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));
22×11 DataFrame
RowNameCASPhaseTcharthetacharDeltaCpphi0SourceCat_1Cat_2Cat_3
String3String15String7Float64Float64Float64Float64String15String7String7?String7?
1C9111-84-2FS5ms98.0430.1789.340.001Leppert2020balkanealkanesmissing
2C10124-18-5FS5ms118.0932.24112.490.001Leppert2020balkaneGrobalkanes
3C111120-21-4FS5ms137.0733.71116.040.001Leppert2020balkaneGrobalkanes
4C12112-40-3FS5ms154.7834.92121.440.001Leppert2020balkanealkanesmissing
5C13629-50-5FS5ms171.3235.93125.620.001Leppert2020balkanealkanesmissing
6C14629-59-4FS5ms186.8336.76126.760.001Leppert2020balkanealkanesmissing
7C15629-62-9FS5ms201.2537.39129.620.001Leppert2020balkanealkanesmissing
8C16544-76-3FS5ms215.138.46142.180.001Leppert2020balkanealkanesmissing
9C17629-78-7FS5ms227.9138.95145.360.001Leppert2020balkanealkanesmissing
10C18593-45-3FS5ms240.139.58153.290.001Leppert2020balkanealkanesmissing
11C19629-92-5FS5ms251.840.21159.470.001Leppert2020balkanealkanesmissing
12C20112-95-8FS5ms262.8140.67164.990.001Leppert2020balkanealkanesmissing
13C21629-94-7FS5ms273.3941.43179.470.001Leppert2020balkanealkanesmissing
14C22629-97-0FS5ms283.5541.89183.350.001Leppert2020balkanealkanesmissing
15C23638-67-5FS5ms293.1142.25188.990.001Leppert2020balkanealkanesmissing
16C24646-31-1FS5ms302.0542.21188.530.001Leppert2020balkanealkanesmissing
17C25629-99-2FS5ms310.6742.26189.510.001Leppert2020balkanealkanesmissing
18C26630-1-3FS5ms320.4244.16216.770.001Leppert2020balkanemissingmissing
19C27593-49-7FS5ms326.6241.9184.170.001Leppert2020balkanealkanesmissing
20C28630-2-4FS5ms334.1941.82183.910.001Leppert2020balkanemissingmissing
21C29630-3-5FS5ms341.441.67183.070.001Leppert2020balkanemissingmissing
22C30638-68-6FS5ms348.3941.57183.280.001Leppert2020balkanealkanesmissing

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)
Example block output

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:

7×12 DataFrame
RowNoNameCAStRτRTRσRuRkRResΔsAnnotations
Int64?StringStringFloat64Float64Float64Float64Float64Float64Float64Float64String
1missingC9111-84-2140.7370.39018246.72810.108270.2774878.1548961.836250.433Leppert2020b, alkane, alkanes
2missingC10124-18-5260.0910.57490556.67430.1116530.19421111.806560.1582241.346Leppert2020b, alkane, Grob, alkanes
3missingC111120-21-4412.80.69432369.40.1115270.16062814.083857.6986230.934Leppert2020b, alkane, Grob, alkanes
4missingC12112-40-3580.1760.75610783.3480.1106970.14640515.098354.1206216.51Leppert2020b, alkane, alkanes
5missingC13629-50-5747.110.78613997.25920.1094050.13916815.492350.2923201.178Leppert2020b, alkane, alkanes
6missingC14629-59-4907.1190.804651110.5930.1080720.1343115.674947.6129190.454Leppert2020b, alkane, alkanes
7missingC15629-62-91061.40.815529123.450.1067950.13095215.7158NaNNaNLeppert2020b, alkane, alkanes

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]);
22×3 DataFrame
RowNametRτR
String3Float64Float64
1C9151.020.452
2C10273.540.654
3C11428.880.801
4C12596.280.872
5C13763.080.918
6C14923.880.926
7C151077.240.944
8C161223.220.936
9C171362.060.94
10C181494.180.951
11C191620.360.956
12C201741.080.988
13C211853.280.657
14C221914.180.466
15C231958.040.391
16C241993.920.38
17C252025.180.343
18C262053.440.333
19C272079.420.327
20C282103.90.311
21C292127.00.318
22C302149.20.306

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

compare = GasChromatographySimulator.compare_measurement_simulation(measurement_D, peaklist)
22×5 DataFrame
RowNamemeasured_tRsimulated_tRΔtRrel_tR
String3Float64RealFloat64Float64
1C9151.02140.73710.2836.80901
2C10273.54260.09113.44864.9165
3C11428.88412.816.07973.74924
4C12596.28580.17616.10442.7008
5C13763.08747.1115.96972.0928
6C14923.88907.11916.76071.81417
7C151077.241061.415.83781.47022
8C161223.22NaNNaNNaN
9C171362.06NaNNaNNaN
10C181494.18NaNNaNNaN
11C191620.36NaNNaNNaN
12C201741.08NaNNaNNaN
13C211853.28NaNNaNNaN
14C221914.18NaNNaNNaN
15C231958.04NaNNaNNaN
16C241993.92NaNNaNNaN
17C252025.18NaNNaNNaN
18C262053.44NaNNaNNaN
19C272079.42NaNNaNNaN
20C282103.9NaNNaNNaN
21C292127.0NaNNaNNaN
22C302149.2NaNNaNNaN

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
Example block output

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)
10×5 DataFrame
RowDeltatTDeltaTpinjpdet
Float64Float64Float64Float64Float64
10.049.323-2.829253.289230.169
20.0549.323-2.829253.289230.169
30.0449.077-2.583253.272230.206
40.0549.323-2.829253.289230.169
50.0449.323-2.829253.289230.169
60.0549.077-2.337253.272230.206
70.0549.077-2.337253.272230.206
80.0449.323-2.583253.289230.169
90.0549.077-2.583253.272230.206
100.0449.077-2.337253.272230.206

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#5"{Matrix{Float64}, String}}([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#5"{Matrix{Float64}, String}([-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], "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], 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#5"{Matrix{Float64}, String}}([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#5"{Matrix{Float64}, String}([-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], "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], 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)
Example block output

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          uR ⋯
     │ Int64?   String  String     Float64  Float64    Float64  Float64     Fl ⋯
─────┼──────────────────────────────────────────────────────────────────────────
   1 │ missing  C9      111-84-2   14.9798  0.0491394   75.482  0.0183973   0. ⋯
   2 │ missing  C10     124-18-5   18.8744  0.0379088   96.402  0.0145225   0.
   3 │ missing  C11     1120-21-4  21.8123  0.03442    111.891  0.0120808   0.
   4 │ missing  C12     112-40-3   24.2789  0.0330324  125.302  0.0104438   0.
   5 │ missing  C13     629-50-5   26.4775  0.0330888  136.986  0.00928725  0. ⋯
   6 │ missing  C14     629-59-4   28.5219  0.0336288  147.958  0.00843696  0.
   7 │ missing  C15     629-62-9   30.4589  0.0343988  158.152  0.00774612  0.
                                                               5 columns omitted, Any[SciMLBase.ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, Float64}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardODEProblem}, OwrenZen5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, OrdinaryDiffEqCore.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, Float64}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, OrdinaryDiffEqLowOrderRK.OwrenZen5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, OrdinaryDiffEqLowOrderRK.OwrenZen5ConstantCache{Float64, Float64}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, Nothing}, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing}([[0.0, 0.0], [0.0011414029062964794, 1.5843086388169421e-6], [0.0267446802522371, 3.711603848429975e-5], [0.10245346420303166, 0.00014210997858276947], [0.3454784436573833, 0.00047840438435933416], [1.5246213824346815, 0.002093632752138591], [1.854028081068109, 0.0025396362497975473], [2.795051696208677, 0.003727953676399829], [3.5341224119887276, 0.004651728967358714], [3.669559170006552, 0.004818091648781353]  …  [11.975176001467975, 0.005991386738769158], [12.040353918528545, 0.005832841023464245], [12.401813973089459, 0.005053434994635211], [12.707981672375873, 0.004506161046996097], [13.109491625755615, 0.003917688050798534], [13.326235040219183, 0.003651504116523339], [13.825161276323996, 0.003146487543900683], [14.216413969666853, 0.0028514719670066635], [14.757881973368649, 0.0025318107544507772], [14.979787030635098, 0.0024146763027818913]], nothing, nothing, [0.0, 9.999999999999999e-5, 0.0023435461079186204, 0.008982244796897989, 0.030338497657189784, 0.1349779073300388, 0.1645269366177424, 0.25021896653560016, 0.318896311293786, 0.3316052318895082  …  1.2300757060641445, 1.2418516530735266, 1.3113626430826064, 1.3761104825648174, 1.4697878757385425, 1.5247015993365098, 1.6632631895234355, 1.78399840696468, 1.9685596110900876, 2.05], [[[0.0, 0.0]], [[11.414116999926641, 0.015843333081800165], [11.414087687480386, 0.015843250849310837], [11.414073031288808, 0.01584320973338718], [11.414029062839276, 0.015843086386891376], [11.414029062839276, 0.015843086386891376], [11.414003938095519, 0.01584301590404025], [11.413963110517996, 0.015842901370742138], [11.41394112650509, 0.015842839699651064]], [[11.41394112650509, 0.015842839699651064], [11.413283519595273, 0.01584099509493188], [11.412954732004213, 0.015840072954062423], [11.411968395711861, 0.0158373070638052], [11.411968395711874, 0.015837307063805352], [11.411404785627449, 0.015835726892861657], [11.410488974850715, 0.015833159755871254], [11.409995839268534, 0.015831777674809974]], [[11.409995839268534, 0.015831777674809974], [11.40805039850285, 0.01582632699580288], [11.407077762580105, 0.01582360290731488], [11.404160027438541, 0.015815435133549067], [11.404160027438717, 0.0158154351335508], [11.402492929468263, 0.015810771052801053], [11.399784170435362, 0.015803196907321064], [11.398325748078914, 0.015799121076174]], [[11.398325748078914, 0.015799121076174], [11.392071239465338, 0.015781658855566948], [11.388944659700693, 0.01577294011225588], [11.379567563191282, 0.015746833121729285], [11.379567563191305, 0.015746833121729552], [11.374211022420697, 0.015731948125418494], [11.36550944930649, 0.01570781174862787], [11.360825436467222, 0.015694841834996965]], [[11.360825436467222, 0.015694841834996965], [11.330250515826506, 0.015610571798486985], [11.314979523211685, 0.0155687359985677], [11.269186825992781, 0.015437049627031992], [11.269186829363251, 0.015437050726650841], [11.242495263390945, 0.015361834638421895], [11.198702530039444, 0.015238078195193077], [11.174903489061835, 0.015170645018826945]], [[11.174903489061835, 0.015170645018826945], [11.165902540039811, 0.01514510892168805], [11.161393867579926, 0.015132311590210496], [11.147834449422925, 0.015093797735315821], [11.147834449449803, 0.015093797735808406], [11.140063725912535, 0.0150717084698388], [11.127401168862596, 0.01503568649086816], [11.117608102604287, 0.014382397244186202]], [[11.117608102604287, 0.014382397244186202], [11.071747811565471, 0.014205914613543664], [11.048989150271874, 0.014119433323200302], [10.981026036955157, 0.01386301794020132], [10.981028005813464, 0.013863065958767604], [10.942482731739068, 0.013719390829076228], [10.880300779829975, 0.013490407061229719], [10.849345722872506, 0.013756255064973563]], [[10.849345722872506, 0.013756255064973563], [10.820146143195286, 0.013654171452576165], [10.805540010836589, 0.013603351543455744], [10.761590579273053, 0.013450750357765611], [10.761590830774093, 0.01345075596587076], [10.736410676625553, 0.013363682563205375], [10.695388789194729, 0.013222397146805542], [10.67324548046684, 0.013146418925339848]], [[10.67324548046684, 0.013146418925339848], [10.66777556149865, 0.01312767897586756], [10.665040307608411, 0.013118316332809105], [10.656829771768473, 0.013090222881674237], [10.656829773361716, 0.013090222916978443], [10.652135649857472, 0.013074173692080263], [10.644503930580306, 0.013048100030080362], [10.640392583069561, 0.01303406347558482]]  …  [[5.769048010425604, -0.014051915903689356], [5.738128580222553, -0.01382634368926915], [5.722919574994504, -0.01371737848513395], [5.6776351610057825, -0.013394072146194272], [5.677644204777852, -0.013394418585448877], [5.652130392074281, -0.013214259522894822], [5.611137734286584, -0.014033503085517778], [5.58813304748308, -0.013852059299760213]], [[5.58813304748308, -0.013852059299760213], [5.570148624073634, -0.01371943392310512], [5.561243078870157, -0.013654474772048819], [5.5346434599111864, -0.013460896336591668], [5.5346453709226795, -0.013460970599044211], [5.519572631593129, -0.013352055444764269], [5.495279748726501, -0.013177882813249015], [5.482298519155696, -0.013085436668236184]], [[5.482298519155696, -0.013085436668236184], [5.381710597844973, -0.012376006692960136], [5.334137959938498, -0.012061664819914239], [5.194655172533028, -0.011146209486370375], [5.19499798059761, -0.011159136272737185], [5.118623710760357, -0.010668719845748686], [5.000360233458619, -0.009956071811159092], [4.939150459279682, -0.009598585549122702]], [[4.939150459279682, -0.009598585549122702], [4.864997916298923, -0.009174014084757612], [4.829554828381319, -0.008981404240343747], [4.725277947829859, -0.008418634667144296], [4.725440594553645, -0.008423626323491903], [4.667963265959073, -0.008120156962250456], [4.578138822546884, -0.007667734761914725], [4.531348346307197, -0.007438330025117125]], [[4.531348346307197, -0.007438330025117125], [4.44338772719282, -0.007015155735597498], [4.401882444320963, -0.00682854761083636], [4.280711983617508, -0.006219459796753446], [4.2810061758340385, -0.0062334123340568775], [4.215254039692972, -0.005932632178803533], [4.113959746698488, -0.005503890017963416], [4.06180449805465, -0.005293414992259819]], [[4.06180449805465, -0.005293414992259819], [4.02200202248745, -0.005133706122237059], [4.0026936523134955, -0.005058683158448254], [3.9456564491155564, -0.004838280601705947], [3.945690566770252, -0.004839010809941795], [3.913962168921229, -0.0047184906070401695], [3.863794848756538, -0.00453275844011999], [3.8374358303898375, -0.0044369040238424525]], [[3.8374358303898375, -0.0044369040238424525], [3.7512149189952626, -0.004128137329998557], [3.7110418844157675, -0.003994721794747351], [3.5946658195993204, -0.0036103990626669188], [3.5950417753282555, -0.0036176329013105305], [3.5323235804842215, -0.003414400213393153], [3.436913029321516, -0.003127706366795295], [3.3889162202451857, -0.002823237305477731]], [[3.3889162202451857, -0.002823237305477731], [3.336039255606639, 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Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, Float64}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.StandardODEProblem}, OwrenZen5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, OrdinaryDiffEqCore.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, 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Nothing}(FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, Float64}}}, FunctionWrappersWrappers.AllowNonIsBits, FunctionWrappersWrappers.SingleCacheStorage}((FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64, String, GasChromatographySimulator.SimpleLinearInterpolation{2, Real}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, GasChromatographySimulator.SimpleLinearInterpolation{1, Float64}, Float64, Float64, Float64, Float64, Float64, GasChromatographySimulator.Options}, Float64}}(Ptr{Nothing} 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0.0017851014289650055], [25.92811037682984, 0.0016655470839871433], [26.176267367378696, 0.0016125705344383423], [27.013775676294266, 0.0014554789881210404], [27.34981727608014, 0.0013995310504680493], [27.862433325283355, 0.0013262154779211032], [28.12207328341219, 0.001294771363530433], [28.728279825200342, 0.0012328061544812784], [29.71878002686749, 0.0011890715231892945], [30.458948264576428, 0.0011832757361002711]], [0.0, 9.999999999999999e-5, 0.0006591673106002476, 0.0008074244838324044, 0.00116363417059531, 0.0013229974658257302, 0.0013919452242091876, 0.0015741353354127175, 0.001604334733126235, 0.0019063287102614103  …  0.7403190486256862, 0.8430955452176729, 0.8998994501215214, 1.1076001724180844, 1.1974063537103508, 1.3402613361960736, 1.4146358444403997, 1.590643696177337, 1.8681877347951947, 2.05], [[[0.0, 0.0]], [[2311.819981256566, 902.4866368787845], [2311.8104299791453, 902.4753619550028], [2311.805658591975, 902.4697314647462], [2311.791361376412, 902.4528676673299], 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796.7162310072092], [2283.140511937068, 788.282296199344], [2273.7184741339797, 774.8048161631398], [2268.6787827820363, 767.6550858065898]], [[2268.6787827820363, 767.6550858065898], [2265.6817685737715, 763.4189344302246], [2264.740184257069, 813.6228592060255], [2262.5044299687747, 810.0260498311757], [2262.507643580218, 811.4541828662893], [2261.229050669438, 808.1758708815028], [2259.1612902914158, 805.3868005308822], [2258.0481614609594, 803.7284159473918]], [[2258.0481614609594, 803.7284159473918], [2257.4068362873763, 802.7902436471514], [2257.0864507761335, 802.3221236858403], [2256.125587531268, 800.9186261405777], [2256.125588220649, 800.918631739738], [2255.5769030303227, 800.117881101631], [2254.685879803684, 798.8186109226391], [2254.206399724743, 798.1199961027771]], [[2254.206399724743, 798.1199961027771], [2252.518124936274, 795.6618281245219], [2251.675910178757, 794.4394171755903], [2249.151291212296, 790.7780765315184], [2249.1513038319717, 790.7781786547181], 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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]);
22×3 DataFrame
RowNametRτR
String3Float64Float64
1C914.76830.0669811
2C1018.22830.0565467
3C1121.02830.0526464
4C1223.50830.0609966
5C1325.76830.0581621
6C1427.88830.0571819
7C1529.88830.0574451
8C1631.80830.0573303
9C1733.66830.0598955
10C1835.46830.0616608
11C1937.22830.0638519
12C2038.90830.0636418
13C2140.54830.0664711
14C2242.12830.068909
15C2343.66830.0718497
16C2445.14830.0726997
17C2546.58830.0772066
18C2648.02830.0816995
19C2749.42830.0847638
20C2850.82830.0920254
21C2952.20830.0987833
22C3053.54830.110653

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)
22×5 DataFrame
RowNamemeasured_tRsimulated_tRΔtRrel_tR
String3Float64RealFloat64Float64
1C914.768314.9798-0.211527-1.43231
2C1018.228318.8744-0.646117-3.54459
3C1121.028321.8123-0.78408-3.72869
4C1223.508324.2789-0.770622-3.27809
5C1325.768326.4775-0.709269-2.75249
6C1427.888328.5219-0.633618-2.27199
7C1529.888330.4589-0.570688-1.90941
8C1631.8083NaNNaNNaN
9C1733.6683NaNNaNNaN
10C1835.4683NaNNaNNaN
11C1937.2283NaNNaNNaN
12C2038.9083NaNNaNNaN
13C2140.5483NaNNaNNaN
14C2242.1283NaNNaNNaN
15C2343.6683NaNNaNNaN
16C2445.1483NaNNaNNaN
17C2546.5883NaNNaNNaN
18C2648.0283NaNNaNNaN
19C2749.4283NaNNaNNaN
20C2850.8283NaNNaNNaN
21C2952.2083NaNNaNNaN
22C3053.5483NaNNaNNaN

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
Example block output

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