI200615707-C02-01). The authors also wish to thank Krist V. Gernaey (BioProcess Engineering Group, Technical University of Denmark) for providing the ASM2d benchmark MatLab-Simulink code to carry out the simulations. Finally, the authors are very grateful to the three anonymous reviewers who have clearly contributed to improving the final manuscript in terms of both quality and comprehensibility.

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Nomenclature Aj ) design option, total number of design options m for a given issue I AE ) aeration energy consumption rate (kWh‚d-1)18 ASM2d ) activated sludge model no. 2d BOD ) biochemical oxygen demand concentration C ) carbon CAPDET ) computer assisted procedure for design and evaluation of wastewater treatment systems20 COD ) chemical oxygen demand DO ) dissolved oxygen EQ ) effluent quality index (kgpollution‚d-1)19 II ) issue to be solved, total number of issues Z IQ ) influent quality index (kgpollution‚d-1)19 ISE ) integral squared error ((gN‚m3)2‚d-1)23 Kp ) proportional gain KLa ) oxygen transfer coefficient (d-1) MCDA ) multicriteria decision analysis N ) nitrogen NO ) nitrate OBJk ) design objective, total number of design objectives P P ) phosphorus PE ) pumping energy consumption rate (kWh‚d-1)18 Pslge ) sludge production rate (kgTSS‚d-1)18 Qintr ) internal recycle flow rate from AER3 to ANOX1 (m3‚d-1) rj,i,f ) loss of objective function for a given option j, moving the variable f, trying to improve the criterion i S ) sensitivity to a given perturbation21,22 Ti ) integral time constant TIV ) time in violation TN ) total nitrogen TP ) total phosphorus TSS ) total suspended solids TKN ) total Kjeldahl nitrogen Vi(Xi) ) value function, total number of value functions W V(xj,i) ) normalized criterion i for a given option j Vj,f ) design variable for a given option j, total number of variables for this option is Y wk ) weight, total number of weights X WWTP ) wastewater treatment plant Xi ) criterion, total number of criteria W, set of criteria for a given issue n xj,i ) quantified criterion i for a given option j Literature Cited (1) Seider, W. D.; Seader, J. D.; Lewin, D. R. Process Design Principles: Synthesis, Analysis and EValuation, 2nd ed.; John Wiley & Sons, Inc.: New York, 2004. (2) Uerdingen, E.; Fischer, U.; Gani, R.; Hungerbu¨hler, K. A New Retrofit Design Methodology for Identifying, Developing, and Evaluating Retrofit Projects for Cost-Efficiency Improvements in Continuous Chemical Processes. Ind. Eng. Chem. Res. 2005, 44 (6), 1842. (3) Rapoport, H. R.; Lavie, R.; Kehat, E. Retrofit Design of New Units into an Existing Plant: Case Study: Adding new Units to an Aromatics Plant. Comput. Chem. Eng. 1994, 18, 743. (4) Chen, H.; Shonnard, D. R. Systematic Framework for Environmentally Conscious Chemical Process Design: Early and Detailed Design Stages. Ind. Eng. Chem. Res. 2004, 43, 535. (5) Shinnar, R. A Systematic Methodology for the Design Development and Scale-up of Complex Chemical Processes. The role of Control and Concurrent Design. Ind. Eng. Chem. Res. 2004, 43, 246.

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ReceiVed for reView November 7, 2006 ReVised manuscript receiVed May 16, 2007 Accepted May 22, 2007 IE061426A

Systematic Procedure to Handle Critical Decisions ... - ACS Publications

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