CHAPTER 10
This chapter describes the aerobic and anaerobic digestion models used in GPS-X.
Basic Anaerobic Digestion Model
This section describes the basic anaerobic digestion model associated with the anaerobic digester object. It is a modified version of the model developed by Andrews (1969), and Andrews et al. (1971). The modifications to the original model are:
· The addition of temperature sensitivity for the hydrolysis of volatile suspended solids (VSS) and the growth of methanogenic organisms. The Arrhenius equation is used with a base temperature of 35 degrees Celsius.
· The introduction of particulate inert inorganic material (xii). This component remains unchanged within the digester and is introduced for the sole purpose of assessing its impact on other processes downstream of the digester.
· The addition of a rate for toxic substance degradation.
Conceptual Model
The basic anaerobic digestion model consists of two reactors: one for the liquid phase and the other for the gaseous phase. Both are modelled as completely mixed reactors. Transfer of gaseous products between the liquid phase and the gaseous phase is modelled using a standard two-film mass transfer equation. Gaseous carbon dioxide (CO2) and methane (CH4) are assumed to follow the ideal gas law. No further reactions take place in the gaseous phase, which has a total gas pressure of 760 mm of Hg (i.e., atmospheric pressure).
Figure 10‑1 - Schematic Diagram of the Anaerobic Digestion Model
A schematic diagram of the anaerobic digestion process is shown in Figure 10‑1, where:
In the gas phase:
qtg: = total gas flow (m 3/d)
qco2 = CO2 gas flow (m3/d)
qch4: = CH4 gas flow (m3/d)
gco2: = partial pressure of CO2 (atm)
gch4 = partial pressure of CH4 (atm)
In the liquid phase:
State Variables
xmh: = methanogens (gCOD/m3)
vss = volatile suspended solids (gCOD/m 3)
slf = total volatile fatty acids (gCOD/m 3)
sco2t = total soluble CO2 (moles/L)
sz = net cations (moles/L)
stox
= toxic substance
(g/m3)
Composite Variables
snhn = free ammonia (moles/L)
snhi = ionized ammonium (moles/L)
slfn = non-ionized volatile fatty acids (moles/L)
slfi = ionized volatile fatty acids (moles/L)
pH = pH
hco3 = bicarbonate (moles/L)
h2co3 = carbonic acid (moles/L)
salk = alkalinity (g/m3)
Mathematical Model
The mathematical equations used in the liquid and gaseous phases are provided in the corresponding Model matrix form in Appendix A. The general reaction pathway is shown in Figure 10‑2.
Figure 10‑2- General Reaction Pathway
Stoichiometry
The relative amounts of chemical components produced by the biological and chemical reactions in the anaerobic digester are specified by stoichiometric coefficients. The chemical reaction stoichiometry is defined by the balanced chemical reaction equations. The biological stoichiometry is defined by the yield coefficients.
Seven yield coefficients are used by the basic model:
ya = slf / vss
yc = xmh / slf
ye = gch4 / xmh
yg = xmh / snhi
In each case the yield is defined as the ratio of the change in a product to the change in a reactant. Volatile acids and volatile suspended solids are expressed as their equivalent chemical oxygen demand (COD).
Components and Processes in the Mathematical Model
Volatile Suspended Solids
The rate of hydrolysis of VSS is assumed to be first order with respect to the concentration of VSS. A temperature correction factor (ftkco) is calculated using the Arrhenius equation with a base temperature of 35 degrees Celsius. The temperature correction factor is incorporated in the equation for the hydrolysis rate:
Equation 10‑1
where:
kco = rate constant for the hydrolysis of VSS
Methanogenic Organisms
The growth of the microorganisms responsible for the generation of methane is modelled using the Monod equation modified by switching functions (similar to the IWA models). The rate of growth of methane producing bacteria (r2) is assumed to be proportional to their concentration (mumh). The model uses un‑ionized volatile acids (slfn) as the substrate and incorporates two switching functions for inhibition: one for inhibition by slfn and the other by free ammonia (snh).
The resulting rate equation is:
Equation 10‑2
where:
ftmum = the temperature correction factor for the growth of methanogens
mumh = maximum specific growth rate for methanogens
ks = the half-saturation coefficient
kia, kin = the inhibition constants for slfn and snh, respectively
As in other biological models, the rate of decay of methane producing bacteria (r3) is assumed to be proportional to their concentration:
Equation 10‑3
where:
kd = the decay rate coefficient
The effect of toxic substances (stox, input as a special component to the influent parameters) is taken into account by using a first order expression for the rate of inactivation of methane bacteria:
Equation 10‑4
where:
ktox = the inactivation rate coefficient
Based on the above rates, the net rate of generation of methanogens (rxmh) is:
Equation 10‑5
Toxic Substances
A rate of toxic substance degradation (r5) is incorporated in the basic model. The rate of degradation is assumed to be first order with respect to the concentration of toxic substances:
Equation 10‑6
where:
kb = toxic substance degradation rate
Total Volatile Fatty Acids
The kinetic expression for total volatile fatty acids (slf) can be established using the previously presented kinetic expressions and appropriate yield coefficients:
Equation 10‑7
where:
(ya r1) = rate of generation of slf by hydrolysis
‑r2/yc = rate of utilization of slf by the growth of methanogens
Methane
The biological generation of methane can be expressed in terms of bacterial growth rates and yield coefficients. The model assumes that the solubility of methane is negligible and all methane generated is immediately transferred to the gas phase:
Equation 10‑8
where:
vm = volume of the liquid phase in the digester
Carbon Dioxide
The mass transfer of carbon dioxide between the liquid and gas phases is calculated using the standard two-film gas transfer equation.
Equation 10‑9
where:
klac2o2 = mass transfer coefficient for CO2
co2sat = saturation concentration of CO2 in the liquid phase, and H2co3=sco2t-hco3-co2
The pH model within the basic digester model calculates bicarbonate (hco3) and carbonate (co2). The concentration of dissolved CO2 in the liquid phase at equilibrium (co2sat) is calculated using Henry's law:
Equation 10‑10
where:
henryco2 = Henry’s law constant for CO2
gco2 = partial pressure of CO2 in the gas phase
Combining the above equations:
Equation 10‑11
The rate of biological generation of total soluble carbon dioxide (rsco2t) can be expressed in terms of bacterial growth rates and yield coefficients. Combined with the above equation results in the total reaction rate for dissolved CO2 (rsco2):
Equation 10‑12
where:
(yb r1) = rate of generation of sco2t by the hydrolysis of vss
(yd r2) = rate of generation of sco2t by the growth of methanogens
gvol = gas constant for CO2 in L/mole
The mass transfer of CO2 between the liquid and gas phases (r6) is negative when CO2 is transferred from the liquid to the gas phase.
Ammonia
Ammonia (snh) is assumed to be produced only at the hydrolysis/acidification stage. Ammonia (snh) is utilized by the methanogenic organisms for growth. The rate of generation of free ammonia (rsnh) is modelled as:
Equation 10‑13
where:
(yf r1) = rate of generation of ammonia by hydrolysis/acidification
-r2/yg = rate of consumption of ammonia due to growth of methanogenic organisms.
The chemical equilibria and the pH calculation used for ammonia (snh) and ammonium ion (snhi) are based on Hydromantis/Hatch's pH Model.
Model Parameters
This section of the chapter discusses the various model parameters and inputs that the user would encounter when using this model. The Parameters menu is shown in Figure 10‑3
Figure 10‑3 – Parameters Menu for the Anaerobic Digester
Physical and Operational Parameters
The physical parameters for the Mantis2 digester model are the volume of the liquid phase or maximum volume (vm), the effective volume fraction (effvol), the headspace volume (vgas), the total gas pressure (itpcon), and the digester temperature (temp). The effective volume fraction accounts for differences in the designed and actual digester volume (due to mixing, inert solids, precipitation, etc).
Figure 10‑4 - Physical Parameters
The Operational parameters shown in Figure 10‑5 are exclusively related to the control of the pumped flow. These parameters are similar to the control parameters used in other models (e.g., CSTR reactor).
Figure 10‑5 –Operational Parameters
Kinetic and Stoichiometric Parameters
The kinetic parameters (shown in Figure 10‑6) are found under Parameters sub-menu item kinetic. The maximum specific growth rate for methanogens (mumh) and the rate constant for hydrolysis of vss (kco) are defined for 35 degrees Celsius and corrected by the model using the Arrhenius equation with the temperature coefficients indicated at the bottom of this menu (tmumh & tkco). The rest of the kinetic parameters in the basic model are not temperature-dependent.
Figure 10‑6 - Kinetic Parameters
The stoichiometric parameters (Figure 10‑7) are found under Parameters sub-menu item Stoichiometric. The first set of stoichiometric parameters consists of conversion factors: particulate COD (xcod) to vss ratio (icvcon), BOD5 (bod) to BODultimate (bodu) ratio (fbodcon).
Conversion factors that are unique to the digester basic model are the mass acetic acid to COD factor(ac2cod), the molecular weight of fatty acids (mwfat) and the gas constant (gvol).
Using these factors and the parameters defined in the Effluent sub-menu, the basic digester model establishes the values for the composite parameters. These parameters will modify the stoichiometry of the effluent stream.
Figure 10‑7 - Stoichiometric Parameters
The second set of stoichiometric parameters consists of yields. The relative amounts of chemical components produced by the biological reactions in the anaerobic digester are specified by these yields.
Other stoichiometric parameters in this sub-menu are the dissociation constants used to calculate the ionized components in the pH model incorporated in the basic model. The dissociation constant for ammonium (kncon) is defined for 20 degrees Celsius and is temperature sensitive, i.e., the model corrects it for temperature changes using the following equation:
Equation 10‑14
The rest of the dissociation constants are not corrected for temperature changes in the basic model.
Gas transfer parameters are also defined on this form. The mass transfer coefficient for carbon dioxide gas (sco2) between the liquid and gas phases (KLaco2) is not corrected by temperature in the basic model. Henry's law constant for carbon dioxide (henryco2) is also included in this item and is not corrected for temperature.
Anaerobic Digestion Model #1 (ADM1)
Anaerobic Digestion Model #1 (ADM1) (Batstone et al., 2002) is implemented in GPS-X according to the ADM1 COST Benchmark (Rosen and Jeppsson, 2002), with the following changes:
· Several differential equations that describe the acid-base equilibrium of the system (equations for Sva-, Sbu-, Spro-, Sac-, Shco3-, and Snh3) have been converted to algebraic equations as described in Table B.3 of Batstone et al. (2002). These processes are very fast and contribute to the stiffness of the system of differential equations.
· The differential equation for Sh2 has been converted to an algebraic equation to improve the simulation speed. This process is very fast and contributes to the stiffness of the system of differential equations. This approach is described by Rosen et al. (2005).
These changes substantially increase the
solution speed of ADM1 in GPS-X and allow an integration algorithm
other than Gear’s Stiff to be used. Double Precision
arithmetic should be used when solving ADM1 in GPS-X
(accessed in
Options > Preferences > Build
tab)
The structured model includes five process steps including disintegration, hydrolysis, acidogenesis, acetogenesis and methanogenesis. The model uses 32 dynamic state variables, 6 acid-base kinetic processes, 19 biochemical processes, and 3 gas-liquid transfer processes.
A simplified ADM1 material flow diagram is shown in Figure 10‑8. For a full description of the model, the reader is referred to Batstone et al,. (2002). Implementation details are found in Rosen and Jeppsson (2002).
Figure 10‑8 - Simplified ADM1 Material Flow Design
In GPS-X, the ADM1 model makes use of an ASM1 to ADM1 interface developed by Copp et al. (2003). This interface allows ADM1 to be used within a full-plant layout that uses ASM1 to model activated sludge processes.
When using ADM1 there are two possible scenarios:
· The influent stream is represented by an influent object. This case is more difficult and requires that you specify the influent in the influent object and in the Influent Form in the digester object. See Figure 10‑9 for a graphical description of this procedure. The section entitled “ADM1 Model Set up Suggestions” gives suggestions on how to characterize the influent.
· The influent stream is an output stream from another object. This case is simpler as the object that precedes the digester will take care of the characterization of the stream itself. The user still needs to specify the parameters found in the Influent form of the digester object. See Figure 10‑10 for a graphical description of this procedure. The section entitled “ADM1 Model Set up Suggestions” gives suggestions on how to characterize the influent.
Figure 10‑9 - Method of Specifying the ADM1 Influent when the Influent Stream is Represented by an Influent Object
Figure 10‑10 - Method of Specifying the ADM1 Influent when the Influent Stream is an Output Stream from another Object
ADM1 Model Set up Suggestions
The following hints are useful for characterizing influent streams to a digester object using the ADM1 model. Because the ADM1 model uses a different set of state variables than the ASM activated sludge models, supplementary information has to be supplied for the ASM1/ADM1 interface.
In typical simulation practice, you will not have all the information you need, and will have to estimate the values for many of the ADM1 influent parameters. These guidelines can be useful for making sure that the estimates are used correctly. The following suggestions are for the Carbon-Nitrogen Library (CNLIB).
ADM1 State Variables Set on the ADM1 “Influent” Parameter Menu
Table 10‑1 – ADM1 State Variables Set on the ADM1 “Influent” Parameter Menu
|
Parameter |
Suggestion |
|
cations |
Must be measured or estimated or can be set to the value of the Sic (inorganic carbon) state in ADM1. |
|
anions |
Must be measured or estimated or can be set to the value of the Sin (inorganic nitrogen) state in ADM1. |
|
long chain fatty acids |
Must be measured or estimated. It is part of Ss in the influent object form. |
|
total valerate
|
Must be measured or estimated. It is part of Ss in the influent object form. |
|
total butyrate |
Must be measured or estimated. It is part of Ss in the influent object form. |
|
total propionate |
Must be measured or estimated. It is part of Ss in the influent object form. |
|
total acetate |
Must be measured or estimated. It is part of Ss in the influent object form. |
|
hydrogen gas |
Set to zero |
|
methane gas |
Set to zero |
|
proteins |
Must be measured or estimated. It is part of Xs in the influent object form. |
|
sugar degraders |
Set to zero |
|
amino acid degraders |
Set to zero |
|
long chain fatty acid degraders |
Set to zero |
|
valerate and butyrate degraders |
Set to zero |
|
propionate degraders |
Set to zero |
|
acetate degraders |
Set to zero |
|
hydrogen degraders |
Set to zero |
ADM1 State Variables Set in the Influent Object
When the influent stream is represented by an influent object, the states influent model should be used in the influent object. Some of the states are ADM1 states and these need to be estimated. Some states are not relevant for ADM1 and can be ignored. Some states form a fraction of an ADM1 state and when added up need to correspond to the values entered into the influent form of the ADM1 object. More detailed descriptions are given below:
Table 10‑2 – ADM1 State Variables Set in the Influent Object
|
Parameter |
Suggestion |
|
inert inorganic suspended solids |
Must be measured or estimated. It is not an ADM1 state but will impact the solids concentration. |
|
soluble inert organic material |
Same as the Si state in ADM1 |
|
readily biodegradable substrate |
Sum of Monosaccharides, Amino acids, Long chain fatty acids, Total valerate, Total butyrate, Total propionate, Total acetate, and Carbohydrates states in ADM1. Make sure this value is the sum of the values entered for these states in the ADM1 influent stream. |
|
particulate inert organic material |
Same as Xi state in ADM1. |
|
slowly biodegradable substrate |
Sum of composites, proteins, and lipids states in ADM1. Make sure this value is the sum of the values entered for these states in the ADM1 influent stream. |
|
active heterotrophic biomass |
Set to zero unless you have an estimate of it. |
|
active autotrophic biomass |
Set to zero unless you have an estimate of it. |
|
unbiodegradable particulates from cell decay |
Becomes part of Xi state in ADM1. Unless you know Xu, use Xi above and set this to zero |
|
internal cell storage product |
Not used. |
|
dissolved oxygen |
Not in ADM1 but used by GPS-X to estimate the COD demand of the influent stream. It is assumed that both oxygen and nitrate will be reduced instantaneously upon entering the anaerobic environment, so the total incoming COD is reduced by this incoming COD demand to compensate for the reduction of the electron acceptors present in the incoming stream. |
|
free and ionized ammonia |
Sin state in ADM1 (inorganic nitrogen). Make sure that correct units are used. |
|
soluble biodegradable organic nitrogen |
(nitrogen faction in amino
acids = 0.098) |
|
particulate biodegradable organic nitrogen |
Use the following formulas:
Xnd = total TKN - Snd - Snh - inxu*Xu -inxi*Xi
total TKN = Sin +
Ni
where:
Snd = conc. of soluble biodegradable organic nitrogen Snh = conc. of free and ionized ammonia inxu = nitrogen fraction of unbiodegradable particulates from cell decay (0.068 in Mantis, 0.06 in ASM1) inxi = nitrogen fraction of particulate inerts (0.068 in Mantis, 0.06 in ASM1) Xu = conc. of unbiodegradable particulates from cell decay Ni = nitrogen fraction of Si and Xi Si = conc. of soluble inerts Xi = conc. of particulate inerts Naa = nitrogen fraction of amino acids (0.098) Saa = conc. of amino acids Nxc = nitrogen fraction of composites (0.0376) Xc = conc. of composites |
|
nitrate and nitrite |
Not in ADM1 but used by GPS-X to estimate the COD demand of the influent stream. It is assumed that both oxygen and nitrate will be reduced instantaneously upon entering the anaerobic environment, so the total incoming COD is reduced by this incoming COD demand to compensate for the reduction of the electron acceptors present in the incoming stream. |
|
dinitrogen |
Set to zero. |
|
alkalinity |
Sic state in ADM1 (inorganic carbon). |
Aerobic Digestion Model
The objective of the aerobic digestion process is to stabilize and reduce the mass of solids for disposal. In this process, microorganisms consume their own protoplasm for energy; they are assumed to be in the endogenous phase. This phase is accounted for in the biological models associated with the CSTR object, but in aerobic digestion, destruction of particulate inert organic material also occurs.
The models associated with the aerobic digester are given the name <model>dig, where <model> is the associated activated sludge model (such as asm1, etc.). The only difference between the activated sludge model and its corresponding aerobic digester model is an added first-order reaction. This additional reaction adjusts the particulate inert organic concentration to account for the destruction of the inert organics:
Equation 10‑15
where:
rxi = rate of reaction for particulate inert organics (xi) (under Parameters – Kinetics menu of the anaerobic digester object)
ki = inert bioconversion rate
No loss of COD is involved in this process, and no electron acceptor is utilized. This destruction process converts particulate inert organics (xi) to slowly biodegradable substrate (xs). The slowly biodegradable substrate formed is then hydrolyzed, releasing an equivalent amount of readily biodegradable COD.
UASB/EGSB Model
The UASB/EGSB model is available only in MANTIS2LIB. The Mantis2 model is used to model the biological-chemical reactions in the reactor. Some of the assumptions made in the development of model are listed below.
1. The hydraulic regime in the UASB/EGSB is modeled as completely mixed reactor.
2. The substrate diffusion into the granule is assumed to be not limiting and the reactions are modeled similar to the suspended growth systems.
3. The average granule properties are used to estimate the granule settling velocity and bed expansion in the reactor.
4. A semi-empirical model is used to estimate the solid concentration distribution above the bed.
The simplified model structure is a first attempt to dynamically model the UASB//EGSB reactors for practical engineering problems.
Some of the important inputs and outputs of the model are described in following sections.
Reactor Parameters
Additional sets of input parameters are required for the UASB/EGSB model to estimate the granule settling velocity, bed fluidization and solid distribution profile above the sludge bed.
The Reactor Parameters can be accessed from the Input Parameters menu item (Figure 10‑11). The ReactorParameters form is as shown in Figure 10‑12.
Figure 10‑11 - Reactor Parameters for UASB/EGSB Reactor
Figure 10‑12 - Reactor Parameters Input Form
Fraction of un-reacted flow-through solids
It is well known that UASB/EGSB reactors are not very effective in treating the suspended solids in the wastewater. A fraction of the solids in the influent stream may just flow through the UASB/EGSB reactor without getting adsorbed or reacted in the reactor. This parameter allows users to specify the fraction of solids which will pass through the reactors un-reacted. Although, this phenomenon is normally observed, it is not very well quantified. The default value of this parameter is set at 0.5. In actual situation, depending on the bed expansion, the value of this parameter may vary.
Average granule size
This parameter is used to calculate the settling velocity of the granules in the granular bed. The estimated settling velocity is also used in estimating the bed expansion in the reactor. A default value of 2mm is used.
Terminal velocity reduction factor
The observed settling velocity of the biological granules is found to be less than the settling velocity estimation procedures. Normally a reduction factor of 0.7-0.8 is suggested in the literature.
Water content in granule
This parameter defines the water content in a granule and is used to estimate the density of the granule required in the settling velocity estimation procedure.
Void ratio of stationary granular bed
This parameter defines the void volume in the granular bed under no flow conditions.
Depth of transition zone
The UASB/EGSB model uses a semi-empirical model to decide the solid profile above the expanded granule bed. In the present model it is assumed that there exists a transition zone above the sludge bed in which the solid concentration changes from the concentration in the bed to a fraction of concentration at the end of transition zone. The depth of this transition zone will affect the solid profile and solid capture efficiency in the reactor.
Ratio of SS in transition zone to sludge bed
As described above, this parameter represents the ratio of solid concentration at the transition zone boundary to the solid concentration in the granule bed.
Fraction of non-settleable solids
This parameter signifies the fraction of finer particles in the bed which are non-settleable. This ratio is expressed with respect to the solid concentration in the reactor.
Solid recovery efficiency of gas solid separator
The solid distribution curve above the granule bed is used to estimate the solids concentration reaching the gas solid separator at the top UASB/EGSB reactors. Depending on the efficiency of the gas solid separator the concentration of solids escaping in effluent is estimated.