{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting interaction parameters of binary systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes Equations of State needs an extra help to better predict behaviours.\n", "\n", "Let's see how we can optimize binary interaction parameters of a Cubic Equation,\n", "using equilibria data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data structure\n", "For all the default approachs of parameter optimization the datapoints must\n", "be in the format of a `pandas` DataFrame, with the following columns:\n", "\n", "- `kind`: Which kind of point is defined `[\"bubble\", \"dew\", \"liquid-liquid\", \"PT\"]`.\n", "- `T`: Temperature (in Kelvin).\n", "- `P`: Pressure (in bar).\n", "- `x1`: Mole fraction of component 1 (lightest component) in heavy phase. \n", "- `y1`: Mole fraction of component 1 (lightest component) in light phase.\n", "\n", "In the following cell we import the datapoints from a `.csv` file" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | kind | \n", "T | \n", "P | \n", "x1 | \n", "y1 | \n", "
---|---|---|---|---|---|
0 | \n", "bubble | \n", "303.15 | \n", "20.24 | \n", "0.2385 | \n", "0.9721 | \n", "
1 | \n", "bubble | \n", "303.15 | \n", "30.36 | \n", "0.3698 | \n", "0.9768 | \n", "
2 | \n", "bubble | \n", "303.15 | \n", "39.55 | \n", "0.5063 | \n", "0.9815 | \n", "
3 | \n", "bubble | \n", "303.15 | \n", "50.95 | \n", "0.7078 | \n", "0.9842 | \n", "
4 | \n", "bubble | \n", "303.15 | \n", "57.83 | \n", "0.8430 | \n", "0.9855 | \n", "
5 | \n", "bubble | \n", "303.15 | \n", "64.68 | \n", "0.9410 | \n", "0.9884 | \n", "
6 | \n", "bubble | \n", "303.15 | \n", "67.46 | \n", "0.9656 | \n", "0.9909 | \n", "
7 | \n", "bubble | \n", "315.15 | \n", "20.84 | \n", "0.2168 | \n", "0.9560 | \n", "
8 | \n", "bubble | \n", "315.15 | \n", "30.40 | \n", "0.3322 | \n", "0.9660 | \n", "
9 | \n", "bubble | \n", "315.15 | \n", "40.52 | \n", "0.4446 | \n", "0.9748 | \n", "
10 | \n", "bubble | \n", "315.15 | \n", "50.66 | \n", "0.5809 | \n", "0.9753 | \n", "
11 | \n", "bubble | \n", "315.15 | \n", "60.29 | \n", "0.7180 | \n", "0.9753 | \n", "
12 | \n", "bubble | \n", "315.15 | \n", "69.11 | \n", "0.8457 | \n", "0.9764 | \n", "
13 | \n", "bubble | \n", "315.15 | \n", "72.89 | \n", "0.8928 | \n", "0.9773 | \n", "
14 | \n", "bubble | \n", "315.15 | \n", "75.94 | \n", "0.9252 | \n", "0.9777 | \n", "
15 | \n", "bubble | \n", "315.15 | \n", "77.50 | \n", "0.9424 | \n", "0.9768 | \n", "
16 | \n", "bubble | \n", "315.15 | \n", "78.66 | \n", "0.9520 | \n", "0.9756 | \n", "