Figure 9.16:

Model fit to all adsorption experiments.

Code for Figure 9.16

Text of the GNU GPL.

main.py

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from paresto import Paresto
from misc import octave_save
import numpy as np
import matplotlib.pyplot as plt
import os
plt.ion()

# Define the data arrays
Hgas1 = np.array([2.659, 27.590, 141.038, 332.613, 546.857, 608.583,
                   875.353, 991.072, 1080.134, 1142.782, 1203.178,
                   1256.244])

Hads1 = np.array([32.31, 40.02, 45.40, 48.49, 50.19, 53.86, 52.77,
                   53.19, 53.67, 54.15, 54.51, 54.73])

Hgas2 = np.array([3.755, 36.331, 189.904, 413.881, 624.665, 817.592])

Hads2 = np.array([33.17, 40.90, 45.59, 47.72, 48.74, 49.43])

Hgas3 = np.array([12.794, 119.331, 339.917, 545.227, 735.746, 890.642])

Hads3 = np.array([36.91, 42.90, 45.65, 47.00, 47.82, 48.60])

Hgas4 = np.array([7.424, 73.312, 251.177, 491.691, 707.806, 873.926])

Hads4 = np.array([39.11, 46.06, 49.87, 51.57, 52.48, 53.18])

Hgas5 = np.array([9.176, 72.065, 259.002, 475.250, 670.034, 818.669])

Hads5 = np.array([39.52, 46.06, 49.92, 51.86, 52.96, 53.88])

Hgas6 = np.array([2.962, 34.350, 176.860, 405.233, 607.476, 799.723, 946.765])

Hads6 = np.array([32.70, 40.11, 44.92, 47.40, 48.62, 49.50, 50.12])

Hgas7 = np.array([3.159, 38.528, 200.877, 433.924, 647.630, 820.673])

Hads7 = np.array([32.42, 39.81, 44.51, 46.79, 48.14, 48.95])

Hgas8 = np.array([34.127, 172.316, 385.633, 616.149, 812.932, 961.191,
                   1061.967, 1155.829, 1219.299])

Hads8 = np.array([43.79, 48.97, 51.57, 53.09, 54.05, 54.67, 55.20,
                   55.60, 55.93])

# Choose a dataset or datasets to fit
cgmeas = np.concatenate([Hgas1, Hgas2, Hgas3, Hgas4, Hgas5, Hgas6, Hgas7, Hgas8])
cadsmeas = np.concatenate([Hads1, Hads2, Hads3, Hads4, Hads5, Hads6, Hads7, Hads8])

Ks0 = 2
cms0 = 40
cmp0 = 0

def alg_model(t, y, p):
    return [
        y.cads - p.cmp - (p.cms * p.sqKs * np.sqrt(y.cgmeas)) / (1 + p.sqKs * np.sqrt(y.cg)),
        y.cg - y.cgmeas
    ]

def lsq(t, y, p):
    return [y.cadsmeas - y.cads]

# Create an instance of the Paresto class with the model
pe = Paresto()
pe.transcription = "shooting"
pe.nlp_solver_options = {'sens_linsol_options': {'eps': 0}}

pe.z = ['cg', 'cads']
pe.p = ['sqKs', 'cms', 'cmp']
pe.d = ['cgmeas', 'cadsmeas']
pe.alg = alg_model
pe.lsq = lsq
pe.tout = np.arange(1, cgmeas.shape[0] + 1)

pe.initialize()

pe.ic.sqKs = np.sqrt(Ks0)
pe.ic.cms = cms0
pe.ic.cmp = cmp0
pe.ic.cg = 100
pe.ic.cads = 30

pe.lb_ub()
pe.lb.sqKs = np.sqrt(1e-3)
pe.lb.cms = 10
pe.lb.cmp = 0
pe.lb.cg = pe.ic.cg
pe.lb.cads = pe.ic.cads

pe.ub.sqKs = np.sqrt(5)
pe.ub.cms = 200
pe.ub.cmp = 100
pe.ub.cg = pe.ic.cg
pe.ub.cads = pe.ic.cads

# Perform optimization
est, yy, pp = pe.optimize(np.vstack([cgmeas, cadsmeas]).reshape(2, len(pe.tout), 1))

# Calculate confidence intervals
conf = pe.confidence(est, 0.95)

# Display results
print('Estimated parameters')
print('\n'.join(f'{k}: {float(v)}' for k, v in est.theta.items()))

print('Bounding box intervals')
print('\n'.join(f'{k}: {float(v)}' for k, v in conf.bbox.items()))

table1 = np.column_stack((Hgas1, Hads1))
table2 = np.column_stack((Hgas2, Hads2))
table3 = np.column_stack((Hgas3, Hads3))
table4 = np.column_stack((Hgas4, Hads4))
table5 = np.column_stack((Hgas5, Hads5))
table6 = np.column_stack((Hgas6, Hads6))
table7 = np.column_stack((Hgas7, Hads7))
table8 = np.column_stack((Hgas8, Hads8))

# Set up plotting values
nplot = 100
Xplot = np.linspace(0, 1.05 * np.max(cgmeas), nplot)
sqKs = est.theta.sqKs
cms = est.theta.cms
cmp = est.theta.cmp
Yplot = cms * sqKs * np.sqrt(Xplot) / (1 + sqKs * np.sqrt(Xplot)) + cmp

# Combine plot data
table_all = np.column_stack((Xplot, Yplot))

octave_save('adsall.dat',
    ('table_all', table_all),
    ('table1', table1),
    ('table2', table2),
    ('table3', table3),
    ('table4', table4),
    ('table5', table5),
    ('table6', table6),
    ('table7', table7),
    ('table8', table8),
)

# Check the environment variable for plotting
if not os.getenv('OMIT_PLOTS') == 'true':
    plt.figure()
    plt.plot(table_all[:, 0], table_all[:, 1], label='Model Fit')
    plt.plot(table1[:, 0], table1[:, 1], '+', label='Table 1')
    plt.plot(table2[:, 0], table2[:, 1], 'x', label='Table 2')
    plt.plot(table3[:, 0], table3[:, 1], '*', label='Table 3')
    plt.plot(table4[:, 0], table4[:, 1], 'o', label='Table 4')
    plt.plot(table5[:, 0], table5[:, 1], '+', label='Table 5')
    plt.plot(table6[:, 0], table6[:, 1], 'x', label='Table 6')
    plt.plot(table7[:, 0], table7[:, 1], '*', label='Table 7')
    plt.plot(table8[:, 0], table8[:, 1], 'o', label='Table 8')

    plt.legend()
    if not os.getenv('OMIT_PLOTS') == 'true':
        plt.show()