5. Vapor + Halite coexistence surface

Calculate VH surface and properties, and compare result with [Driesner, 2007].

Python code

import os
import numpy as np
import time
import linecache
import matplotlib.pyplot as plt
import matplotlib as mpl
from matplotlib import patches
import matplotlib.ticker as ticker
from matplotlib.ticker import MultipleLocator
from tabulate import tabulate
from matplotlib.patches import Patch
import copy
import warnings
warnings.filterwarnings("ignore", category=RuntimeWarning)
# 3d plot
import helpfunc
mpl.rcParams['font.family'] = 'Arial'  # default font family
mpl.rcParams['mathtext.fontset'] = 'cm'  # font for math
dpi=100
fmt_figs = []  # ['svg','pdf']
figpath = '.'
result_path='../../../gallery_H2ONaCl/pT'
def savefig(figname):
    for fmt_fig in fmt_figs:
        figname_full = '%s/%s.%s' % (figpath, figname, fmt_fig)
        plt.savefig(figname_full, bbox_inches='tight',dpi=dpi)
        print('figure saved: ', figname_full)
compare = lambda a,b : float(str('%.6e'%(a)))-float(str('%.6e'%(b)))
# Import package of xThermo
from xThermo import H2O
from xThermo import NaCl
from xThermo import H2ONaCl
sw_84 = H2ONaCl.cH2ONaCl("IAPS84")
sw_95 = H2ONaCl.cH2ONaCl("IAPWS95")

def plot_3d(sw,scale='linear'):
    fig=plt.figure(figsize=(14,14))
    ax = fig.add_subplot(111,projection='3d',facecolor='None')
    xcenter=1 # X<1% wt.% use log scale, if X>=1% wt.% NaCl, use linear scale
    axtrans=[]
    if(scale=='loglinear'):
        axtrans=helpfunc.set_axis_diagram_3D_loglinearx(ax,xcenter=xcenter,ratio_log_lin=(1,1),zlim=(sw.pmin()/1E5,600),xMajor_loc_log=2,xMajor_loc_linear=10,xMinor_loc_linear=2,zMajor_loc=100,zMinor_loc=20,ylim=(90,820),xlim=(1E-14,100),xlabel='log$_{\mathregular{10}}$(Wt.% NaCl)')
    else:
        helpfunc.set_axis_diagram_3D(ax,zlim=(sw.pmin()/1E5,600),zMajor_loc=100,zMinor_loc=20)
    transform_X = lambda X : helpfunc.data2axis_loglin(axtrans,X) if(scale=='loglinear') else X
    # plot VLH surface as reference
    T = np.linspace(H2ONaCl.T_MIN_VLH, sw.Tmax_VLH(), 100)
    P_vlh = np.array(sw.P_VLH(T))
    # X_haliteLiquidus=np.array(sw.X_HaliteLiquidus(T,P))
    Xl_vlh, Xv_vlh = np.array(sw.X_VLH(T,P_vlh))
    # plot
    n_log,n_linear=20,40
    X = np.linspace(H2ONaCl.X_MIN, H2ONaCl.X_MAX, n_log+n_linear)
    TT,XX = np.meshgrid(T, X)
    PP = np.zeros_like(TT)
    for i in range(0,PP.shape[0]):
        PP[i,:]=P_vlh
    # 1. vapor -> liquid region
    for j in range(0,PP.shape[1]):
        XX[:,j] = np.append(10**np.linspace(np.log10(Xv_vlh[j]),np.log10(xcenter/100),n_log), np.linspace(xcenter/100,Xl_vlh[j],n_linear))
    xx_plot = transform_X(XX*100)
    ax.plot_surface(xx_plot,TT-273.15,PP/1E5,color='w',alpha=0.5)
    ax.plot_wireframe(xx_plot,TT-273.15,PP/1E5,ec='b',lw=0.8,label='VLH: V->L')
    # 2. liquid -> halite region
    for j in range(0,PP.shape[1]):
        XX[:,j] = np.linspace(Xl_vlh[j], 1,len(X))
    xx_plot = transform_X(XX*100)
    ax.plot_surface(xx_plot,TT-273.15,PP/1E5,color='w',alpha=0.5)
    ax.plot_wireframe(xx_plot,TT-273.15,PP/1E5,ec='orange',lw=0.8,label='VLH: L->H')
    # 3. Halite saturated vapor in VH region
    P = np.linspace(0,1,40)
    TT,PP = np.meshgrid(T,P)
    for i in range(0,len(T)):
        PP[:,i] = np.linspace(sw.pmin(),P_vlh[i],len(P))
    XX_VH = np.array(sw.X_VH(TT.reshape(-1,),PP.reshape(-1,)))
    xx_plot = transform_X(XX_VH.reshape(TT.shape)*100)
    ax.plot_surface(xx_plot,TT-273.15,PP/1E5,color='w',alpha=0.5)
    ax.plot_wireframe(xx_plot,TT-273.15,PP/1E5,ec='purple',lw=0.8,label='VH: vapor')
    # halite
    ax.plot(transform_X(Xl_vlh*0+100), T-273.15, P_vlh/1E5, color='k',label='VLH: halite',lw=4)
    # halite liquidus
    ax.plot(transform_X(Xl_vlh*100), T-273.15, P_vlh/1E5, color='g',label='VLH: liquid',lw=4)
    # upper pressure bound
    ax.plot(transform_X(Xv_vlh*100), T-273.15, P_vlh/1E5, color='r',label='VLH: vapor',lw=4)
    # lower pressure bound
    Xv_pmin = np.array(sw.X_VH(T,T*0 + sw.pmin()))
    ax.plot(transform_X(Xv_pmin*100), T-273.15, T*0+sw.pmin()/1E5, color='blue',label='VH: vapor (P=%.0f bar)'%(sw.pmin()/1E5),lw=4)
    # plot several isotherm profile on X-p plane: Fig. 8a in Driesner(2007a)
    for i,T0 in enumerate([300, 450, 500, 550, 650]):
        P_ = np.linspace(sw.pmin(),sw.P_VLH(T0+273.15),100)
        X_ = np.array(sw.X_VH(P_*0 + T0 + 273.15, P_))
        l,=ax.plot(transform_X(X_*100), X_*0 + ax.get_ylim()[1], P_/1E5)
        helpfunc.text3d(ax, (transform_X(10**(-13+1.2*i)),800,50+i*50), 'T=%.0f$^{\circ}$C'%(T0),zdir='y',size=0.05, fc=l.get_color(), ec="None",ha='left',va='bottom')
        # # add line of VLH
        # Xl_=sw.X_HaliteLiquidus(T0+273.15, P_[-1])
        # ax.plot(np.log10(np.array([X_[-1],Xl_])*100),np.array([ax.get_ylim()[1]]*2),np.array([P_[-1]]*2)/1E5,color='b')
        # ax.plot(np.log10(np.array([Xl_,1])*100),np.array([ax.get_ylim()[1]]*2),np.array([P_[-1]]*2)/1E5,color='orange')
    # ax.plot(np.log10(Xv_vlh*100), T*0 + ax.get_ylim()[1], P_vlh/1E5, color='r',label='VLH: vapor',lw=1,ls='dashed')
    # legend
    leg=ax.legend()
    # change legend handle of wireframe of phase boundaries to wireframe hatch
    for i in [0,1,2]:
        leg.legendHandles[i]=Patch(facecolor='white', edgecolor=leg.legendHandles[i]._color,linewidth=0.0,label=leg.texts[i]._text,hatch='++++')
    ax.legend(handles=leg.legendHandles, loc='upper left',ncol=7)
    # text
    helpfunc.text3d(ax,(transform_X(1E-12),800,sw.pmin()/1E5),"P$_{min}$=%.0f bar"%(sw.pmin()/1E5),size=0.07,angle=-90,ec='None',fc='k')
    ax.view_init(elev=25, azim=-145)
    savefig('PhaseBoundary_VH_3D_%s'%(scale))

General 3D view: linear scale (left panel) and log-linear scale (right panel)

The VH surface connect to the Vapor side of VLH surface which can be calculated by function Xl_vlh, Xv_vlh = V_VLH(T, P)

plot_3d(sw_84,scale='linear')
plot_3d(sw_84,scale='loglinear')

• 
• 

Benchmark comparison

Compare halite saturated vapor composition of xThermo and [Driesner, 2007], and also compare result based on different EOS of water.

Python code

def benchmark_VL(sw,mmc4='../Driesner2007a/1-s2.0-S0016703707002943-mmc4.txt'):
    # compare
    if(not os.path.exists(mmc4)):
        print('Please set correct mmc4 file path: %s'%(mmc4))
        exit()
    T0,P0,X0=data=np.loadtxt(mmc4, skiprows=7,unpack=True)
    XL0_wt= np.array(sw.Mol2Wt(X0))*100
    # 1. calculate halite saturated vapor composition: XV_VH
    X_ = np.array(sw.X_VH(T0+273.15,P0*1E5))
    X_mol_ = np.array(sw.Wt2Mol(X_))
    # compare result dict
    Data0 = {'Xv':X0}
    Data_ = {'Xv':X_mol_}
    Err,RErr={},{}
    for key in Data0.keys(): Err[key],RErr[key] = Data0[key]-Data_[key], np.abs(Data0[key]-Data_[key])/(Data0[key])*100.0
    # print to file
    fpout = open('%s/mmc4a_%s.csv'%(result_path,sw.name_backend()),'w')
    fpout.write('T[C],P[bar],XV(Driesner)[mol],XV(xThermo)[mol],XV(diff)[mol]\n')
    for i in range(0,len(T0)):
        fpout.write('%.6e,%.6e'%(T0[i]-273.15,P0[i]))
        for key in Data0.keys():
            fpout.write(',%.6e,%.6e,%.6e'%(Data0[key][i], Data_[key][i],compare(Data0[key][i],Data_[key][i])))
        fpout.write('\n')
    fpout.close()
    # plot data
    fig=plt.figure(figsize=(8,8))
    ax=plt.gca()
    cmap,vmin,vmax='YlGnBu_r',sw.pmin()/1E5,H2ONaCl.P_Peak_VLH/1E5
    CS=ax.scatter(X0,T0,c=P0,cmap=cmap,vmin=vmin,vmax=vmax,s=5)
    ax_cb=ax.inset_axes([1.02,0,0.05,1])
    plt.colorbar(CS,cax=ax_cb,label='Pressure (bar)')
    # also plot VLH: vapor curve
    T = np.linspace(H2ONaCl.T_MIN_VLH, sw.Tmax_VLH(), 100)
    P_vlh = np.array(sw.P_VLH(T))
    # X_haliteLiquidus=np.array(sw.X_HaliteLiquidus(T,P))
    Xl_vlh, Xv_vlh = np.array(sw.X_VLH(T,P_vlh))
    helpfunc.plot_coloredline(ax,np.array(sw.Wt2Mol(Xv_vlh)), T-273.15, P_vlh/1E5,cmap=cmap,vmin=vmin,vmax=vmax,lw=2)
    XV_VH_pmin = np.array(sw.X_VH(T,T*0+sw.pmin()))
    helpfunc.plot_coloredline(ax,np.array(sw.Wt2Mol(XV_VH_pmin)), T-273.15, T*0+sw.pmin()/1E5 ,cmap=cmap,vmin=vmin,vmax=vmax,lw=2)
    ax.annotate("VLH: vapor",ha='center',va='center', xy=(1E-6,320),xytext=(1E-6,150), bbox={'fc':'None','ec':'r'},fontsize=14,fontweight='bold', arrowprops=dict(arrowstyle="->",connectionstyle="arc3"),)
    ax.annotate("Halite saturated vapor\nat $P_{min}$=%.0f bar"%(sw.pmin()/1E5),ha='center',va='top', xy=(2E-13,290),xytext=(2E-13,500), bbox={'fc':'None','ec':'b'},fontsize=14,fontweight='bold', arrowprops=dict(arrowstyle="->",connectionstyle="arc3"),)
    ax.grid(lw=0.2,color='gray')
    ax.set_ylim(H2ONaCl.T_MIN_VLH-273.15, H2ONaCl.T_MAX_VLH-273.15)
    ax.set_xscale('log')
    ax.set_ylabel('Temperature ($^{\circ}$C)')
    ax.set_xlabel('X$_{\mathregular{NaCl}}$ (mole fraction)')

    # savefig('mmc4a')
    # statistics of the difference
    table=[]
    for key,name in zip(list(Err.keys()),['XV (mole fraction)']):
        RErr[key] = RErr[key][~(np.isnan(RErr[key]) | np.isinf(RErr[key]))]
        table.append([name,Err[key].min(),Err[key].max(),RErr[key].min(),RErr[key].max()])
    print(tabulate(table, headers=['Critical property', 'Err. Min', 'Err. Max','RE. Min(%)','RE. Max(%)'],numalign="right",floatfmt=".6f"))

Based on IAPS84 EOS

benchmark_VL(sw_84)

Out:

Critical property      Err. Min    Err. Max    RE. Min(%)    RE. Max(%)
-------------------  ----------  ----------  ------------  ------------
XV (mole fraction)    -0.000000    0.000000      0.000000      0.000105

Based on IAPWS95 EOS

benchmark_VL(sw_95)

Out:

Critical property      Err. Min    Err. Max    RE. Min(%)    RE. Max(%)
-------------------  ----------  ----------  ------------  ------------
XV (mole fraction)    -0.000000    0.000000      0.000000      0.884347

Result table

See also

Electronic Annex EA-4 in [Driesner & Heinrich, 2007] and Fig. 8 in [Driesner & Heinrich, 2007].

Result data calculated by xThermo based on both water EOS of IAPS84 and IAPWS95.

IAPS84

Table 18 Comparison between result of [Driesner, 2007] and result calculated by xThermo.

T[C]	P[bar]	XV(Driesner)[mol]	XV(xThermo)[mol]	XV(diff)[mol]
1.685000e+01	5.000000e+01	2.759550e-07	2.759550e-07	0.000000e+00
2.185000e+01	5.000000e+01	2.318952e-07	2.318952e-07	0.000000e+00
2.685000e+01	5.000000e+01	1.931804e-07	1.931804e-07	0.000000e+00
3.185000e+01	5.000000e+01	1.593317e-07	1.593317e-07	0.000000e+00
3.685000e+01	5.000000e+01	1.302618e-07	1.302618e-07	0.000000e+00
4.185000e+01	5.000000e+01	1.058254e-07	1.058254e-07	0.000000e+00
4.685000e+01	5.000000e+01	8.569633e-08	8.569633e-08	0.000000e+00
5.185000e+01	5.000000e+01	6.939659e-08	6.939659e-08	0.000000e+00
5.685000e+01	5.000000e+01	5.637183e-08	5.637183e-08	0.000000e+00
6.185000e+01	5.000000e+01	4.606286e-08	4.606286e-08	0.000000e+00
6.685000e+01	5.000000e+01	3.795396e-08	3.795396e-08	0.000000e+00
7.185000e+01	5.000000e+01	3.159766e-08	3.159766e-08	0.000000e+00
7.685000e+01	5.000000e+01	2.662167e-08	2.662167e-08	0.000000e+00
8.185000e+01	5.000000e+01	2.272487e-08	2.272487e-08	0.000000e+00
8.685000e+01	5.000000e+01	1.966743e-08	1.966743e-08	0.000000e+00
9.185000e+01	5.000000e+01	1.725747e-08	1.725747e-08	0.000000e+00
9.685000e+01	5.000000e+01	1.533012e-08	1.533012e-08	0.000000e+00
1.018500e+02	5.000000e+01	1.362180e-08	1.362180e-08	0.000000e+00
1.068500e+02	5.000000e+01	1.221553e-08	1.221553e-08	0.000000e+00
1.118500e+02	5.000000e+01	1.124970e-08	1.124970e-08	0.000000e+00
1.168500e+02	5.000000e+01	1.056732e-08	1.056732e-08	0.000000e+00
1.218500e+02	5.000000e+01	1.008300e-08	1.008300e-08	0.000000e+00
1.268500e+02	5.000000e+01	9.746070e-09	9.746070e-09	0.000000e+00
1.318500e+02	5.000000e+01	9.525190e-09	9.525190e-09	0.000000e+00
1.368500e+02	5.000000e+01	9.400591e-09	9.400591e-09	0.000000e+00
1.418500e+02	5.000000e+01	9.359899e-09	9.359899e-09	0.000000e+00
1.468500e+02	5.000000e+01	9.395722e-09	9.395722e-09	0.000000e+00
1.518500e+02	5.000000e+01	9.504212e-09	9.504212e-09	0.000000e+00
1.568500e+02	5.000000e+01	9.684200e-09	9.684200e-09	0.000000e+00
1.618500e+02	5.000000e+01	9.936664e-09	9.936664e-09	0.000000e+00
1.668500e+02	5.000000e+01	1.026443e-08	1.026443e-08	0.000000e+00
1.718500e+02	5.000000e+01	1.067203e-08	1.067203e-08	0.000000e+00
1.768500e+02	5.000000e+01	1.116564e-08	1.116564e-08	0.000000e+00
1.818500e+02	5.000000e+01	1.175312e-08	1.175312e-08	0.000000e+00
1.868500e+02	5.000000e+01	1.244412e-08	1.244412e-08	0.000000e+00
1.918500e+02	5.000000e+01	1.325023e-08	1.325023e-08	0.000000e+00
1.968500e+02	5.000000e+01	1.418521e-08	1.418521e-08	0.000000e+00
2.018500e+02	5.000000e+01	1.526524e-08	1.526524e-08	0.000000e+00
2.068500e+02	5.000000e+01	1.650923e-08	1.650923e-08	0.000000e+00
2.118500e+02	5.000000e+01	1.793926e-08	1.793926e-08	0.000000e+00
2.168500e+02	5.000000e+01	1.958098e-08	1.958098e-08	0.000000e+00
2.218500e+02	5.000000e+01	2.146415e-08	2.146415e-08	0.000000e+00
2.268500e+02	5.000000e+01	2.362331e-08	2.362331e-08	0.000000e+00
2.318500e+02	5.000000e+01	2.610101e-08	2.610101e-08	0.000000e+00
2.368500e+02	5.000000e+01	2.894310e-08	2.894311e-08	-1.000000e-14
2.418500e+02	5.000000e+01	3.219789e-08	3.219789e-08	0.000000e+00
2.468500e+02	5.000000e+01	3.592073e-08	3.592073e-08	0.000000e+00
2.518500e+02	5.000000e+01	4.017492e-08	4.017493e-08	-1.000000e-14
2.568500e+02	5.000000e+01	4.503268e-08	4.503269e-08	-1.000000e-14
2.618500e+02	5.000000e+01	5.057621e-08	5.057622e-08	-1.000000e-14
2.668500e+02	5.000000e+01	5.689899e-08	5.689901e-08	-2.000000e-14
2.718500e+02	5.000000e+01	6.410715e-08	6.410716e-08	-1.000000e-14
2.768500e+02	5.000000e+01	7.232101e-08	7.232103e-08	-2.000000e-14
2.818500e+02	5.000000e+01	8.167690e-08	8.167692e-08	-2.000000e-14
2.868500e+02	5.000000e+01	9.232902e-08	9.232904e-08	-2.000000e-14
2.918500e+02	5.000000e+01	1.044517e-07	1.044517e-07	0.000000e+00
2.968500e+02	5.000000e+01	1.182418e-07	1.182418e-07	0.000000e+00
3.018500e+02	5.000000e+01	1.339213e-07	1.339213e-07	0.000000e+00
3.068500e+02	5.000000e+01	1.517404e-07	1.517404e-07	0.000000e+00
3.118500e+02	5.000000e+01	1.719808e-07	1.719808e-07	0.000000e+00
3.168500e+02	5.000000e+01	1.949593e-07	1.949594e-07	-1.000000e-13
3.218500e+02	5.000000e+01	2.210319e-07	2.210320e-07	-1.000000e-13
3.268500e+02	5.000000e+01	2.505982e-07	2.505982e-07	0.000000e+00
3.318500e+02	5.000000e+01	2.841061e-07	2.841062e-07	-1.000000e-13
3.368500e+02	5.000000e+01	3.220579e-07	3.220579e-07	0.000000e+00
3.418500e+02	5.000000e+01	3.650152e-07	3.650152e-07	0.000000e+00
3.468500e+02	5.000000e+01	4.136063e-07	4.136064e-07	-1.000000e-13
3.518500e+02	5.000000e+01	4.685330e-07	4.685331e-07	-1.000000e-13
3.568500e+02	5.000000e+01	5.305785e-07	5.305786e-07	-1.000000e-13
3.618500e+02	5.000000e+01	6.006158e-07	6.006159e-07	-1.000000e-13
3.668500e+02	5.000000e+01	6.796173e-07	6.796175e-07	-2.000000e-13
3.718500e+02	5.000000e+01	7.686652e-07	7.686654e-07	-2.000000e-13
3.768500e+02	5.000000e+01	8.689623e-07	8.689625e-07	-2.000000e-13
3.818500e+02	5.000000e+01	9.818444e-07	9.818445e-07	-1.000000e-13
3.868500e+02	5.000000e+01	1.108793e-06	1.108794e-06	-1.000000e-12
3.918500e+02	5.000000e+01	1.251452e-06	1.251453e-06	-1.000000e-12
3.968500e+02	5.000000e+01	1.411641e-06	1.411641e-06	0.000000e+00
4.018500e+02	5.000000e+01	1.591370e-06	1.591370e-06	0.000000e+00
4.068500e+02	5.000000e+01	1.792866e-06	1.792866e-06	0.000000e+00
4.118500e+02	5.000000e+01	2.018584e-06	2.018585e-06	-1.000000e-12
4.168500e+02	5.000000e+01	2.271235e-06	2.271235e-06	0.000000e+00
4.218500e+02	5.000000e+01	2.553804e-06	2.553805e-06	-1.000000e-12
4.268500e+02	5.000000e+01	2.869582e-06	2.869582e-06	0.000000e+00
4.318500e+02	5.000000e+01	3.222186e-06	3.222186e-06	0.000000e+00
4.368500e+02	5.000000e+01	3.615593e-06	3.615593e-06	0.000000e+00
4.418500e+02	5.000000e+01	4.054171e-06	4.054172e-06	-1.000000e-12
4.468500e+02	5.000000e+01	4.542712e-06	4.542712e-06	0.000000e+00
4.518500e+02	5.000000e+01	5.086468e-06	5.086469e-06	-1.000000e-12
4.568500e+02	5.000000e+01	5.691194e-06	5.691195e-06	-1.000000e-12
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2.468500e+02	2.000000e+02	9.536395e-06	9.536400e-06	-5.000000e-12
2.518500e+02	2.000000e+02	9.193646e-06	9.193652e-06	-6.000000e-12
2.568500e+02	2.000000e+02	8.912888e-06	8.912893e-06	-5.000000e-12
2.618500e+02	2.000000e+02	8.687126e-06	8.687131e-06	-5.000000e-12
2.668500e+02	2.000000e+02	8.510621e-06	8.510626e-06	-5.000000e-12
2.718500e+02	2.000000e+02	8.378674e-06	8.378679e-06	-5.000000e-12
2.768500e+02	2.000000e+02	8.287458e-06	8.287463e-06	-5.000000e-12
2.818500e+02	2.000000e+02	8.233878e-06	8.233883e-06	-5.000000e-12
2.868500e+02	2.000000e+02	8.215461e-06	8.215466e-06	-5.000000e-12
2.918500e+02	2.000000e+02	8.230266e-06	8.230270e-06	-4.000000e-12
2.968500e+02	2.000000e+02	8.276807e-06	8.276812e-06	-5.000000e-12
3.018500e+02	2.000000e+02	8.354002e-06	8.354007e-06	-5.000000e-12
3.068500e+02	2.000000e+02	8.461117e-06	8.461121e-06	-4.000000e-12
3.118500e+02	2.000000e+02	8.597730e-06	8.597735e-06	-5.000000e-12
3.168500e+02	2.000000e+02	8.763705e-06	8.763710e-06	-5.000000e-12
3.218500e+02	2.000000e+02	8.959160e-06	8.959165e-06	-5.000000e-12
3.268500e+02	2.000000e+02	9.184454e-06	9.184459e-06	-5.000000e-12
3.318500e+02	2.000000e+02	9.440167e-06	9.440173e-06	-6.000000e-12
3.368500e+02	2.000000e+02	9.727095e-06	9.727101e-06	-6.000000e-12
3.418500e+02	2.000000e+02	1.004624e-05	1.004624e-05	0.000000e+00
3.468500e+02	2.000000e+02	1.039879e-05	1.039879e-05	0.000000e+00
3.518500e+02	2.000000e+02	1.078615e-05	1.078615e-05	0.000000e+00
3.568500e+02	2.000000e+02	1.120990e-05	1.120991e-05	-1.000000e-11
3.618500e+02	2.000000e+02	1.167184e-05	1.167185e-05	-1.000000e-11
3.668500e+02	2.000000e+02	1.217395e-05	1.217396e-05	-1.000000e-11
3.718500e+02	2.000000e+02	1.271842e-05	1.271843e-05	-1.000000e-11
3.768500e+02	2.000000e+02	1.330765e-05	1.330766e-05	-1.000000e-11
3.818500e+02	2.000000e+02	1.394426e-05	1.394426e-05	0.000000e+00
3.868500e+02	2.000000e+02	1.463108e-05	1.463108e-05	0.000000e+00
3.918500e+02	2.000000e+02	1.537118e-05	1.537119e-05	-1.000000e-11
3.968500e+02	2.000000e+02	1.616788e-05	1.616789e-05	-1.000000e-11
4.018500e+02	2.000000e+02	1.702475e-05	1.702476e-05	-1.000000e-11
4.068500e+02	2.000000e+02	1.794562e-05	1.794563e-05	-1.000000e-11
4.118500e+02	2.000000e+02	1.893460e-05	1.893461e-05	-1.000000e-11
4.168500e+02	2.000000e+02	1.999611e-05	1.999611e-05	0.000000e+00
4.218500e+02	2.000000e+02	2.113484e-05	2.113485e-05	-1.000000e-11
4.268500e+02	2.000000e+02	2.235585e-05	2.235586e-05	-1.000000e-11
4.318500e+02	2.000000e+02	2.366451e-05	2.366452e-05	-1.000000e-11
4.368500e+02	2.000000e+02	2.506656e-05	2.506657e-05	-1.000000e-11
4.418500e+02	2.000000e+02	2.656813e-05	2.656814e-05	-1.000000e-11
4.468500e+02	2.000000e+02	2.817572e-05	2.817573e-05	-1.000000e-11
4.518500e+02	2.000000e+02	2.989629e-05	2.989630e-05	-1.000000e-11
4.568500e+02	2.000000e+02	3.173721e-05	3.173722e-05	-1.000000e-11
4.618500e+02	2.000000e+02	3.370633e-05	3.370634e-05	-1.000000e-11
1.768500e+02	2.500000e+02	1.219090e-04	1.219090e-04	0.000000e+00
1.818500e+02	2.500000e+02	1.090070e-04	1.090070e-04	0.000000e+00
1.868500e+02	2.500000e+02	9.783645e-05	9.783645e-05	0.000000e+00
1.918500e+02	2.500000e+02	8.809633e-05	8.809634e-05	-1.000000e-11
1.968500e+02	2.500000e+02	7.957025e-05	7.957025e-05	0.000000e+00
2.018500e+02	2.500000e+02	7.209468e-05	7.209468e-05	0.000000e+00
2.068500e+02	2.500000e+02	6.553974e-05	6.553974e-05	0.000000e+00
2.118500e+02	2.500000e+02	5.979778e-05	5.979778e-05	0.000000e+00
2.168500e+02	2.500000e+02	5.477663e-05	5.477663e-05	0.000000e+00
2.218500e+02	2.500000e+02	5.039579e-05	5.039579e-05	0.000000e+00
2.268500e+02	2.500000e+02	4.658416e-05	4.658416e-05	0.000000e+00
2.318500e+02	2.500000e+02	4.328763e-05	4.328765e-05	-2.000000e-11
2.368500e+02	2.500000e+02	4.044548e-05	4.044551e-05	-3.000000e-11
2.418500e+02	2.500000e+02	3.799293e-05	3.799295e-05	-2.000000e-11
2.468500e+02	2.500000e+02	3.587629e-05	3.587631e-05	-2.000000e-11
2.518500e+02	2.500000e+02	3.405086e-05	3.405088e-05	-2.000000e-11
2.568500e+02	2.500000e+02	3.247928e-05	3.247930e-05	-2.000000e-11
2.618500e+02	2.500000e+02	3.113021e-05	3.113023e-05	-2.000000e-11
2.668500e+02	2.500000e+02	2.997732e-05	2.997734e-05	-2.000000e-11
2.718500e+02	2.500000e+02	2.899845e-05	2.899847e-05	-2.000000e-11
2.768500e+02	2.500000e+02	2.817491e-05	2.817493e-05	-2.000000e-11
2.818500e+02	2.500000e+02	2.749095e-05	2.749097e-05	-2.000000e-11
2.868500e+02	2.500000e+02	2.693333e-05	2.693335e-05	-2.000000e-11
2.918500e+02	2.500000e+02	2.649089e-05	2.649091e-05	-2.000000e-11
2.968500e+02	2.500000e+02	2.615428e-05	2.615430e-05	-2.000000e-11
3.018500e+02	2.500000e+02	2.591570e-05	2.591572e-05	-2.000000e-11
3.068500e+02	2.500000e+02	2.576868e-05	2.576870e-05	-2.000000e-11
3.118500e+02	2.500000e+02	2.570790e-05	2.570791e-05	-1.000000e-11
3.168500e+02	2.500000e+02	2.572904e-05	2.572906e-05	-2.000000e-11
3.218500e+02	2.500000e+02	2.582868e-05	2.582870e-05	-2.000000e-11
3.268500e+02	2.500000e+02	2.600417e-05	2.600419e-05	-2.000000e-11
3.318500e+02	2.500000e+02	2.625356e-05	2.625358e-05	-2.000000e-11
3.368500e+02	2.500000e+02	2.657552e-05	2.657554e-05	-2.000000e-11
3.418500e+02	2.500000e+02	2.696930e-05	2.696931e-05	-1.000000e-11
3.468500e+02	2.500000e+02	2.743464e-05	2.743466e-05	-2.000000e-11
3.518500e+02	2.500000e+02	2.797179e-05	2.797181e-05	-2.000000e-11
3.568500e+02	2.500000e+02	2.858143e-05	2.858144e-05	-1.000000e-11
3.618500e+02	2.500000e+02	2.926465e-05	2.926467e-05	-2.000000e-11
3.668500e+02	2.500000e+02	3.002297e-05	3.002299e-05	-2.000000e-11
3.718500e+02	2.500000e+02	3.085827e-05	3.085829e-05	-2.000000e-11
3.768500e+02	2.500000e+02	3.177281e-05	3.177282e-05	-1.000000e-11
3.818500e+02	2.500000e+02	3.276920e-05	3.276922e-05	-2.000000e-11
3.868500e+02	2.500000e+02	3.385043e-05	3.385045e-05	-2.000000e-11
3.918500e+02	2.500000e+02	3.501985e-05	3.501987e-05	-2.000000e-11
3.968500e+02	2.500000e+02	3.628114e-05	3.628116e-05	-2.000000e-11
4.018500e+02	2.500000e+02	3.763836e-05	3.763838e-05	-2.000000e-11
4.068500e+02	2.500000e+02	3.909594e-05	3.909596e-05	-2.000000e-11
4.118500e+02	2.500000e+02	4.065866e-05	4.065868e-05	-2.000000e-11
4.168500e+02	2.500000e+02	4.233170e-05	4.233172e-05	-2.000000e-11
4.218500e+02	2.500000e+02	4.412061e-05	4.412064e-05	-3.000000e-11
4.268500e+02	2.500000e+02	4.603137e-05	4.603139e-05	-2.000000e-11
4.318500e+02	2.500000e+02	4.807034e-05	4.807036e-05	-2.000000e-11
4.368500e+02	2.500000e+02	5.024432e-05	5.024434e-05	-2.000000e-11
4.418500e+02	2.500000e+02	5.256056e-05	5.256058e-05	-2.000000e-11
2.118500e+02	3.000000e+02	1.891858e-04	1.891858e-04	0.000000e+00
2.168500e+02	3.000000e+02	1.717410e-04	1.717410e-04	0.000000e+00
2.218500e+02	3.000000e+02	1.567415e-04	1.567415e-04	0.000000e+00
2.268500e+02	3.000000e+02	1.437999e-04	1.437999e-04	0.000000e+00
2.318500e+02	3.000000e+02	1.326407e-04	1.326407e-04	0.000000e+00
2.368500e+02	3.000000e+02	1.230069e-04	1.230070e-04	-1.000000e-10
2.418500e+02	3.000000e+02	1.146548e-04	1.146549e-04	-1.000000e-10
2.468500e+02	3.000000e+02	1.073907e-04	1.073908e-04	-1.000000e-10
2.518500e+02	3.000000e+02	1.010585e-04	1.010585e-04	0.000000e+00
2.568500e+02	3.000000e+02	9.553037e-05	9.553043e-05	-6.000000e-11
2.618500e+02	3.000000e+02	9.070090e-05	9.070095e-05	-5.000000e-11
2.668500e+02	3.000000e+02	8.648216e-05	8.648221e-05	-5.000000e-11
2.718500e+02	3.000000e+02	8.280039e-05	8.280044e-05	-5.000000e-11
2.768500e+02	3.000000e+02	7.959337e-05	7.959342e-05	-5.000000e-11
2.818500e+02	3.000000e+02	7.680835e-05	7.680840e-05	-5.000000e-11
2.868500e+02	3.000000e+02	7.440051e-05	7.440056e-05	-5.000000e-11
2.918500e+02	3.000000e+02	7.233164e-05	7.233169e-05	-5.000000e-11
2.968500e+02	3.000000e+02	7.056911e-05	7.056916e-05	-5.000000e-11
3.018500e+02	3.000000e+02	6.908506e-05	6.908510e-05	-4.000000e-11
3.068500e+02	3.000000e+02	6.785568e-05	6.785572e-05	-4.000000e-11
3.118500e+02	3.000000e+02	6.686063e-05	6.686067e-05	-4.000000e-11
3.168500e+02	3.000000e+02	6.608259e-05	6.608263e-05	-4.000000e-11
3.218500e+02	3.000000e+02	6.550685e-05	6.550690e-05	-5.000000e-11
3.268500e+02	3.000000e+02	6.512097e-05	6.512101e-05	-4.000000e-11
3.318500e+02	3.000000e+02	6.491448e-05	6.491452e-05	-4.000000e-11
3.368500e+02	3.000000e+02	6.487867e-05	6.487872e-05	-5.000000e-11
3.418500e+02	3.000000e+02	6.500640e-05	6.500644e-05	-4.000000e-11
3.468500e+02	3.000000e+02	6.529188e-05	6.529192e-05	-4.000000e-11
3.518500e+02	3.000000e+02	6.573056e-05	6.573060e-05	-4.000000e-11
3.568500e+02	3.000000e+02	6.631901e-05	6.631905e-05	-4.000000e-11
3.618500e+02	3.000000e+02	6.705480e-05	6.705485e-05	-5.000000e-11
3.668500e+02	3.000000e+02	6.793644e-05	6.793648e-05	-4.000000e-11
3.718500e+02	3.000000e+02	6.896325e-05	6.896329e-05	-4.000000e-11
3.768500e+02	3.000000e+02	7.013537e-05	7.013542e-05	-5.000000e-11
3.818500e+02	3.000000e+02	7.145366e-05	7.145371e-05	-5.000000e-11
3.868500e+02	3.000000e+02	7.291967e-05	7.291971e-05	-4.000000e-11
3.918500e+02	3.000000e+02	7.453560e-05	7.453564e-05	-4.000000e-11
3.968500e+02	3.000000e+02	7.630428e-05	7.630433e-05	-5.000000e-11
4.018500e+02	3.000000e+02	7.822916e-05	7.822920e-05	-4.000000e-11
4.068500e+02	3.000000e+02	8.031424e-05	8.031428e-05	-4.000000e-11
4.118500e+02	3.000000e+02	8.256412e-05	8.256416e-05	-4.000000e-11
4.168500e+02	3.000000e+02	8.498395e-05	8.498400e-05	-5.000000e-11
2.518500e+02	3.500000e+02	2.535087e-04	2.535088e-04	-1.000000e-10
2.568500e+02	3.500000e+02	2.379103e-04	2.379104e-04	-1.000000e-10
2.618500e+02	3.500000e+02	2.242973e-04	2.242975e-04	-2.000000e-10
2.668500e+02	3.500000e+02	2.123784e-04	2.123786e-04	-2.000000e-10
2.718500e+02	3.500000e+02	2.019188e-04	2.019189e-04	-1.000000e-10
2.768500e+02	3.500000e+02	1.927265e-04	1.927266e-04	-1.000000e-10
2.818500e+02	3.500000e+02	1.846434e-04	1.846435e-04	-1.000000e-10
2.868500e+02	3.500000e+02	1.775376e-04	1.775377e-04	-1.000000e-10
2.918500e+02	3.500000e+02	1.712985e-04	1.712986e-04	-1.000000e-10
2.968500e+02	3.500000e+02	1.658324e-04	1.658325e-04	-1.000000e-10
3.018500e+02	3.500000e+02	1.610600e-04	1.610601e-04	-1.000000e-10
3.068500e+02	3.500000e+02	1.569135e-04	1.569136e-04	-1.000000e-10
3.118500e+02	3.500000e+02	1.533349e-04	1.533350e-04	-1.000000e-10
3.168500e+02	3.500000e+02	1.502743e-04	1.502744e-04	-1.000000e-10
3.218500e+02	3.500000e+02	1.476890e-04	1.476891e-04	-1.000000e-10
3.268500e+02	3.500000e+02	1.455422e-04	1.455422e-04	0.000000e+00
3.318500e+02	3.500000e+02	1.438021e-04	1.438021e-04	0.000000e+00
3.368500e+02	3.500000e+02	1.424415e-04	1.424416e-04	-1.000000e-10
3.418500e+02	3.500000e+02	1.414371e-04	1.414372e-04	-1.000000e-10
3.468500e+02	3.500000e+02	1.407689e-04	1.407690e-04	-1.000000e-10
3.518500e+02	3.500000e+02	1.404201e-04	1.404201e-04	0.000000e+00
3.568500e+02	3.500000e+02	1.403761e-04	1.403762e-04	-1.000000e-10
3.618500e+02	3.500000e+02	1.406251e-04	1.406252e-04	-1.000000e-10
3.668500e+02	3.500000e+02	1.411573e-04	1.411573e-04	0.000000e+00
3.718500e+02	3.500000e+02	1.419645e-04	1.419646e-04	-1.000000e-10
3.768500e+02	3.500000e+02	1.430405e-04	1.430406e-04	-1.000000e-10
3.818500e+02	3.500000e+02	1.443805e-04	1.443806e-04	-1.000000e-10

IAPWS95

Table 19 Comparison between result of [Driesner, 2007] and result calculated by xThermo.

T[C]	P[bar]	XV(Driesner)[mol]	XV(xThermo)[mol]	XV(diff)[mol]
1.685000e+01	5.000000e+01	2.759550e-07	2.735146e-07	2.440400e-09
2.185000e+01	5.000000e+01	2.318952e-07	2.298831e-07	2.012100e-09
2.685000e+01	5.000000e+01	1.931804e-07	1.915206e-07	1.659800e-09
3.185000e+01	5.000000e+01	1.593317e-07	1.579744e-07	1.357300e-09
3.685000e+01	5.000000e+01	1.302618e-07	1.291649e-07	1.096900e-09
4.185000e+01	5.000000e+01	1.058254e-07	1.049489e-07	8.765000e-10
4.685000e+01	5.000000e+01	8.569633e-08	8.500223e-08	6.941000e-10
5.185000e+01	5.000000e+01	6.939659e-08	6.885002e-08	5.465700e-10
5.685000e+01	5.000000e+01	5.637183e-08	5.594240e-08	4.294300e-10
6.185000e+01	5.000000e+01	4.606286e-08	4.572509e-08	3.377700e-10
6.685000e+01	5.000000e+01	3.795396e-08	3.768722e-08	2.667400e-10
7.185000e+01	5.000000e+01	3.159766e-08	3.138561e-08	2.120500e-10
7.685000e+01	5.000000e+01	2.662167e-08	2.645162e-08	1.700500e-10
8.185000e+01	5.000000e+01	2.272487e-08	2.258707e-08	1.378000e-10
8.685000e+01	5.000000e+01	1.966743e-08	1.955444e-08	1.129900e-10
9.185000e+01	5.000000e+01	1.725747e-08	1.716364e-08	9.383000e-11
9.685000e+01	5.000000e+01	1.533012e-08	1.525106e-08	7.906000e-11
1.018500e+02	5.000000e+01	1.362180e-08	1.355351e-08	6.829000e-11
1.068500e+02	5.000000e+01	1.221553e-08	1.215911e-08	5.642000e-11
1.118500e+02	5.000000e+01	1.124970e-08	1.120139e-08	4.831000e-11
1.168500e+02	5.000000e+01	1.056732e-08	1.052490e-08	4.242000e-11
1.218500e+02	5.000000e+01	1.008300e-08	1.004502e-08	3.798000e-11
1.268500e+02	5.000000e+01	9.746070e-09	9.711557e-09	3.451300e-11
1.318500e+02	5.000000e+01	9.525190e-09	9.493427e-09	3.176300e-11
1.368500e+02	5.000000e+01	9.400591e-09	9.371044e-09	2.954700e-11
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3.518500e+02	3.000000e+02	6.573056e-05	6.573060e-05	-4.000000e-11
3.568500e+02	3.000000e+02	6.631901e-05	6.631905e-05	-4.000000e-11
3.618500e+02	3.000000e+02	6.705480e-05	6.705485e-05	-5.000000e-11
3.668500e+02	3.000000e+02	6.793644e-05	6.793648e-05	-4.000000e-11
3.718500e+02	3.000000e+02	6.896325e-05	6.896329e-05	-4.000000e-11
3.768500e+02	3.000000e+02	7.013537e-05	7.013542e-05	-5.000000e-11
3.818500e+02	3.000000e+02	7.145366e-05	7.145371e-05	-5.000000e-11
3.868500e+02	3.000000e+02	7.291967e-05	7.291971e-05	-4.000000e-11
3.918500e+02	3.000000e+02	7.453560e-05	7.453564e-05	-4.000000e-11
3.968500e+02	3.000000e+02	7.630428e-05	7.630433e-05	-5.000000e-11
4.018500e+02	3.000000e+02	7.822916e-05	7.822920e-05	-4.000000e-11
4.068500e+02	3.000000e+02	8.031424e-05	8.031428e-05	-4.000000e-11
4.118500e+02	3.000000e+02	8.256412e-05	8.256416e-05	-4.000000e-11
4.168500e+02	3.000000e+02	8.498395e-05	8.498400e-05	-5.000000e-11
2.518500e+02	3.500000e+02	2.535087e-04	2.535088e-04	-1.000000e-10
2.568500e+02	3.500000e+02	2.379103e-04	2.379104e-04	-1.000000e-10
2.618500e+02	3.500000e+02	2.242973e-04	2.242975e-04	-2.000000e-10
2.668500e+02	3.500000e+02	2.123784e-04	2.123786e-04	-2.000000e-10
2.718500e+02	3.500000e+02	2.019188e-04	2.019189e-04	-1.000000e-10
2.768500e+02	3.500000e+02	1.927265e-04	1.927266e-04	-1.000000e-10
2.818500e+02	3.500000e+02	1.846434e-04	1.846435e-04	-1.000000e-10
2.868500e+02	3.500000e+02	1.775376e-04	1.775377e-04	-1.000000e-10
2.918500e+02	3.500000e+02	1.712985e-04	1.712986e-04	-1.000000e-10
2.968500e+02	3.500000e+02	1.658324e-04	1.658325e-04	-1.000000e-10
3.018500e+02	3.500000e+02	1.610600e-04	1.610601e-04	-1.000000e-10
3.068500e+02	3.500000e+02	1.569135e-04	1.569136e-04	-1.000000e-10
3.118500e+02	3.500000e+02	1.533349e-04	1.533350e-04	-1.000000e-10
3.168500e+02	3.500000e+02	1.502743e-04	1.502744e-04	-1.000000e-10
3.218500e+02	3.500000e+02	1.476890e-04	1.476891e-04	-1.000000e-10
3.268500e+02	3.500000e+02	1.455422e-04	1.455422e-04	0.000000e+00
3.318500e+02	3.500000e+02	1.438021e-04	1.438021e-04	0.000000e+00
3.368500e+02	3.500000e+02	1.424415e-04	1.424416e-04	-1.000000e-10
3.418500e+02	3.500000e+02	1.414371e-04	1.414372e-04	-1.000000e-10
3.468500e+02	3.500000e+02	1.407689e-04	1.407690e-04	-1.000000e-10
3.518500e+02	3.500000e+02	1.404201e-04	1.404201e-04	0.000000e+00
3.568500e+02	3.500000e+02	1.403761e-04	1.403762e-04	-1.000000e-10
3.618500e+02	3.500000e+02	1.406251e-04	1.406252e-04	-1.000000e-10
3.668500e+02	3.500000e+02	1.411573e-04	1.411573e-04	0.000000e+00
3.718500e+02	3.500000e+02	1.419645e-04	1.419646e-04	-1.000000e-10
3.768500e+02	3.500000e+02	1.430405e-04	1.430406e-04	-1.000000e-10
3.818500e+02	3.500000e+02	1.443805e-04	1.443806e-04	-1.000000e-10

Tip

The help function for 3D plot can be downloaded at here: helpfunc.py