Ind. Eng. Chem. Res. 2009, 48, 2605–2615
2605
Bifurcation Behavior of a Large Scale Waste Water Treatment Plant Antonio Flores-Tlacuahuac,* Margarita Herna´ndez Esparza, and Rodrigo Lo´pez-Negrete de la Fuente Departamento de Ingenierı´a y Ciencias Quı´micas, UniVersidad Iberoamericana, Prolongacio´n Paseo de la Reforma 880, Me´xico D.F., 01210, Me´xico
Because water has become a major natural resource, it is important to address several important issues that may lead to its better use and conservation. From a process system engineering point of view, the approaches that could be taken for improving the quality of treated domestic and industrial water streams are related to the modeling, simulation, optimization, and control of waste water treatment plants (WWTPs). Although there have been important contributions from the modeling, simulation, and control research communities, practically there is not reported research work addressing the nonlinear analysis, and its control or operability implications, on large scale WWTPs. Such studies could provide some indications about potential operability problems and suggest potential ways of avoiding them. Because in the traditional biological treatment of polluted streams there are embedded complex interactions due to the highly nonlinear nature of the kinetic relationships and because the traditional activated sludge process involves process recycle streams, strong interactions among the main processing variables should be expected. In this paper, we address the bifurcation analysis of an industrial scale WWTP with the aim of learning how a typical WWTP process features complex interactions mainly among potential controlled, manipulated, and disturbance variables. It was found that nonlinear behavior was only present when considering disturbances in the main flow rate of the polluted stream. The rest of analyzed bifurcation variables led to rather smooth behavior. This behavior seems to be an indication that WWTP plants could be properly controlled with simple proportional, integral, and derivative (PID) controllers making probably unnecessary the use of advanced control systems. The model used in this work reflects operating conditions closely resembling those found in a real WWTP. 1. Introduction Waste water treatment plants (WWTPs) are widely used systems for pollutant removal from domestic and industrial effluents. Although the mathematical modeling of industrial scale WWTP has been addressed, there are no reported studies concerning the nonlinear behavior embedded into such complex systems. However, the presence of nonlinear behavior in biological reactors has been assessed.1 The nonlinearities present in WWTP models stem from several sources. First, complex reactions in living organisms usually take place in biological reactors used for wastewater treatment. Even when most of the reported WWTP models assume constant temperature, some nonlinearities emerge as bilinearities. Another potential source of nonlinear behavior stems from process design. To improve process operation, most WWTPs feature mass recycle streams. Recycle plants are very well-known examples of complex systems leading to operational difficulties. It has been reported that recycle streams are responsible for nonlinear behavior such as nonminimum phase behavior, input multiplicities, etc. Moreover, recycle streams, being an example of positive feedback systems, tend to lead to unstable operation. Nonlinearities can also be introduced even by the simplest closedloop control systems.2 In fact, the integral part of PI controllers can embed input multiplicities into plant behavior.3,2 Nonlinear analysis tools can be used for addressing optimal process design4 or for analyzing potential operability problems.5 For existing processes, nonlinear analysis provides information about multiple steady states, highly sensitivity operating regions, and oscillatory and chaotic behavior patterns. The information gathered during nonlinear analysis can be used to propose ways * To whom correspondence should be addressed. E-mail:
[email protected]. Phone/fax: +52(55)59504074. Website: http:// 200.13.98.241/∼antonio.
of improving process operability or to learn how process design changes can modify patterns of nonlinear behavior.6 There is a recent work7 dealing with the nonlinear behavior analysis of a small scale WWTP. In ref 7, the authors used simplified models to allow an analytical treatment of the bifurcation phenomena; they report interesting nonlinear behavior. However, it is difficult to conclude if such nonlinearities stem as product of model simplifications or if they can really occur in a real WWTP. In fact, using a more detailed model and industrial processing conditions typical of WWTP, we could not find most of the strange nonlinear behavior reported in ref 7. In this work our aim is to carry out the bifurcation analysis of a WWTP to detect the kind and source of nonlinear behavior embedded into a particular type of such plants. To carry out this analysis, we have used the mathematical model of an industrial scale WWTP previously formulated as a benchmark problem to test simulation, optimization, and control strategies in WWTP systems.8 Because the model reflects operating conditions closely resembling those found in a real WWTP, the nonlinearities detected in this work should probably be observed in a real plant environment. 2. Plant Description Domestic or urban wastewater pollution control is mostly carried out using the activated sludge process. The process is based on the metabolic characteristics of microorganisms that form the activated sludge for pollutant degradation. It consists in mixing a waste polluted water stream with a solid biomass formed by the microorganisms responsible of the biological transformation of the pollutants. Initially used for removal of organic matter and further applied to nitrification of organic and ammonia nitrogen sources, the activated sludge process has been extended and combined with other processes for the
10.1021/ie8003072 CCC: $40.75 2009 American Chemical Society Published on Web 01/29/2009
2606 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
Figure 1. Flowsheet of the wastewater treatment plant. Table 1. Parameter Values for the Anoxic and Aerobic Reactors under Normal Operating Conditions symbol
value
description
units
YA YH fp iXB iXP KS KOH KNO bA bH ng nh KH KX KNH KOA Ka µA µH Qf Qwr Qsr Qair 3 Qair 4 Qair 5 S Osat V1 V2 V3 V4 V5
0.24 0.67 0.08 0.08 0.06 10 0.2 0.5 0.002083 0.0125 0.8 0.8 0.125 0.1 1 0.4 0.002083 0.02083 0.1667 768.6 2305.8 768.6 2 2 0.7 8.637 1000 1000 1333 1333 1333
autotrophic yield heterotrophic yield fraction of biomass yielding particulate products mass N/mass COD in biomass mass N/mass COD in products from biomass half-saturation coefficient for heterotrophs oxygen half-saturation coefficient for heterotrophs nitrate half-saturation coefficient for denitrifying H autotrophic decay rate heterotrophic decay rate correction factor for anoxic growth of heterotrophs correction factor for anoxic hydrolysis max specific hydrolysis rate half-saturation coefficient for hydrolysis ammonia half-saturation coefficient for autotrophs oxygen half-saturation coefficient for autotrophs ammonification rate autotrophic max spec growth rate heterotrophic max spec growth rate flow rate of the water polluted stream flow rate of water recycle stream flow rate of sludge recycle stream air flow rate to the first aerobic reactor air flow rate to the second aerobic reactor air flow rate to the third aerobic reactor oxygen saturation concentration first anoxic reactor volume second anoxic reactor volume first aerobic reactor volume second aerobic reactor volume third aerobic reactor volume
g cell COD formed/g N oxidized g cell COD formed/g COD oxidized g N/(g COD) in biomass g N/(g COD) in endogenous mass g COD/m3 g O2/m3 g NO3-N/m3 1/h 1/h g biod. COD/(g COD · h) g biod. COD/(g COD) g NH3-N/m3 g O2/m3 m3/(g COD · h)) 1/h 1/h m3/h m3/h m3/h m3/h m3/h m3/h mg/L m3 m3 m3 m3 m3
Table 2. Settler Parameters symbol
value
description
V A h Ns Nf Qw Vo Vop rh rp XT fNS f1 f2 f3
6000 1500 0.4 10 6 16.04 19.75 10.4167 0.000576 0.00286 3000 0.00228 0.75 0.75 0.891
settler volume area length of each layer number of layers feed layer (numbered from top to bottom) flow rate of sludge purge stream maximum theoretical settling velocity maximum practical settling velocity settling parameter associated with the hindered settling component settling parameter associated with the low concentration threshold suspended solids concentration nonsettleable fraction of the influent suspended solids conversion factor of particulate matter to COD conversion factor of suspended solids to COD conversion factor of biomass solids (heterotrophic and autotrophic) to COD
removal of biological nutrients, such as nitrogen in the form of nitrate and ammonium, commonly present in domestic waste discharges. This has been achieved combining the aerobic with an anoxic process that carries out the denitrification process. As shown in the WWTP flowsheet depicted in Figure 1, the selected system is a preanoxic integrated with an activated sludge process or modified Ludzak-Ettinger process. This is one of the most simple of the combined nitrification-denitrification processes. The wastewater inlet stream is initially treated in the anoxic reactor whose aim, as stated before, is to transform nitrate compounds into nitrogen gas. To carry out this task, the process
units m3 m2 m m3/h m/h m/h m3/g m3/g g/m3 g ss/g COD g ss/g COD
features heterotrophic bacteria operating under oxygen free or anoxic process operating environments. It is based on the benefit from using the incoming organic matter of the raw wastewater as the readily biodegradable carbon source in the anoxic reactors. This eliminates or reduces the amount of external additional carbon source (generally methanol) needed for this stage in a postanoxic treatment. To improve the quality of the effluent and to maximize the use of sludge flocs, two recycle streams are fed back to the anoxic reactor: one from the last aerobic stage and the other one from the bottom of the settler. The transformation of the nitrogen sources
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2607
dZji Q f Qwr wr Qsr sr ) (Zi - Zji) + (Zi - Zji) + (Z - Zji) + Rji, dt Vj Vj Vj i ∀ i, j ) 1 (1) where Z stands for the system states, Q is the volumetric flow rate, V is the reactor volume, R is the reaction rate. The superscripts f, wr, and sr represent the polluted water feed stream, intermediate water recycle, and sludge recycle streams, respectively; j is the reactor number, and i are the system components. For the rest of the biological reactors, the material balances are given as follows, f
dZji (Qf + Qwr + Qsr) ) (Zj-1,i - Zji) + Rji, ∀ i, j ) 2, ... , 5 dt Vj (2) For the three aerobic reactors (j ) 3, 4, 5), the dissolved oxygen mass balances are as follows: dZj,SO dt
Figure 2. Settler divided into a series of layers. Inside each layer, water properties remain constant.
to nitrate and removal of ammonium compounds takes place in a sequence of two series of connected biological continuous reactors which operate under aerobic conditions and use autotrophic bacteria. These reactors are also responsible for the degradation of organic matter or carbonaceous material. Since the biological wastewater treatment process ends at the third aerobic reactor, as mentioned above, a portion of the mixed liquor exiting is recycled to the anoxic zone as a source of nitrate for the heterotrophic bacteria and where the nitrate concentration is reduced, in order to meet treated water quality specifications. The aerobic stage also allows the liberation of the nitrogen gas formed in the previous stage and improves the settleability of the sludge. The portion of the biologically treated water effluent that is not recycled is sent to a settler whose aim is to perform the physical separation between the treated water and the biological sludge flocs. The concentrated sludge embedded with bacteria is recycled to improve both process operation and economics. As a result, the presence of recycle streams in the WWTP flowsheet creates a highly mass integrated complex process that intuitively should feature nonlinear behavior patterns.
)
(Qf + Qwr + Qsr) (Zj-1,SO - Zj,SO) + Rj,SO + Vj KLA,j(ZSOsat - Zj,SO), j ) 3, ... , 5 (3)
where KLA is the mass transfer coefficient, the superscript sat stands for saturation concentration. KLA expressions were correlated against the volumetric air flow rate Qair j for the aerobic reactors and are given as follows: KLA,j ) 10(1 - e-1.2Qj ), j ) 3, 4 air
KLA,j ) 10(1 - e
), j ) 5
(5)
The kinetic rate expressions are the same regardless of the type of reactor, but, of course, they reflect the processing conditions at each reactor:
{ ( )[
Rj,XBH ) µH
SSj
SOj
Ks + SSj
KOH + SOj
(
ng
{(
Rj,XBA ) µA
+
KOH KOH + SOj
SNHj KNH + SNHj
)(
Rj,XS ) (1 - fp)(bHXBHj + bAXBAj) -
)(
(
nH
KNO + SNOj
KOA + SOj XSj XBHj
KX +
XSj
{ )(
KOH KOH + SOj
Rj,XND ) (iXB - fpiXP)(bHXBHj + bAXBAj) -
SOj
(
+ nH
- bA XBAj
SOj KOH + SOj
KOH KOH + SOj
+
SNOj KNO + SNOj
)}
XBHj XSj
( )( )( ( )(
XBHj
)(
SNOj KNO + SNOj
)
SSj SOj 1 - YH X YH Ks + SSj KOH + SOj BHj
µA
XBHj (8)
×
)}
Rj,XP ) fp(bHXBHj + bAXBAj)
Rj,SO ) -µH
(7)
XNDj
KX +
KOH + SOj
-bH XBHj (6)
XBHj
Kh
{
)] } ) }
SNOj
SOj
Kh
3. Mathematical Model The mathematical model used in this work to take care of the dynamic behavior of the anoxic and aerobic reactors corresponds to the first version of the activated sludge model (ASM1) proposed by the International Association of Water Quality (IAWQ).9 The model is a deterministic one and consists of a system of ordinary differential equations whose numerical solution should not present difficulties even in the presence of stiffness problems. 3.1. Biological Reactors. The wastewater treatment plant comprises a set of two anoxic reactors, three aerobic reactors, and a settler connected as displayed in Figure 1. It has been assumed that the reactors can be modeled as isothermal continuous stirred tank reactors. No reactions are considered to take place in the settler where essentially only a physical separation is carried out. The material balances for the first anoxic reactor take a different form since it considers the contribution of the water and sludge recycled streams:
(4)
-0.55Qjair
)(
XBHj (9)
(10)
)
SNHj SOj 4.57 - YA X (11) YA KNH + SNHj KOA + SOj BAj
2608 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
{ ( ) [( ( )] }
Rj,SNH ) -iXBµH SNOj
SSj
SOj
Ks + SSj
KOH + SOj
+ KaSNDj XBHj - µA iXB +
KNO + SNOj
{
Kh
SOj
XNDj XBHj
KX +
nh
(
(
XSj XBHj
[(
SOj KOH + SOj
)
XBAj (12)
+
)(
SNOj KOH KOH + SOj KNO + SNOj
)(
)(
×
SNHj 1 × YA KNH + SNHj KOA + SOj
Rj,SND ) -KaSNDj +
)]
)
}
XBHj (13)
SSj 1 - YH KOH × 2.86YH Ks + SSj KOH + SOj SNOj SNHj SOj µA XBHj + X (14) KNO + SNOj YA KNH + SNHj KOA + SOj BAj
Rj,SNO ) -µhng
(
(
) ( ) )( ) ( ) KOH KOH + SOj
+ ng
{
)
( ) [(
SSj µH Rj,SS ) YH Ks + SSj
(
SNOj KNO + SNOj
(
SOj KOH + SOj
)]
Kh +
(
nh
{
)
) (
XBHj
)
XSj XBHj
[(
KOH KOH + SOj
SOj KOH + SOj
)(
)
(
µA
• Thickening section: j < Nf dXj Vdn(Xj+1 - Xj) + Fj+1 - Fj ) dt h (Qf + Qsr)Xf - (Vup + Vdn)Xj - Fj + Fj+1 A ) dt h
dXNf
(17)
(18)
• Clarification section: j > Nf, j < Ns +
SNOj KNO + SNOj
)]
}
dXj Vup(Xj-1 - Xj) + Fj+1 - Fj ) dt h
(19)
• Top stage: j ) Ns dXj Vup(Xj-1 - Xj) - Fj ) dt h
XBHj (15)
( )[ ( ) )( )( )] } ( )( )( )
SSj SOj iXB KaSND + µH + 14 Ks + SSj 14 KOH + SOj 1 - YH SNOj iXB YH KOH ng XBHj 40.04 14 KOH + SOj KNO + SNOj
Rj,SALK )
Material Balance.
• Feed stage: j ) Nf
KOH + ng × KOH + SOj
XSj
KX +
)(
the clarification zone where the intended physical separation mostly takes place. The lower settler operating zone is the thickening zone used for compacting or concentrating the activated sludge for recycling back to the anoxic reactors. From a modeling point of view, it is clear that the settler properties change along the vertical distance and time. This suggests that taking into account dynamic longitudinal properties variation should lead to a distributed properties model described in terms of a system of partial differential equations. However, to simplify the numerical solution of the dynamic distributed settler model, it is customary to assume that the settler can be divided into a set of longitudinal segments and that, inside each element (or layer), the settler physical properties remain constant. This is equivalent to perform a naive discretization of the longitudinal settler component, therefore leading to a simplified model version, in terms of a system of ordinary differential equations. Hence, mass conservation equations are stated around each layer. This settler modeling approach closely resembles that used for the dynamic modeling of staged distillation columns. The model described in this section, and parameter values shown in Table 2, were taken from ref 10.
SNHj SOj iXB 1 + X (16) 14 7YA KNH + SNHj KOA + SOj BAj
In Table 1, typical parameter values for the operation of the anoxic and aerobic reactors are shown. The depicted values were taken from ref 9. 3.2. Settler. As stated before, the aim of the settler is to carry out a physical separation between the treated water and the sludge flocs. This is mostly done by gravity settling. As displayed in Figure 2, the settler is commonly divided into two operating zones separated by the place where the treated water stream enters to the settler. The upper zone is called
(20)
where, Vdn )
Qsr + Qw A
(21)
Qf - Qw A Flow of Solids Due to Gravity Setting. Vup )
(22)
fs fs + XBA ) Xin ) f1(XSfs + XPfs) + f2(XBH
(23)
Xmin ) fnsXin
(24)
• j ) 2,..., Ns-1
{
min(Vs1Xj-1, Vs2Xj) j e Nf j > Nf and Fj ) Vs2Xj min(Vs1Xj-1, Vs2Xj) j > Nf and
Xj-1 e XT Xj-1 > XT
(25)
where Vs1 ) max{0, min[Vop, Voe-rh(Xj-1-Xmin) - Voe-rp(Xj-1-Xmin)]} (26) Vs2 ) max{0, min[Vop, Voe-rh(Xj-Xmin) - Voe-rp(Xj-Xmin)]} (27)
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2609
Particle Concentration at the Treated Water Stream. e ) XBH
e XBA )
XSe )
fs XNs f2 f3XBH
Xin fs XNs f2 f3XBA
Xin f1 f3XSfsXNs Xin
(28)
(29)
(30)
fs XNs f2 f3XND e XND ) Xin
(31)
f1 f3XPfsXNs e XP ) Xin
(32)
sr XBH )
fs f2 f3XBH X1 Xin
(33)
sr XBA )
fs f2 f3XBA X1 Xin
(34)
f1 f3XSfsX1 Xin
(35)
fs f2 f3XND X1 Xin
(36)
f1 f3XPfsX1 Xin
(37)
XSsr ) sr XND )
XPsr ) Soluble Components.
dZi (Qf + Qsr)(Zfsi - Zi) ) , i ) SO, SNH, SND, SNO, SS, SALK dt V (38) In Table 2, the physical and hydraulic parameters for the settler are shown. 4. Bifurcation Analysis In this section, we perform a bifurcation analysis to understand the way the WWTP behavior changes according to a set of variables that can be considered as manipulated, disturbances, or design variables. Hopefully, this analysis will allow us to identify potential operability problems that could lead to plant operation improvement. To carry out the nonlinear analysis we selected a typical polluted domestic wastewater stream whose composition information is shown in Table 3; those values were taken from ref 11. To test the quality of the effluent, the following performance indexes have been proposed.8 e e TSS ) 0.75(XPe + XSe + XBA + XBH )
(39)
e e + XBA COD ) SSe + XSe + XPe + XBH
(40)
e e + XBA )) BOD ) 0.25(SSe + XSe + (1 - fp)(XBH
(41)
e e e e e + SND + XND + ixb(XBH + XBA ) + ixpXPe (42) TKN ) SNH e NO ) SNO
(43)
Ntot ) TKN + NO
(44)
Table 3. Pollutant Concentration in the Example Domestic Waste Water Stream state XBH XBA XS XND XP SO SNH SND SNO SS SALK
description
value
heterotrophic biomass 20 autotrophic biomass 0 slowly biodegradable substrate particles 160 particulate organic nitrogen 18.28 particulate products arising from biomass decay 40 dissolved oxygen 0 ammonia nitrogen 12.5 soluble organic nitrogen 10.1 nitrate nitrogen 1 readily biodegradable substrate 64 alkalinity 7
units mg COD/L mg COD/L mg COD/L mg N/L mg COD/L mg COD/L mg N/L mg N/L mg N/L mg/L COD mmol/L
These performance indexes were followed as several operating conditions were varied, while maintaining the other parameters constant. The manipulated variables considered, the range of their variation, and the response of the performance indexes due to these variations are presented below. In the following plots, the solid continuous line stands for open-loop stable steady states, the dashed lines indicate open-loop unstable steady states, the empty circles represent the nominal operating conditions, and the empty diamonds denote Hopf bifurcation points. (a) Qf (Feed Flow): from 0 to 1500 m3/h. As shown in Figure 3, the WWTP response depicts strong steady state and dynamic nonlinear behavior patterns which can be attributed to the complex interactions among competing factors and plant design. Reaction kinetics, as shown in eqs 6-16, is a major source of nonlinear behavior. Since in a real operational scenario, sudden and wide variations of the pollutant streamflow rate can be expected, the results displayed in Figure 3 indicate that the WWTP could feature multiple steady states slightly below the nominal operating region. As indicated, multiple steady states are only obtained if Qf gets reduced below 600 m3/h. At approximately 310 m3/h, the WWTP steady-state behavior reaches a Hopf bifurcation point that clearly indicates that the plant might exhibit oscillatory response. At this point several unstable steady-state operating branches emerge, so the WWTP displays unstable operating regions. Of course openloop stability problems could be coped with using a proper control system. However, control systems might also introduce additional nonlinearities as has been reported by Koppel.3 Moreover, the aim of Figure 3 is to demonstrate that, under the plant design conditions, the addressed WWTP could easily get unstable when the pollutant flow rate decreases, a situation likely to occur during dry season operation of WWTPs. It should be noted that no stability and multiple steady-state behavior problems were detected for pollutant flow rates larger than the nominal one. (b) Qwr (Internal Water Recycle from the Last Aerobic Reactor to the First Anoxic Reactor): from 0 to 3000 m3/ h [Since It Is Common to Use in These Type of Systems Variations in Internal Recycle from 0 to 300% of Qf]. Most of these types of WWTPs feature a recycle stream consisting of a partially treated stream. In our case, the water recycle stream is fed back from the outlet of the last aerobic reactor to the first reactor of the biological reaction train. The aim of such a water recycle stream as stated before, is to provide the source of nitrate species necessary for the denitrification stage, using the incoming carbon source from the plant influent. From an operational point of view, the water recycle stream can be used as an additional degree of freedom to improve process control, meaning that it may be considered as an extra manipulated variable. Therefore, from a process control point of view, it turns out to be relevant to realize the way the water recycle stream influences the process response.
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Figure 3. (a) Total Kjeldahl nitrogen concentration (TKN). (b) Total suspended solids concentration (TSS). (c) Biodegradable organic matter concentration (BOD). (d) Chemical oxygen demand concentration (all organic matter present) (COD). (e) Soluble nitrate (and nitrite) concentration (NO). (f) Total nitrogen concentration. All of these quantities are expressed as milligrams per liter. The bifurcation parameter is volumetric flowrate of the feedstream [m3/h].
This behavior is depicted in Figure 4, that shows that a smooth behavior is always observed between the water recycle stream and the plant response. On one hand responses as those shown in Figure 4 indicate that process control should not be a difficult matter. However, disturbance rejection could be a hard task to achieve because large control actions are required to change the plant response. From this short discussion, we might conclude that the
internal water recycle stream probably should not be considered as relevant for quality control purposes as other variables. (c) Qsr (Sludge Recycle from the Bottom of the Settler to the First Anoxic Reactor): from 0 to 1500 m3/h [Since It Is Common to Use in These Types of Systems Recycle Ratios of Qsr/Qf of 0 to 100%]. To maintain the necessary biomass (heterotrophic and autotrophic) in the biological reactors,
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2611
Figure 4. (a) Total Kjeldahl nitrogen concentration (TKN). (b) Total suspended solids concentration (TSS). (c) Biodegradable organic matter concentration (BOD). (d) Chemical oxygen demand concentration (all organic matter present) (COD). (e) Soluble nitrate (and nitrite) concentration (NO). (f) Total nitrogen concentration. All of these quantities have been expressed as milligrams per liter. The bifurcation parameter is internal water recycle, Qint ) Qwr [m3/h].
a major part of the sludge obtained in the settler is recycled to the first anoxic reactor of the biological reaction train. However, from a process control point of view, the recycle sludge stream provides also an additional degree of freedom aiming to improve water quality during plant operation. Figure 5 displays the steady-state behavior between the recycle sludge stream and plant response. As shown, most of the water quality variables (with the exception of NO) display sensitivity with respect to the sludge stream. Again,
there is not a region that displays oscillatory behavior. This clearly indicates that quality control loops could use the sludge stream as a manipulated variable. Moreover, in the region that displays monotonic and smooth steady-state behavior, smooth closed-control behavior should be achieved. As noted in Figure 5, no multiplicity regions were observed. However, as stated previously, closed-loop control loops could outperform process behavior by introducing undesired nonlinear behavior.3,2
2612 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
Figure 5. (a) Total Kjeldahl nitrogen concentration (TKN). (b) Total suspended solids concentration (TSS). (c) Biodegradable organic matter concentration (BOD). (d) Chemical oxygen demand concentration (all organic matter present) (COD). (e) Soluble nitrate (and nitrite) concentration (NO). (f) Total nitrogen concentration. All of these quantities are expressed as milligrams per liter. The bifurcation parameter is sludge recycle, Qsl [m3/h].
(d) Air Flow in the First and Third Aerobic Reactors: from a Value of 0 to 10 m3/h. Controlling the right amount of oxygen concentration turns out to be crucial to ensure aerobic conditions and good pollutant removal in the aerobic reaction train leading to good water quality control. It is important that the air flow maintains the needed aerobic conditions. Lower air flows will have an adverse effect on the effluent water quality. Figures 6 and 7 display the effluent water quality response for air flow rate
variations in the first and third aerobic reactors (results for variations in the second aerobic reactor are not shown since they are similar to responses obtained from the first aerobic reactor). Practically, air flow rate variations in any aerobic reactor lead to the same final steady state. In this WWTP, there is a limit in the response of the first two biological aerobic reactors that is independent of the increase in air flow. From the figures it is obvious that 2 m3/h is the limit for the aerobic condition and response in the reactors. In
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2613
Figure 6. (a) Total Kjeldahl nitrogen concentration (TKN). (b) Total suspended solids concentration (TSS). (c) Biodegradable organic matter concentration (BOD). (d) Chemical oxygen demand concentration (all organic matter present) (COD). (e) Soluble nitrate (and nitrite) concentration (NO). (f) Total nitrogen concentration. All of these quantities are expressed as milligrams per liter. The bifurcation parameter is air flow rate in the third reactor [m3/h].
the case of the last aerobic reactor, although a slightly better response could be achieved at higher air rates, the level of oxygen in the effluent has to be limited to the minimum, because the internal water recycle that flows from this reactor to the first anoxic reactor, would affect its efficiency or behavior. However, if smaller air flow rate variations take place in the last aerobic reactor no propagation effect will occur leading to a smaller impact on water
quality response. Figure 6 also show that air flow rate in the first two aerobic reactors should not be directly used for water quality control purposes due to the small process sensitivity among these variables. However, the last one shows a stronger sensitivity than the previous ones and could be considered in the quality control scheme, since it directly impacts the response of the first anoxic reactor.
2614 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
Figure 7. (a) Total Kjeldahl nitrogen concentration (TKN). (b) Total suspended solids concentration (TSS). (c) Biodegradable organic matter concentration (BOD). (d) Chemical oxygen demand concentration (all organic matter present) (COD). (e) Soluble nitrate (and nitrite) concentration (NO). (f) Total nitrogen concentration. All of these quantities are expressed as milligrams per liter. The bifurcation parameter is air flow rate in the fifth reactor [m3/h].
5. Conclusions WWTPs are complex systems with embedded highly nonlinear behavior. The nonlinear behavior stems from the complex mass and kinetic interactions that take place inside the anoxic and aerobic biological reactors, therefore leading to multiple steady states and high parametric sensitivity operating regions. In this work we have carried out a bifurcation analysis aimed to detect potential
operability problems and to propose operation changes leading to improved plant operation such to achieve water quality specifications. To improve plant operation to meet water quality specifications, most WWTP use recycle streams. However, this design practice might exacerbate nonlinearities. However, in this work, we found that nonlinear behavior is absent from
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2615
the addressed system when both recycle streams are changed around the nominal operating point. On the other hand, nonlinear behavior was observed when disturbances in the pollutant volumetric feed flow rate stream hit the system. It is clear that such sources of disturbances could be removed or smoothed by feeding the treatment plant from buffer tanks. Nonlinearities were also absent when variations in the volumetric flow rate of the recycle streams and in the air feed stream were carried out. This result might have relevance from a control point of view since these variables could be used for closed-loop control purposes as manipulated variables. Therefore, smooth variations in these variables would lead also to similar smooth responses in the controlled variables reducing the control effort and the complexity in the design of the control system. Finally, bifurcation analysis was also done changing the composition of the inlet polluted stream. However, in this situation, nonlinearities were not observed as this is the reason why they are not discussed in the present work. Up to our best knowledge, no studies have been published on the bifurcation analysis of large scale WWTPs. Because of the major role that water plays in modern societies, it becomes relevant to address all aspects related to its conservation. In this work we use bifurcation analysis tools to learn how nonlinearities embedded in the traditional activated sludge process for the treatment of polluted streams could lead to potential operability problems. As discussed in the present work the only serious nonlinear behavior was observed when the main flow rate of the polluted stream was considered as a potential disturbance. Therefore, our results indicate that the addressed WWTP could be properly controlled by proportional, integral, and derivative (PID) controllers making the use of advanced control systems unnecessary. Even when normally PID controllers are the first option to consider for the closed-loop control of systems, it is important to have an indication that such control
systems could be enough for the proper control of WWTPs around a desired steady-state operating region. Literature Cited (1) Agrawal, P.; Lee, C.; Lim, H. C.; Ramkrishna, D. Theoretical Investigations of Dynamic Behavior of Isothermal Continuous Stirred Tank Biological Reactors. Chem. Eng. Sci. 1982, 37 (3), 453–462. (2) Chang, H.; Chen., L. Bifurcation Characteristics of Nonlinear Systems under Conventional PID Control. Chem. Eng. Sci. 1984, 39, 1127– 1142. (3) Koppel, L. B. Input Multiplicities in Nonlinear Multivariable Control Systems. AIChE J. 1982, 28 (6), 935–945. (4) Marquardt W.; Monnigmann, M. Constructive Nonlinear Dynamics in Process System Engineering. Proceedings of the European Symposium on Computer Aided Process Engineering, Escape-14, Lisbon, Portugal, May 16-19, 2004; pp 99-116. (5) Seider, W.; Brengel, D.; Provost, A.; Widagdo, S. Nonlinear Analysis in Process Design. Why Overdesign To Avoid Complex Nonlinearities? Ind. Eng. Chem. Res. 1990, 29, 805. (6) Lemoine-Nava, R.; Flores-Tlacuahac, A.; Saldı´var-Guerra, E. Nonlinear Bifurcation Analysis of the Living Nitroxide-Mediated Radical Polymerization of Styrene in a CSTR. Chem. Eng. Sci. 2006, 61 (2), 370– 387. (7) Vasudeva Kumar, M.; Sree Rama Raju, V.; Pushpavanam, S.; Kienle, A. Effect of the Minimum Flux Condition in the Settler on the Nonlinear Behavior of the Activated Sludge Process. Ind. Eng. Chem. Res. 2006, 45, 5596–6006. (8) Corp, J. B. The COST Simulation Benchmark. http://www.ensic. inpl-nancy.fr/COSTWWTP/Pdf/Simulator_manual.pdf. (9) Henze, M.; Grady, C.; Gujer, W.; Matsuo, T. Activated Sludge Model No. 1. IAWQ. Scientific and Technical Report No. 1; London, 1987. (10) Takacs, I.; Patry, G. G.; Nolasco, D. A Dynamic Model of the Clarification-Thickening Process. Water Res. 1991, 25 (10), 1263–1271. (11) http://www.ensic.inpl-nancy.fr/COSTWWTP (accesed Sep 2008).
ReceiVed for reView February 22, 2008 ReVised manuscript receiVed September 4, 2008 Accepted December 9, 2008 IE8003072
