calc.stoich.basis {stoichcalc}

Calculate Basis of Stoichiometric Space

Description

Calculate the basis of the stoichiometry space that is compatible with mass balances of elementary constituents and additional constraints

Usage

calc.stoich.basis(alpha, subst = NA, constraints = list(), eps = 1e-5, verbose = TRUE)

Arguments

alpha

Substance composition matrix of all substances (labelled columns) and mass fractions of elementary constituents (labelled rows). Typically calculated by the function calc.comp.matrix.

subst

Character vector of names of substances to be used for analysis (this must be a subset of the column names of alpha).

constraints

list of stoichiometric constraints in addition to mass conservation of elementary constituents. Each stoichiometric constraint must be stored as a vector containing the coefficients of the linear equation in elementary constituents that defines the constraint. The elements of this vector must be labelled by the names of the corresponding elementary constituents.

eps

relative tolerance for checking ratios of stoichiometric coefficients (only used for informing user about substance pairs with fixed stoichiometric ratio)

verbose

indicator for whether or not to write basic information to the console.

Details

This function is primarily used in the function calc.stoich.coef. However, it can also be used to check the number of required stoichiometric constraints in addition to mass conservation of elementary constituents for a given process. In this case the composition matrix should only contain the substances relevant for this process. The number of required constraints is then equal to the row dimension of the output matrix minus 1.

Value

Matrix of basis vectors (in rows) that span the compatible stoichiometric space.

Author(s)

Peter Reichert <[e-mail]>

References

Reichert, P. and Schuwirth, N., A generic framework for deriving process stoichiometry in environmental models, Environmental Modelling and Software 25, 1241-1251, 2010.

See Also

calc.comp.matrix, calc.stoich.coef

Examples

subst.comp <- 
  list(NH4  = c(H      = 4*1/14,  # gH/gNH4-N
                N      = 1,       # gN/gNH4-N
                charge = 1/14),   # chu/gNH4-N
       NO3  = c(O      = 3*16/14, # gO/gNO3-N
                N      = 1,       # gN/gNO3-N
                charge = -1/14),  # chu/gNO3-N
       HPO4 = c(O      = 4*16/31, # gO/gHPO4-P
                H      = 1*1/31,  # gH/gHPO4-P
                P      = 1,       # gP/gHPO4-P
                charge = -2/31),  # chu/gHPO4-P
       HCO3 = c(C      = 1,       # gC/gHCO3-C
                O      = 3*16/12, # gO/gHCO3-C
                H      = 1*1/12,  # gH/gHCO3-C
                charge = -1/12),  # chu/gHCO3-C
       O2   = c(O      = 1),      # gO/gO2-O
       H    = c(H      = 1,       # gH/molH
                charge = 1),      # chu/molH
       H2O  = c(O      = 1*12,    # gO/molH2O
                H      = 2*1),    # gH/molH2O
       ALG  = c(N      = 0.06,    # gN/gALG
                P      = 0.005,   # gP/gALG
                O      = 0.50,    # gO/gALG
                H      = 0.07,    # gH/gALG
                C      = 0.365),  # gC/gALG
       ZOO  = c(N      = 0.06,    # gN/gZOO
                P      = 0.01,    # gP/gZOO
                O      = 0.50,    # gO/gZOO
                H      = 0.07,    # gH/gZOO
                C      = 0.36),   # gC/gZOO
       POM  = c(N      = 0.04,    # gN/gPOM
                P      = 0.007,   # gP/gPOM
                O      = 0.40,    # gO/gPOM
                H      = 0.07,    # gH/gPOM
                C      = 0.483),  # gC/gPOM
       DOM  = c(N      = 0.04,    # gN/gDOM
                P      = 0.007,   # gP/gDOM
                O      = 0.40,    # gO/gDOM
                H      = 0.07,    # gH/gDOM
                C      = 0.483))  # gC/gDOM
                
Y.ZOO <- 0.2; f.POM <- 0.2; f.DOM <- 0.1

alpha <- calc.comp.matrix(subst.comp)

subst.gro.ALG.NO3 <- c("NO3","HPO4","HCO3",
                       "O2","H","H2O","ALG")

basis.gro.ALG.NO3 <- 
  calc.stoich.basis(alpha,subst.gro.ALG.NO3)

subst.gro.ZOO <- c("NH4","HPO4","HCO3","O2","H",
                   "H2O","ALG","ZOO","POM","DOM")

basis.gro.ZOO <- 
  calc.stoich.basis(alpha,subst.gro.ZOO)

const.gro.ZOO <- list(c("ZOO" = 1,"ALG" = Y.ZOO),
                      c("POM" = 1,"ALG" = f.POM),
                      c("DOM" = 1,"ALG" = f.DOM)) 

basis.gro.ZOO <- 
  calc.stoich.basis(alpha,subst.gro.ZOO,const.gro.ZOO)