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stoichiometry_and_thermodynamics.py
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stoichiometry_and_thermodynamics.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Dec 30 15:35:20 2021
@author: Arjun Chakrawal
https://twitter.com/ArjunChakrawal
"""
# %%
import os
# import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
from scipy import optimize
import warnings
warnings.filterwarnings("ignore")
# %%
plt.style.use("ggplot")
# %%
if not os.path.exists("fig"):
os.makedirs("fig/tif")
os.makedirs("fig/svg")
# %% [markdown]
# ### function to estimate efficiency
# %%
def dGox_func(gamma):
return 60.3 - 28.5 * (4 - gamma)
def dCG_O2(gamma):
return dGox_func(gamma) + (gamma / gamma_O2) * dGred_O2
def efficiency_CNED_Inf(gamma, T, eA, CNB, NSource, CNED):
if gamma > 8:
print("Error. wrong values of DR of S of P")
return
# Ts = 298
# pre-assign std G of formation from CHNOSZ
dfGH2O = -237.2 # kJ/mol
dfGO2aq = 16.5 # kJ/mol
dfGNH4 = -79.5 # kJ/mol
# dfGHCO3aq = -586.9 #kJ/mol
# dfGglu = -919.8 #kJ/mol
# dfGbio = -67 #kJ/mol
# dfGeth = -181.8 #kJ/mol
dfGNO3 = -111 # kJ/mol
# dfGNO2 = -32.2 #kJ/mol
# dfGNO = 102 #kJ/mol
# dfGN2H4 = 159.17 #kJ/mol
# dfGNH2OH = -43.6 #kJ/mol
dfGN2 = 18.2 # kJ/mol
# dfGH2 = 17.7
gamma_B = 4.2 # e- mol/Cmol
# define epectron acceptor and some other DR
if eA == "O2":
gamma_eA = 4
dGred_eA = 2 * dfGH2O - dfGO2aq
elif eA == "NO3":
gamma_eA = 8
dGred_eA = dfGNH4 + 3 * dfGH2O - dfGNO3
elif eA == "Denitrification":
gamma_eA = 5
dGred_eA = 0.5 * dfGN2 + 3 * dfGH2O - dfGNO3
elif eA == "Fe(III)": # ferrihydrite
# dGred_eA values are taken from La Rowe 2015
gamma_eA = 1
dGred_eA = -100 * gamma_eA
elif eA == "FeOOH": # goethite
gamma_eA = 1
dGred_eA = -75.58 * gamma_eA
elif eA == "Mn4": # goethite
gamma_eA = 2
dGred_eA = -120.03 * gamma_eA
elif eA == "SO4": # goethite
gamma_eA = 8
dGred_eA = -24.04 * gamma_eA
# define NSource
if NSource == "NO3":
gamma_NS = 8
dGred_NS = dfGNH4 + 3 * dfGH2O - dfGNO3
elif NSource == "NH4":
# 0.5N2 + 4e + 5H -> NH4 + 0.5H2
gamma_NS = 0
dGred_NS = 0
# dGred_NS values are taken from La Rowe 2015
# growth yield calculations
if gamma < 4.67:
dGrX = -(666.7 / gamma + 243.1) # kJ/Cmol biomass
else:
dGrX = -(157 * gamma - 339) # kJ/Cmol biomass
# Anbolic reaction
dCGX = dCG_O2(gamma_B)
dGana = (gamma_B / gamma) * dCG_O2(gamma) - dCGX
dGana1 = dGana
dG_ox = dGox_func(gamma)
if gamma_NS == 0: # NSource = NH4
dGcat = dG_ox + gamma * dGred_eA / gamma_eA
Y = dGcat / (dGrX - dGana1 + gamma_B / gamma * dGcat)
xN_cat = 0
xEA_cat = (gamma) / gamma_eA
dGrS = dGcat
else:
def xN(y1):
return (y1 / CNB - 1 / CNED) * (1 - y1 * gamma_B / gamma) ** -1
def dGcat(y2):
return (
dG_ox
+ dGred_NS * xN(y2)
+ dGred_eA * (gamma - gamma_NS * xN(y2)) / gamma_eA
)
def fun(y3):
return y3 - dGcat(y3) / (dGrX - dGana1 + gamma_B / gamma * dGcat(y3))
sol = optimize.root_scalar(fun, bracket=[0, 3], method="brentq")
Y = sol.root
xN_cat = xN(Y)
xEA_cat = (gamma - gamma_NS * xN_cat) / gamma_eA
TER = CNB / Y
dGrS = dGcat(Y)
if CNED < TER: # true means N rich ED
xN_cat = 0
xEA_cat = gamma / gamma_eA
dGcatNoNS = dG_ox + dGred_eA * gamma / gamma_eA
Y = dGcatNoNS / (dGrX - dGana1 + gamma_B / gamma * dGcatNoNS)
if dGcatNoNS > 0:
print("Error. dGcat POSITIVE")
return
dGrS = dGcatNoNS
else:
if dGcat(Y) > 0:
print("Error. dGcat POSITIVE")
return
v_EA = (1 - Y * gamma_B / gamma) * xEA_cat
v_N = Y / CNB - 1 / CNED
YCO2 = 1 - (Y)
if xEA_cat < 0:
print("eTransferEA <0")
return
return [Y, YCO2, dGrS, xN_cat, xEA_cat, v_EA, v_N]
# %%
T = 273 + 25
dfGH2O = -237.2 # kJ/mol
dfGO2aq = 16.5 # kJ/mol
# DeltaG of complete oxidation of organic matter
gamma_O2 = 4
dGred_O2 = 2 * dfGH2O - dfGO2aq
eA = ["O2", "NO3", "Fe(III)", "FeOOH", "SO4"] # Electron acceptors
gammaB = 4.2 # Degree of reduction of biomass
xycolor = np.array([1, 1, 1]) * 0.2
lstyle = ["-", "--", "-.", "."]
labelfont = 16
# backcolor = [0.9412, 0.9412, 0.9412]
backcolor = np.array([1, 1, 1]) * 0.975
GridCol = np.array([1, 1, 1]) * 0.9
# backcolor=[1 1 1]
axisfont = 12
LC = [
"#1f77b4",
"#ff7f0e",
"#2ca02c",
"#d62728",
"#9467bd",
"#8c564b",
"#e377c2",
"#7f7f7f",
"#bcbd22",
"#17becf",
]
xycol = np.array([1, 1, 1]) * 0.4
gamma_B = 4.2
CNB = 5 # CN ratio of biomass
INORM = (
np.arange(0.001, 0.1 + 0.0005, 0.0005) / 0.5
) # normalized inorganic N supply rate
delta_psi = 120 * 0.001 # volt # Membrane potential
R = 8.314 # J/ mol K , Gas constant
FaradayC = 96.48534 # Coulomb per mol e or kJ/ volt, faraday constant
# %% [markdown]
# # Figure 2 matplotllib
# %%
gamma = np.arange(0.5, 8 + 0.05, 0.05)
dGred = -np.array([5.0, 24.0, 40.0, 75.6, 85.0, 122.7])
# dGred = -np.array([122])
dGrX = np.zeros((len(gamma)))
dCGX = dCG_O2(gamma_B)
dGB_ana = (gamma_B / gamma) * dCG_O2(gamma) - dCGX
# viridis = plt.cm.get_cmap('viridis', len(dGred))
# LC = viridis.colors
for i in range(0, len(gamma)):
if gamma[i] < 4.67:
dGrX[i] = -(666.7 / gamma[i] + 243.1) # kJ/Cmol biomass
else:
dGrX[i] = -(157 * gamma[i] - 339) # kJ/Cmol biomass
fig = plt.figure(figsize=(5.5, 4.5), facecolor="w")
axs = fig.subplots(nrows=1, ncols=1)
for i in range(0, len(dGred)):
dGcat = (60.3 - 28.5 * (4 - gamma)) + gamma * dGred[i]
Y = dGcat / (dGrX - dGB_ana + (4.2 / gamma) * dGcat)
Ycat = 1 - (Y * 4.2 / gamma)
# nTh = (Y * dGB_ana) / (-Ycat * dGcat)
# nTh = dGB_ana / (dGrX - dGB_ana)
nTh = dCGX / (dGcat / Y)
axs.plot(gamma, Y, label=" " + str(-dGred[i]), linewidth=3.0, color=LC[i])
# axs.set_ylim([0, 0.65])
axs.set_ylim(bottom=0)
# axs.set_xlim([0, 3])
axs.tick_params(axis="x", labelsize=axisfont)
axs.tick_params(axis="y", labelsize=axisfont)
axs.set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs.legend(
loc="upper left",
bbox_to_anchor=(-0.125, 1.3),
frameon=False,
fontsize=labelfont - 4,
title=r"$ \frac{-\Delta_{red}G_{EA}}{\gamma_{EA}}$ kJ $\mathrm{(e^- mol)^{-1}}$",
title_fontsize=labelfont,
)
axs.text(2.3, 0.595, r"($\mathrm{{SO_4}^{2-}}$)", fontsize=labelfont - 4)
axs.text(2.3, 0.490, r"(goethite)", fontsize=labelfont - 4)
axs.text(2.3, 0.38, r"($\mathrm{O_2}$)", fontsize=labelfont - 4)
axs.set_ylabel(r"$G_{norm} = e$", fontsize=labelfont)
fig.tight_layout()
fig.savefig("fig/tif/Figure3.tif", dpi=300)
fig.savefig("fig/svg/Figure3.svg", dpi=300)
plt.show()
# %% [markdown]
# ## Figure3 Aerobic condition Nitrate and ammonium as N source
# %%
CNED = np.inf
gamma_S = [3, 4, 5]
# LC = linspecer(length(gamma_S))
NS = ["NH4", "NO3"]
fig = plt.figure(figsize=(6, 4), facecolor="w")
ax = plt.axes()
plt.style.use("ggplot")
for m in range(0, len(NS)):
for j in range(0, len(gamma_S)):
emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N = efficiency_CNED_Inf(
gamma_S[j], T, eA[0], CNB, NS[m], CNED
)
Gnorm = np.minimum(emax_S * np.ones((len(INORM)),), (emax_S / v_N) * INORM)
plt.plot(
INORM,
Gnorm,
lstyle[m],
linewidth=3,
color=LC[j],
label=r"{$\gamma_{OM}}$ = " + str(gamma_S[j]),
)
# ax.set(xlabel = r'${I_{norm}}$', ylabel=r'$G_{norm}}$')
plt.ylabel(r"${G_{norm}}$", fontsize=labelfont)
plt.xlabel(r"${I_{norm}}$", fontsize=labelfont)
lstr = []
for i in gamma_S:
lstr.append(r"$\gamma_{OM} =" + str(i) + "$")
leg1 = ax.legend(lstr, loc="best", frameon=False, fontsize=labelfont - 4)
ax.text(0.7, 1.05, "C limited", transform=ax.transAxes, fontsize=labelfont)
ax.text(0.1, 0.35, "N limited", transform=ax.transAxes, rotation=45, fontsize=labelfont)
ax.xaxis.set_major_formatter(lambda x, pos: "%.2f" % x)
(p1,) = ax.plot(np.nan, np.nan, linewidth=3, linestyle=lstyle[0], color="k")
(p2,) = ax.plot(np.nan, np.nan, linewidth=3, linestyle=lstyle[1], color="k")
ax.legend(
[p1, p2],
[r"$\mathrm{NH_4^+}$", r"$\mathrm{NO_3^-}$"],
loc="lower right",
frameon=False,
fontsize=labelfont - 4,
title="Inorg. N source",
title_fontsize=labelfont - 2,
)
ax.add_artist(leg1)
fig.tight_layout()
fig.savefig("fig/tif/Figure4.tif", dpi=300)
fig.savefig("fig/svg/Figure4.svg", dpi=300)
plt.show()
# %% [markdown]
# # Figure 4
# %%
fig = plt.figure(figsize=(14, 6), facecolor="w")
axs = fig.subplots(nrows=1, ncols=2)
INORM = [0.01, 0.1, 0.2, 0.3, 0.5, 1.5]
# INORM = [0.01]
gamma_S = np.arange(0.05, 8, 0.1)
NS = "NO3"
eA = ["NO3", "Denitrification"]
vN = np.zeros((len(gamma_S), len(eA)))
e = np.zeros((len(gamma_S), len(eA)))
for i in range(0, len(INORM)):
Gnorm = np.zeros((len(gamma_S), len(eA)))
for m in range(0, len(eA)):
for j in range(0, len(gamma_S)):
emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N = efficiency_CNED_Inf(
gamma_S[j], T, eA[m], CNB, NS, CNED
)
vN_met = (xN + xEA) * (1 - emax_S * gammaB / gamma_S[j])
Gnorm[j, m] = np.minimum(emax_S, (emax_S / (vN_met) * INORM[i]))
e[j, m] = emax_S
vN[j, m] = vN_met
# fig = plt.figure(figsize=(14, 6), facecolor='w')
# axs = fig.subplots(nrows=1, ncols=2)
axs[0].plot(gamma_S, Gnorm[:, 0], lstyle[0], linewidth=3, color=LC[i])
axs[0].plot(gamma_S, Gnorm[:, 1], lstyle[1], linewidth=3, color=LC[i])
GN = (e[:, 0] / vN[:, 0]) * INORM[i]
GC = e[:, 0]
id = GC < GN
idGN = sum(id)
axs[1].plot(
gamma_S[0:idGN], GN[0:idGN], lstyle[0], linewidth=3, color=LC[i], alpha=0.3
)
axs[1].plot(gamma_S[idGN:], GN[idGN:], lstyle[0], linewidth=3, color=LC[i])
GN = (e[:, 1] / vN[:, 1]) * INORM[i]
GC = e[:, 1]
id = GC < GN
idGN = sum(id)
axs[1].plot(
gamma_S[0:idGN], GN[0:idGN], lstyle[1], linewidth=3, color=LC[i], alpha=0.3
)
axs[1].plot(gamma_S[idGN:], GN[idGN:], lstyle[1], linewidth=3, color=LC[i])
axs[1].plot(gamma_S, e[:, 0], lstyle[0], linewidth=3, color="k")
axs[1].plot(gamma_S, e[:, 1], lstyle[1], linewidth=3, color="k")
for i in axs:
i.tick_params(axis="x", labelsize=axisfont + 4)
i.tick_params(axis="y", labelsize=axisfont + 4)
lstr = []
lhlist = []
for i in range(0, len(INORM)):
(p1,) = axs[0].plot(np.nan, np.nan, linestyle="-", linewidth=3, color=LC[i])
lstr.append(str(INORM[i]))
lhlist.append(p1)
leg1 = axs[0].legend(
lhlist,
lstr,
loc="lower left",
frameon=False,
fontsize=labelfont - 2,
title=r"$I_{norm}$",
title_fontsize=labelfont,
bbox_to_anchor=(0, 0.2),
ncol=1,
)
(p1,) = axs[0].plot(np.nan, np.nan, linestyle=lstyle[0], color="k", linewidth=3)
(p2,) = axs[0].plot(np.nan, np.nan, linestyle=lstyle[1], color="k", linewidth=3)
leg2 = axs[0].legend(
[p1, p2],
[r"$\mathrm{NO_3^- → NH_4^+}$", r"$\mathrm{NO_3^- → N_2}$"],
loc="upper left",
frameon=False,
fontsize=labelfont - 2,
)
axs[0].add_artist(leg1)
# axs[1].text('Black lines = $G_{C, norm}$ and Colored lines = $G_{N, norm}$', fontsize=labelfont)
axs[0].set_ylabel(r"${G_{norm}}$", fontsize=labelfont + 6)
axs[0].set_xlabel(r"${\gamma_{OM}}$", fontsize=labelfont + 6)
axs[1].set_xlabel(r"${\gamma_{OM}}$", fontsize=labelfont + 6)
axs[0].text(0.0, 1.05, "(A)", transform=axs[0].transAxes, fontsize=labelfont)
axs[1].text(0.0, 1.05, "(B)", transform=axs[1].transAxes, fontsize=labelfont)
fig.tight_layout()
fig.savefig("fig/tif/Figure5.tif", dpi=300)
fig.savefig("fig/svg/Figure5.svg", dpi=300)
plt.show()
# %% [markdown]
# # Figure 4 zoomed out
# %%
INORM = [0.01]
gamma_S = np.arange(0.05, 8, 0.1)
NS = "NO3"
eA = ["NO3", "Denitrification"]
Gnorm = np.zeros((len(gamma_S), len(eA)))
vN = np.zeros((len(gamma_S), len(eA)))
e = np.zeros((len(gamma_S), len(eA)))
i = 0
for m in range(0, len(eA)):
for j in range(0, len(gamma_S)):
emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N = efficiency_CNED_Inf(
gamma_S[j], T, eA[m], CNB, NS, CNED
)
vN_met = (xN + xEA) * (1 - emax_S * gammaB / gamma_S[j])
Gnorm[j, m] = np.minimum(emax_S, (emax_S / (vN_met) * INORM[i]))
e[j, m] = emax_S
vN[j, m] = vN_met
fig = plt.figure(figsize=(14, 6), facecolor="w")
axs = fig.subplots(nrows=1, ncols=2)
axs[0].plot(gamma_S, Gnorm[:, 0], lstyle[0], linewidth=3, color=LC[i])
axs[0].plot(gamma_S, Gnorm[:, 1], lstyle[1], linewidth=3, color=LC[i])
axs[1].plot(gamma_S, e[:, 0], lstyle[0], linewidth=3, color="k", alpha=0.3)
axs[1].plot(gamma_S, e[:, 1], lstyle[1], linewidth=3, color="k", alpha=0.3)
axs[0].set_ylabel(r"${G_{norm}}$", fontsize=labelfont + 6)
axs[0].set_xlabel(r"${\gamma_{OM}}$", fontsize=labelfont + 6)
axs[1].set_xlabel(r"${\gamma_{OM}}$", fontsize=labelfont + 6)
axs[1].set_ylabel(r"$G_{C, norm}$", fontsize=labelfont + 6)
ax2 = axs[1].twinx() # instantiate a second axes that shares the same x-axis
ax2.plot(gamma_S, (e[:, 0] / vN[:, 0]) * INORM[i], lstyle[0], linewidth=3, color=LC[i])
ax2.plot(gamma_S, (e[:, 1] / vN[:, 1]) * INORM[i], lstyle[1], linewidth=3, color=LC[i])
# we already handled the x-label with ax1
ax2.set_ylabel(r"$G_{N, norm}$", color=LC[i], fontsize=labelfont + 6)
ax2.tick_params(axis="y", labelcolor=LC[i], labelsize=axisfont + 4)
for i in axs:
i.tick_params(axis="x", labelsize=axisfont + 4)
i.tick_params(axis="y", labelsize=axisfont + 4)
lstr = []
for i in INORM:
lstr.append(str(i))
leg1 = axs[0].legend(
lstr,
loc="lower center",
frameon=False,
fontsize=labelfont - 2,
title=r"$I_{norm}$",
title_fontsize=labelfont,
)
(p1,) = axs[0].plot(np.nan, np.nan, linestyle=lstyle[0], color="k", linewidth=3)
(p2,) = axs[0].plot(np.nan, np.nan, linestyle=lstyle[1], color="k", linewidth=3)
leg2 = axs[0].legend(
[p1, p2],
[r"$\mathrm{NO_3^- → NH_4^+}$", r"$\mathrm{NO_3^- → N_2}$"],
loc="upper right",
frameon=False,
fontsize=labelfont - 2,
)
axs[0].add_artist(leg1)
axs[0].text(0.0, 1.05, "(A)", transform=axs[0].transAxes, fontsize=labelfont)
axs[1].text(0.0, 1.05, "(B)", transform=axs[1].transAxes, fontsize=labelfont)
fig.tight_layout()
fig.savefig("fig/tif/FigureS1.tif", dpi=300)
fig.savefig("fig/svg/FigureS1.svg", dpi=300)
plt.show()
# %% [markdown]
# # Figure 5
# %%
INORM = [0.01, 0.001]
eA = "O2"
CNS = np.arange(1, 20.1, 0.1)
CNS = np.append(CNS, np.arange(21, 1001, 1))
gamma_S = np.arange(1, 7, 1)
NS = "NH4"
fig = plt.figure(figsize=(7, 5), facecolor="w")
ax = plt.axes()
for j in range(0, len(INORM)):
Gnorm = np.zeros((len(CNS), 1))
for m in range(0, len(gamma_S)):
for i in range(0, len(CNS)):
[emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N] = efficiency_CNED_Inf(
gamma_S[m], T, eA, CNB, NS, CNS[i]
)
if v_N < 0: # NH4 mineralization occurs
Gnorm[i] = emax_S
else:
Gnorm[i] = np.minimum(emax_S, (emax_S / v_N) * INORM[j])
ax.plot(CNS, Gnorm, linestyle=lstyle[j], linewidth=3, color=LC[m])
plt.ylabel(r"${G_{norm}}$", fontsize=labelfont)
plt.xlabel(r"${CN_{OM}}$", fontsize=labelfont)
plt.ylim([0.005, 1])
plt.yscale("log")
plt.xscale("log")
lhlist = []
lstr = []
for j in gamma_S:
lstr.append(str(j))
leg1 = ax.legend(lstr, loc="lower left", frameon=False, title=r"$\gamma_{OM}}$")
lstr = []
for i in range(0, len(INORM)):
(p1,) = ax.plot(np.nan, np.nan, linestyle=lstyle[i], linewidth=3, color="k")
lstr.append(r"$I_{norm} =" + str(INORM[i]) + "$")
lhlist.append(p1)
ax.legend(lhlist, lstr, loc="upper right", frameon=False)
ax.add_artist(leg1)
ax.grid(True, which="both")
fig.savefig("fig/tif/Figure6.tif", dpi=300)
fig.savefig("fig/svg/Figure6.svg", dpi=300)
plt.show()
# %% [markdown]
# # Figure 6
# %%
eA = ["O2", "Fe(III)", "FeOOH", "SO4"]
# eA = ['O2']
String_eA = [r"$\mathrm{O_2}$", "ferrihydrite", "goethite", r"$\mathrm{SO_4^{2-}}$"]
color_map = plt.cm.get_cmap("Spectral")
color_map = color_map.reversed()
gamma_S = np.linspace(1, 8, 71)
INORM = 0.01
fig = plt.figure(figsize=(11, 7), facecolor="w")
axs = fig.subplots(nrows=2, ncols=2, sharey="row", sharex="col")
axs = axs.reshape((2 * 2, 1))
NS = "NH4"
# CNS=[10000]
for k in range(0, len(eA) - 1):
Gnorm = np.zeros((len(CNS), len(gamma_S)))
e = np.zeros((len(CNS), len(gamma_S)))
for m in range(0, len(gamma_S)):
for i in range(0, len(CNS)):
[emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N] = efficiency_CNED_Inf(
gamma_S[m], T, eA[k], CNB, NS, CNS[i]
)
e[i, m] = emax_S
if emax_S < 0:
print("negative CUE")
else:
if v_N < 0: # NH4 mineralization occurs
Gnorm[i, m] = emax_S
else:
Gnorm[i, m] = np.minimum(emax_S, (emax_S / v_N) * INORM)
[gY, CNX] = np.meshgrid(gamma_S, CNS)
cl = np.arange(0.05, 0.6 + 0.05, 0.05)
cs = axs[k][0].contourf(gY, CNX, Gnorm, cl, cmap=color_map, vmin=0.0, vmax=0.6)
axs[k][0].set_yscale("log")
# fig.colorbar(cs,ax=axs[k][0])
fig.colorbar(
cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap),
ticks=np.arange(0, 0.6 + 0.1, 0.1),
ax=axs[k][0],
)
axs[k][0].set_title(String_eA[k], fontsize=labelfont)
k = len(eA) - 1
Gnorm = np.zeros((len(CNS), len(gamma_S)))
for m in range(0, len(gamma_S)):
for i in range(0, len(CNS)):
[emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N] = efficiency_CNED_Inf(
gamma_S[m], T, eA[k], CNB, NS, CNS[i]
)
if v_N < 0: # NH4 mineralization occurs
Gnorm[i, m] = emax_S
else:
Gnorm[i, m] = np.minimum(emax_S, (emax_S / v_N) * INORM)
[gY, CNX] = np.meshgrid(gamma_S, CNS)
cl = np.arange(0, 0.1 + 0.01, 0.01)
cs = axs[k][0].contourf(gY, CNX, Gnorm, cl, cmap=color_map, vmin=0.0, vmax=0.1)
axs[k][0].set_yscale("log")
# fig.colorbar(cs,ax=axs[k][0])
fig.colorbar(
cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap),
ticks=np.arange(0, 0.1 + 0.02, 0.02),
ax=axs[k][0],
)
axs[k][0].set_title(String_eA[k], fontsize=labelfont)
fcaption = ["(A)", "(B)", "(C)", "(D)"]
for i in range(len(axs)):
axs[i][0].text(
0.0, 1.05, fcaption[i], transform=axs[i][0].transAxes, fontsize=labelfont
)
axs[2][0].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs[3][0].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs[0][0].set_ylabel(r"$CN_{OM}$", fontsize=labelfont)
axs[2][0].set_ylabel(r"$CN_{OM}$", fontsize=labelfont)
axs[0][0].text(
0.4, 0.8, "N limited", transform=axs[0][0].transAxes, fontsize=labelfont, color="w"
)
axs[0][0].text(
0.075,
0.15,
"Energy\nlimited",
transform=axs[0][0].transAxes,
fontsize=labelfont,
color="k",
)
axs[0][0].text(
0.6, 0.15, "C limited", transform=axs[0][0].transAxes, fontsize=labelfont, color="w"
)
axs[1][0].text(
0.4, 0.8, "N limited", transform=axs[1][0].transAxes, fontsize=labelfont, color="w"
)
axs[1][0].text(
0.05,
0.15,
"Energy\nlimited",
transform=axs[1][0].transAxes,
fontsize=labelfont,
color="k",
)
axs[1][0].text(
0.5, 0.15, "C limited", transform=axs[1][0].transAxes, fontsize=labelfont, color="w"
)
axs[2][0].text(
0.4, 0.8, "N limited", transform=axs[2][0].transAxes, fontsize=labelfont, color="w"
)
axs[2][0].text(
0.05,
0.15,
"Energy\nlimited",
transform=axs[2][0].transAxes,
fontsize=labelfont,
color="k",
)
axs[2][0].text(
0.6, 0.15, "C limited", transform=axs[2][0].transAxes, fontsize=labelfont, color="k"
)
axs[3][0].text(
0.075,
0.9,
"N limited",
transform=axs[3][0].transAxes,
fontsize=labelfont,
color="k",
)
axs[3][0].text(
0.7,
0.5,
"Energy\nlimited",
transform=axs[3][0].transAxes,
fontsize=labelfont,
color="k",
)
axs[3][0].text(
0.15,
0.15,
"C limited",
transform=axs[3][0].transAxes,
fontsize=labelfont,
color="k",
)
plt.subplots_adjust(left=0.1, bottom=0.1, right=0.6, top=0.8)
fig.tight_layout()
fig.savefig("fig/tif/Figure7.tif", dpi=300)
fig.savefig("fig/svg/Figure7.svg", dpi=300)
plt.show()
# %% [markdown]
# # Appendix
# ## Figure S2
#
# %%
gamma = np.arange(0.5, 8.1, 0.1) # Degree of reduction of ED
dGrX = np.zeros((len(gamma)))
# dGB_ana = -2.7
# Anbolic reaction
dCGX = dCG_O2(gamma_B)
dGB_ana = gamma_B / gamma * dCG_O2(gamma) - dCGX
for i in range(len(gamma)):
if gamma[i] < 4.67:
dGrX[i] = -(666.7 / gamma[i] + 243.1) # kJ/Cmol biomass
else:
dGrX[i] = -(157 * gamma[i] - 339) # kJ/Cmol biomass
dGred = np.array([0, 5, 24.04, 40, 75.6, 85, 122.7])
# dGred = np.array([0, 5,24])
fig = plt.figure(figsize=(12, 4.5), facecolor="w")
axs = fig.subplots(nrows=1, ncols=3)
axs[0].plot(
gamma,
60.3 - 28.5 * (4 - gamma) + -dGred[0] * gamma,
linewidth=3,
color="k",
label=str(dGred[0]),
)
for i in range(1, len(dGred)):
dGcat = (60.3 - 28.5 * (4 - gamma)) + gamma * -dGred[i]
axs[0].plot(
gamma, dGcat, linewidth=2, color=LC[i - 1], label=str(dGred[i]),
)
Y = dGcat / (dGrX - dGB_ana + (gammaB / gamma) * dGcat)
# above Y is same as Y = dGcat / (dGrX + dCGX)
denom = dGrX - dGB_ana + (gammaB / gamma) * dGcat
axs[1].plot(gamma, dGrX * Y, linewidth=2, color=LC[i - 1])
axs[2].plot(gamma, denom, "--", linewidth=2, color=LC[i - 1])
axs[2].plot(gamma, dGcat, "-", linewidth=2, color=LC[i - 1])
axs[1].plot(gamma, dGrX, "--", linewidth=3, color="k")
# axs[1].set_ylim([-1000, 200])
axs[0].set_ylim([-800, 200])
# axs[2].set_ylim(bottom=0)
# axs[2].set_ylim([0, -2000])
axs[0].plot([1.88, 1.88], axs[0].get_ylim(), "--", linewidth=1, color="k")
axs[0].plot(axs[0].get_xlim(), [0, 0], "--", linewidth=1, color="k")
axs[0].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs[1].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs[2].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont)
axs[0].set_ylabel(
r"$ \Delta_{cat}G_{OM}$ kJ $\mathrm{(C mol \ OM)^{-1}}$", fontsize=labelfont
)
axs[1].set_ylabel(r"$ \Delta_{r}G$", fontsize=labelfont)
axs[0].text(0.0, 1.05, "(A)", transform=axs[0].transAxes, fontsize=labelfont)
axs[1].text(0.0, 1.05, "(B)", transform=axs[1].transAxes, fontsize=labelfont)
axs[2].text(0.0, 1.05, "(C)", transform=axs[2].transAxes, fontsize=labelfont)
axs[1].text(
0.1,
1.05,
r" Dashed line = $ \Delta_{r}G_{B}$",
transform=axs[1].transAxes,
fontsize=labelfont - 2,
)
axs[1].text(
0.1,
0.95,
r" Solid lines = $ \Delta_{r}G_{OM}$",
transform=axs[1].transAxes,
fontsize=labelfont - 2,
)
fig.tight_layout(pad=5, w_pad=0.5, h_pad=1)
lhlist = []
lstr = []
p1 = []
(p1,) = axs[0].plot(np.nan, np.nan, linestyle=lstyle[0], color="k", linewidth=3)
lstr.append(str(dGred[0]))
lhlist.append(p1)
for i in range(1, len(dGred)):
(p1,) = axs[0].plot(
np.nan, np.nan, linestyle=lstyle[0], color=LC[i - 1], linewidth=3
)
lstr.append(str(dGred[i]))
lhlist.append(p1)
axs[0].legend(
lhlist,
lstr,
loc="lower left",
frameon=False,
fontsize=labelfont - 2,
ncol=4,
bbox_to_anchor=(0.75, 1.15),
)
axs[0].text(
-0.1,
1.35,
r"$ \frac{-\Delta_{red}G_{EA}}{\gamma_{EA}}$ kJ $\mathrm{(e^- mol)^{-1}}$",
transform=axs[0].transAxes,
fontsize=labelfont,
color="k",
)
lhlist = []
p1 = []
for i in range(0, 2):
(p1,) = axs[2].plot(np.nan, np.nan, linestyle=lstyle[i], color="k", linewidth=3)
lhlist.append(p1)
axs[2].legend(
lhlist,
[r"$ \Delta_{cat}G_{OM}$", "denominator Eq. (34)"],
loc="lower left",
frameon=False,
fontsize=labelfont - 2,
)
fig.savefig("fig/svg/FigureS2.svg", dpi=300)
fig.savefig("fig/tif/FigureS2.tif", dpi=300)
plt.show()
# %% [markdown]
# # Figure S3
# %%
# eA = ["NO3", "Denitrification"]
# gamma_S = np.linspace(0.5, 8, 100)
# # INORM = np.array([0.01,0.2,1.5])
# INORM = np.array([0.01, 0.1, 0.2, 0.5, 1.5])
# # INORM = np.array([0.005]) / 0.5
# NS = "NO3"
# GG = []
# for j in range(0, len(INORM)):
# G = []
# for k in range(0, len(eA)):
# Gnorm = np.zeros((len(CNS), len(gamma_S)))
# for m in range(0, len(gamma_S)):
# for i in range(0, len(CNS)):
# [emax_S, YCO2, dGrS, xN, xEA, v_EA, v_N] = efficiency_CNED_Inf(
# gamma_S[m], T, eA[k], CNB, NS, CNS[i]
# )
# vN_met = (xN + xEA) * (1 - emax_S * gammaB / gamma_S[m])
# Gnorm[i, m] = np.minimum(emax_S, (emax_S / vN_met) * INORM[j])
# G.append(Gnorm)
# GG.append(G)
# color_map = plt.cm.get_cmap("cividis")
# color_map = color_map.reversed()
# j = 0
# fig = plt.figure(figsize=(12, 7), facecolor="w")
# axs = fig.subplots(nrows=3, ncols=len(INORM), sharey="row", sharex="col")
# G = GG[j]
# Gnorm_diff = G[0] - G[1] # Gnorm_diff = DNRA- Denitrification
# id = Gnorm_diff > 0
# Gnorm_diff_norm = Gnorm_diff
# Gnorm_diff_norm[:] = 0
# Gnorm_diff_norm[id] = 1
# [gY, CNX] = np.meshgrid(gamma_S, CNS)
# cs = axs[0, j].contourf(gY, CNX, G[0], cmap=color_map)
# axs[0, j].set_yscale("log")
# # v1= np.linspace(np.amin(G[0]), np.amax(G[0]),5)*1000
# v1 = np.linspace(5, 15, 5)
# norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(cm.ScalarMappable(norm=norm, cmap=cs.cmap), ticks=v1, ax=axs[0, j])
# # cbar= fig.colorbar(cs,ax=axs[0,j])
# # v1=cbar.get_ticks()
# cbar.ax.set_yticklabels(["{:1.0f}".format(i) for i in v1])
# cbar.ax.set_title(r" $\mathrm{x10^{-3}}$", fontsize=10)
# cs = axs[1, j].contourf(gY, CNX, G[1], cmap=color_map)
# axs[1, j].set_yscale("log")
# # v1= np.linspace(np.amin(G[1]), np.amax(G[1]),5)*1000
# norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(cm.ScalarMappable(norm=norm, cmap=cs.cmap), ticks=v1, ax=axs[1, j])
# cbar.ax.set_yticklabels(["{:1.0f}".format(i) for i in v1])
# cbar.ax.set_title(r" $\mathrm{x10^{-3}}$", fontsize=10)
# v1 = np.array([0, 1])
# cs = axs[2, j].contourf(
# gY, CNX, Gnorm_diff_norm, cmap=color_map, vmin=v1.min(), vmax=v1.max()
# )
# axs[2, j].set_yscale("log")
# # norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(
# cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap), ticks=v1, ax=axs[2, j]
# )
# cbar.ax.set_yticklabels(["{:1.1f}".format(i) for i in v1])
# maxv = [0.015, 0.15, 0.3, 0.6, 0.6]
# vstep = [0.001, 0.05, 0.1, 0.1, 0.1]
# for j in range(1, len(INORM)):
# G = GG[j]
# Gnorm_diff = G[0] - G[1] # Gnorm_diff = DNRA- Denitrification
# id = Gnorm_diff > 0
# Gnorm_diff_norm = Gnorm_diff
# Gnorm_diff_norm[:] = 0
# Gnorm_diff_norm[id] = 1
# [gY, CNX] = np.meshgrid(gamma_S, CNS)
# v1 = np.arange(0, maxv[j] + vstep[j], vstep[j])
# cs = axs[0, j].contourf(gY, CNX, G[0], cmap=color_map, vmin=v1.min(), vmax=v1.max())
# axs[0, j].set_yscale("log")
# # norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(
# cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap), ticks=v1, ax=axs[0, j]
# )
# cbar.ax.set_yticklabels(["{:1.1f}".format(i) for i in v1])
# cs = axs[1, j].contourf(gY, CNX, G[1], cmap=color_map, vmin=v1.min(), vmax=v1.max())
# axs[1, j].set_yscale("log")
# # norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(
# cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap), ticks=v1, ax=axs[1, j]
# )
# cbar.ax.set_yticklabels(["{:1.1f}".format(i) for i in v1])
# v1 = np.array([0.0, 1.0])
# cs = axs[2, j].contourf(
# gY, CNX, Gnorm_diff_norm, cmap=color_map, vmin=v1.min(), vmax=v1.max()
# )
# axs[2, j].set_yscale("log")
# # cbar= fig.colorbar(cs,ax=axs[2,j])
# # norm = mpl.colors.Normalize(vmin=v1.min(), vmax=v1.max())
# cbar = fig.colorbar(
# cm.ScalarMappable(norm=cs.norm, cmap=cs.cmap), ticks=v1, ax=axs[2, j]
# )
# # cbar.ax.set_yticklabels(["{:1.1f}".format(i) for i in v1])
# for row in [0, 1, 2]:
# axs[row, 0].set_ylabel(r"$CN_{OM}$", fontsize=labelfont)
# txt = ["(A)", "(B)", "(C)", "(D)", "(E)", "(F)"]
# for col in range(0, len(INORM)):
# axs[2, col].set_xlabel(r"$\gamma_{OM}$", fontsize=labelfont - 2)
# axs[0, col].set_title(
# txt[col] + "\n" + r"$I_{norm} =" + str(INORM[col]) + "$", fontsize=labelfont - 2
# )
# fig.tight_layout()
# fig.savefig("fig/tif/FigureS3.tif", dpi=300)
# fig.savefig("fig/svg/FigureS3.svg", dpi=300)
# plt.show()
# %% [markdown]
# # Figure S
# %%
INORM = 0.2
eA = ["NO3", "Denitrification"]
eAstr = ["DNRA", "Denitrification"]
CNS = np.arange(1, 20.1, 0.1)
CNS = np.append(CNS, np.arange(21, 1001, 1))
gamma_S = np.arange(1, 8 + 1, 1)
#
# gamma_S = np.array([2]);
NS = "NO3"
fig = plt.figure(figsize=(20, 10), facecolor="w")