simulation study of anaerobic digestion control

Simulation Study of Anaerobic Digestion Control

Alberto Dalla Torre and Gregory Stephanopoulos Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91 125

Accepted for publication August 79, 7985

A mixed culture anaerobic digestion model developed previously was applied to the evaluation of several digester control strategies. It was found that pH control by base addition or flow rate manipulation is inadequate. Based on an analysis of digester dynamics, a new controi of the total suspended solids concentration at the feed was proposed through the manipulation of the underflow flow rate of the preceeding sedimentation unit. This control was tested in a variety of simulated runs and proved very effective in eliminating most of the usual causes of digester failure.

INTRODUCTION

During anaerobic digestion organic solids are hy- drolyzed and biologically transformed into volatile organic acids which in turn are converted to gas, mainly methane and carbon dioxide, in subsequent steps. Al- though biomass is also formed during the process, there is a substantial volatile solids reduction and a subsequent organic matter stabilization due to the methane produced in the absence of oxygen. Figure 1 is a very simplified illustration of the various steps of anaerobic digestion.

Low costs, relevant solids reduction and useful end products (methane and solids that can sometimes be used as soil conditioners) make anaerobic digestion a useful process for treating civil as well as industrial and agricultural wastes. However, various operational difficulties, such as low methane production and thus low stabilization of organic matter and frequent process failures (no methane production and organic acids accumulation), have been encountered in the operation of these systems. For this reason an increasing interest in the stability and control strategies for anaerobic digesters has recently developed.

Experimental studies with anaerobic digesters are difficult to perform and very time consuming to carry out, for residence times of the order of ten days are quite typical in the operation of the systems. There- fore, mathematical models and simulation studies are

particularly attractive for the investigation of the dynamic features of digesters.

The first dynamic model of anaerobic digestion, due to Graef and Andrews,'*= consisted of one species (methane formers) and one substrate (acetic acid). This model was used in the evaluation of several control strategies. Thus, the pH control through the addition of a basic solution, gas composition control by sludge recycle and pH control by carbon-dioxide-free gas recycle were investigated. In addition to these controls, Collins and Gilliland, also examined the possibility of pH control by sludge recycle and by feed flow rate reduction. Both feedback and feedforward controllers were investigated and a digital adaptive flow rate controller based on the digester model was finally proposed. However, this model did not account for the presence of several types of microorganisms in the digesting sludge with distinct functions in the overall digestion process. For this reason, delays and other dynamic features resulting from the ensuing mixed culture interactions were absent from the model and the potential cause-effect relationships were inadequately represented.

Lately, multiple species, mixed culture type models have been propo~ed.~J One such model5 was shown to be quite accurate in predicting observed steady state and dynamic features of anaerobic digesters. Distinc- tive features of this model are that 1) all basic steps of anaerobic digestion (hydrolysis-acidogenesis-methanogenesis) are accounted for; 2) commensal relationships between acid formers (lumped into a single species B , ) and methane formers are identified and basic properties of commensalism considered in evaluating the digester dynamics; and 3 ) three distinct groups of methanogenic bacteria (B2, B,, and B4) are considered, each acting on a different substrate (acetic, propionic, and butyric acid, respectively). The model is based on rate expressions appearing in the literature, material balances and ionic equilibria equations. Perfect mixing and constant temperature are assumed. Equations, pa-

Biotechnology and Bioengineering, Vol. XXVIII, Pp. 1138-1 153 (1986) 0 1986 John Wiley & Sons, Inc. CCC 0006-35921861081 138-16$04.00

Suspended Organic Matter

(carbohydrates, 1 ipids. nitrogenous material)

Enzymatic Hydrolysis

I Solubilized Organic Matter

I 1 I

Acidogenic Bacteria

Volatile Organic Acids (C,-C,)

Methanogenic Bacteria

Figure 1. Basic anaerobic digestion steps.

rameter values and an extensive discussion have been already r e p ~ r t e d . ~ The use of the model in the evaluation of startup procedures has been previously discussed.

Given the reliability of the model in predicting digester dynamics and the various difficulties associated with the experimental study of digester control, the developed model was employed for the examination of ex- isting, proposed, and new control strategies. Results of these studies are presented in this publication. The main limitation was the assumption of constant temperature and perfect mixing. The one species-one substrate model was modified by Buhr and Andrews6 to include temperature dependence for digestion in the thermophilic range. Temperature dependences were not included in the model employed here for they further complicate the system and they cannot be justified on the basis of available information about the type of functions applicable and values of the parameters in- volved. Some mixing effects will be considered. Grit and scum accumulation can be simulated with lower available digester volumes or lower residence times. Inadequate mixing also imposes some upper limits on the solids density that can be fed into the digester.

In the following sections, the most frequent causes of digester failure are reviewed and the results of a digester stability study presented. In the sequel, several control strategies are analyzed and some useful conclusions on the appropriate control policies are presented.

ANALYSIS OF DIGESTER STABILITY AND DYNAMICS

In order to put the discussion on digester stability and dynamics in perspective, the various causes of digester failure should be reviewed. This will allow a more direct investigation later with the use of the available mixed culture model.

Causes of Digester Failure

Difficulties with the operation of digesters and process failures were observed in a pilot plant by Torpey7 and in the laboratory by Andrews and Pearson,* Law- rence and McCarty? Hurst and Hushley,’O Pohland and Ghosh,” and Cox.’* After a successful startup, the systems were quite stable and rather large perturbations from normal operating conditions were required to bring about serious digester upsets. However, once those upsets get in, they were difficult to control and frequently led to system failure. Another observation was that usual process indicators such as pH, gas composition, and volatile acids concentrations remained at a normal range until failure was incipient and did not give any kind of early warning of the coming disturbance. Similar features were exhibited by the model and they point to the possible inadequacy of process feedback controllers for effective control. Feedfor- ward action is possibly more appropriate which, however, requires for successful implementation either accurate quantitative model predictions or experimental determination of a transfer function for small perturbations.

The most common cause of digester failure is the imbalance between production and consumption rates of volatile acids. These acids are the substrate for methanogenic bacteria, and are also inhibitory in large concentrations. When such concentrations are in the inhibitory range, a substrate increase causes a decrease in methanogenic bacteria growth rate which in turn decreases acids consumption rate and increases the concentration of acids. This unstable situation corresponds to operation on the descending side of the specific growth rate curve with a negative slope.

The above production-consumption imbalance can be caused by several factors: poor mixing, low residence time, high inlet solids concentration, toxic substances, or temperature shocks.

Mixing is accomplished in a number of ways: frequent or continuous feeding, circulation through an external heat exchanger, gas recirculation, mechanical mixing, internal draft tube mixers, and rising bubbles of gas produced during digestion (see refs. thirteen and fourteen). Mixing avoids grit and scum accumulation, that reduce the actual volume of the digester, and also provides uniform substrates and biomass concentration. It is commonly accepted that a good mixing is necessary for satisfactory digester performance and that, with the usual designs, there is a maximum allowable feed solids concentration beyond which adequate mixing is not p0ssib1e.l~ This limit varies from plant to plant up to 10-12%. Sometimes the maximum solids concentration is determined by the ability of pumps to handle thick sludges.

All mathematical models of anaerobic digestion as- sume perfect mixing, since it would be very difficult

DALLA TORRE AND STEPHANOPOULOS: ANAEROBIC DIGESTION CONTROL 1139

to account for nonideal mixing effects with the present level of process understanding. This means that model predictions will not be meaningful at high feed density. In any case, such operating conditions should be care- fully avoided.

A decrease in the mean residence time can decrease the biomass concentration of methane formers with respect to acid formers, since methanogens have lower specific growth rate maxima. This will increase volatile acids concentration. If the inhibitory range is reached, the digester gets “sour” because of acids accumulation and methanogens are washed out.

Due to very fast solid solubilization and acidogenesis, an increase in volatile suspended solids (VSS) in the feed causes a fast rise in solubilized organics and acid concentration which, if large enough, can cause inhibition of methanogenic bacteria. The latter are then washed out because of the low growth rates and this makes the digester sour.

Many chemicals have been reported to be toxic to bacteria active in anaerobic digestion: heavy metals, organic bactericides; oxidants such as nitrates and sul- phates; and sodium, calcium, and ammonium ions. These ions are important in pH control of digester operation. Other substances only occasionally are present in significant concentrations, due to exceptional cases, such as an industrial spill.

Heating can be provided by internal or external heat exchangers or feed preheating and is necessary since digesters are usually operated in the mesophilic temperature range (30-40°C). It is likely that poor temperature control can cause digester failure and that kinetics parameters will vary with temperature. Due to insufficient knowledge and data on temperature de- pendencies, this possibility will not be examined for control purposes. In any case the range for satisfactory operation would be quite narrow.

Digester Stability

Digester stability was examined by simulating the system response to step changes of the two main op-

Table I. Feed and steady-state values.

erating parameters, namely, the residence time and volatile suspended solids. As expected, the digester was able to handle small perturbations of these parameters (T = 5 days; VSS = 75 g/L) but failed when large disturbances were introduced ( T = 2.5 days; VSS = 160 g/L). The initial condition before the introduction of these changes was that indicated in Table I. Feed values are after data measured by Eastman and Fer- guson.I6 Figures 2-5 are representative examples of the obtained responses and show the progress with time of the system variables when subjected to the indicated hydraulic (residence time) and organic matter (VSS) perturbations.

It is interesting to follow the values of the various digester parameters for the purpose of identifying good indicators of an imminent failure. Different scales should be noted in comparing Figures 2-5. Drops in pH, alkalinity, methane production, and rises in volatile acids concentration and acids-alkalinity ratio are evident near failure and reproduce what is observed on the field. The above variables have often been considered to be the best indicators of digester condition. However, our simulations showed that they can vary significantly even when the digester is operating normally and they cannot be used as early indicators of digester failure, in agreement with MOP 1615 and Ashley and Hurst.Io This behavior can be explained, on the basis that the observed changes are not the cause, but rather an effect of volatile acids production/consumption imbalance. It would seem that the rate of change of acids concentration would be more appropriate, as suggested by MOP 16ls; but this variable is more difficult to measure. These simulations also contrast the result of Graef and Andrews2 and Collins and Gilliland,3 who used the one species model and found that pH, gas composition, and acid concentrations responded immediately to step load changes. This disagreement can be probably explained since the present model takes into account all three consecutive steps of digestion (hydrolysis- acidogenesis-methanogenesis), while the single species model accounts only for the last. In agreement with Graef and Andrews,2 simulations confirmed that

Variable Feed Steady-state value -~~

Degradable solids concentration (g/L) Hydrolysis product concentration (g/L) B , biomass concentration (g/L) Acetic acid concentration (mol/L) Propionic acid concentration (moVL) Butyric acid concentration (moVL) Bz biomass concentration (g/L) B, biomass concentration (g/L) Bq biomass concentration (g/L) Ammonia concentration (mol/L) Total carbon dioxide concentration (mol/L) Methane gas molar fraction

26.3 1.86 0 0.026 0.01 1 0.006 0 0 0 0.041 0 -

0.848 0.161 3.930

0.291 x 0.422 x 1.946 0.359 0.133

0.892 x 10-3

0.0728 0.0812 0.548

1140 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 28, AUGUST 1986

. L . L .

tLL+ L o x'

0.000 1.600 3.200 4 . BOO 6.400 8.000 TIME C d a y l

Figure 2. Residence time shift down to 5 days. Acids refer to the sum of volatile organic acids expressed as acetic. Alkalinity refers to bicarbonate alkalinity expressed as CaC03. Ratio refers to the ratio of acids to alkalinity.


Figure 4. Feed VSS concentration shift up to 75 g/L. Acids refer to the sum of volatile organic acids expressed as acetic. Alkalinity refers to bicarbonate alkalinity expressed as CaCO,. Ratio refers to the ratio of acids to alkalinity.


Figure 5. Feed VSS concentration shift up to 160 glL. Acids refer to the sum of volatile organic acids expressed as acetic. Alkalinity refers to bicarbonate alkalinity expressed as CaCO,. Ratio refers to the ratio of acids to alkalinity.

1144 BIOTECHNOLOGY A N D BIOENGINEERING, VOL. 28, AUGUST 1986

methane production rate is not a good process indicator; in fact it increases initially and drops only very near to failure.

In Figures 3 and 5 an increase in methane gas content can be noted when failure has occurred. This is un- important, since gas production is nearly zero, at that point. The extremely low amounts of carbon dioxide produced leave the reactor mainly in the liquid stream, resulting in a low carbon dioxide gas content. A certain redissolution of gaseous carbon dioxide could even occur.

The relative magnitudes of the concentrations of the volatile acids and the mixed culture components change significantly near failure. At steady-state acetic, propionic, and butyric acid concentrations are in the ratio 21 :6.9: 1. From Figures 2-5 it can be seen that near failure there is a large relative increase of butyric acid. Such increase of butyric acid concentration and other higher acids not included in the model has been observed experimentally by Ashley and Hurst'O and Cox.'* Acetic acid is predominant at normal operation and in Figures 2-5 but, with a residence time shift down to 4 days, the model predicts that propionic acid will dom- inate. In fact, while at 2.5 days there is a complete wash out of methanogenic bacteria, at 4 days only B3 is washed out, because the maximum specific growth rate of only this population has been exceeded by the dilution rate. Failures where acetic or propionic acid are in largest concentration have also been observed in practice (see ref. 17). It should be noted that, while the model allows for the attainment of a new steady state, after a catastrophic perturbation, with some vi- able methanogenic bacteria, in practice, life would stop after a certain time because of the excessively low pH.

A conclusion that can be drawn from the above simulation results is that there is probably no variable that can be followed in time as an indicator of possible digester failure. Some are more reliable than others but even with them there is little that could be done to avoid the approaching acid accumulation with a usual control system.

The next series of simulations examined the magnitude of step changes in the residence time and feed VSS concentration, alone or in combination, required to bring about digester failure. Step changes in the residence time and VSS feed concentration were used because they provide good tests of system stability. Results are summarized in Figure 6. A digester operating at steady states indicated by points 1-7 in terms of the values of the main operating parameters (residence time and VSS feed concentration) was subjected to various levels of perturbation of these two parameters and the subsequent dynamics was observed. All other feed values were as in Table I. The limit curves shown in Figure 6 represent the smallest step changes in the two parameters required to make the system unstable when starting from the indicated steady-state

7 r

20 1 steady states

15 4, 2 x 6 x

0 0 50 100 150

TSS [g/11

Figure 6. Reactor stability to step changes in residence time and feed solids content. Limit curves relative to various steady states.

point. The abscissa represents total suspended solids (TSS) rather than VSS, which is better for result inter- pretation. It was assumed that VSS is a constant fraction of TSS; a typical value of 73% was taken from Chynoweth and Mah.'* If it is further assumed that solids have constant density (a typical value for sewage water would be 1.4), then there is a one to one cor- respondence between TSS and sludge density, which, for the usual range, is approximately a proportionality relation. Therefore, any result can be expressed in terms of density, TSS, or VSS equivalently.

Figure 6 indicates that the effect of a hydraulic load is approximately the same for all steady states of operation. Regardless of the normal operating condition washout occurs when the residence time drops to the level of 4.3 days or lower. Furthermore, there is noth- ing that one can do about controlling the system other than reducing the flow rate through the digester to a level that can be accommodated by the culture growth rates.

The effect of the total solids (TSS) feed concentration is more interesting. The lines of Figure 6 show the magnitude of a disturbance in TSS feed concentration alone or in combination with a disturbance in residence time which are sufficient to destabilize the steady state indicated by the corresponding number. The stabilizing effect of increasing TSS feed concentration is evident: larger perturbations are needed to drive unstable a steady state. In comparing the stability results of Figure 6 steady states of equal productivity should be considered. It is easy to show that such steady states lie on a straight line through the origin (e.g., points 1, 2 and 7 are all equivalent in terms of digester productivity). Consequently, one should operate at as high a residence time and feed TSS concentration as mixing and other constraints allow in order to enjoy the highest degree of stability with respect to such disturbances.

Concentration of digester feed is generally advised since it reduces tank volumes, heating requirements, and boiler capacity. Here, based on simulations results, it is cIaimed that concentration of digester feed has also positive effects on digester stability. The re-


sulting increase in residence time has also expected benefits in VSS reduction and methane production. Therefore, while design efforts should be made to reduce feed TSS constraints imposed by mixing and pumping, one should choose an operating point close to the maximum allowed density. Since fluctuations in feed characteristics are wide, some density control will be necessary as examined in a later section.

It should be also pointed out that, in addition to step changes, digester stability was examined with respect to other types of perturbations such as pulse disturbances. Figure 7 shows some of the results obtained with a 3-day pulse disturbance of both parameters (curve b). The effects seem to be somewhat less severe, especially at low resistance times. No generalizations, however, can be made, for the effects of oscillatory inputs are more difficult to predict. Table I1 summa- rizes the results of simulations starting at steady state 1 of Figure 6 and with feed VSS varying as a square wave between 5 g/L and VSS,,, at various frequen- cies. In some cases this type of disturbance is more severe then a step increase. In fact, if the feed stays at low values for long times, biomass concentrations decrease and this makes the system more sensitive to the step increase of the next cycle as illustrated in Table 11.

Toxic Substances

The effect of a toxic substance was modelled through a growth-rate decrease. Assuming linearity with respect to the toxic substance concentration, T, the new specific growth rate, p,, is:

( 1 )

for speciesj, where l / K , is the threshold concentration of the toxic substance necessary to produce zero growth and p, is the specific growth rate for T = 0. A value l / K T I = 0.35 moVL was chosen for B,, while a smaller value 0.25 mol/L was chosen for the weaker BZ, Bj, and B4. These values as well as feed concentrations of toxic materials are purely indicative. The material bal- ance for the toxic substance is:

- P; = P,41 - K,T)

dT - = (Tf - T)/T dt

in C 1 s

0 50 100 TSS [ g i l l

Figure 7. Limit curves relative to steady state 1: (a) uncontrolled system with step disturbance; (b) uncontrolled system with pulse disturbance; (c) controlled system (base addition) with step disturbance; (d) controlled system (Row manipulation) with step disturbance.

Table 11. Stability with oscillatory feed concentration.

Semiperiod VSS,,, (days) (dL) Failure?

1 85 no 5 85 Yes 15 85 Yes I 75 no 5 75 no

15 75 Yes

where T represents the mean residence time and Tf is the feed concentration. Starting from steady state 1 of Figure 6 , a 2-day square pulse of Tf has been simulated. The system recovers for Tfup to 1.05 mol/L and fails for larger values.

CONTROL STRATEGIES

The objective of all digester control structures employed to date is the control of pH or other indicator of volatile acid concentration, since acid accumulation is the predominant cause of digester failure. These controls are basically feedback systems with no anticipatory qualities due to lack of quantitative models of digester operation. The most common manipulated variables are the feed flow rate, basic substance addition rate, and the rate of sludge recycle. Effects of such variables are qualitatively evident. A lower flow rate reduces the amount of solids fed to the digester and thus the amount of acids produced; also biomass concentrations benefit from higher residence time. The addition of a base increases the pH and avoids inhibition, because methanogens are inhibited by undis- sociated acids. The pH control is the most popular control employed because it is based on a straightfor- ward measurement and depends directly on volatile acids concentrations even though the buffering capacity of digesting sludge prevents pH from giving an im- mediate indication of souring. Finally, biomass recycle increases biomass concentration and reduces the like- lihood of wash out. The last case (anaerobic contact process) will not be considered here and control strategies will be examined for the case of no sludge recycle only.

On the basis of the above discussion, it was decided to examine two representative and promising schemes already proposed and analyzed by Graef and Andrews2 and Collins and Gilliland.3 Feedback control was chosen with on-off band controllers since proportional and proportional integral controllers did not seem to offer significant advantages.

pH Control by Base Addition

With a pH band of 6.8-7.0 and starting from steady state 1 in Figure 7 , the limit curve was determined that


defines the magnitude of the perturbations of residence time and TSS feed concentration that can destabilize the system under pH control. This curve is shown as curve (c) in Figure 7. NaOH was used as the base. It was reported elsewhere5 that NaOH performs better than lime for pH control. In practice, however, low costs and toxicity are such that lime is preferred. To avoid a possible unknown carbonate supersaturation and longer computing times, NaOH rather than lime was used for simulations.

As seen in Figure 7, no improvement was obtained at low residence times. This is in agreement with Graef and Andrews’ and can be readily explained: when the dilution rate is higher than the maximum specific growth rate, the species is washed out no matter what pH is chosen. A higher pH can only reduce inhibition and delay the washout. This indicates that pH control with base addition will be more effective for pulse disturbances.

Some improvement is obtained at large feed VSS. This improvement, however, is quite marginal and such a control not justified for these large feed VSS concentrations are at the limit of allowed operation. Any stability enhancement in this region is inconsequential for this region lies outside the operability limits and, also, in this region model predictions are not very accurate.

Thus, in contrast with other workers, pH control by base addition does not seem to be very effective. It should be noted, however, that base addition is useful in other cases, especially those where large acid concentrations exist. These situations may arise during start up of normal operation or in the control of sour digesters. The usefulness of base addition in such cases has been proved in field operation.

pH Control by Flow Reduction

Reduction of flow through the digester implies either additional costs for a holding tank before anaerobic digestion or the inconvenience of some feed discharged without anaerobic treatment, which would be acceptable only if a failure could be avoided this way.

The control needs are: 1 ) reduce the flow rate only when there is a danger of reactor failure due to low residence time and 2) bypass the smallest possible amount of feed. This is accomplished by the control scheme of Figure 8(a) where a flow control is cascaded with a pH control. The outer loop has an on-off band controller such that the flow rate is uncontrolled for normal operation. When the pH is in the low range and the residence time is below a minimum limit, 7sp,

the controller activates the inner loop with set point vAD/7sp, where VAD is the digester volume. A simple proportional or PI controller can be used. 7sp = 5 day was chosen on the basis that 0.20 day-’ is smaller than the maximum growth rate of all populations present

DIGESTED SLUDGE

1 BYPASS

(a)

DIGESTER Fi FEED I I

DIGESTED SLUDGE

BYPASS

(b) Figure 8. pH control (a) cascaded with flow control; (b) by flow manipulation.

and also leaves a safety margin. After operating for some time with T~~ = 5 day, one could try to reduce this value. The above control action avoids an exces- sive flow reduction (7 > 7sp) that would not only increase the amount of the bypass, but also would not be significantly beneficial for the process. In fact the methanogens of the digester are largely affected by the residence time only when the dilution rate, I h , is close to their maximum’specific growth rate.

Effecting pH control by manipulation of the bypass flow rate, represented in Figure 8 (b), is simpler, but does not fully satisfy the control needs explained above. In fact, since the flow rate is not measured, the controller is not able to determine if the operating difficulties are due to low residence time or to any other process disturbance. Also the lower limit for the digester feed flow rate (fully open valve) will depend on the total flow rate (before bypass) and could be unneces- sarily low. Another advantage of the cascade scheme is that, when the digester has already operating difficulties, any significant hydraulic disturbance is elimi- nated by the inner loop before it reaches the digester.

Since the inner loop has undoubtedly a dynamics much faster than the outer loop, the control scheme is equivalent to a pH on-off controller with “off’ cor-


responding to a residence time of 5 days and “on” to uncontrolled flow. This fact was used in the following simulations.

With a pH band of 6.8-7.0 and with steady state 1 as initial condition, the limit curve (d) was constructed in Figure 7 for the magnitude of the perturbations that can destabilize the controlled system.

The above results indicate that neither base addition nor the flow rate manipulation can provide a robust and efficient control for anaerobic digesters. Such controls are useless if the maximum allowable density is reached. Finally, they involve extra costs and may cause toxicity problems as discussed in an earlier section. For these reasons a new control strategy based on the density control of primary sedimentation is analyzed below as another possibility for the control of anaerobic digestion systems.

Density Control of Primary Sedimentation

The stability results of Figure 6 pointed to several advantages that could be gained by operating at high feed solids densities and the corresponding higher residence times. In order to control these parameters it is necessary to control the operation of the next unit upstream in an anaerobic digestion process. In most cases this is a primary sedimentation unit whose underflow output is the input to the digester. A schematic of the unit arrangement is given in Figure 9 and the characteristics and operation of these units are briefly described before and used in the sequel for the control of the digester.

Primary sedimentation is accomplished in rectangular or circular basins at retention times of 1.5-2.5 h. The underflow is a concentrated suspension of solids and the overflow a low solids concentration stream of approximately the same flow rate as the incoming stream due to the very high concentrations achieved.

Let /? be the solids removal efficiency:

F,TSS, /?=- F,TSS, (3)

where F indicates the flow rate and subscripts u and o refer to settler underflow and feed. Since the underflow is the feed to the digester, then:

dTSs, = vAD/(pF,Tss,) (4)

where VAD is the digester volume. Parameter p is at least 50% and depends essentially on the overftow velocity, defined as the ratio of the overflow volumetric flow rate to the basin sedimentation area. This dependence is deduced from statistical data by Eckenfelder and O’ConnorI3 and measurements by Thereoux and Betz.I9 Since for constant F, the overflow velocity is almost constant, then the efficiency /3 is constant and eq. (4) represents a straight line through the origin in

PRIMARY S E D I M E N T A T I O N ANAEROBIC D I G E S T I O N

G A S I-----

PRIMARY SLUDGE

DIGESTED SLUDGE

Figure 9. Proposed control scheme for sedimentation and digestion.

Figure 10. When F, and/or TSS, increase, the slope changes according to eq. (4) and the operating line moves from (a) to (b), (c), or (d) in Figure 8. TSS, and 7 are determined by the sedimentation operation along the operating line. However, once they are determined, they define a steady state for the digester indicated by the corresponding point in the 7-vs.-TSS,, diagram. Figure 10 also shows line (e) of the maximum solids that can be handled by the digester and the limit curve (f) for the magnitude of perturbations that can destabilize the system operating at point S.

Various control strategies are possible for the output of sedimentation unit or the feed to the digester. All these controls are, in some respect, anticipatory for they aim at controlling the input to the digester at the desired point instead of responding to indicators of souring when very little is possible to prevent failure. One possibility is to control F,, (using a positive dis- placement pump) which is equivalent to staying (at steady state) on a horizontal line through S indicated with (1) in Figure 10. Another option is to control TSS, with a PI controller which means that the operating variables lie on a vertical line (2) through S. Inter- mediate control actions are also possible as shown by lines (3) and (4) in Figure 10.

In practice density control can be more complicated and require an on-off mode to allow solids collection and consolidation in hoppers. The need for time cycles is described by Garrison and Nage120 and most of the

0 20 4 0 TSS [ g / l l

Figure 10. Digester feed characteristics diagram: (a)-(d) primary sedimentation operating lines; (e) maximum allowable solids concentration; (f) digester limit curve relative to steady state S; (1)-(4) sedimentation control strategies.


conclusions reached here would apply also to these types of controllers.

Starting from steady state S, the digester can handle all feed conditions within the limits imposed by Iines (e) and (f). If the controller keeps F, constant (line 1 in Fig. lo), all raw wastewater conditions resulting in lines above OP are acceptable; a TSS, proportional-integral controller (line 2) can handle all lines above OQ; a TSS, proportional controller (line 3) would further improve system capabilities. A special purpose controller (line 4), based on the knowledge of lines (e) and (f), could handle all lines above (c).

Raw wastewater conditions corresponding to lines such as shown in Figure 10(d) cannot be handled by any TSS, controller and the addition of a basic substance can do little to correct this problem. On the other hand, flow reduction enlarges the stability domain for values of TSS just around the steady state and seems very well suited to complement density control. The resulting control scheme appears in Figure 9; the bypass can be replaced by a holding tank if any undigested sludge discharge cannot be tolerated even in exceptional cases. The position of the holding tank in the wastewater treatment flowsheet should be between primary sedimentation and anaerobic digestion and not before the settler. This would drastically increase required volumes and .cause more problems with scum and sludge (see ref. 21, p. 189). The bypass could also be actuated before the settler.

Steady state S corresponds to 1 in Figure 6; similar conclusions can be drawn for steady states 2 or 7. In particular it should be noted that the system can at least double its normal feed rate without activating the bypass.

Based on the above considerations, the control of TSS, by F, manipulation is proposed. Proportional control was tested against PI control and steady state designed feedforward control. In addition to the men- tioned steady state advantages, proportional control is the fastest and gives no overshoot as response to step input changes in TSS, andlor F,. The proportional controller is defined by:

-- F,, = F, + Kp(TSS, - TSS,)

Here the overbar indicates setpoint values. A large value of the proportional gain, K p , can be selected with no stability problems; K, = 25 m3 Llg day gives a suitably low offset, while larger values give marginally

Figure 11. model.

Structure and symbols of the primary sedimentation

Table 111. Primary settler model equations.

d - (VTSSI) = F,,TSS, - (Fay + F,)TSSI - fTSSi dl

d - (VTSS,) F,,(TSS,- - TSS,) - fTSS, (i = 2,3,4,5) dt

dV - = ( IW(F,J - F,,, - Fu) dt

5v A

h = - - H

F,,, = 153,082 bh3'2 (empirical weir equation)

f = F,>,[(I - /3-1 '5 - 11

dTSS, dt

5

vh- - - F,,(TSSI - TSSJ + fC TSS, I - I

better performance. The above value was used in the simulations. mu = 36.03 g1L (VSS = 26.3 g1L) and F, = 61.685

m3/day were chosen. For V,, = 618.65 m3, this is the digester feed corresponding to steady state 1. For a larger digester more settlers could be employed operating in parallel.

The performance of the above controller was tested with a variety of dynamic simulations. For the sedimentation unit a rectangular basin primary settler model from Tanthapanichakoon and HimmelblauZz was used. According to this model (Fig. 11) the settler is ideally divided into a solids separator with a sludge hopper at the bottom and five completely mixed compartments to account for hydraulic mixing. Only volumetric and suspended solids balances have been included, though it is possible to treat dissolved species in an obvious way. Details on the model can be found in Tantha- panichakoon and Himmelblau.22 For completeness symbols are illustrated in Figure 11 where F refers to flow rates, TSS to total suspended solids, and V to volumes. Equations are reported in Table 111. Param- eter values (Table IV) were determined with a settler sizing procedure from Metcalf and Eddy.*' The steady- state solids removal efficiency, p, was computed after an experimental curve from Thereoux and Betz.I9 It seems that equipment sizing is generous if such a curve

Table IV. Primary settler sizing parameters.

Parameter Value

Total volume Settling area ( A ) Lengths Weir length (b) ' Weir height ( H ) Average load Average residence time Average weir load

1092 m3 273 m2 34.125 m 48 m 4.0 m 50 rn3/m2 day 1.92 h 283 m3/m day

DALLA TORRE AND STEPHANOPOULOS: ANAEROBIC DlGESTlON CONTROL 1149

Figure 12. wastewater conditions to F,, = 22,000 m3/day and TSS, = 0.2796 g/L.

Performance of the control scheme in Figure 9 for a step change in raw


SCALE FAClOR - 1.E 1 I I

0 .000 0.480 0.960 1 . 4 4 0 1.920 2.400 TIME [ d a y ]

Figure 13. wastewater conditions to F, = 22,000 m3/day and TSS, = 0.350 g/L.

Performance of the control scheme in Figure 9 for a step change in raw

DACM TORRE AND STEPHANOPOULOS: ANAEROBIC DIGESTION CONTROL 1151

is employed. For design purposes F, = 13650 m31day; TSS, = 0.22 glL; and a peak value of 2F, were assumed.

Density Control Performance

The performance of the control strategy in Figure 9 was tested with step changes in F, andlor TSS,. It should be noted that these are equivalent. For example, we can get the same underflow straight line with 13,650 m3/day and 0.4273 gIL, 31,936 m3/day and 0.22 g/L, or 22,000 m3/day and 0.2796 g/L. All these conditions give F,TSS, = 4330.55 kglday which defines line (b) in Figure 10. Also, the dynamic response of F, and TSS, is very similar. Therefore, there is practically no difference for the digester if F, or TSS, increase. Curves could be drawn in the F, vs. TSS, plane as loci of raw wastewater conditions with constant F, TSS,. If the digester can handle a point on this line, it will handle any point on and below the line. A curve corresponding to (c) in Figure 10 would determine conditions that could be handled with suitable control action and no flow reduction.

Results with a step change to 22,000 m3/day and 0.2795 glL are reported in Figure 12. Flow reduction is not needed.

Line (d) in Figure 10 corresponds, for example, to F, = 28,000 m3/day and TSS, = 0.350 g1L (F,TSS, = 6598.9 kg/day). With such a step increase, Figure 13 was obtained. Flow reduction acts effec- tively in this case. In both cases the F, constant control would lead to TSS, beyond the allowable limit of line (e).

Low time constants for the settler and speedy action of the proportional controiler are such that steady state conclusions match closely with dynamic performance. Figures 12 and 13 show satisfactory operation of the control scheme in Figure 9.

Toxic Substance

A toxic substance spill was simulated as a two-day pulse in To. Starting from steady state 1, the uncontrolled system fails for T’ > 1.05 mol/L. With pH control by base addition as in a previous paragraph, the limit shifts to 1.25 mol1L. This was expected since such a control offers some advantages with disturbances lasting for short periods of time. The density control scheme with flow reduction is not effective for such a disturbance. Steady state 2 is much more resistant and fails for Tf > 1.8 mol/L (uncontrolled). This is essentially due to the larger methane forms biomass concentration (52% increase) which provides another good reason to increase steady-state feed VSS.

CONCLUSIONS Causes of anaerobic digester failure have been ex-

amined qualitatively and with the aid of computer sim-

ulations based on a mixed culture model. The model accounts for the three basic steps of digestion: hydrolysis of organic solids, acidogenesis, and methanogenesis.

Digester stability was tested with respect to step input changes in feed flow rate andlor feed concentration of volatile suspended solids. Souring due to acids accumulation following sufficiently large step input is reproduced by the model. Results can be conveniently expressed in a mean residence time versus feed of total suspended solids diagram, where lines can be drawn separating allowed from failure-causing step inputs. The position of these lines depends mainly on the steady state of operation for the corresponding feed VSS; by increasing VSS, the stability domain increases. Based on these results, it is suggested that one should try to operate at a total suspended solids (TSS is assumed to be approximately proportional to VSS) which is near the maximum allowed by mixing or pumping capabilities. This also saves boiler capacity and digester volume, and reduces heat addition.

Some control strategies have been proposed in the past. Essentially, the controlled variable is pH (or another equivalent variable such as gas composition) and the manipulated variables are feed flow rate or the rate of base addition. The first is effective against low residence times, but implies the construction of a holding tank or bypass of a fraction of the feed. The second is ineffective against low residence times and has some effect at high TSS which, however, is outside the allowed region of operation. While the effect of poor mixing is not included in the model and the performance of this control scheme cannot be fully evaluated, it seems more reasonable to act on the cause (high TSS) rather than on the effect (low pH). If lime were used, carbonate precipitation could increase mixing problems. Base addition alone is useful only when a large acid concentration already exists, such as in a startup of a sour digester.

The necessity to guard against high feed TSS and to operate at relatively large VSS suggests the use of a TSS control. It was assumed, as often is the case, that anaerobic digestion follows primary sedimentation, so that TSS control was applied to the settler underflow. Settler steady-state operation can be well approxi- mated by a straight line in the digester residence time- versus-feed TSS plane, the slope of the straight line depending on raw wastewater flow rate and TSS. Based on steady-state performance of control strategies, represented in Figure 10, a TSS proportional control was selected. The system can now handle a much wider range of raw wastewater conditions. For exceptional cases a pH control by flow reduction is adequate, since it acts only against large feed rates and at TSS near the setpoint. The resulting control scheme (Fig. 9) gives good resuits in a wide range of conditions (Figs. 12 and 13).


A limited advantage is offered by a pH control with base addition against a two-day square pulse of a toxic substance in the feed. The control scheme of Figure 9 does not act against such a disturbance. Larger steady- state feed VSS increase greatly stability to a toxic substance pulse, since the starting methane formers biomass concentration is larger.

Support in the form of a graduate fellowship to one of the authors (Albert0 Dalla Torre) by the Rotary Foundation of Rotary International is gratefully acknowledged. This work was also supported in part by Kraft, Inc., E. I . duPont de Nemours, Inc., and Monsanto through their participation in the Caltech Process Biocatalysis Program.

NOMENCLATURE settling area (mZ) weir length (m) acidogenic bacteria population methanogenic bacteria population (acetic acid) methanogenic bacteria population (propionic acid) methanogenic bacteria population (butyric acid) TSS removal rate coefficient (m3/day) flow rate (m3/day) settler overflow flow rate (m3/day) liquid level above the settler outlet weir (m) weir height (m) proportional gain (m3 L/g day) toxicity constant (L/mol for population j ) methane production rate (mol/L day) toxic substance concentration (mol/L) toxic substance concentration in digester feed (rnol/L) total suspended solids or total suspended solids concentration in digester feed (dL) total suspended solids concentration in settler stage j ( d L ) settler stage volume (m3) digester volume (m3) hopper volume (m3) volatile suspended solids or volatile suspended solids concentration in digester feed (dL) maximum VSS concentration in digester feed (square wave input) (g/L) methane gas molar fraction

Greek letters B settler solids removal efficiency PI specific growth rate of populationj [day-’]

P, specific growth rate of population j in presence of a toxic substance [day-’]

residence time corresponding to Row controller set point 7 digester mean residence time [day] T~~

Subscripts 0

U

refers to settler feed values refers to settler underflow values (equal to digester feed values) overbar refers to set point values

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DALLA JORRE AND STEPHANOPOULOS: ANAEROBIC DIGESTION CONTROL 1153

simulation study of anaerobic digestion control

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