DKsludge/3_typical_mass_balance.Rmd at master · LiguanLi/DKsludge · GitHub

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# Typical Mass balance calculation

```{r "load functions, warning=FALSE, message=FALSE"}
source('R/functions.R')
```

  - inf = influent
  - eff = effluent
  - WAS = waste activated sludge
  - AS  = activated sludge
  - WW  = wet weight
  - DW  = dry weight
  - OM  = organic matter
  - OM  = DW  -> inorganic matter assumed negligible
  - COD = Chemical oxygen demand
  - Vp   = total plant volume
  - Xp   = total plant biomass

## Define Constants

```{r "define constants"}
# Nominal plant volume
Vp        <- 1
# Hydrolyic retension time
HRT       <- 1       # days
# Solids retension time
SRT       <- 30      # days
# Assumed yield
Y_assumed <- 0.28

# unit conversion factors
um3_per_cm3  <- 1e12
g_per_kg     <- 1e3
cm3_per_m3   <- 1e6
```

## Dry weather influent

```{r "Dry weather influent"}
# COD to organic matter ratio
COD_per_OM_inf  <- 1.42 # kg-COD kg-OM^-1 [2]
# mean influent COD
COD_inf         <- 0.582   # kg-COD m⁻³        [1]
# mean influent cell concentration
cells_inf       <- 1.0e8   # cells cm⁻³        [1, 4]
# influent flow
flow_inf        <- Vp * HRT # V day⁻¹

cells_inf <- cells_inf * cm3_per_m3   # cells m^-3
OM_inf    <- COD_inf / COD_per_OM_inf # kg-OM m⁻³

# calculation of cell fraction of organic matter
# cell mass = 95 fg cell⁻¹     [3]
# cell mass = 9.5e-13 g cell⁻¹

cell_volume     <- 0.285 # µm³-cell cell⁻¹ [1]
cell_density    <- 1.1   # g-cell cm⁻³     [1, 3]
OM_per_cell_WW  <- 0.22  # g-OM g-cell⁻¹   [1, 3]

cell_OM          <- calculate_cell_OM(cell_volume, cell_density, OM_per_cell_WW)
cell_OM_inf      <- cells_inf * cell_OM
# g-OM m⁻³          cell m⁻³ * g-OM cell⁻¹
cell_OM_inf      <- cell_OM_inf / g_per_kg
# kg-OM m⁻³
cell_OM_percent  <- round(cell_OM_inf / OM_inf * 100, 1)
```

## Waste activated sludge

```{r "Waste activated sludge"}
# mean AS cell concentration
cells_AS <- 1.0e10                 # cells cm⁻³
cells_AS <- cells_AS * cm3_per_m3  # cells m⁻³
# WAS OM & COD
OM_AS    <- 5.0           # kg-OM  m⁻³

COD_per_VSS_AS <- 1.42   # kg-COD kg-VSS⁻¹
VSS_per_OM_AS  <- 0.75   # kg-VSS kg-OM⁻¹
COD_AS  <- OM_AS * VSS_per_OM_AS * COD_per_VSS_AS  # kg-COD m⁻³

# WAS thickening
WAS_thick <- 3.0
OM_WAS    <- OM_AS    * WAS_thick  # kg-OM  m⁻³
COD_WAS   <- COD_AS   * WAS_thick  # kg-COD m⁻³

cells_WAS <- cells_AS * WAS_thick

# WAS flow
flow_WAS <- Vp * (1 / SRT) / WAS_thick # V day⁻¹
```

## Dry weather effluent

```{r "Dry weather effluent"}
# effluent flow
flow_eff <- Vp - flow_WAS            # V day⁻¹
# effluent OM & COD
OM_eff   <- 20                       #  g-OM m⁻³
OM_eff   <- OM_eff / g_per_kg        # kg-OM m⁻³
COD_eff  <- OM_eff * COD_per_OM_inf  # kg-COD m⁻³
# mean effleunt cell concentration
cells_eff <- 1.0e7                   # cells cm⁻³  [4, 5]
cells_eff <- cells_eff * cm3_per_m3  # cells m⁻³
```

## Mass balance

```{r}
# Cell budget
ncells_in  <-  cells_inf * flow_inf
ncells_eff <-  cells_eff * flow_eff
ncells_AS  <-  cells_AS  * Vp
ncells_WAS <-  cells_WAS * flow_WAS
ncells_out <-  ncells_eff + ncells_WAS

pprint <- function(x) {paste0(round(x * 100, 1), "%")}
# % of out cells in effluent
pprint(ncells_eff / ncells_out)
# % of out cells in waste
pprint(ncells_WAS / ncells_out)
# fraction of out cells coming with WW
pprint(ncells_in  / ncells_out)
# Daily effluent fraction of AS
pprint(ncells_eff / ncells_AS)
# Daily waste fraction of AS
pprint(ncells_WAS / ncells_AS)
```


## References
  [1]: Vollertsen et al. 2001. Comparison of methods for determination of microbial biomass in wastewater

  [2]: Henze et al. 2002.

  [3]: Loferer-Krössbacher et al. 1998. Determination of bacterial cell dry mass by transmission electron microscopy and densitometric image analysis.

  [4]: Snaidy. 2009. PhD Thesis. Detection and Enumeration of E. coli and Campylobacter in wastewater and treated water by CARD-FISH.

  [5]: Morgan-Sagastume 2008

  [6]: Frølund 1996