Examples

Notebooks

In the folder notebooks several notebooks, using Pluto.jl, for the simulation of GC-systems are available.

To use these notebooks Julia, v1.6 or above, must be installed and Pluto must be added:

julia> ]
(v1.7) pkg> add Pluto

To run Pluto, use the following commands:

julia> using Pluto
julia> Pluto.run()

Pluto will open your browser. In the field Open from file the URL of a notebook or the path to a locally downloaded notebook can be insert and the notebook will open and load the necessary packages.

Overview of notebooks

• simulation_conventional_GC.jl - Simulation of a conventional GC-system (constant temperature, constant diameter and constant film thickness along the column) and outlet pressure as "vacuum" or "atmospheric", with option of flow or pressure control and temperature program notation in the typical form used in commercial GC software (temperature levels, holding times and heating ramps). Results can be exported.
• simulation_conventional_GC_TL.jl - Simulation of a conventional GC-system (constant temperature, constant diameter and constant film thickness along the column) with an attached transfer line (at a fixed temperature) and outlet pressure as "vacuum" or "atmospheric", with option of flow or pressure control and temperature program notation in the typical form used in commercial GC software (temperature levels, holding times and heating ramps). Results can be exported.
• simulation_conventional_GC_load_2dbs.jl - Simulation of a conventional GC-system (constant temperature, constant diameter and constant film thickness along the column) and loading of up to two different substance databases and simulation of the common substances with the same GC-system and comparing the result. Also, an option is given, to load measured retention times and compare these to the simulations. Same setting for programs as in simulation_conventional_GC.jl
• simulation_example.jl - General example of simulation of a GC-system with optional thermal gradient (exponential/linear model of temperature change along the column) and constant diameter and constant film thickness along the column. Results can be exported.
• simulation_example_input_gradient_function.jl - Simulation of a GC-system with optional thermal gradient where the temperature change along the column is defined by a user-defined equation (cosine-function as example).

Simulation of measurements

Two measurements from [7] will be simulated and compared to the measured chromatograms. The n-alkanes from n-nonane (C9) to n-triacontane (C30) are separated in a conventional GC and a thermal gradient GC . The database with the thermodynamic parameters is Database_Leppert2020b.csv.

Conventional GC

The conventional GC program simulated here is Prog. D from [7], a temperature program with two heating ramps, constant inlet pressure and a flame ionization detector (FID, atmospheric outlet pressure).

The standard options are used, beside the option ng (non-gradient) is changed to true. Because the conventional GC does not use non-uniform temperature, diameter or film thickness, the model can be simplified and the calculation of the separation is faster.

opt = GasChromatographySimulator.Options(ng=true)

GasChromatographySimulator.Options(OwrenZen5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, static(false)), 1.0e-6, 0.001, "inlet", true, true, "Blumberg", "Pressure", 1.0e12)

The column has a length of 11.18 m, a diameter of 0.104 mm and a film thickness of 0.104 µm. The stationary phase is labeled as FS5ms and the mobile phase gas is helium:

col = GasChromatographySimulator.Column(11.18, 0.104e-3, 0.104e-6, "FS5ms", "H2");

GasChromatographySimulator.Column(11.18, 0.000104, [0.000104], 1.04e-7, [1.04e-7], "FS5ms", "H2")

The temperature program starts at 40°C, which is hold for 1 min. The column is heated up to 180°C in 28 min (5°C/min heating ramp), where the temperature is also hold for 1min. Than the column is heated to 300°C in 6 min (20°C/min heating ramp), where the temperature again is kept for 1 min. The inlet pressure is at constant 411564 Pa (absolute) and the outlet pressure is at constant 101300 Pa (absolute) during the program.

prog_D = GasChromatographySimulator.Program([0.0, 60.0, 1680.0, 60.0, 360.0, 60.0], [40.0, 40.0, 180.0, 180.0, 300.0, 300.0], 411564.0*ones(6), 101300.0.*ones(6), col.L);

We want to use all solutes for the stationary phase FS5ms, which are in the database Database_Leppert2020b.csv. We load the database into a dataframe:

db_dataframe = DataFrame(CSV.File("../../data/Leppert2020b/Database_Leppert2020b.csv", header=1, silencewarnings=true));

and extract all the names of the substances with: To keep the documentation concise, tables in this section are truncated to the first 10 rows in the output.

solutes = String.(GasChromatographySimulator.all_solutes(col.sp, db_dataframe));
println("Showing first 10 of $(length(solutes)) solutes:")
first(solutes, 10)

10-element Vector{String}:
 "C9"
 "C10"
 "C11"
 "C12"
 "C13"
 "C14"
 "C15"
 "C16"
 "C17"
 "C18"

The injection is assumed to be ideal with initial peak widths τ₀ of 0 seconds and occuring at the beginning of the temperature program (t₀ of 0 seconds). The data for all solutes is finally loaded with:

t₀ = zeros(length(solutes))
τ₀ = zeros(length(solutes))
sub = GasChromatographySimulator.load_solute_database(db_dataframe, col.sp, col.gas, solutes, t₀, τ₀)

7-element Vector{GasChromatographySimulator.Substance}:
 GasChromatographySimulator.Substance("C9", "111-84-2", 371.19, 30.17, 89.34, 0.001, "Leppert2020b, alkane, alkanes", 0.00012532067220845386, 0.0, 0.0)
 GasChromatographySimulator.Substance("C10", "124-18-5", 391.24, 32.24, 112.49, 0.001, "Leppert2020b, alkane, Grob, alkanes", 0.00011884992834775946, 0.0, 0.0)
 GasChromatographySimulator.Substance("C11", "1120-21-4", 410.21999999999997, 33.71, 116.04, 0.001, "Leppert2020b, alkane, Grob, alkanes", 0.00011323854194900686, 0.0, 0.0)
 GasChromatographySimulator.Substance("C12", "112-40-3", 427.92999999999995, 34.92, 121.44, 0.001, "Leppert2020b, alkane, alkanes", 0.00010831150224729054, 0.0, 0.0)
 GasChromatographySimulator.Substance("C13", "629-50-5", 444.46999999999997, 35.93, 125.62, 0.001, "Leppert2020b, alkane, alkanes", 0.00010394000406156419, 0.0, 0.0)
 GasChromatographySimulator.Substance("C14", "629-59-4", 459.98, 36.76, 126.76, 0.001, "Leppert2020b, alkane, alkanes", 0.00010002699641573172, 0.0, 0.0)
 GasChromatographySimulator.Substance("C15", "629-62-9", 474.4, 37.39, 129.62, 0.001, "Leppert2020b, alkane, alkanes", 9.649766997034015e-5, 0.0, 0.0)

The parameters are combined:

par = GasChromatographySimulator.Parameters(col, prog_D, sub, opt);

The temperature program and the pressure/flow program can be plotted:

p_flow = GasChromatographySimulator.plot_flow(par)
p_press = GasChromatographySimulator.plot_pressure(par)
p_temp = GasChromatographySimulator.plot_temperature(par)
l = @layout([a{0.65w} [b; c]])
p_TpF = plot(p_temp, p_press, p_flow, layout=l)

The temperatures at the column inlet and outlet are identical, the temperature along the colum is uniform. With the temperature program and the constant pressures, the flow decreases during the temperature program.

Finally, the simulation is executed:

peaklist, sol = GasChromatographySimulator.simulate(par);

with the peaklist:

We know can compare the simulation results with the measured chromatogram. The file Leppert2020b_measured_RT_progD.csv contains the retention times and peak widths (as standard deviations) from the measurement.

measurement_D = DataFrame(CSV.File("../../data/Leppert2020b/Leppert2020b_measured_RT_progD.csv", header=1, silencewarnings=true));
measurement_D[!, 2] = measurement_D[!, 2] .* 60.0; # conversion from min -> s
rename!(measurement_D, [:Name, :tR, :τR]);

The simulated and measured separations can be compared by comparing measured and simulated retention times:

compare = GasChromatographySimulator.compare_measurement_simulation(measurement_D, peaklist)

Differences between measured and simulated retention times are in the range of some seconds, while the retention times are in minutes. Most differences are below 1%. The measured peak widths are 10 to 15% higher than the calculated peak widths.

The measured and simulated separation can also be compared by a plot of the chromatograms:

chrom_D = DataFrame(CSV.File("../../data/Leppert2020b/Leppert2020b_measured_Chrom_progD.csv", header=1, silencewarnings=true))
p_chrom, t, chrom = GasChromatographySimulator.plot_chromatogram(peaklist, (0.0, round(chrom_D[end,1];sigdigits=2)); annotation=false, number=true, mirror=true, offset=0.0)
plot!(p_chrom, chrom_D[!,1], chrom_D[!,2].*400.0.+0.1)
ylims!(-1.6,1.6)
xlims!(0.0,round(chrom_D[end,1];sigdigits=2))
p_chrom

The measured chromatogram is plotted in orange, while the simulated chromatogram is plotted in blue and mirrored.

Thermal gradient GC

The following example of a thermal gradient GC is the example medium gradient from [7].

Standard options are used (here the option ng has to be false):

opt_tg = GasChromatographySimulator.Options()

GasChromatographySimulator.Options(OwrenZen5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, static(false)), 1.0e-6, 0.001, "inlet", true, false, "Blumberg", "Pressure", 1.0e12)

And the column is 2.05 m long and has the same diameter, film thickness and stationary phase as in the example before. Here Helium is used as mobile phase.

col_tg = GasChromatographySimulator.Column(2.05, 0.104e-3, 0.104e-6, "FS5ms", "He");

GasChromatographySimulator.Column(2.05, 0.000104, [0.000104], 1.04e-7, [1.04e-7], "FS5ms", "He")

The program is taken from the measured temperatures and pressures during the GC run, stored in the file Leppert2020b_prog_settings_med_gradient_x90.csv.

prog_settings = DataFrame(CSV.File("../../data/Leppert2020b/Leppert2020b_prog_settings_med_gradient_x90.csv", header=1, silencewarnings=true));
println("Showing first 10 of $(nrow(prog_settings)) rows:")
first(prog_settings, 10)

We do not need the measured temperatures and pressures at such a high measurement rate (every 40 to 50 ms). Only every 20th measurement point is used to re-construct the temperature and pressure program. The curvature factor $α$ is set to a value of -3.0, based on separate measurements of the temperature profile along the column.

# use only every 20th measurement
time = cumsum(prog_settings.Deltat)[1:20:end]
time_steps = Array{Float64}(undef, length(time))
for i=2:length(time)
    time_steps[i] = time[i]-time[i-1]
end
time_steps[1] = 0.0
temp_steps = prog_settings.T[1:20:end]
ΔT_steps = prog_settings.DeltaT[1:20:end]
pin_steps = prog_settings.pinj[1:20:end].*1000.0 .+ 101300.0
pout_steps = prog_settings.pdet[1:20:end].*1000.0
α_steps = -3.0.*ones(length(ΔT_steps))
x₀_steps = zeros(length(ΔT_steps))
L₀_steps = col_tg.L.*ones(length(ΔT_steps))
prog_med_grad = GasChromatographySimulator.Program(time_steps, temp_steps, pin_steps, pout_steps, ΔT_steps, x₀_steps, L₀_steps, α_steps, "outlet", col_tg.L);

GasChromatographySimulator.Program{GasChromatographySimulator.var"#gf#2"{String, Matrix{Float64}}}([0.0, 0.9200000000000003, 0.9100000000000007, 0.9199999999999986, 0.9199999999999995, 0.910000000000001, 0.9199999999999999, 0.9199999999999982, 0.9200000000000008, 0.9300000000000006  …  0.9199999999999875, 0.9100000000000108, 0.9200000000000017, 0.9099999999999966, 0.9200000000000017, 0.9099999999999966, 0.9200000000000017, 0.9099999999999966, 0.9099999999999966, 0.9200000000000017], [49.323, 48.954, 49.323, 49.077, 49.569, 49.446, 48.831, 49.323, 49.077, 49.077  …  63.099, 56.211, 51.414, 48.339, 46.74, 45.51, 44.895, 44.28, 43.911, 43.542], [354589.48, 354562.67000000004, 354589.48, 354571.61, 354607.32, 354598.4, 354553.72, 354589.48, 354571.61, 354571.61  …  355560.34, 355082.14, 354740.58, 354517.9, 354400.94, 354310.42000000004, 354264.98, 354219.43, 354192.04000000004, 354164.6], [230168.87, 230224.3, 230168.87, 230205.81999999998, 230131.96, 230150.41, 230242.79, 230168.87, 230205.81999999998, 230205.81999999998  …  228154.50999999998, 229148.40000000002, 229856.25, 230316.84999999998, 230558.51, 230745.38999999998, 230839.16, 230933.15000000002, 230989.65000000002, 231046.23], GasChromatographySimulator.var"#gf#2"{String, Matrix{Float64}}("outlet", [-2.829 0.0 2.05 -3.0; -2.46 0.0 2.05 -3.0; … ; -1.23 0.0 2.05 -3.0; -0.984 0.0 2.05 -3.0]), [-2.829 0.0 2.05 -3.0; -2.46 0.0 2.05 -3.0; … ; -1.23 0.0 2.05 -3.0; -0.984 0.0 2.05 -3.0], GasChromatographySimulator.SimpleLinearInterpolation{2, Real}((Real[0.0, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009  …  2.041, 2.042, 2.043, 2.044, 2.045, 2.046, 2.047, 2.048, 2.049, 2.05], Real[0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996]), Real[319.644 319.644 … 315.83099999999996 315.70799999999997; 319.64427497550935 319.64423910913854 … 315.8311195545693 315.7080956436554; … ; 322.4687943216368 322.1003428883798 … 317.0591714441899 316.6905371553519; 322.47299999999996 322.104 … 317.061 316.692]), GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}(([0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996],), [354589.48, 354562.67000000004, 354589.48, 354571.61, 354607.32, 354598.4, 354553.72, 354589.48, 354571.61, 354571.61  …  355560.34, 355082.14, 354740.58, 354517.9, 354400.94, 354310.42000000004, 354264.98, 354219.43, 354192.04000000004, 354164.6]), GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}(([0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996],), [230168.87, 230224.3, 230168.87, 230205.81999999998, 230131.96, 230150.41, 230242.79, 230168.87, 230205.81999999998, 230205.81999999998  …  228154.50999999998, 229148.40000000002, 229856.25, 230316.84999999998, 230558.51, 230745.38999999998, 230839.16, 230933.15000000002, 230989.65000000002, 231046.23]))

The same solutes sub are used as in the previous example.

The parameters are combined:

par_tg = GasChromatographySimulator.Parameters(col_tg, prog_med_grad, sub, opt_tg);

GasChromatographySimulator.Parameters(GasChromatographySimulator.Column(2.05, 0.000104, [0.000104], 1.04e-7, [1.04e-7], "FS5ms", "He"), GasChromatographySimulator.Program{GasChromatographySimulator.var"#gf#2"{String, Matrix{Float64}}}([0.0, 0.9200000000000003, 0.9100000000000007, 0.9199999999999986, 0.9199999999999995, 0.910000000000001, 0.9199999999999999, 0.9199999999999982, 0.9200000000000008, 0.9300000000000006  …  0.9199999999999875, 0.9100000000000108, 0.9200000000000017, 0.9099999999999966, 0.9200000000000017, 0.9099999999999966, 0.9200000000000017, 0.9099999999999966, 0.9099999999999966, 0.9200000000000017], [49.323, 48.954, 49.323, 49.077, 49.569, 49.446, 48.831, 49.323, 49.077, 49.077  …  63.099, 56.211, 51.414, 48.339, 46.74, 45.51, 44.895, 44.28, 43.911, 43.542], [354589.48, 354562.67000000004, 354589.48, 354571.61, 354607.32, 354598.4, 354553.72, 354589.48, 354571.61, 354571.61  …  355560.34, 355082.14, 354740.58, 354517.9, 354400.94, 354310.42000000004, 354264.98, 354219.43, 354192.04000000004, 354164.6], [230168.87, 230224.3, 230168.87, 230205.81999999998, 230131.96, 230150.41, 230242.79, 230168.87, 230205.81999999998, 230205.81999999998  …  228154.50999999998, 229148.40000000002, 229856.25, 230316.84999999998, 230558.51, 230745.38999999998, 230839.16, 230933.15000000002, 230989.65000000002, 231046.23], GasChromatographySimulator.var"#gf#2"{String, Matrix{Float64}}("outlet", [-2.829 0.0 2.05 -3.0; -2.46 0.0 2.05 -3.0; … ; -1.23 0.0 2.05 -3.0; -0.984 0.0 2.05 -3.0]), [-2.829 0.0 2.05 -3.0; -2.46 0.0 2.05 -3.0; … ; -1.23 0.0 2.05 -3.0; -0.984 0.0 2.05 -3.0], GasChromatographySimulator.SimpleLinearInterpolation{2, Real}((Real[0.0, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009  …  2.041, 2.042, 2.043, 2.044, 2.045, 2.046, 2.047, 2.048, 2.049, 2.05], Real[0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996]), Real[319.644 319.644 … 315.83099999999996 315.70799999999997; 319.64427497550935 319.64423910913854 … 315.8311195545693 315.7080956436554; … ; 322.4687943216368 322.1003428883798 … 317.0591714441899 316.6905371553519; 322.47299999999996 322.104 … 317.061 316.692]), GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}(([0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996],), [354589.48, 354562.67000000004, 354589.48, 354571.61, 354607.32, 354598.4, 354553.72, 354589.48, 354571.61, 354571.61  …  355560.34, 355082.14, 354740.58, 354517.9, 354400.94, 354310.42000000004, 354264.98, 354219.43, 354192.04000000004, 354164.6]), GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}(([0.0, 0.9200000000000003, 1.830000000000001, 2.7499999999999996, 3.669999999999999, 4.58, 5.5, 6.419999999999998, 7.339999999999999, 8.27  …  90.99999999999996, 91.90999999999997, 92.82999999999997, 93.73999999999997, 94.65999999999997, 95.56999999999996, 96.48999999999997, 97.39999999999996, 98.30999999999996, 99.22999999999996],), [230168.87, 230224.3, 230168.87, 230205.81999999998, 230131.96, 230150.41, 230242.79, 230168.87, 230205.81999999998, 230205.81999999998  …  228154.50999999998, 229148.40000000002, 229856.25, 230316.84999999998, 230558.51, 230745.38999999998, 230839.16, 230933.15000000002, 230989.65000000002, 231046.23])), GasChromatographySimulator.Substance[GasChromatographySimulator.Substance("C9", "111-84-2", 371.19, 30.17, 89.34, 0.001, "Leppert2020b, alkane, alkanes", 0.00012532067220845386, 0.0, 0.0), GasChromatographySimulator.Substance("C10", "124-18-5", 391.24, 32.24, 112.49, 0.001, "Leppert2020b, alkane, Grob, alkanes", 0.00011884992834775946, 0.0, 0.0), GasChromatographySimulator.Substance("C11", "1120-21-4", 410.21999999999997, 33.71, 116.04, 0.001, "Leppert2020b, alkane, Grob, alkanes", 0.00011323854194900686, 0.0, 0.0), GasChromatographySimulator.Substance("C12", "112-40-3", 427.92999999999995, 34.92, 121.44, 0.001, "Leppert2020b, alkane, alkanes", 0.00010831150224729054, 0.0, 0.0), GasChromatographySimulator.Substance("C13", "629-50-5", 444.46999999999997, 35.93, 125.62, 0.001, "Leppert2020b, alkane, alkanes", 0.00010394000406156419, 0.0, 0.0), GasChromatographySimulator.Substance("C14", "629-59-4", 459.98, 36.76, 126.76, 0.001, "Leppert2020b, alkane, alkanes", 0.00010002699641573172, 0.0, 0.0), GasChromatographySimulator.Substance("C15", "629-62-9", 474.4, 37.39, 129.62, 0.001, "Leppert2020b, alkane, alkanes", 9.649766997034015e-5, 0.0, 0.0)], GasChromatographySimulator.Options(OwrenZen5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, static(false)), 1.0e-6, 0.001, "inlet", true, false, "Blumberg", "Pressure", 1.0e12))

The temperature program and the pressure/flow program can be plotted:

p_flow_tg = GasChromatographySimulator.plot_flow(par_tg)
p_press_tg = GasChromatographySimulator.plot_pressure(par_tg)
p_temp_tg = GasChromatographySimulator.plot_temperature(par_tg)
l = @layout([a{0.65w} [b; c]])
p_TpF_tg = plot(p_temp_tg, p_press_tg, p_flow_tg, layout=l)

The temperature at the outlet side of the column is programmed linearly starting with 50°C (hold for 10 s), heating to 370°C in 60 s (heating ramp of 5.33°C/s). During this heating ramp the temperature at the inlet side of the column is heated faster, resulting in an increasing temperature difference, until around 40 s where the temperature at the inlet increases slower than on the outlet resulting in an decreasing temperature difference.

Finally the simulation is run by:

peaklist_tg, sol_tg = GasChromatographySimulator.simulate(par_tg);

(7×12 DataFrame
 Row │ No       Name    CAS        tR       τR         TR        σR          u ⋯
     │ Int64?   String  String     Float64  Float64    Float64   Float64     F ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ missing  C9      111-84-2   14.9798  0.0491823   75.482   0.0184134   0 ⋯
   2 │ missing  C10     124-18-5   18.8744  0.0379631   96.4019  0.0145433   0
   3 │ missing  C11     1120-21-4  21.8124  0.0344197  111.891   0.0120807   0
   4 │ missing  C12     112-40-3   24.2789  0.0330431  125.302   0.0104472   0
   5 │ missing  C13     629-50-5   26.4776  0.0330922  136.986   0.00928826  0 ⋯
   6 │ missing  C14     629-59-4   28.5219  0.0336204  147.958   0.00843483  0
   7 │ missing  C15     629-62-9   30.4589  0.0343998  158.152   0.00774631  0
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typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}([30.458910917451977, 0.0011833482566892043], [30.307624549856953, 0.0011809040662810629], [4.272714908287408, 3.924040260559845e-5], [4.299026748400564, 4.913044870445541e-5], [4.31236042901033, 5.4124601214178714e-5], [4.353550724247017, 6.979746039633729e-5], [4.353545160087672, 6.978429222255435e-5], [4.37780288091976, 7.912389458713067e-5], [4.418360070235023, 9.48861070081946e-5], [4.440803168933174, 0.00010370139561969899], [-4.519822574781128e-8, -2.340685140216422e-11], [30.439675098014295, 0.0011829175184827267], [-1.4838594200193474e-6, -1.0720622021911433e-5], OrdinaryDiffEqLowOrderRK.OwrenZen5ConstantCache{Float64, Float64}(0.16666666666666666, 0.0625, 0.1875, 0.25, -0.75, -0.75, 3.75, -3.0, 0.5, 0.26895043731778423, -0.7084548104956269, 0.8658892128279884, 0.15462307371928363, 0.06184922948771345, -0.02947695035460993, 0.18500664893617022, 0.4802345261121857, 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nothing, false), true, 0, SciMLBase.DEStats(1669, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 134, 0.0), nothing, SciMLBase.ReturnCode.Success, nothing, nothing, nothing)])

The file Leppert2020b_measured_RT_med_gradient.csv contains the retention times and peak widths (as standard deviations) from the measured chromatogram.

measurement_tg = DataFrame(CSV.File("../../data/Leppert2020b/Leppert2020b_measured_RT_med_gradient.csv", header=1, silencewarnings=true));
measurement_tg[!, 3] = measurement_tg[!, 3] ./ 1000.0; # conversion from ms -> s
rename!(measurement_tg, [:Name, :tR, :τR]);

The simulated and measured separations can be compared by comparing measured and simulated retention times:

compare_tg = GasChromatographySimulator.compare_measurement_simulation(measurement_tg, peaklist_tg)

Differences in retention times are below 1 s, while the retention times are in the range of several seconds. Relative retention time differences are below 4%. The peak widths on the other hand are partly more than 50% higher in the measurement than in the simulation. Main reasons are peak broadening effects outside the scope of this simulation, e.g. extra-column broadening (in the detector) and asymmetric peak broadening (tailing of the peaks, especially for the later substances).

The measured and simulated separation can also be compared by a plot of the chromatograms:

chrom_tg = DataFrame(CSV.File("../../data/Leppert2020b/Leppert2020b_measured_Chrom_med_gradient_x90.csv", header=1, silencewarnings=true))
p_chrom_tg, t_, chrom_ = GasChromatographySimulator.plot_chromatogram(peaklist_tg, (0.0, 55.0); annotation=false, number=true, mirror=true, offset=0.0)
plot!(p_chrom_tg, chrom_tg[!,1].*60.0, chrom_tg[!,2].*8e-5)
ylims!(-13,13)
xlims!(0.0,55.0)
p_chrom_tg

The measured chromatogram is plotted in orange, while the simulated chromatogram is plotted in blue and mirrored.