CHAPTER 16

Legacy Libraries

Appendix E: State Variables

Carbon – Nitrogen Library (CNLIB)

Sixteen state variables are available in the Carbon – Nitrogen library (Table 16‑1)

Table 16‑1 - Carbon – Nitrogen Library (CNLIB) State Variables

	State Variables	GPS-X Cryptic Symbols	Units
1.	inert inorganic suspended solids	xii	g/m3
2.	soluble inert organic material	si	gCOD/m3
3.	readily biodegradable substrate	ss	gCOD/m3
4.	particulate inert organic material	xi	gCOD/m3
5.	slowly biodegradable substrate	xs	gCOD/m3
6.	active heterotrophic biomass	xbh	gCOD/m3
7.	active autotrophic biomass	xba	gCOD/m3
8.	unbiodegradable particulates from cell decay	xu	gCOD/m3
9.	internal cell storage product	xsto	gCOD/m3
10.	dissolved oxygen	so	gO2/m3
11.	free and ionized ammonia	snh	gN/m3
12.	soluble biodegradable organic nitrogen	snd	gN/m3
13.	particulate biodegradable organic nitrogen	xnd	gN/m3
14.	nitrate and nitrite	sno	gN/m3
15.	dinitrogen	snn	gN/m3
16.	alkalinity	salk	mole/m3

Industrial Pollutant Library (CNIPLIB)

Forty-six (46) state variables are available in the Industrial Pollutant library. Sixteen (16) are pre-defined and thirty (30) are user-definable (15 soluble, 15 particulate). They are listed in Table 16‑2.

Table 16‑2 - Industrial Pollutant (CNIPLIB) Library State Variables.

	State Variables	GPS-X Cryptic Symbols	Units
1.	inert inorganic suspended solids	xii	g/m3
2.	soluble inert organic material	si	gCOD/m3
3.	readily biodegradable substrate	ss	gCOD/m3
4.	particulate inert organic material	xi	gCOD/m3
5.	slowly biodegradable substrate	xs	gCOD/m3
6.	active heterotrophic biomass	xbh	gCOD/m3
7.	active autotrophic biomass	xba	gCOD/m3
8.	unbiodegradable particulates from cell decay	xu	gCOD/m3
9.	internal cell storage product	xsto	gCOD/m3
10.	dissolved oxygen	so	gO2/m3
11.	free and ionized ammonia	snh	gN/m3
12.	soluble biodegradable organic nitrogen	snd	gN/m3
13.	particulate biodegradable organic nitrogen	xnd	gN/m3
14.	nitrate and nitrite	sno	gN/m3
15.	dinitrogen	snn	gN/m3
16.	alkalinity	salk	mole/m3
17.	soluble component "a"	sza	notset
18.	soluble component "b"	szb	notset
19.	soluble component "c"	szc	notset
20.	soluble component "d"	szd	notset
21.	soluble component "e"	sze	notset
22.	soluble component "f"	szf	notset
23.	soluble component "g"	szg	notset
24.	soluble component "h"	szh	notset
25.	soluble component "i"	szi	notset
26.	soluble component "j"	szj	notset
27.	soluble component "k"	szk	notset
28.	soluble component "l"	szl	notset
29.	soluble component "m"	szm	notset
30.	soluble component "n"	szn	notset
31.	soluble component "o"	szo	notset
32.	particulate component "a"	xza	notset
33.	particulate component "b"	xzb	notset
34.	particulate component "c"	xzc	notset
35.	particulate component "d"	xzd	notset
36.	particulate component "e"	xze	notset
37.	particulate component "f"	xzf	notset
38.	particulate component "g"	xzg	notset
39.	particulate component "h"	xzh	notset
40.	particulate component "i"	xzi	notset
41.	particulate component "j"	xzj	notset
42.	particulate component "k"	xzk	notset
43.	particulate component "l"	xzl	notset
44.	particulate component "m"	xzm	notset
45.	particulate component "n"	xzn	notset
46.	particulate component "o"	xzo	notset

Carbon – Nitrogen – Phosphorus Library (CNPLIB)

Twenty-seven (27) state variables are available in the Carbon – Nitrogen – Phosphorus library (Table 16‑3).

Table 16‑3 - Carbon – Nitrogen – Phosphorus (CNPLIB) Library State Variables

	State Variables	GPS-X Cryptic Symbols	Units
1.	inert inorganic suspended solids	xii	g/m3
2.	soluble inert organic material	si	gCOD/m3
3.	readily biodegradable substrate	ss	gCOD/m3
4.	fermentable readily biodegradable substrate	sf	gCOD/m3
5.	volatile fatty acids	slf	gCOD/m3
6.	particulate inert organic material	xi	gCOD/m3
7.	slowly biodegradable substrate	xs	gCOD/m3
8.	active heterotrophic biomass	xbh	gCOD/m3
9.	active autotrophic biomass	xba	gCOD/m3
10.	active poly-P accumulating biomass	xbp	gCOD/m3
11.	unbiodegradable particulates from cell decay	xu	gCOD/m3
12.	internal cell storage product	xsto	gCOD/m3
13.	poly-hydroxy-alkanoates (PHA)	xbt	gCOD/m3
14.	stored glycogen	xgly	gCOD/m3
15.	dissolved oxygen	so	gO2/m3
16.	soluble ortho-phosphate	sp	gP/m3
17.	stored polyphosphate	xpp	gP/m3
18.	stored polyphosphate (releasable)	xppr	gP/m3
19.	free and ionized ammonia	snh	gN/m3
20.	soluble biodegradable organic nitrogen	snd	gN/m3
21.	particulate biodegradable organic nitrogen	xnd	gN/m3
22.	nitrate and nitrite	sno	gN/m3
23.	soluble unbiodegradable organic nitrogen	sni	gN/m3
24.	dinitrogen	snn	gN/m3
25.	alkalinity	salk	mole/m3
26.	metal-hydroxides	xmeoh	g/m3
27.	metal-phosphates	xmep	g/m3

CNP Industrial Pollutant Library (CNPIPLIB)

Fifty-seven (57) state variables are available in the CNP Industrial Pollutant Library (CNPIPLIB). These include the 27 state variables from CNPLIB, as well as 30 user‑definable variables (15 soluble and 15 particulate) as shown in Table 16‑4.

Table 16‑4 - CNP Industrial Pollutant (CNPIPLIB) Library State Variables

	State Variables	GPS-X Cryptic Symbols	Units
1.	inert inorganic suspended solids	xii	g/m3
2.	soluble inert organic material	si	gCOD/m3
3.	readily biodegradable substrate	ss	gCOD/m3
4.	fermentable readily biodegradable substrate	sf	gCOD/m3
5.	volatile fatty acids	slf	gCOD/m3
6.	particulate inert organic material	xi	gCOD/m3
7.	slowly biodegradable substrate	xs	gCOD/m3
8.	active heterotrophic biomass	xbh	gCOD/m3
9.	active autotrophic biomass	xba	gCOD/m3
10.	active poly-P accumulating biomass	xbp	gCOD/m3
11.	unbiodegradable particulates from cell decay	xu	gCOD/m3
12.	internal cell storage product	xsto	gCOD/m3
13.	poly-hydroxy-alkanoates (PHA)	xbt	gCOD/m3
14.	stored glycogen	xgly	gCOD/m3
15.	dissolved oxygen	so	gO2/m3
16.	soluble ortho-phosphate	sp	gP/m3
17.	stored polyphosphate	xpp	gP/m3
18.	stored polyphosphate (releasable)	xppr	gP/m3
19.	free and ionized ammonia	snh	gN/m3
20.	soluble biodegradable organic nitrogen	snd	gN/m3
21.	particulate biodegradable organic nitrogen	xnd	gN/m3
22.	nitrate and nitrite	sno	gN/m3
23.	soluble unbiodegradable organic nitrogen	sni	gN/m3
24.	dinitrogen	snn	gN/m3
25.	alkalinity	salk	mole/m3
26.	metal-hydroxides	xmeoh	g/m3
27.	metal-phosphates	xmep	g/m3
28.	soluble component "a"	sza	notset
29.	soluble component "b"	szb	notset
30.	soluble component "c"	szc	notset
31.	soluble component "d"	szd	notset
32.	soluble component "e"	sze	notset
33.	soluble component "f"	szf	notset
34.	soluble component "g"	szg	notset
35.	soluble component "h"	szh	notset
36.	soluble component "i"	szi	notset
37.	soluble component "j"	szj	notset
38.	soluble component "k"	szk	notset
39.	soluble component "l"	szl	notset
40.	soluble component "m"	szm	notset
41.	soluble component "n"	szn	notset
42.	soluble component "o"	szo	notset
43.	particulate component "a"	xza	notset
44.	particulate component "b"	xzb	notset
45.	particulate component "c"	xzc	notset
46.	particulate component "d"	xzd	notset
47.	particulate component "e"	xze	notset
48.	particulate component "f"	xzf	notset
49.	particulate component "g"	xzg	notset
50.	particulate component "h"	xzh	notset
51.	particulate component "i"	xzi	notset
52.	particulate component "j"	xzj	notset
53.	particulate component "k"	xzk	notset
54.	particulate component "l"	xzl	notset
55.	particulate component "m"	xzm	notset
56.	particulate component "n"	xzn	notset
57.	particulate component "o"	xzo	notset

Appendix F: Composite Variable Calculations

State Variables in CNLIB

Figure 16‑1 shows the relationship between the CNLIB state variables and the TSS, BOD, and COD composite state variables. Table 16‑5 illustrates the same composite variable calculations in the tabular format.

Figure 16‑1 – Carbon – Nitrogen Library (CNLIB): BOD, COD, and Suspended Solids Composite Variables and their Relationship to the State Variables

>Table 16‑5 – CNLIB BOD, COD, and TSS Composite Variables (All Models)

SBODU

XBODU

BODU

SBOD

XBOD

BOD

SCOD

XCOD

COD

VSS

XISS

X

si

1

1

ss

1

1

fbod

fbod

1

1

xi

1

1

icv^-1

icv^-1

xs

1

1

fbod

fbod

1

1

icv^-1

icv^-1

xbh

1

1

fbod

fbod

1

1

icv^-1

icv^-1

xba

1

1

fbod

fbod

1

1

icv^-1

icv^-1

xu

1

1

icv^-1

icv^-1

xsto

1

1

fbod

fbod

1

1

icv^-1

icv^-1

xii

1

1

The COD composite variables are a sum of state variables (where units are gCOD/m³). Soluble COD (SCOD) is the sum of the soluble inert organics (si) and readily biodegradable substrate (ss), while particulate COD (XCOD) is the sum of the slowly biodegradable substrate (xs), active heterotrophic biomass (xbh), active autotrophic biomass (xba), cell internal storage product (xsto), un-biodegradable particulates from cell decay (xu), and particulate inert organics (xi). The total COD (COD) is the sum of the soluble and particulate COD.

The suspended solids composite variable (X) is calculated from the particulate COD (XCOD) by dividing it by the XCOD: VSS ratio (icv), which changes the units of the XCOD to mgVSS/L, resulting in the volatile suspended solids (VSS) composite variable. To calculate the suspended solids composite variable (X), VSS is added to particulate inert inorganic material (XII). By default, in the CN library, particulate inert suspended solids (XISS) is equal to xii.

The biochemical oxygen demand (BOD) composite variables are calculated from the state variables. First, the biodegradable state variables (the state variables that exert BOD, which are in units of gO/m³) are summed to provide both a particulate and a soluble ultimate BOD (XBODU, SBODU). The sum of these components is the total ultimate BOD measurement (BODU).  To determine BOD₅, the calculated BODU is multiplied by a stoichiometric fraction, fbod, which is the ratio of BOD₅:BOD_U.

In terms of variables containing nitrogen, the calculation of the composite variables involves adding up various state variables and multiplying other state variables by fractions as appropriate (Figure 16‑2). The soluble total Kjeldahl nitrogen (STKN) is the sum of the free and ionized ammonia (snh), soluble biodegradable organic nitrogen (snd), and (in asm3 only) the nitrogen components of soluble substrate (ss) and soluble inerts (si). The particulate total Kjeldahl nitrogen (XTKN) is the particulate biodegradable organic nitrogen (xnd), plus the nitrogen component of biomass (xbh and xba), unbiodegradable cell products (xu), particulate substrate (xs) and particulate inerts (xi). Total Kjeldahl nitrogen (TKN) is the sum of soluble (STKN) and particulate TKN (XTKN). The total nitrogen (TN) is the sum of the TKN and the nitrate nitrogen (sno).

Figure 16‑2 – Carbon – Nitrogen Library: Composite Variables and their Relationships to the State Variables

The nitrogen fractions of xbh, xba, xu, xi, ss and si vary from model to model. The nitrogen composite variable relationships for the mantis, asm1 and asm3 models are shown in Table 16‑6, Table 16‑7, and Table 16‑8

Table 16‑6 – CNLIB Nitrogen Composite Variables – Mantis Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
snd	1		1	1
xnd		1	1	1
xbh		ibhn	ibhn	ibhn
xba		ibhn	ibhn	ibhn
xu		iuhn	iuhn	iuhn
xi		iuhn	iuhn	iuhn

Table 16‑7 – CNLIB Nitrogen Composite Variables – ASM1 Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
snd	1		1	1
xnd		1	1	1
xbh		ixbn	ixbn	ixbn
xba		ixbn	ixbn	ixbn
xu		ixun	ixun	ixun
xi		ixun	ixun	ixun

Table 16‑8 - CNLIB Nitrogen Composite Variables - ASM3 Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
si	insi		insi	insi
ss	inss		inss	inss
xbh		inbm	inbm	inbm
xba		inbm	inbm	inbm
xs		inxs	inxs	inxs
xi		inxi	inxi	inxi
snd	1		1	1
xnd		1	1	1

Composite Variables in CNIPLIB

The relationship between the state and composite variables are the same as those for CNLIB (Figure 16‑2 and Table 16‑8). Table 16‑6 through Table 16‑8 illustrates the composite variable calculations for the mantis1, asm1, and asm3 models in CNIPLIB.

Composite Variables in CNPLIB

Figure 16‑3 shows the relationships between CNPLIB state variables and the TSS, BOD and COD composite variables. Table 16‑9 illustrates the same composite variable calculations in tabular format.

As all the state variables are in units of gCOD/m³, the COD composite variables are simply a sum of the appropriate state variables. In general, the soluble COD (SCOD) is a sum of the soluble inert organics (si), volatile fatty acids (slf), fermentable readily biodegradable substrate (sf), and readily biodegradable substrate (ss). The particulate COD (XCOD) is a sum of the slowly biodegradable substrate (xs), active heterotrophic biomass (xbh), active autotrophic biomass (xba), polyphosphate accumulating biomass (xbp), stored glycogen (xgly), poly-hydroxy-alkanoates (xbt), unbiodegradable particulates from cell decay (xu), cell internal storage product (xsto) and particulate inert organics (xi). The total COD (COD) is the sum of the soluble and particulate COD.

Figure 16‑3 – Carbon – Nitrogen – Phosphorus Library: BOD, COD, and Suspended Solids Composite Variables and their Relationship to the State Variables

The suspended solids composite variable is calculated from the particulate COD (XCOD) by dividing it by the XCOD:VSS ratio (icv). This changes the units of the XCOD to gVSS/m³, resulting in the composite variable for volatile suspended solids (VSS). To calculate the suspended solids composite variable (X), VSS is added to the concentration of inert inorganic particulates (XII), metal hydroxides (xmeoh) and metal phosphates (xmep), and stored polyphosphate (multiplied by 3 to change from gP/m³ to g/m³).

The biochemical oxygen demand (BOD) composite variables are calculated from the state variables. The biodegradable state variables (the state variables that exert BOD, which are in units of gCOD/m³) are summed to provide a particulate and a soluble ultimate BOD (XBODU, SBODU). The sum of these components is the total ultimate BOD measurement (BODU). To determine BOD₅, a stoichiometric fraction, fbod, which is the ratio of BOD₅:BOD₂₀, is multiplied by the calculated BODU.

Table 16‑9 - CNPLIB BOD, COD, and TSS Composite Variables

	SBODU	XBODU	BODU	SBOD	XBOD	BOD	SCOD	XCOD	COD	VSS	XISS	X
ss	1		1	fbod		fbod	1		1
sf	1		1	fbod		fbod	1		1
slf	1		1	fbod		fbod	1		1
xs		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xbh		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xba		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xpb		1	1		fbod	fbod		1	1	icv^-1		icv^-1
si							1		1
xi								1	1	icv^-1		icv^-1
xu								1	1	icv^-1		icv^-1
xgly		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xbt		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xsto		1	1		fbod	fbod		1	1	icv^-1		icv^-1
xii											1	1
xmeoh											1	1
xmep											1	1
xpp											3	3
xppr											3	3

In terms of variables containing nitrogen, the calculation of the composite variables is similar to the calculations done in the Carbon - Nitrogen library. The differences include the addition of a new state variable, soluble unbiodegradable organic nitrogen (sni), to the soluble TKN (STKN), the inclusion of nitrogen components of the new substrate type (sf), and the inclusion of nitrogen components of poly‑phosphate-accumulating organisms (xbp). See Figure 16‑4 for a general diagram of the nitrogen composite variable calculations.

Figure 16‑4 - Carbon - Nitrogen - Phosphorus Library: Nitrogen Composite Variables and their Relationships to the State Variables

Table 16‑10 - CNPLIB Nitrogen Composite Variables - Mantis Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
sni	1		1	1
snd	1		1	1
xnd		1	1	1
xbh		ibhn	ibhn	ibhn
xba		ibhn	ibhn	ibhn
xi		iuhn	iuhn	iuhn
xu		iuhn	iuhn	iuhn

The calculation for nitrogen state variables differs slightly from model to model. In particular, the nitrogen fractions of biomass and other particulate components have different names from model to model. Table 16‑10 through Table 16‑14 shows the nitrogen composite variable calculations for the mantis, asm1, asm2d, asm3 and newgeneral models in CNPLIB.

Table 16‑11 - CNPLIB Nitrogen Composite Variables - ASM1 Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
sni	1		1	1
snd	1		1	1
xnd		1	1	1
xbh		ixbn	ixbn	ixbn
xba		ixbn	ixbn	ixbn
xi		ixun	ixun	ixun
xu		ixun	ixun	ixun

Table 16‑12 - CNPLIB Nitrogen Composite Variables - ASM2d Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
sni	1		1	1
snd	1		1	1
xnd		1	1	1
si	insi		insi	insi
sf	insf		insf	insf
xbp		inbm	inbm	inbm
xbh		inbm	inbm	inbm
xba		inbm	inbm	inbm
xi		inxi	inxi	inxi
xs		inxs	inxs	inxs

Table 16‑13 - CNPLIB Nitrogen Composite Variables - ASM3 Model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
sni	1		1	1
snd	1		1	1
xnd		1	1	1
xbh		inbm	inbm	inbm
xba		inbm	inbm	inbm
xi		inxi	inxi	inxi
xs		inxs	inxs	inxs
ss	inss		inss	inss
si	insi		insi	insi

Table 16‑14 - CNPLIB Nitrogen Composite Variables - NEWGENERAL model

	STKN	XTKN	TKN	TN
sno				1
snh	1		1	1
sni	1		1	1
snd	1		1	1
xnd		1	1	1
xbp		fnzh	fnzh	fnzh
xbh		fnzh	fnzh	fnzh
xba		fnzh	fnzh	fnzh
xi		fnzeh	fnzeh	fnzeh
xu		fnzeh	fnzeh	fnzeh

Generally, soluble total phosphorus (STP) is equal to the sum of soluble phosphorus (sp) and the phosphorus components of ss, si, and sf, as appropriate. Particulate total phosphorus (XTP) is the sum of stored polyphosphate (xpp and xppr) and the phosphorus components of xs, xi, xbh, xba, xbp and xmeoh. See Figure 16‑5 for a schematic of these calculations. The calculations differ slightly from model to model. Table 16‑15 to

Table 16‑18 describe the phosphorus composite variable calculations.

Figure 16‑5 - Carbon - Nitrogen - Phosphorus Library: Phosphorus Composite Variables and their Relationship to the State Variables

Table 16‑15 - CNPLIB Phosphorus Composite Variables - ASM1/Mantis Models

	STP	XTP	TP
sp	1		1
xi		ixup	ixup
xu		ixup	ixup
xbh		ixbp	ixbp
xba		ixbp	ixbp
xbp		ixbp	ixbp
xmep		0.205	0.205
xpp		1	1
xppr		1	1

Table 16‑16 – CNPLIB Phosphorus Composite Variables – ASM3 Model

	STP	XTP	TP
sp	1		1
ss	ipss		ipss
si	ipsi		ipsi
xi		ipxi	ipxi
xs		ipxs	ipxs
xbh		ixbp	ixbp
xba		ixbp	ixbp
xbp		ixbp	ixbp
xmep		0.205	0.205
xpp		1	1
xppr		1	1

Table 16‑17 - CNPLIB Phosphorus Composite Variables - ASM2d Model

	STP	XTP	TP
sp	1		1
sf	ipsf		ipsf
si	ipsi		ipsi
xi		ipxi	ipxi
xs		ipxs	ipxs
xbh		ipbm	ipbm
xba		ipbm	ipbm
xbp		ipbm	ipbm
xmep		0.205	0.205
xpp		1	1
xppr		1	1

Table 16‑18 - CNPLIB Phosphorus Composite Variables - NEWGENERAL Model

	STP	XTP	TP
sp	1		1
xpp		1	1
xppr		1	1
xi		fpzeh	fpzeh
xu		fpzeh	fpzeh
xbh		fpzh	fpzh
xba		fpzh	fpzh
xbp		fpzh	fpzh
xmep		0.205	0.205

Composite Variables in CNPIPLIB

The relationships between the state variables and composite variables are similar to the Carbon-Nitrogen-Phosphorus library (CNPLIB). Table 16‑10 through

Table 16‑18 shows the relationships between the state and composite variables that are used in the models in CNPIPLIB.

Composite Variables Calculated from Non-Modelled States

Whether stoichiometry has been set globally or locally within each object, the list of composite variables that are available to be displayed will depend on which library has been used for that particular GPS-X layout (CNLIB, CNPLIB, etc.).

It is possible to use a model in the layout that does not simulate the fate of all components of a given library (e.g. mantis in CNPLIB, which does not model phosphorus even though there are phosphorus state variables in CNPLIB). In these cases, these extra components will be modelled as if they were inert (i.e. no biological transformation applied, but mixing and settling are applied).

The composite variable list displayed in the Output Variables > Concentrations menu is the list associated with the library used to create the layout (e.g. CNPLIB). All composite variables are calculated for the given library, even if the component states are not modelled biologically in the reactor. For the example above (mantis model in CNPLIB), soluble phosphorus (sp) is not modelled biologically, and therefore behaves the same as si (soluble inerts); however, because CNPLIB contains the composite variable TP (total phosphorus), it will be calculated (from sp and other components) even though sp was modelled as an inert.

It is important to take this into consideration when selecting which model and library you will be using when creating your plant layout.

Appendix G: Legacy Library Influent Model

Influent Objects in CNLIB, CNPLIB, CNIPLIB, CNPIPLIB

There are five (5) influent objects in GPS-X:

Table 16‑19 – Influent Objects

Name	Object	Use	Models Available
Wastewater Influent		Continuous wastewater flows (steady or dynamic)	bodbased codbased codstates sludge states tssfrac
Batch Influent		Batch deliveries of septage or other discontinuous wastewater flows	bodbased codbased codstates sludge states tssfrac
Water Influent		Clean water input (steady or dynamic)	water
COD Chemical Dosage		Dosage of COD into streams or objects	codfeed
Acid Dosage		Dosage of acid for pH control	acidfeed

The influent objects contain models, options, and features that are relevant to the type of influent being used.  For example, the continuous wastewater model has options for specifying a diurnal pattern for influent flow, a feature not found in the chemical dosage object.

Wastewater Influent Object

The wastewater influent object (brown arrow) is used to characterize continuous streams of wastewater flow.  The continuous influent flow rate is specified in the influent object’s Flow > Flow Data menu. (Figure 16‑6 and Figure 16‑7)

Figure 16‑6 - Selecting the Influent Flow Data Menu

Figure 16‑7 - Influent Flow Data Menu, showing Flow Type Options

The flow is specified via one of the four methods:

1. Data – users set the flow rate directly, via menu entry or read from file.

2. Sinusoidal – GPS-X applies a sinusoidal curve to the influent flow set in the menu or read from file.

3. Diurnal Flow – a daily diurnal patter is set via flow rates at different times of the day.

4. Diurnal Flow Factor – a daily diurnal pattern is set via flow rates at different times of the day.

Wastewater Influent Models

The influent models available in GPS-X depend on the model library and the local biological model used to relate the state variables to the composite variables. The manner in which the state variables are calculated sometimes differs from model to model and library to library. This chapter discusses the models available and the flow choices available with the batch influent object.

Figure 16‑8 - The Influent Models

Each influent model calculates a complete set of library-dependent state variables that are passed to the rest of the plant layout. The influent models differ only in the type of information required as inputs to the model.

The descriptions of the influent models that follow are an overview of how they work; however, due to their complexity and their dependence on the local biological model, and the library currently in use, users are referred to the Influent Advisor to understand the calculations being made in each model.

BODbased

The BODbased influent model is the choice when BOD data is available and COD data is not available; however, due to the approximations and the nature of the BOD measurement, special care must be taken to properly estimate influent particulate inerts. If this model is selected, the user inputs total carbonaceous BOD₅, total TKN, total suspended solids, a few state variables. The state variables are normally zero, except for the soluble inert organics, soluble ortho-phosphate (CNPLIB) and alkalinity (Figure 16‑9 and Figure 16‑10 and several stoichiometric fractions).

These inputs are used to calculate the remaining influent state variables: readily biodegradable substrate (ss), slowly biodegradable substrate (xs), particulate inert organics (xi), free and ionized ammonia (snh), particulate biodegradable organic nitrogen (xnd), and soluble biodegradable organic nitrogen (snd).

Figure 16‑9 – Mantis2 Library BODbased Influent Model Inputs

The relationships between the calculated state variables and the composite and stoichiometric fractions are library-specific and the relationships are shown in the Figure 16‑11 and Figure 5‑7. BODultimate is assumed to be equivalent to the biodegradable COD.

The stoichiometric fraction fss (soluble substrate:BODultimate), is used to determine what fraction of the total BODultimate is soluble substrate (sf for asm2d or ss for all other biological models). In terms of sampling measurements, the fraction fss can be estimated from the ratio of filtered BOD₂₀ :BOD₂₀. The particulate substrate state variable (xs) is then calculated by difference (i.e. in CNLIB, xs = BODultimate * (1-fss) -xba-xbh-xsto)). The particulate inert organics (xi) state variable is calculated by subtracting all the other particulate carbonaceous organic states (xsto, xbh, xba, xu (all input by user) and xs (calculated above)) from the particulate COD (XCOD).

Calculation of the three unknown nitrogen state variables depends on the calculation of TKN which is biological model-dependent.  For instance, with the asm1 or mantis models the amount of free and ionized ammonia (snh) is the fraction of ammonia (fnh)multiplied by the TKN. The remainder is the biodegradable organic nitrogen, which is partitioned into three areas including nitrogen associated with particulate state variables (i.e. xbh, xba, xi and xu), and soluble and particulate organic nitrogen (snd and xnd) using the fxn fraction and the nitrogen fractions of the particulate state variables (Figure 16‑10).

Figure 16‑10 – Mantis2 Library Nutrient Fractions for the BODbased Influent Model

This differs from the calculations made when asm3 has been chosen as the local biological model because snd and xnd are not state variables in asm3. In this case, soluble TKN is calculated as the difference between the total TKN and the particulate TKN. The nitrogen associated with the soluble state variables (ss and si) is subtracted from the soluble TKN and the remaining TKN is equated to ammonia (snh). Hence, in the asm3 BOD based influent model, fnh and fxn are not used. Influent Advisor will help users determine what parameters are necessary for each mode.

Figure 16‑11 - Influent Specific Stoichiometric Parameters

Figure 16‑12 - Fixed Stoichiometric Parameters in Mantis2LIB

CODFractions

This model requires an input of total COD, total TKN, total phosphorus (in CNPLIB), state variables (the state variables are normally zero except for ammonia, soluble ortho‑phosphate and alkalinity) and several stoichiometric fractions. From these inputs, the complete set of state variables, composite variables and nutrient fractions are calculated (Figure 16‑19, Figure 16‑20 and Figure 16‑21).

The calculation of the nitrogen and phosphorus (CNPLIB) state variables and fractions is complicated in the codfractions influent models. This is because some of the nitrogen and phosphorus in the influent is associated with the organic state variables.(i.e. N content of active biomass). Therefore, the model must adjust itself depending on the applicable composite variable model and the current organic states. As with the other influent models, these nutrient fractions are specified in this model. However, in the event that a mass balance is not achievable with the user input data, the codfractions model will recalculate these nutrient fractions to force the mass balance. It is recommended that Influent Advisor be used to set-up and understand these calculations.

This model has the advantage that each of the calculations is based on the total COD, total TKN, total phosphorus (CNPLIB), soluble ortho-phosphate (CNPLIB) and ammonia inputs. Therefore, (as often is available in practice) a series of these data over a period of time can be read in from a data file and the influent state variables will vary with the load. This is in contrast to other influent models in which some state variables are input directly and will not automatically vary with a load change.

CODStates

This model works similarly to the codfractions influent model, however all COD input fractions are set as a fraction of total COD.  This allows users to specify total COD, TKN and ammonia as their main characterization inputs.  Soluble inert COD (si), readily biodegradable substrate (ss, sf or slf), particulate inert material (xi), unbiodegradable cell products (xu) and biomass concentrations (xbh, xba and xbp) are specified via fractions of total COD, as shown in Figure 16‑13.

Figure 16‑13 - CODstates Influent Model Inputs

This model has been designed to mimic the input of a sludge stream. The user inputs the total suspended solids, a few state variables, and a couple of stoichiometric fractions. From these inputs, the organic solids are partitioned into heterotrophic biomass (i.e. degradable particulate material), polyphosphate accumulating biomass (CNPLIB only) and un-biodegradable particulate material. The remaining particulate organic state variables are set to zero. All the soluble state variables are defaulted to zero in this model, except for dissolved oxygen and alkalinity.

This model is appropriate if a full influent characterization has been performed and the influent state variables have been calculated manually. If the user selects the states model, input values for the state variables, and a few stoichiometric fractions used for calculating the composite variables are required. The CNLIB states data entry form (Composition > Influent Composition) is shown in Figure 16‑13, and the stoichiometry entry form (Composition > Influent Stoichiometry) is shown in Figure 16‑14.

Figure 16‑14 - CN Library States Influent Model Influent Stoichiometry Inputs

TSSCOD

The tsscod influent model can be used successfully if the influent was characterized using COD and suspended solids as the main components. The tsscod influent model was developed based on the Activated Sludge Model No. 2 report (Henze et al., 1995).

If this model is selected, the user inputs total COD, total TKN, total suspended solids, a few state variables (the state variables are normally zero except for the soluble inert organics, soluble ortho-phosphate (CNPLIB) and alkalinity and several stoichiometric fractions. These inputs are then used to calculate the remaining state variables (Figure 16‑9 and Figure 16‑10).

Particulate COD (XCOD) is calculated from the TSS using two stoichiometric fractions. This is then divided into its component parts via stoichiometric fractions or explicitly as read from the data input forms leaving the particulate inert organics component (xi) to be calculated by subtraction.  Figure 16‑16 shows how the soluble COD (SCOD) components are calculated from the COD, XCOD and the stoichiometric parameter, frsi. See the bodbased model for the calculation of the nitrogen and phosphorus (CNPLIB) state variables. It is recommended that Influent Advisor be used to understand these calculations.

Figure 16‑15 - CN Library tsscod Model Particulate Inert Calculation

Figure 16‑16 - CN Library tsscod Influent Soluble Components Calculation

Chemical Dosage Influent Object

The chemical dosage influent object (blue arrow) is used to characterize streams which are not typical wastewater inputs, but rather chemical or water inputs to a wastewater treatment process.  The models found in the chemical dosage influent have been developed specifically for this purpose, and are set up for easy conversion of typical chemical components into the state variables used in the biological models.  The flow is specified only through the Data option as described in Figure 16‑7.

Acetate

The acetate influent model can be used to simulation the addition of acetate to the treatment process. The acetate dose (as acetic acid) can be entered as a percentage of purity, or in a variety of units (mol acetate/L, g (acetate*COD)/m³, g(acetate)/L, etc.), by selecting from the drop-down units menu (Figure 16‑17). The COD equivalent of the acetate dose is automatically converted to slf if asm2d or newgeneral have been chosen for the local biological model or ss (readily biodegradable substrate) for all other local biological models.

Figure 16‑17 - CN Library Acetate Influent Model - Acetate Dose Form

The methanol influent model can be used to simulate the addition of methanol to the treatment process. The methanol dose can be entered as a percentage of purity, or in a variety of other units (mol methanol/L, g(methanol*COD)/m³, g(methanol)/L, etc.), by selecting from the units drop-down menu (Figure 16‑18). The COD equivalent of the methanol dose is automatically converted to sf if asm2d has been chosen for the local biological model or ss (readily biodegradable substrate) for all other local biological models.

Figure 16‑18 - CN Library Methanol Influent Model Inputs

This influent model was developed to simulate a rain event or alkalinity addition whereby the influent hydraulic load could be increased without increasing the organic or nitrogen load to the plant. In the water influent, the only variable to be provided in the composition menu is the alkalinity. All other state variables are set to zero.

Influent Appendices

Model-Dependent State and Composite Variables

When setting up your influent model, it is important that you realize what state variables are used in each biological model. The following sections outline the state variables used in the models in the different libraries.

Of similar importance is an understanding of how the composite variables are calculated from the state variables. This is important because many of the influent models go backwards (i.e. from the composite variables to the state variables); hence, an understanding of these relationships will help if debugging is necessary. Influent Advisor has been developed specifically to help navigate the more complicated influent models. The following figures were developed to help with this understanding.

The composite variable figures are copies of the figures presented in the composite variables chapter of this Reference; however, they are repeated here because of their importance to the influent model calculations.

CN and CNIP Libraries

This section contains one table and two figures which are to help the user understand how GPS-X has calculated the CNLIB state variables, and what state variables should be calculated depending on which biological model you are using.

Table 16‑20 - State Variables Used in Each Biological Model Included in CNLIB and CNIPLIB

State Variable	Mantis	ASM1	ASM3
si	✓	✓	✓
ss	✓	✓	✓
xi	✓	✓	✓
xs	✓	✓	✓
xu	✓	✓
xsto			✓
xbh	✓	✓	✓
xba	✓	✓	✓
so	✓	✓	✓
snh	✓	✓	✓
snd	✓	✓
xnd	✓	✓
sno	✓	✓	✓
snn	✓	✓	✓
salk	✓	✓	✓
xii	✓	✓	✓

CNP and CNPIP Libraries

This section contains one table and three figures which are to help the user understand how GPS-X has calculated the CNPLIB state variables, and what state variables should be calculated depending on which biological model you are using.

Table 16‑21 – State Variables Used in Each Biological Model included in CNPLIB and CNPIPLIB

State Variable	Mantis	ASM1	ASM2d	ASM3	NewGeneral
si	✓	✓	✓	✓	✓
ss	✓	✓		✓	✓
sf			✓
slf			✓		✓
xi	✓	✓	✓	✓	✓
xs	✓	✓	✓	✓	✓
xu	✓	✓			✓
xbh	✓	✓	✓	✓	✓
xba	✓	✓	✓	✓	✓
xbp			✓		✓
xbt			✓		✓
xsto				✓
so	✓	✓	✓	✓	✓
sp			✓		✓
xpp			✓		✓
xppr					✓
snh	✓	✓	✓	✓	✓
snd	✓	✓			✓
xnd	✓	✓			✓
sno	✓	✓	✓	✓	✓
snn	✓	✓		✓
salk	✓	✓	✓	✓	✓
xmeoh			✓
xmep			✓
xii	✓	✓	✓	✓	✓

Figure 16‑19 - CNP Library Organic State and Composite Variables

Figure 16‑20 - CNP Library Nitrogen State and Composite Variables

Figure 16‑21 - CNP Library Phosphorus State and Composite Variables

Appendix H: Suspended Growth Model

Activated Sludge Model No. 1 (ASM1)

Introduction

The International Association on Water Pollution Research and Control (IAWPRC) Task Group realized that due to the long solids retention times and low growth rates of the bacteria, the actual effluent substrate concentrations between different activated sludge treatment plants did not vary greatly. What were significantly different were the levels of MLSS and electron acceptor (oxygen or nitrate). Thus the focus of the Activated Sludge Model No. 1 (called asm1 in GPS-X) is the prediction of the amount and change of the solids and electron acceptor.

The Task Group considered the trade-off between model accuracy and practicality. They identified the major biological processes occurring in the system and characterized these processes with the simplest rate expressions that could be used, resembling the real reactions.

The use of switching functions was made by the Task Group since some reactions depended on the type of electron acceptor present. These functions were of the form:

Equation 16‑1

At low concentrations of dissolved oxygen (S_O), the parameter K_OH dominates the expression and approaches a value of zero. At high values of S_O, the parameter K_OH would be negligible and the expression approaches unity. If the switching function was inverted, then the limits when S_O were high or low are reversed. A consequence of using switching functions of this form is that they are continuous functions unlike discontinuous on/off switches which are more difficult to simulate.

Conceptual Model

In the development of activated sludge modelling, the manner in which the quantity of organic matter is measured (BOD, COD or TOC) is inconsistent. The Task Group decided to use COD since mass balances can be carried out and since it has links to the electron equivalents in the organic substrate, biomass and electron acceptor.

The organic material is categorized according to a number of characteristics. First, is the biodegradability of the material. The non-biodegradable organics pass through the system unchanged and can be further categorized according to their physical state (soluble or particulate), which is removed from the system by different pathways. The particulate material is generally removed with the waste activated sludge, while the soluble material leaves with the effluent. The biodegradable material is categorized as either readily or slowly biodegradable. The Task Group treated the former as soluble material, while the latter was treated as particulate material (this is not strictly correct, but simplifies matters). The readily biodegradable organics may be utilized for cell maintenance or growth with a transfer of electrons to the acceptors. The particulate (slowly) biodegradable substrate is hydrolyzed to readily biodegradable material, assuming no energy utilization and no corresponding use of electron acceptor.

The hydrolysis rate is usually slower than the utilization of readily biodegradable substrate so that it is the rate limiting step, if only slowly biodegradable substrate is available.

Two types of biomass are modelled:

1. heterotrophic; and

2. autotrophic

The heterotrophic biomass is generated by the growth on readily biodegradable substrate under aerobic or anoxic conditions and decays (including endogenous respiration, death, predation and lysis) under all conditions. The autotrophic biomass is generated under aerobic conditions only utilizing ammonia for energy and decays under all conditions.

The nitrogenous material is categorized according to its biodegradability and physical state. The non-biodegradable particulate material is modelled as a fraction of the non-biodegradable particulate COD, while the non-biodegradable soluble material is ignored. The biodegradable nitrogenous material is divided into ammonia (free and ionized), soluble organic and particulate organic. Particulate organic is hydrolyzed to soluble organic, while soluble organic is converted to ammonia by the heterotrophic biomass. The conversion of ammonia to nitrate by the autotrophs is assumed to take place in one step.

The Model Matrix for asm1 is found in Appendix A.

Activated Sludge Model No. 2 (ASM2)

Asm2 is no longer implemented in GPS-X, in favour of using the asm2d model (see below), which corrects errors and deficiencies from the original published model.

Activated Sludge Model No. 2d (ASM2d)

Introduction

This model (asm2d) is an implementation of the Activated Sludge Model No. 2d (Henze et al., 1998). The model structure, default values and all other model aspects follow the publication in every detail.

This model is an extension of asm1, primarily to handle biological phosphorus removal systems. The model matrix is shown with the nomenclature used in the GPS-X implementation. Users of this model should consult the reference (Henze et al., 1998) for details of this model.

The asm2d model is implemented in the CNP and CNPIP libaries, and the Model Matrix is found in Appendix A.

ASM2d Model Components

One major difference in the way this model is presented compared with the other models is seen in its matrix description. The stoichiometric coefficients for ammonia and soluble phosphorus are listed outside the table. The reason behind this is that to eliminate the organic nitrogen state variables (xnd and snd); they are now incorporated into the other soluble and particulate organic components as a fixed fraction. Similarly, a fixed fraction of phosphorus is included in the organic components.

State Variables

Each of these state variables represents a spectrum of organic biodegradable material. Another state variable is used to model the other soluble organic material, which is not biodegradable (si). This material is part of the influent and can be produced during some hydrolysis processes. The soluble nitrogen components consist of 1) ammonia and ammonium (snh); and 2) nitrate and nitrite (sno). The dinitrogen gas produced (snn) is also modelled, but is considered insoluble and immediately comes out of solution. Oxygen (so) and inorganic soluble phosphorus (sp) are the other two soluble states. The inorganic soluble phosphorus is typically ortho-phosphate.

Looking at the particulate states, the model includes three types of biomass:

1. heterotrophic organisms (xbh);

2. nitrifying organisms (xba); and

3. phosphate accumulating organisms (xbp)

The phosphate accumulating organisms’ state variables do not include the internal storage products, which are separate state variables. Particulate non-biodegradable organic material is also modelled (xi). Although it is not removed from the system, it may be generated during cell decay. The two internal storage products of the phosphorus accumulating organisms are:

1. internally stored COD (xbt); and

2. poly-phosphate (xpp).

Neither of these two components is included in the mass of the phosphorus accumulating organism. The last state variable is the slowly biodegradable substrates (xs) which must undergo hydrolysis before available as a substrate. Particulate inorganic inert solids (xii) are present in the system, but do not interact with the biological model.

Processes

The processes described by this model are separated into four groups:

1. processes involving hydrolysis;

2. processes involving heterotrophs;

3. process involving autotrophs; and

4. processes involving phosphorus accumulators.

The hydrolysis processes include the aerobic, anoxic and anaerobic hydrolysis of slowly biodegradable organic material into soluble substrate (processes 1-3). The rate equations are similar for the three processes; however, the rate constants under these different environmental conditions are not well known. The hydrolysis of organic nitrogen is not explicitly included in this model. Rather, a fraction of the organic particulate material is assumed to be organic nitrogen and therefore hydrolyzes at the same rate as the organic particulate substrate.

The heterotrophic processes include the aerobic growth on two substrates (processes 4 and 5), their corresponding anoxic growth (processes 6 and 7). The fermentation of organic material under anaerobic conditions is also accounted for by process 8. This process has been identified as one requiring more research into its understanding. Since little is known about this process, a large range of kinetic parameters for this rate may be found during the modelling exercise. Process 9 models the death and lysis of the heterotrophs.

Processes 10-15 describe the phosphorus accumulating bacteria:

1. the internal storage of fermentable products (process 10);

2. the internal storage of poly-phosphate (process 11);

3. the aerobic growth of polyP bacteria (process 12); and

4. the lysis of the bacteria and their corresponding internally stored products (processes 13-15)

The final two processes in the model are the aerobic growth of the nitrifiers (process 16) and their death and lysis (process 17). The kinetic parameters of this model, like those of the mantis model, are temperature dependent. A similar Arrhenius type function is used to describe this dependency.

This model is a minor extension of the original asm2 model. It includes two additional processes to account for phosphorus accumulating organisms (PAOs) using cell internal storage products for denitrification. Whereas the asm2 model assumed PAOs to grow only under aerobic conditions, the asm2d model includes denitrifying PAOs.

Activated Sludge Model No. 3 (ASM3)

The Activated Sludge Model No. 3 (Gujer et al., 1999) relates to ASM1 and corrects for some inadequacies of ASM1. The main features of the model are:

· Hydrolysis is independent of the electron donor, and occurs at the same rate under aerobic and anoxic conditions.

· Lower anoxic yield coefficients are introduced.

· Decay of biomass is modelled as endogenous respiration (vs. the “death regeneration” concept used in asm1).

· Storage of COD by heterotrophs under anoxic and aerobic conditions is modelled.

· It is possible to differentiate between anoxic and aerobic nitrifier decay rates.

· Ammonification of SND and hydrolysis of biodegradable, particulate nitrogen (XND) are omitted.  Instead, a constant composition of all organic components has been assumed (constant N to COD ratio).

· Alkalinity limitation on the process rates is considered.

Figure 16‑22 shows a schematic of the processes simulated in the asm3 model.

Figure 16‑22 - ASM3 Model Processes

The Model Matrix for asm3 is found in Appendix A.

Mantis Model (MANTIS)

The mantis model is identical to the IAWPRC Activated Sludge Model No. 1 (asm1), except for the following modifications:

· Two additional growth processes are introduced, to allow for growth of heterotrophic biomass with nitrate as a nutrient.

· Switching functions for nitrogen as a nutrient (and phosphorus, in applicable libraries) and alkalinity for growth

· Separate half-saturation coefficients for oxygen for aerobic and anoxic growth, to allow for calibration of simultaneous nitrification/denitrification.

The additional growth processes account for the observed growth of organisms during conditions of low ammonia and high nitrate. Under these conditions, the organisms can uptake nitrate as a nutrient source.

The temperature dependence of the kinetic parameters is described by an Arrhenius equation. See Appendix A for the Model matrix describing this model.

Aerobic denitrification is included in the model according to the Münch modification (Münch et al., 1996). In many cases modellers have seen nitrate levels overpredicted in their models due to the simplifications in spatial resolution (ideally mixed aeration tanks, no oxygen diffusion limitation in floc cores, etc.). The new modification, consisting of one new anoxic oxygen half-saturation coefficient makes anoxic growth rates adjustable independently from aerobic growth, and the coefficient itself is an indication of the degree of aerobic denitrification occurring within the plant modelled. The default value of the new constant is set equal to the aerobic oxygen half saturation.

New General Model (NEWGENERAL)

Introduction

Dold's general model is not implemented in GPS-X, in favour of the newgeneral model. However, a description of the general model (which makes up the basis for the newgeneral model) is presented here.

In the following sections, the general model of Dold (1990) is described. This model was derived from a combination of the asm1 model for non-polyP heterotrophic organisms and autotrophic organisms (Henze et al., 1987a, 1987b) and the Wentzel et al. (1989b) model for polyP organisms.

General Model Components (Non-PolyP Organisms)

The general model component proposed for describing the kinetic response of the non‑polyP heterotrophic and autotrophic organism masses is based on the asm1 model (Henze et al., 1987a, 1987b), with three modifications/extensions:

1. The nitrogen source for cell synthesis

2. Conversion of soluble readily biodegradable COD to short-chain fatty acids (SCFA’s).

3. Growth of non-polyP heterotrophs on SCFA.

Nitrogen Source for Cell Synthesis

In reviewing the initial asm1 model version, Dold and Marais (1986) postulated that under certain circumstances, nitrate, instead of ammonia nitrogen, may serve as the nitrogen source for cell synthesis purposes. This postulate was confirmed from analysis of data collected over an extensive period, particularly in multiple series reactor configurations operated at long sludge ages and which exhibited high nitrification rates. The use of nitrate as a nitrogen source for polyP organism synthesis, when the ammonia concentration dropped to low levels, was also observed by Wentzel et al., (1989b). On the basis of this information, an additional two processes have been incorporated into the asm1 model version to give four growth processes: aerobic and anoxic growth of non-polyP heterotrophs with either ammonia or nitrate as the N source for synthesis.

Growth of non-polyP heterotrophs on SCFA

In the asm1 model, readily biodegradable soluble COD is utilized by the non-polyP organisms (i.e. heterotrophs) in four possible growth modes - under aerobic or anoxic conditions with either ammonia or nitrate as the nitrogen source for synthesis purposes. For biologically-enhanced phosphorus removal (BEPR) systems it is necessary to distinguish between "complex" and SCFA readily biodegradable COD; therefore, it is necessary to duplicate the four growth processes in the asm1 model to account for possible growth on the two components of the readily biodegradable COD for the mixed culture system. With regard to growth on SCFA it is likely that only one of the four processes would be of consequence - anoxic growth with ammonia as the N source. This is because SCFAs are removed in the unaerated zones at the "front end" of the continuous flow systems and do not enter the aerobic zones in appreciable concentrations. However, for completeness all four growth processes in the asm1 model (for "complex" COD) were duplicated in the general model for growth of non-polyP organisms with SCFA as substrate. The same kinetic formulations and stoichiometry for growth on "complex" readily biodegradable COD and SCFA have been used.

General Model Components (PolyP Organisms)

The general model component proposed for describing the kinetic response of the polyP heterotrophic organism mass is based on the enhanced culture model of Wentzel et al. (1989b), with one additional process for anoxic growth of polyP organisms described by Dold (1990) (and the one additional stoichiometric constant, fup, for anoxic growth). It should be noted that the phenomenon of accumulation of un-biodegradable soluble COD from endogenous processes in the enhanced cultures also received attention. Wentzel et al. (1989a) suggested that this material would be used as a substrate source by non-polyP organisms in mixed culture systems.

While this is likely, no change was made to the model in this respect because the amount of generation in the mixed culture systems is small.

The values of the kinetic parameters, as with the asm1 model, are those for 20^°C.

The general model is no longer available in GPS-X, in favour of using the newgeneral model (see below), which corrects deficiencies of the general model.

New General Extension

The newgeneral model is based on the general model with significant changes to account for so-called 'COD losses' that have been reported in nutrient removal systems.

Some key features of the newgeneral model include:

· ‘COD’ loss yields

· Hydrolysis efficiency factors

· Heterotrophic yield coefficients for different electron acceptor conditions.

The modelling of BNR activated sludge systems has identified mass balance problems in some facilities. That is, several experimental and full-scale evaluations of BNR facilities have revealed imbalances between what is going into the plant and what is going out (i.e. less COD is going out than going in, hence the COD 'loss'). Both from a theoretical and modelling point of view this causes some problems, and there is no world-wide accepted explanation for these imbalances. Nevertheless, these discrepancies must be modelled. To account for these mass balance problems (referred to as anaerobic stabilization or COD losses), four COD loss terms are included in the newgeneral model. These include:

· Hydrolysis efficiency factor (anoxic)

· Hydrolysis efficiency factor (anaerobic)

· Fermentation volatile fatty acid (VFA) yield.

· PolyP PHB yield on sequestration of VFAs.

The newgeneral model has proven itself to be a reliable predictive tool for the BNR process. Nevertheless, users should be aware that the newgeneral model in its default condition does not result in a COD balance across the system. To eliminate COD losses (and thus force a COD balance across a newgeneral -based layout) each of these stoichiometric loss terms should be set to 1.0.

Included in newgeneral are two new heterotrophic yield terms to account for differences in yield under varying electron acceptor conditions. Where the general model assumed the same yield irrespective of the electron acceptor, newgeneral differentiates the yield depending on the presence of oxygen and nitrate. The added stoichiometric terms include:

· Yield (anoxic)

· Yield (anaerobic)

In total, two state variables and eight processes have been added to the general model.

State Variables

· Non-releasable polyphosphate (XPP)

· Soluble inorganic nitrogen (SNI)

Processes

· Anoxic hydrolysis of stored/enmeshed COD

· Anaerobic hydrolysis of stored/enmeshed COD

· XPP lysis on aerobic decay

· XPP lysis on anaerobic decay

· Anoxic decay of PolyP organisms

· XPPR lysis on anoxic decay

· XPP lysis on anoxic decay

· XBT lysis on anoxic decay

Phosphorus Uptake

As evidence exists that not all polyphosphate is releasable, a new state variable to represent non-releasable polyphosphate was incorporated. The uptake of phosphorus (both aerobically and anoxically) in newgeneral results in the storage of both releasable and non-releasable polyphosphate. The partitioning of the storage is stoichiometrically determined based on the total phosphorus taken up.

PolyP Decay

In the general model decay of PolyP organisms was modelled as an aerobic or anaerobic process. The newgeneral model includes anoxic decay of XBP to those processes. This results in the anoxic lysis of XBT and XPPR modelled in a similar way to the aerobic lysis of these variables in the general model. To account for the lysis of XPP, newgeneral includes three new processes: one for aerobic lysis, one for anoxic lysis and one for anaerobic lysis.

Hydrolysis

The hydrolysis of particulate COD to soluble material suitable for growth is a critical step in the COD cycle. The general model modelled hydrolysis as an aerobic process only, but newgeneralincludes hydrolysis under anoxic and anaerobic conditions and uses these processes as a sink for COD 'loss.

Fermentation

Whereas the fermentation of SS to SLF was a non-growth related process in the general model, in newgeneral, this process is associated with the growth of heterotrophic organisms and hence, a portion of the fermented COD winds up as new biomass; however, equally important is the stoichiometry of this process because, like hydrolysis, this process includes a COD 'loss' component.

The Model Matrix for the newgeneral model is found in Appendix A.

Pre-fermenter Model (Prefermenter)

The pre-fermentation model implemented in GPS-X is based on the Munch et al. model (1999), which is a mechanistic model aiming at describing the effect of design and operating parameters on the rate of VFAs production. The pre-fermenter model is found in the CSTR object only.

A general reaction pathway is shown in Figure 16‑23.

Figure 16‑23 - General Reaction Pathway

The state variables in the prefermenter model are as follows:

· C_is:  insoluble substrate (not passing through a 0.45 mm filter) such as cellulose, fats, insoluble proteins (mg COD/L).

· C_ss: soluble, high molecular weight substrate, such as soluble carbohydrates (starch), and soluble proteins (globular) (mg COD/L).

· C_mo: monomer species such as glucose, long-chain fatty acids, amino acids (mg COD/L).

· S_lf: volatile fatty acids (mg COD/L).

· C_e: hydrolytic enzymes which act as a catalyst to hydrolyse insoluble substrate, soluble high-molecular-weight substrate and proteins (mg COD/L).

· C_xa: acidogenic bacteria which utilize monomers (C_mo) as their substrate (mg COD/L).

· C_xm: methanogenic bacteria, which utilize volatile fatty acids (VFAs) as their substrate then transforming it into methane gas (mg COD/L).

· C_prot: organic nitrogen contained in particulate proteins which is converted into ammonia nitrogen in the ammonification process as particulate proteins are hydrolysed. It is also produced from the decay of bacteria cells (mg N/L).

· S_nh: ammonia nitrogen (mg N/L).

· CH_4,g:  methane gas.

Stoichiometric Parameters

The stoichiometric parameters to be specified in the influent section are used to calculate the concentration of soluble, high molecular weight substrate (C_is) from the influent readily biodegradable substrate (ss) and the concentration of methanogenic biomass (C_xm) from the influent slowly biodegradable substrate (X_s):

· f_ss: fraction of soluble high molecular weight substrate (C_is) in the influent readily biodegradable substrate (ss).

· f_xm: fraction of methanogenic biomass (C_xm) in the influent slowly biodegradable substrate (X_s).

· f_m: conversion factor from COD to cubic meters for methane production (m³ CH₄/g COD).

The stoichiometric parameters specified in the “hydrolysis”, “acidogens” and “methanogens” sections are the following yield coefficients:

· Y_e: Yield for hydrolytic enzymes on insoluble or soluble substrate (C_e/C_ss).

· Y_a: yield for acidogens on monomers species (C_xa/C_mo).

· Y_m: Yield for methanogens on volatile fatty acids (C_xm/S_lf).

Kinetic Parameters

The model kinetic parameters are:

· k_his: hydrolysis rate constant for insoluble substrate (g COD/m³.d).

· k_hs: hydrolysis rate constant for soluble substrate (g COD/m³.d).

· k_amm: ammonification rate constant for organic nitrogen contained in proteins (g N/m³.d).

· k_mo: maximum specific consumption rate of monomers by acidogenic biomass (g COD/m³.d).

· k_ac: maximum specific consumption rate of volatile fatty acids by methanogenic biomass (g COD/m³.d).

· d_a: decay rate constant of acidogens (g COD/m³.d).

· d_m: decay rate constant of methanogens (g COD/m³.d).

· d_e : deactivation rate constant of hydrolytic enzymes (g COD/m³.d).

Process Rates

The process rates described in the model are:

Hydrolysis of insoluble substrate

Equation 16‑2

The hydrolysis rate of insoluble substrate is considered to be first order with respect to the concentration of insoluble substrate and to the concentration of hydrolytic enzymes, and to be inversely proportional to the concentration of acidogenic biomass, due to a limited surface area available which could cause mass transfer limitations.

Hydrolysis of soluble substrate

Equation 16‑3

The hydrolysis of soluble substrate is considered to be first order with respect to the concentration of soluble substrate and to the concentration of hydrolytic enzymes.

Ammonification of proteins

Equation 16‑4

The ammonification of proteins is considered to be proportional to the concentration of proteins, to the concentration of hydrolytic enzymes and inversely proportional to the acidogenic biomass concentration.  Proteins are regarded as particulate matter with surface area limitations.

Consumption of monomers by acidogens

Equation 16‑5

The consumption rate of monomers is assumed to be proportional to monomers and to ammonia nitrogen saturation functions and to the concentration of acidogenic biomass.

Consumption of VFAs by methanogens

Equation 16‑6

The consumption rate of volatile fatty acids is considered to be proportional to the volatile fatty acids and ammonia nitrogen saturation functions and to the concentration of methanogenic biomass.

Decay of acidogens

Equation 16‑7

The rate of decay of acidogens is assumed to be proportional to their concentration.

Decay of methanogens

Equation 16‑8

The rate of decay of methanogens is assumed to be proportional to their concentration.

Decay of enzymes

Equation 16‑9

The rate of decay of enzymes is assumed to be proportional to their concentration

Model Structure

A schematic diagram of the prefermenter model is shown in Figure 16‑24 (adapted from Munch et al., 1999).

Figure 16‑24 – Schematic Diagram of the prefermenter Model

The Model Matrix for the prefermenter model can be found in Appendix A.

Suggestions for Selecting an Activated Sludge Model

With a large number of models available in the provided literature and used in GPS-X, it can be a challenge to select which model is best for each modelling application. The following simple guide gives a few suggestions and “rules of thumb” for selecting an activated sludge model.

1. The first choice to be made is the GPS-X macro library. If you are only concerned with carbon and nitrogen processes, then you should use the CN (1‑step nitrification) library. If you are interested in modelling phosphorus, then the CNP or Comprehensive libraries should be used. If you are interested in modelling pH, inorganic precipitation and/or side stream processes, use the Comprehensive library.  Extra user-defined components can be added to the models by selecting the associated IP (Industrial Pollutant) library – CNIP or CNPIP.

2. It is a good rule of practice to keep the model as simple as possible at the beginning, until you interpret the results and are comfortable with that model's level of complexity. You can then move to more complicated models. If you are unsure of which model to start with we recommend using asm1, or mantis.

3. The choice of model should depend on the amount and type of data that is available to support its use. For example, if you have little information about different substrate types in your system, it is advisable to use models that have fewer substrates. 

4. If you are modelling a plant that has recycling of flows back from the solids handling process back to the activated sludge line, the Mantis2 model is best suited for handling this situation.  The Comprehensive (Mantis2) library contains a full set of state variables that cover both activated sludge and anaerobic digestion processes.

The choice of model should reflect the need to simulate certain processes. For example, if you are interested in exploring P-removal or alkalinity control, you will need to use models that contain processes that are relevant to those components. Table 16‑22 summarizes the processes in each model, and may be useful in choosing a model. You can consult the model descriptions earlier in this chapter or the Model matrices found in Appendix A to see the details of the processes contained in each model.

Table 16‑22 – Model Processes in GPS-X

Process	asm1	asm3	mantis (and 3dmantis)	asm2d	new general	mantis2	mantis3
Fermentation Step				X	X	X	X
Nitrification/Denitrification	X	X	X	X	X	X	X
Aerobic Denitrification			X
Aerobic Substrate Storage		X
COD "Loss"					X
2-Step Nitrification/denitrification						X	X
NO3^- as a N source for cell synthesis			X		X
Alkalinity consumption/generation	X	X	X	X		X	X
Alkalinity (as a limiting factor for growth processes)				X
Biological phosphorus removal				X	X	X	X
Precipitation of P with metal hydroxides				X		X	X
Temperature dependency	X*	X*	X	X	X	X	X
pH						X	X
Struvite, other Calcium and Magnesium ppt.						X	X
Anammox						X	X
Methylotroph						X	X
N2O gas production							X

* not part of the published model, but added in GPS-X.

Figure 16‑25 – CN Library Organic State and Composite Variables

Figure 16‑26 - CN Library Nitrogen State and Composite Variables

Special Activated Sludge Units

Deep Shaft Reactor

The model associated with the deep shaft object is an adaptation of the mantis suspended-growth model. It takes into account the specific hydraulics and hydrostatic pressure found in a deep shaft reactor.

The deep shaft header tank is modelled with two complete-mix reactors (by default), and is under atmospheric pressure.  The downcomer and the riser shafts are modelled with twenty complete-mix reactors (by default).

Pond/Lagoon

The pond object contains only the empiric model, which simulates the transformation, dilution and mixing of state variables in a pond. Unlike the activated sludge models, the empiric model is empirical in nature. It does not use fundamental mechanistic dynamic processes to determine the rate of change of the states (such as those found in the Model Matrices in Appendix A), but simulates behavior that has been observed in existing ponds, bench‑scale studies and pilot-scale studies.

The empiric model simulates three different kinds of ponds: anaerobic, facultative, and aerated. The pond models are discussed in detail below.

Note that Pond/Lagoon object is only available in the GPS-X legacy libraries (CNLIB, CNIPLIB, CNPLIB, CNPIPLIB)

Anaerobic Ponds

In the anaerobic pond model, the BOD and TSS removal is simulated using a simple regression model derived from anaerobic pond behavior in North America (Beier, 1987).

The following equations describe the amount of BOD and TSS removal:

Equation 16‑10

Equation 16‑11

where:

A_TSS, A_BOD, B_TSS, B_BOD, K_hrt = calibration parameters

n  = number of ponds in series

As the empirical equations above only deal with GPS-X composite variables (BOD and TSS), a methodology is required to transfer this information back to the state variables. The following list outlines the relationships for the state variables in CNLIB.

A fraction is calculated for each particulate state variable (xbh, xba, xs, xi, xu, xsto for CNLIB) that is equal to that variable's concentration over incoming xcod.

A new TSS value (x) is calculated from the above empirical REMOVAL equation.

New VSS (vss) and particulate COD (xcod) concentrations are calculated as:

vss = ivt * x
xcod = icv * vss

A new BOD value is calculated from the above empirical REMOVAL equation, and then compared to the BOD value calculated as the sum of the fractions from step 1 multiplied by the new xcod multiplied by fbod.

If the BOD calculated from the fractions is less than the BOD calculated from the empirical equation, excess soluble BOD (the difference between bod and xbod) is assigned to ss.

If the BOD calculated in step 3 from the fractions is greater than the BOD calculated from the empirical equation, the excess particulate BOD (xbodu) is assumed to be converted to xu.  Soluble substrate (and soluble BOD) is then assumed to be zero.

Inert and non-reacting variables are mapped through the pond object (si, salk, and snn).

The effluent oxygen concentration (so) and nitrate concentration (sno) are assumed to be zero in the anaerobic pond environment.

Particulate biodegradable organic nitrogen (xnd) is assumed to be converted to snh as per the conversion of xs.

Soluble biodegradable organic nitrogen (snd) is assumed to be converted to ammonia (snh) as per the conversion of ss.

The loss of heterotrophic (xbh) and autotrophic (xba) biomass results in the production of ammonia (snh).

Facultative Ponds

The approach for facultative ponds is similar to that for anaerobic ponds, but uses a different model for BOD reduction, and a slightly different approach for determining state variable concentrations. The empirical BOD removal model used for facultative ponds is from Thirumurthi (1974):

Equation 16‑12

where:

BOD_EFF            = effluent BOD (g/m³)

BOD_INF             = influent BOD (g/m³)

K_S                    = first order BOD removal rate coefficient (1/d) at 20°C

C_TEMP               = correction factor for temperature

C_O                    = correction factor for organic loading

and

Equation 16‑13

Equation 16‑14

where:

TEMP              = temperature, °C

θ                      = temperature correction constant

SLR                  = standard loading rate (kg/ha/d)

LR                    = current loading rate (kgBOD/ha/d)

The methodology for the determination of the state variables xba, xbh, xs, xu, xi, xsto, si, salk, snn, ss, snd and xnd are identical to that for anaerobic ponds.

Oxygen is determined by assuming that the DO is saturated in the aerobic zone, and zero in the anaerobic zone. The concentration of so is determined from the following equation:

Equation 16‑15

where:

SOST               = saturated oxygen concentration (gO₂m³)

AERDEPTH     = fraction of depth that is aerobic (unitless)

For the nitrogen composite variables, nitrate is assumed to be converted to nitrogen gas in the anaerobic zone; therefore:

Equation 16‑16

As anaerobic conversion of biomass and biodegradable nitrogen only happens in a fraction of the pond, the increase in ammonia (snh) as shown in the anaerobic model is multiplied by AERDEPTH.

Aerated Ponds

The aerated pond uses the same empirical BOD and TSS reduction models as the facultative pond model. However, the default value for the BOD removal rate coefficient has been changed to reflect aerated conditions (Eckenfelder, 1980).

The methodology for the determination of the state variables xba, xbh, xs, xu, xi, xsto, si, salk, snn, ss, snd and xnd is identical to that for facultative ponds.

Oxygen is assumed to be saturated at the effluent point of the aerated pond. Due to this completely oxic environment, nitrate is assumed to remain unchanged, and is mapped through the pond object.

Ammonia is assumed not to change, due to the assumption that most of the biomass will be settled out of the water column. Therefore, snh is mapped through the pond object.

Calibration

The parameters found in the Parameters > Physical page of the pond object include pond type and settings for pond size. Number of cells in series describes the degree of plug flow for the pond system. Typically, BOD and TSS removal increases with increasing numbers of cells in series. The temperature values found on the More... page are used in the temperature correction equations in the facultative and aerated pond models.

The parameters found on the Parameters > Empirical Model Constants include those used to calibrate the BOD and TSS removal, and the half-saturation coefficient K_HRT that is used to decrease removal efficiency for very short HRTs.

Table 16‑23 summarizes suggested calibration techniques for the empirical pond models found in the empiric model.

Table 16‑23 – Calibration Suggestions

Model	Calibration
anaerobic	Calibrate with the A coefficients for TSS removal first, then adjust A coefficient for BOD.
facultative	Calibrate with the A coefficients for TSS removal first, then adjust BOD removal rate constant. Further tuning can be performed by adjusting KHRT and temp/loading coefficients. Lastly, adjust depth of aerobic zone to calibrate ammonia.
aerated	Calibrate with the A coefficients for TSS removal first, then adjust BOD removal rate constant. Further tuning can be performed by adjusting KHRT and temp/loading coefficients.

Pond Models in Other Libraries

The above methods for determining the values of state variables from the empirical pond models are for CNLIB only. These methods have been extended to the other libraries by making small additions and changes based on the new and/or different state variables. Table 16‑24 describes these differences.

Table 16‑24 - Library-specific Algorithms for Empiric Pond Model

Library	Additions/Changes from CNLIB pond methodology
CNIPLIB	All particulate IP components (xza to xzo) settle similarly to xi (not changed biologically, but undergo settling and mixing, as appropriate). Soluble IP components (sza to szo) are unaffected by biological activity, but undergo mixing.
CNPLIB	slf and sf behave similarly to ss. PAOs are transformed similarly to xbh and xba.  sp is not modelled, and is treated the same as si.
CNPIPLIB	slf and sf behave similarly to ss. PAOs are transformed similarly to xbh and xba.  sp is not modelled, and is treated the same as si. All particulate IP components (xza to xzo) settle similarly to xi (not changed biologically, but undergo settling and mixing, as appropriate). Soluble IP components (sza to szo) are unaffected by biological activity, but undergo mixing.

Powdered Activated Carbon

The powdered activated carbon (PAC) object is a normal CSTR object that has been enhanced with powdered activated carbon addition.  The carbon sorbs one or more components using a competitive sorption isoterm.  The sorbed components are then converted to particulate inerts before moving downstream.  The version of the PAC model is different in the IP libraries, where 3 user-defined components can be added to the existing sorbable set of state variables and used as toxic inhibitors to biological activity.

Note the Powdered Activated Carbon object is only available in the GPS-X legacy libraries (CNLIB, CNIPLIB, CNPLIB, CNPIPLIB)

Sorption Isotherms

In the CN and CNP libraries, the only components being sorbed from solution onto the PAC are ss (soluble substrate) and si (soluble inerts).  In this two-component system, the sorption rates are:

Equation 16‑17

Equation 16‑18

where:

adsrate_SI           = adsorption rate of SI (gCOD/m³/d)

adsrate_SS = adsorption rate of SS (gCOD/m³/d)

MA_SI                 = maximum sorption capacity for SI (gCOD/gPAC)

MA_SS                = maximum sorption capacity for SS (gCOD/gPAC)

KL_SI                  = SI sorption half-sat coefficient (gCOD/m³)

KL_SS                 = SS sorption half-sat coefficient (gCOD/m³)

X_PAC                 = PAC concentration in liquid (gPAC/m³)

R_ADS                 = adsorption rate (1/d)

The PAC model calculates the amount of “fresh” PAC (PAC that is available to sorb components), and “used” PAC (PAC that has components sorbed onto it, and is not available to sorb more), and the fraction of total PAC that is “fresh” and available to sorb.

The model calculates the concentrations of individual components that are bound to PAC.  For PAC-bound soluble substrate, the biomass will grow at an enhanced rate, due to the presence of a concentrated substrate source.  This enhancement of growth is controlled by the bioregeneration factor, by which all of the biological growth rates (that grow on ss) are multiplied.  The consumption of PAC-bound ss frees up the “used” PAC to become “fresh” PAC again.

Toxic Inhibition in IP Libraries

In the CNIP and CNPIP libraries, the above-described functionality is enhanced by the addition of user-defined toxic components and their sorption properties.  Users can use the IP library versions of the PAC object to investigate the relationship between toxic inhibition and PAC addition to sorb the toxics.

Toxic Inhibition

The growth rates for biomass (both heterotrophic and autotrophic) in the Mantis biological model is appended with a switching function for the presence of toxic inhibitors.  The user must identify which components are the toxic components and specify the relative inhibition of each component.  The Toxic Inhibition menu contains the parameters used in the inhibition switching function.  Figure 16‑27 shows the Toxic Inhibition menu, with sza (IP state variable “soluble component ‘a’”) filled in as Toxic Component #1.

Figure 16‑27 – Toxic Inhibition Menu

Note, the user must specify the cryptic variable name without labels.  The user may specify any state variable as a toxic component, including regular states (sno, snh, xnd, etc.) and any of the IP state variables (sza, szb, xza, xzb, etc.).

The toxic component # 1 inhibition constant is a half-saturation coefficient that represents the concentration at which the biological growth rate will be half of its normal value.

Sorption of Toxic Components

The sorption parameters for the toxic components are found in the PAC Addition menu, in the More… button.  These components are added to the ss and si sorption isotherms described above, to make a 5-component competitive sorption system.  The sorption rates for a five-component system are all on the form.

Equation 16‑19

where:

var1, var2, var3            = toxic component concentrations (g/m³)

MA_var                           = maximum adsorption capacity (g/gPAC)

KL_var                            = sorption half-saturation coeff (g/m³)

The multi-component competitive sorption model will favour sorption of those components with the lowest sorption half-saturation coefficient.

Appendix I: Sedimentation and Flotation Models

This section provides a description of the legacy sedimentation and flotation models available in GPS-X.

Sedimentation Models

In reactive models, biological reactions are included, and the model names are associated with the corresponding suspended-growth models, described in Chapter 6 (page 141).  For example, the asm1 sedimentation model uses the asm1 suspended-growth model.

· One-dimensional, reactive: mantis,asm1, asm2d, asm3, newgeneral

Appendix J: Digestion Model for Legacy Libraries

pH Solver Set up Parameters

These parameters, found under the Parameters sub-menu item pH Solver Set up (Figure 16‑28) define the initial pH value (ph), the pH boundaries: minimum (lowph), and maximum (highph) values, and the required pH accuracy (errorph). Parameters for the search routine of the pH are presented in this sub-menu.

Figure 16‑28 - pH Solver Set up

Influent and Effluent Parameters

These menu items are found under Parameters sub-menu items Influent and Effluent.

The Influent sub-menu, shown in Figure 16‑29, allows the user to define influent parameters that are exclusive to the basic digester model: soluble total CO₂ (sco2t), toxic substance concentration (stox), methanogens concentration (xmh) and net cations (strong bases)(sz).

The Effluent sub-menu, shown in Figure 16‑30, allows the user to define special components to the effluent of the anaerobic digester: inert soluble COD (si) and the fraction of the effluent VSS that is inert (frinert).

Figure 16‑29 - Influent Parameters (Basic Digester Model)

Figure 16‑30 – Effluent Parameters (Basic Digester Model)

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 16‑31 - 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 BOD_ultimate (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 16‑32 - 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 16‑20

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.

Appendix K: Tools and Process Control Objects

pH Tool

Figure 16‑33 - Modelling Toolbox Object pH Model

The ph tool is found in the Toolbox object in some libraries, and allows the user to estimate the pH of a wastewater stream in the layout, or do pH estimation directly from parameters entered into the menu.  These two options are available in the pH Model Set up menu (Figure 16‑34).

Figure 16‑34 - pH Model Set up Menu

The pH model operation menu item specifies whether the calculation is a standalone pH estimation using the components under the Wastewater Components (stand-alone model) header, or uses the components from a specific flow point in the plant layout. 

If you select link pH estimation to label, the calculation will use the concentrations of ammonia, nitrate, etc., from the stream label specified in label of point where pH is to be estimated.   If you would like to estimate the pH at several different points throughout the plant, place one Toolbox object per pH calculation into the layout, and link each box to a different point in the layout where pH is to be estimated.

The calculation is based on a model developed by Vavilin et al. (1995). The model is simplified to include only strong bases, strong acids, total ammonia, total acetate, and total carbon dioxide. The model uses an iterative process, in combination with the concentration of each component, to determine the pH value.

The relationship between the concentration of a component and the concentration of its ions is related through a dissociation constant (K). The concentration of hydrogen ion is used to determine pH:

Equation 16‑21

The initial pH identified on the pH solver set up control form is used to calculate the initial concentration of hydrogen ion. An example of this control form is shown in Figure 16‑34. The default initial guess for pH is 7.

A second control form, shown in Figure 16‑35, is used to input various equilibrium and temperature constants.

Figure 16‑35 – Component Control Form

These concentrations are used in a series of five equilibrium equations that form the basis for the pH model:

Equation 16‑22

Equation 16‑23

Equation 16‑24

Equation 16‑25

Equation 16‑26

where:

K_n        = ammonium dissociation constant (mol/L)

K_a        = acetate dissociation constant (mol/L)

K_w        = water dissociation constant (mol/L)

K_c1        = CO₂ dissociation constant – step 1 (mol/L)

K_c2        CO₂ dissociation constant – step 2 (mol/L)

The dissociation constants used in these equations can also be input on the control form shown in Figure 16‑35.  The default dissociation constants are taken from the literature. The ammonium dissociation constant is corrected for temperature.

To properly reflect the presence/absence of added alkalinity (lime addition, etc.) the alkalinity state variable salk is assumed to be all carbonate alkalinity that is available (and completely dissociated) for acid neutralization.

In the above equations, totalCO₂ is the total CO₂ available (converted to equivalent charge).  Because the alkalinity is assumed to be in the form of completely dissociated CaCO₃, a 2+ charge cation is also assumed present in the equilibrium system.

The above equations are combined with the charge balance shown below:

Equation 16‑27

An implicit nonlinear equation solver is used to solve this system of equations for [H+]. The calculated pH values are bounded by the low bound and high bound parameters shown in Figure 16‑34.

Once the solution is complete and the concentrations of the ionized components have been calculated, the concentrations of the non-ionized components are calculated from the speciation equation shown above.

The calculated pH and the concentrations of the individual components can be displayed on an output form similar to that shown in Figure 16‑36.  This pH model is also used in the HPO (High Purity Oxygen) object for pH estimation.

Figure 16‑36 – Sample pH Outputs

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