funcKinetics.py

"""
Function for kinetic reactions of biomass pyrolysis from Sadhukhan 2009.
"""

# modules
# -----------------------------------------------------------------------------
import numpy as np

# Kinetics Function
# -----------------------------------------------------------------------------

def kn(T, B, C1, C2, rhow, dt, i, H):
    """
    Kinetic reactions for biomass pyrolysis of a woody particle. Kinetic scheme
    from Sadhukhan 2009 paper.

    Example:
        B[i], C1[i], C2[i], g = kn(T, B, C1, C2, rhow, dt, i, H)
    Inputs:
        T = temperature, K
        B = mass fraction of biomass, (-)
        C1 = mass fraction of char 1, (-)
        C2 = mass fraction of char 2, (-)
        rhow = density of wood, kg/m^3
        dt = time step, s
        i = row index
        H = heat of reaction, J/kg
    Output:
        B[i] = biomass mass fraction vector for row index i
        C1[i] = char 1 mass fraction vector for row index i
        C2[i] = char 2 mass fraction vector for row index i
        g = heat generation, W/m^3
    """

    R = 0.008314 # universal gas constant, kJ/mol*K

    # A as pre-factor (1/s) and E as activation energy (kJ/mol)
    A1 = 168.4;     E1 = 51.965;    # biomass -> (vol+gas)
    A2 = 13.2;      E2 = 45.960;    # biomass -> char
    A3 = 5.7e6;     E3 = 92.4;      # (vol+gas) + char -> (vol+gas)2 + char2
    S = 1.38                        # deposition coefficient

    # evaluate reaction rate constant for each reaction, 1/s
    K1 = A1 * np.exp(-E1 / (R*T[i]))    # biomass -> (vol+gas)
    K2 = A2 * np.exp(-E2 / (R*T[i]))    # biomass -> char
    K3 = A3 * np.exp(-E3 / (R*T[i]))    # (vol+gas) + char -> (vol+gas)2 + char2

    # reaction rates as mass fraction basis
    rB = -(K1+K2) * B[i-1]          # biomass rate
    rC1 = K2*B[i-1] - K3*C1[i-1]    # primary char rate
    rC2 = S*K3*C1[i-1]              # secondary char rate

    # update biomass and char mass fractions, (-)
    Bnew = B[i-1] + rB*dt
    C1new = C1[i-1] + rC1*dt
    C2new = C2[i-1] + rC2*dt

    # calculate heat of generation term
    rp = rhow*(rB+rC1+rC2)  # rate of pyrolysis
    g = H*rp                # heat generation

    # return the biomass and char mass fractions and heat of generation
    return Bnew, C1new, C2new, g