diff --git a/media/Distillation Column.png b/media/Distillation Column.png new file mode 100644 index 00000000..895bc230 Binary files /dev/null and b/media/Distillation Column.png differ diff --git a/media/Distillation_column.png b/media/Distillation_column.png new file mode 100644 index 00000000..895bc230 Binary files /dev/null and b/media/Distillation_column.png differ diff --git a/media/rxn_equation.jpeg b/media/rxn_equation.jpeg new file mode 100644 index 00000000..8071c73a Binary files /dev/null and b/media/rxn_equation.jpeg differ diff --git a/media/rxn_equation.png b/media/rxn_equation.png new file mode 100644 index 00000000..8071c73a Binary files /dev/null and b/media/rxn_equation.png differ diff --git a/notebooks/assignments/ProblemSet2_F23.ipynb b/notebooks/assignments/ProblemSet2_F23.ipynb index 6903a609..4de0748e 100644 --- a/notebooks/assignments/ProblemSet2_F23.ipynb +++ b/notebooks/assignments/ProblemSet2_F23.ipynb @@ -47,7 +47,9 @@ " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", " import colab_helper\n", " colab_helper.install_idaes()\n", - " colab_helper.install_ipopt()" + " colab_helper.install_ipopt()\n", + "\n", + "import pyomo.environ as pyo" ] }, { @@ -593,36 +595,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. Portfolio Data Analysis\n", - "\n", - "Portfolio management is a classic example of quadratic programming (optimization). The idea is to find the optimal blend of investments that achieves a specified rate of return (or better) while minimizing the variance in rate of return. In this problem, you will use your skills in statistical analysis to analyze the stock data.\n", - "\n", - "### Historical Stock Data\n", - "\n", - "Historical daily adjusted closing prices for the last five years (obtained from Yahoo! Finance) are available for the $N=5$ stocks listed in table below. (We are actually considering index funds, but this detail does not change the analysis.) \n", - "\n", - "| Symbol | Name |\n", - "|-|-|\n", - "| GSPC | S&P 500 | \n", - "| DJI | Dow Jones Industrial Average | \n", - "| IXIC | NASDAQ Composite | \n", - "| RUT | Russell 2000 |\n", - "| VIX | CBOE Volatility Index |" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4a. Return Rate\n", - "\n", - "You are given a Stock\\_Data.csv file. Using the stock data, calculate the 1-day return rate:\n", - "\n", - "\\begin{equation}\n", - "\tr_{t,i} = \\frac{p_{t+1,i} - p_{t,i}}{p_{t,i}}\n", - "\\end{equation}\n", - "\n", - "where $p_{t+1,i}$ and $p_{t,i}$ are the *Adjusted Closing Prices* at the end of days $t+1$ and $t$, respectively, for stock $i$. These results are stored in matrix `R`. *Hint*: Use Pandas." + "## 4. Numeric Integration of Partial Differential Equations with Pyomo" ] }, { @@ -631,81 +604,117 @@ "metadata": {}, "outputs": [], "source": [ - "# This is the long path to the folder containg data files on GitHub (for the class website)\n", - "data_folder = 'https://raw.githubusercontent.com/ndcbe/data-and-computing/main/noteboohttps://raw.githubusercontent.com/ndcbe/data-and-computing/main/notebooks/data/'\n", + "%matplotlib inline\n", "\n", - "# Load the data file into Pandas\n", - "df_adj_close = pd.read_csv(data_folder + 'Stock_Data.csv')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Add your solution here" + "# Import plotting libraries\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d.axes3d import Axes3D \n", + "\n", + "# Import Pyomo\n", + "import pyomo.environ as pyo\n", + "\n", + "# Import Pyomo numeric integration features\n", + "from pyomo.dae import DerivativeVar, ContinuousSet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### 4b. Visualization\n", + "During your time at Notre Dame, you will likely want (or at least need) to solve a partial differential equation (PDE) system. In this problem, we will practice using Pyomo to numerically integrate a simple and common PDE. (Special thanks to Prof. Kantor for this problem.)\n", "\n", - "Plot the single day return rates for the 5 stocks you obtain in the previous section and check if you obtain the following profiles:\n", + "Transport of heat in a solid is described by the familiar thermal diffusion model:\n", "\n", - "![ad](https://raw.githubusercontent.com/ndcbe/data-and-computing/main/media/stock_return_plots.png)\n", + "$$\n", + "\\begin{align*}\n", + "\\rho C_p\\frac{\\partial T}{\\partial t} & = \\nabla\\cdot(k\\nabla T)\n", + "\\end{align*}\n", + "$$\n", "\n", + "We will assume the thermal conductivity $k$ is a constant, and define thermal diffusivity in the conventional way\n", "\n", - "The first plot is made for you. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Create figure\n", - "plt.figure(figsize=(9,15))\n", + "$$\n", + "\\begin{align*}\n", + "\\alpha & = \\frac{k}{\\rho C_p}\n", + "\\end{align*}\n", + "$$\n", "\n", - "# Create subplot for DJI\n", - "plt.subplot(5,1,1)\n", - "plt.plot(R[\"DJI\"]*100,color=\"blue\",label=\"DJI\")\n", - "plt.legend(loc='best')\n", + "We will further assume symmetry with respect to all spatial coordinates except $x$ where $x$ extends from $-X$ to $+X$. The boundary conditions are\n", "\n", - "# Add your solution here\n", + "$$\n", + "\\begin{align*}\n", + "T(t,X) & = T_{\\infty} & \\forall t > 0 \\\\\n", + "\\nabla T(t,0) & = 0 & \\forall t \\geq 0 \n", + "\\end{align*}\n", + "$$\n", "\n", - "# Show plot\n", - "plt.show()" + "where we have assumed symmetry with respect to $r$ and uniform initial conditions $T(0, x) = T_0$ for all $0 \\leq r \\leq X$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### 4c. Covariance and Correlation Matrices\n", + "### 4a. Rescaling and Dimensionless Model\n", + "\n", + "We would like a dimensionless model for two reasons: first, we only need to solve the dimensionless model once, i.e., it becomes independent of input data. Second, the dimensionless models are often scaled better for numerical solutions.\n", + "\n", + "Let's consider the following proposed scaling procedure:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "T' & = \\frac{T - T_0}{T_\\infty - T_0} \\\\\n", + "x' & = \\frac{r}{X} \\\\\n", + "t' & = t \\frac{\\alpha}{X^2}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "Show this scaling procedure gives the following dimensionless system:\n", "\n", - "Write Python code to:\n", - "1. Calculate $\\bar{r}$, the average 1-day return for each stock. Store this as the variable `R_avg`.\n", - "2. Calculate $\\Sigma_{r}$, the covariance matrix of the 1-day returns. This matrix tells us how returns for each stock vary with each other (which is important because they are correlated!). Hint: pandas has a function `cov`\n", - "3. Calculate the correlation matrix for the 1-day returns. Hint: pandas has a function `corr`.\n", + "$$\n", + "\\begin{align*}\n", + "\\frac{\\partial T'}{\\partial t'} & = \\nabla^2 T'\n", + "\\end{align*}\n", + "$$\n", "\n", - "Looking at the correlation matrix, answer the follwing questions:\n", + "with auxiliary conditions\n", "\n", - "1. Which pair of stocks have the highest **positive** correlation?\n", - "2. Which pair of stocks have the highest **negative** correlation?\n", - "3. Which pair of stocks have the lowest **absolute** correlation?\n", + "$$\n", + "\\begin{align*}\n", + "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1\\\\\n", + "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", + "\\nabla T'(t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", + "\\end{align*}\n", + "$$\n", "\n", - "Hint: Read ahead in the class website for more information on [correlation and covariance](../..//notebooks/14/Correlation-Covariance-and-Independence.ipynb)" + "Turn in your work (pencil and paper) via **Gradescope**. *Important:* Here the prime $'$ indicates the scaled variables and coordinates. It does not indicate a derivative. Thus $T'$ is scaled temperature, NOT the derivative of temperature (which begs the question of \"with respect to what?\")." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Please write one or two sentences for each question:" + "### 4b. Numeric Integration via Pyomo\n", + "\n", + "For simplicity, let's consider planar coordinates. For a slab geometry, we want to numerical integrate the following PDE:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\frac{\\partial T'}{\\partial t'} & = \\frac{\\partial^2 T'}{\\partial x'^2}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "with auxiliary conditions\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1 \\\\\n", + "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", + "\\frac{\\partial T'}{\\partial x'} (t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", + "\\end{align*}\n", + "$$\n", + "\n", + "Complete the following Pyomo code to integrate this PDE." ] }, { @@ -714,188 +723,129 @@ "metadata": {}, "outputs": [], "source": [ - "# Add your solution here" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "nbgrader": { - "grade": true, - "grade_id": "check-R_avg", - "locked": true, - "points": "0.5", - "solution": false - } - }, - "outputs": [], - "source": [ - "# Removed autograder test. You may delete this cell." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4c. Markowitz Mean/Variance Portfolio Model\n", + "# Create Pyomo model\n", + "m = pyo.ConcreteModel()\n", "\n", - "The Markowitz mean/variance model, shown below, computes the optimal allocation of funds in a portfolio:\n", + "# Define sets for spatial and temporal domains\n", + "m.x = ContinuousSet(bounds=(0,1))\n", + "m.t = ContinuousSet(bounds=(0,2))\n", "\n", - "\\begin{align}\n", - "\t\t\\min_{{x} \\geq {0}} \\qquad & z:= {x}^T \\cdot {\\Sigma_r} \\cdot {x} \\\\\n", - "\t\t\\text{s.t.} \\qquad & {\\bar{r}}^T \\cdot {x} \\geq \\rho \\\\\n", - "\t\t & \\sum_{i =1}^N x_i = 1 \n", - "\\end{align} \n", + "# Define scaled temperature indexed by time and space\n", + "m.T = pyo.Var(m.t, m.x)\n", "\n", + "# Define variables for the derivates\n", + "m.dTdt = DerivativeVar(m.T, wrt=m.t)\n", + "m.dTdx = DerivativeVar(m.T, wrt=m.x)\n", + "m.d2Tdx2 = DerivativeVar(m.T, wrt=(m.x, m.x))\n", "\n", - "where $x_i$ is the fraction of funds invested in stock $i$ and $x = [x_1, x_2, ..., x_N]^T$. The objective is to minimize the variance of the return rate. (As practice for the next exam, try deriving this from the error propagation formulas.) This requires the expected return rate to be at least $\\rho$. Finally, the allocation of funds must sum to 100%.\n", + "# Define PDE equation\n", + "def pde(m, t, x):\n", + " if t == 0:\n", + " return pyo.Constraint.Skip\n", + " elif x == 0 or x == 1:\n", + " return pyo.Constraint.Skip\n", + " # Add your solution here\n", "\n", - "Write Python code to solve for $\\rho = 0.08\\%.$ Report both the optimal allocation of funds and the standard deviation of the return rate. \n", - "*Hint*:\n", - "1. Be mindful of units.\n", - "2. You can solve with problem using the Pyomo function given below\n", - "3. $:=$ means ''defined as''\n", + "m.pde = pyo.Constraint(m.t, m.x, rule=pde)\n", "\n", - "Store your answer in `std_dev`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "R_avg_tolist = R_avg.values.tolist()\n", - "Cov_list = Cov.values.tolist()\n", + "# Define first auxilary condition\n", + "def initial_condition(m, x):\n", + " if x == 0 or x == 1:\n", + " return pyo.Constraint.Skip\n", + " # Add your solution here\n", "\n", - "# Optimization Problem\n", - "def create_model(rho,R_avg,Cov):\n", - " \n", - " '''\n", - " This function solves for the optimal allocation of funds in a portfolio \n", - " by minimizing the variance of the return rate\n", - " \n", - " Arguments:\n", - " rho: required portfolio expected return\n", - " Ravg: average return rates (list)\n", - " Cov: covariance matrix\n", - " \n", - " Returns:\n", - " m: Pyomo concrete model\n", - " \n", - " '''\n", - " \n", - " m = pyo.ConcreteModel()\n", - " init_x = {}\n", - " m.idx = pyo.Set(initialize=[0,1,2,3,4])\n", - " for i in m.idx:\n", - " init_x[i] = 0\n", - " m.x = pyo.Var(m.idx,initialize=init_x,bounds=(0,None))\n", - " \n", - " def Obj_func(m):\n", - " b = []\n", - " mult_result = 0\n", - " for i in m.idx:\n", - " a = 0\n", - " for j in m.idx:\n", - " a+= m.x[j]*Cov[j][i]\n", - " b.append(a)\n", - " for i in m.idx:\n", - " mult_result += b[i]*m.x[i]\n", - " \n", - " return mult_result\n", - " m.OBJ = pyo.Objective(rule=Obj_func)\n", - " \n", - " def constraint1(m):\n", - " # Add your solution here\n", + "m.ic = pyo.Constraint(m.x, rule = initial_condition)\n", "\n", - " m.C1 = pyo.Constraint(rule=constraint1)\n", - " \n", - " def constraint2(m):\n", - " # Add your solution here\n", + "# Define second auxilary condition\n", + "def boundary_condition1(m, t):\n", + " # Add your solution here\n", "\n", - " m.C2 = pyo.Constraint(rule=constraint2)\n", - " \n", - " return m\n" + "m.bc1 = pyo.Constraint(m.t, rule = boundary_condition1)\n", + "\n", + "# Define third auxilary condition\n", + "@m.Constraint(m.t)\n", + "def boundary_condition2(m, t):\n", + " # Add your solution here \n", + "\n", + "m.bc2 = pyo.Constraint(m.t, rule=boundary_condition2)\n", + "\n", + "# Define dummy objective\n", + "m.obj = pyo.Objective(expr=1)\n", + "\n", + "# Discretize spatial coordinate with forward finite difference and 50 elements\n", + "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.x)\n", + "\n", + "# Discretize time coordinate with forward finite difference and 50 elements\n", + "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.t)\n", + "pyo.SolverFactory('ipopt').solve(m, tee=True).write()" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "rho = 0.0008\n", - "model1 = create_model(rho,R_avg_tolist,Cov_list)\n", - "\n", - "#Solve Pyomo in the method learned in Class 11\n", - "\n", - "# Add your solution here" + "### 4c. Visualize Solution " ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "nbgrader": { - "grade": true, - "grade_id": "standard-deviation", - "locked": true, - "points": "0.5", - "solution": false - } - }, - "outputs": [], - "source": [ - "# Removed autograder test. You may delete this cell." - ] - }, - { - "cell_type": "markdown", "metadata": {}, + "outputs": [], "source": [ - "### 4e. Volatility and Expected Return Tradeoff\n", + "# Extract indices\n", + "x = sorted(m.x)\n", + "t = sorted(m.t)\n", "\n", - "We will now perform sensitivity analysis of the optimization problem in 3d to characterize the tradeoff between return and risk.\n", + "# Create numpy arrays to hold the solution\n", + "xgrid = np.zeros((len(t), len(x)))\n", + "# Hint: define tgrid and Tgrid the same way\n", + "# Add your solution here\n", + "\n", + "# Loop over time\n", + "for i in range(0, len(t)):\n", + " # Loop over space\n", + " for j in range(0, len(x)):\n", + " # Copy values\n", + " xgrid[i,j] = x[j]\n", + " tgrid[i,j] = t[i]\n", + " # Hint: how to access values from Pyomo variable m.T?\n", + " # Add your solution here\n", "\n", - "Write Python code to:\n", - "1. Solve the optimization problem for many values of $\\rho$ between min($\\bar{r}$) and max($\\bar{r}$) and save the results. Use the Pyomo function created in 3d.\n", - "2. Plot $\\rho$ versus $\\sqrt{z}$ (using the saved results).\n", - "3. Write at least one sentence to interpret and discuss your plot.\n", + "# Create a 3D wireframe plot of the solution\n", + "# Hint: consult the matplotlib documentation\n", + "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", "\n", - "Submit your plot and discussion via **Gradescope**." + "# Add your solution here" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "rho_vals = np.arange(0.0005,0.0038,0.0001)\n", - "std_dev = []\n", + "Write a few sentences to describe the PDE solution. Is it what you expect based on your prior knowledge of this system? Each person brings different prior knwoledge to this class, you everyone should have a distinct answer. In other words, there is no \"right answer\". Instead, this is helping you practice interpreting results based on your knowledge which is a critical skill in graduate school.\n", "\n", - "# Add your solution here" + "**Discussion:**" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "#Plot\n", + "## Submission Instructions and Tips\n", "\n", - "# Add your solution here" + "1. Answer discussion questions in this notebook.\n", + "2. When asked to store a solution in a specific variable, please also print that variable.\n", + "3. Turn in this notebook via Gradescope.\n", + "4. Also turn in written (pencil and paper) work via Gradescope.\n", + "5. Even if you are not required to turn in pseudocode, you should always write pseudocode. It takes only a few minutes and can save you *hours* of time.\n", + "6. We are not using the autograder for CBE 60258, so please skip those instructions." ] }, { "cell_type": "markdown", "metadata": {}, - "source": [ - "**Discussion**:" - ] + "source": [] } ], "metadata": { diff --git a/notebooks/assignments/ProblemSet3_F23.ipynb b/notebooks/assignments/ProblemSet3_F23.ipynb index 22c5545e..c5f3bcd0 100644 --- a/notebooks/assignments/ProblemSet3_F23.ipynb +++ b/notebooks/assignments/ProblemSet3_F23.ipynb @@ -45,7 +45,16 @@ "import math\n", "import numpy as np\n", "import scipy.stats as stats\n", - "from scipy import optimize" + "from scipy import optimize\n", + "\n", + "import sys\n", + "if \"google.colab\" in sys.modules:\n", + " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", + " import colab_helper\n", + " colab_helper.install_idaes()\n", + " colab_helper.install_ipopt()\n", + "\n", + "import pyomo.environ as pyo" ] }, { @@ -1088,310 +1097,363 @@ "# Removed autograder test. You may delete this cell." ] }, - { - "cell_type": "markdown", - "metadata": { - "id": "1y6sHpO5d-fR" - }, - "source": [ - "## 3. Numeric Integration of Partial Differential Equations with Pyomo" - ] - }, { "cell_type": "code", "execution_count": null, "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 357 + }, "executionInfo": { - "elapsed": 404, + "elapsed": 1668, "status": "ok", - "timestamp": 1664677364866, + "timestamp": 1664677559084, "user": { "displayName": "Alexander Dowling", "userId": "00988067626794866502" }, "user_tz": 240 }, - "id": "OyvMIfLdd-fR" + "id": "qLQGM8Urd-fT", + "outputId": "751136c4-d2eb-4edc-c183-e30b80d82128" }, "outputs": [], "source": [ - "%matplotlib inline\n", + "# Extract indices\n", + "x = sorted(m.x)\n", + "t = sorted(m.t)\n", "\n", - "# Import plotting libraries\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.mplot3d.axes3d import Axes3D \n", + "# Create numpy arrays to hold the solution\n", + "xgrid = np.zeros((len(t), len(x)))\n", + "# Hint: define tgrid and Tgrid the same way\n", + "# Add your solution here\n", "\n", - "import sys\n", - "if \"google.colab\" in sys.modules:\n", - " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", - " import colab_helper\n", - " colab_helper.install_idaes()\n", - " colab_helper.install_ipopt()\n", + "# Loop over time\n", + "for i in range(0, len(t)):\n", + " # Loop over space\n", + " for j in range(0, len(x)):\n", + " # Copy values\n", + " xgrid[i,j] = x[j]\n", + " tgrid[i,j] = t[i]\n", + " # Hint: how to access values from Pyomo variable m.T?\n", + " # Add your solution here\n", "\n", - "# Import Pyomo\n", - "import pyomo.environ as pyo\n", + "# Create a 3D wireframe plot of the solution\n", + "# Hint: consult the matplotlib documentation\n", + "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", "\n", - "# Import Pyomo numeric integration features\n", - "from pyomo.dae import DerivativeVar, ContinuousSet" + "# Add your solution here" ] }, { "cell_type": "markdown", - "metadata": { - "id": "_GdDQNuud-fR" - }, + "metadata": {}, "source": [ - "During your time at Notre Dame, you will likely want (or at least need) to solve a partial differential equation (PDE) system. In this problem, we will practice using Pyomo to numerically integrate a simple and common PDE. (Special thanks to Prof. Kantor for this problem.)\n", + "## 3. Portfolio Data Analysis\n", "\n", - "Transport of heat in a solid is described by the familiar thermal diffusion model:\n", + "Portfolio management is a classic example of quadratic programming (optimization). The idea is to find the optimal blend of investments that achieves a specified rate of return (or better) while minimizing the variance in rate of return. In this problem, you will use your skills in statistical analysis to analyze the stock data.\n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\rho C_p\\frac{\\partial T}{\\partial t} & = \\nabla\\cdot(k\\nabla T)\n", - "\\end{align*}\n", - "$$\n", + "### Historical Stock Data\n", "\n", - "We will assume the thermal conductivity $k$ is a constant, and define thermal diffusivity in the conventional way\n", + "Historical daily adjusted closing prices for the last five years (obtained from Yahoo! Finance) are available for the $N=5$ stocks listed in table below. (We are actually considering index funds, but this detail does not change the analysis.) \n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\alpha & = \\frac{k}{\\rho C_p}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "We will further assume symmetry with respect to all spatial coordinates except $x$ where $x$ extends from $-X$ to $+X$. The boundary conditions are\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "T(t,X) & = T_{\\infty} & \\forall t > 0 \\\\\n", - "\\nabla T(t,0) & = 0 & \\forall t \\geq 0 \n", - "\\end{align*}\n", - "$$\n", - "\n", - "where we have assumed symmetry with respect to $r$ and uniform initial conditions $T(0, x) = T_0$ for all $0 \\leq r \\leq X$. " + "| Symbol | Name |\n", + "|-|-|\n", + "| GSPC | S&P 500 | \n", + "| DJI | Dow Jones Industrial Average | \n", + "| IXIC | NASDAQ Composite | \n", + "| RUT | Russell 2000 |\n", + "| VIX | CBOE Volatility Index |" ] }, { "cell_type": "markdown", - "metadata": { - "id": "S9E0AZB2d-fR" - }, + "metadata": {}, "source": [ - "### 3a. Rescaling and Dimensionless Model\n", + "### 3a. Return Rate\n", "\n", - "We would like a dimensionless model for two reasons: first, we only need to solve the dimensionless model once, i.e., it becomes independent of input data. Second, the dimensionless models are often scaled better for numerical solutions.\n", + "You are given a Stock\\_Data.csv file. Using the stock data, calculate the 1-day return rate:\n", "\n", - "Let's consider the following proposed scaling procedure:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "T' & = \\frac{T - T_0}{T_\\infty - T_0} \\\\\n", - "x' & = \\frac{r}{X} \\\\\n", - "t' & = t \\frac{\\alpha}{X^2}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "Show this scaling procedure gives the following dimensionless system:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "\\frac{\\partial T'}{\\partial t'} & = \\nabla^2 T'\n", - "\\end{align*}\n", - "$$\n", - "\n", - "with auxiliary conditions\n", + "\\begin{equation}\n", + "\tr_{t,i} = \\frac{p_{t+1,i} - p_{t,i}}{p_{t,i}}\n", + "\\end{equation}\n", "\n", - "$$\n", - "\\begin{align*}\n", - "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1\\\\\n", - "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", - "\\nabla T'(t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", - "\\end{align*}\n", - "$$\n", + "where $p_{t+1,i}$ and $p_{t,i}$ are the *Adjusted Closing Prices* at the end of days $t+1$ and $t$, respectively, for stock $i$. These results are stored in matrix `R`. *Hint*: Use Pandas." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# This is the long path to the folder containg data files on GitHub (for the class website)\n", + "data_folder = 'https://raw.githubusercontent.com/ndcbe/data-and-computing/main/noteboohttps://raw.githubusercontent.com/ndcbe/data-and-computing/main/notebooks/data/'\n", "\n", - "Turn in your work (pencil and paper) via **Gradescope**. *Important:* Here the prime $'$ indicates the scaled variables and coordinates. It does not indicate a derivative. Thus $T'$ is scaled temperature, NOT the derivative of temperature (which begs the question of \"with respect to what?\")." + "# Load the data file into Pandas\n", + "df_adj_close = pd.read_csv(data_folder + 'Stock_Data.csv')" ] }, { - "cell_type": "markdown", - "metadata": { - "id": "vY4nyAGid-fS" - }, + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ - "### 3b. Numeric Integration via Pyomo" + "# Add your solution here" ] }, { "cell_type": "markdown", - "metadata": { - "id": "y3qGQ6Had-fS" - }, + "metadata": {}, "source": [ - "For simplicity, let's consider planar coordinates. For a slab geometry, we want to numerical integrate the following PDE:\n", + "### 3b. Visualization\n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\frac{\\partial T'}{\\partial t'} & = \\frac{\\partial^2 T'}{\\partial x'^2}\n", - "\\end{align*}\n", - "$$\n", + "Plot the single day return rates for the 5 stocks you obtain in the previous section and check if you obtain the following profiles:\n", "\n", - "with auxiliary conditions\n", + "![ad](https://raw.githubusercontent.com/ndcbe/data-and-computing/main/media/stock_return_plots.png)\n", "\n", - "$$\n", - "\\begin{align*}\n", - "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1 \\\\\n", - "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", - "\\frac{\\partial T'}{\\partial x'} (t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", - "\\end{align*}\n", - "$$\n", "\n", - "Complete the following Pyomo code to integrate this PDE." + "The first plot is made for you. " ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "executionInfo": { - "elapsed": 2497, - "status": "ok", - "timestamp": 1664677371426, - "user": { - "displayName": "Alexander Dowling", - "userId": "00988067626794866502" - }, - "user_tz": 240 - }, - "id": "yM3uKVfGd-fS", - "outputId": "4150d75e-328b-4ce3-a77e-7951f7c2a89d" - }, + "metadata": {}, "outputs": [], "source": [ - "# Create Pyomo model\n", - "m = pyo.ConcreteModel()\n", + "# Create figure\n", + "plt.figure(figsize=(9,15))\n", "\n", - "# Define sets for spatial and temporal domains\n", - "m.x = ContinuousSet(bounds=(0,1))\n", - "m.t = ContinuousSet(bounds=(0,2))\n", + "# Create subplot for DJI\n", + "plt.subplot(5,1,1)\n", + "plt.plot(R[\"DJI\"]*100,color=\"blue\",label=\"DJI\")\n", + "plt.legend(loc='best')\n", "\n", - "# Define scaled temperature indexed by time and space\n", - "m.T = pyo.Var(m.t, m.x)\n", + "# Add your solution here\n", "\n", - "# Define variables for the derivates\n", - "m.dTdt = DerivativeVar(m.T, wrt=m.t)\n", - "m.dTdx = DerivativeVar(m.T, wrt=m.x)\n", - "m.d2Tdx2 = DerivativeVar(m.T, wrt=(m.x, m.x))\n", + "# Show plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3c. Covariance and Correlation Matrices\n", "\n", - "# Define PDE equation\n", - "def pde(m, t, x):\n", - " if t == 0:\n", - " return pyo.Constraint.Skip\n", - " elif x == 0 or x == 1:\n", - " return pyo.Constraint.Skip\n", - " # Add your solution here\n", + "Write Python code to:\n", + "1. Calculate $\\bar{r}$, the average 1-day return for each stock. Store this as the variable `R_avg`.\n", + "2. Calculate $\\Sigma_{r}$, the covariance matrix of the 1-day returns. This matrix tells us how returns for each stock vary with each other (which is important because they are correlated!). Hint: pandas has a function `cov`\n", + "3. Calculate the correlation matrix for the 1-day returns. Hint: pandas has a function `corr`.\n", "\n", - "m.pde = pyo.Constraint(m.t, m.x, rule=pde)\n", + "Looking at the correlation matrix, answer the follwing questions:\n", "\n", - "# Define first auxilary condition\n", - "def initial_condition(m, x):\n", - " if x == 0 or x == 1:\n", - " return pyo.Constraint.Skip\n", - " # Add your solution here\n", + "1. Which pair of stocks have the highest **positive** correlation?\n", + "2. Which pair of stocks have the highest **negative** correlation?\n", + "3. Which pair of stocks have the lowest **absolute** correlation?\n", "\n", - "m.ic = pyo.Constraint(m.x, rule = initial_condition)\n", + "Hint: Read ahead in the class website for more information on [correlation and covariance](../..//notebooks/14/Correlation-Covariance-and-Independence.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Please write one or two sentences for each of the above questions:\n", + "1. Fill in here\n", + "2. Fill in here\n", + "3. Fill in here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3d. Markowitz Mean/Variance Portfolio Model\n", "\n", - "# Define second auxilary condition\n", - "def boundary_condition1(m, t):\n", - " # Add your solution here\n", + "The Markowitz mean/variance model, shown below, computes the optimal allocation of funds in a portfolio:\n", "\n", - "m.bc1 = pyo.Constraint(m.t, rule = boundary_condition1)\n", + "\\begin{align}\n", + "\t\t\\min_{{x} \\geq {0}} \\qquad & z:= {x}^T \\cdot {\\Sigma_r} \\cdot {x} \\\\\n", + "\t\t\\text{s.t.} \\qquad & {\\bar{r}}^T \\cdot {x} \\geq \\rho \\\\\n", + "\t\t & \\sum_{i =1}^N x_i = 1 \n", + "\\end{align} \n", "\n", - "# Define third auxilary condition\n", - "@m.Constraint(m.t)\n", - "def boundary_condition2(m, t):\n", - " # Add your solution here \n", "\n", - "m.bc2 = pyo.Constraint(m.t, rule=boundary_condition2)\n", + "where $x_i$ is the fraction of funds invested in stock $i$ and $x = [x_1, x_2, ..., x_N]^T$. The objective is to minimize the variance of the return rate. (As practice for the next exam, try deriving this from the error propagation formulas.) This requires the expected return rate to be at least $\\rho$. Finally, the allocation of funds must sum to 100%.\n", "\n", - "# Define dummy objective\n", - "m.obj = pyo.Objective(expr=1)\n", + "Write Python code to solve for $\\rho = 0.08\\%.$ Report both the optimal allocation of funds and the standard deviation of the return rate. \n", + "*Hint*:\n", + "1. Be mindful of units.\n", + "2. You can solve with problem using the Pyomo function given below\n", + "3. $:=$ means ''defined as''\n", "\n", - "# Discretize spatial coordinate with forward finite difference and 50 elements\n", - "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.x)\n", + "Store your answer in `std_dev`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "R_avg_tolist = R_avg.values.tolist()\n", + "Cov_list = Cov.values.tolist()\n", "\n", - "# Discretize time coordinate with forward finite difference and 50 elements\n", - "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.t)\n", - "pyo.SolverFactory('ipopt').solve(m, tee=True).write()" + "# Optimization Problem\n", + "def create_model(rho,R_avg,Cov):\n", + " \n", + " '''\n", + " This function solves for the optimal allocation of funds in a portfolio \n", + " by minimizing the variance of the return rate\n", + " \n", + " Arguments:\n", + " rho: required portfolio expected return\n", + " Ravg: average return rates (list)\n", + " Cov: covariance matrix\n", + " \n", + " Returns:\n", + " m: Pyomo concrete model\n", + " \n", + " '''\n", + " \n", + " m = pyo.ConcreteModel()\n", + " init_x = {}\n", + " m.idx = pyo.Set(initialize=[0,1,2,3,4])\n", + " for i in m.idx:\n", + " init_x[i] = 0\n", + " m.x = pyo.Var(m.idx,initialize=init_x,bounds=(0,None))\n", + " \n", + " def Obj_func(m):\n", + " b = []\n", + " mult_result = 0\n", + " for i in m.idx:\n", + " a = 0\n", + " for j in m.idx:\n", + " a+= m.x[j]*Cov[j][i]\n", + " b.append(a)\n", + " for i in m.idx:\n", + " mult_result += b[i]*m.x[i]\n", + " \n", + " return mult_result\n", + " m.OBJ = pyo.Objective(rule=Obj_func)\n", + " \n", + " def constraint1(m):\n", + " # Add your solution here\n", + "\n", + " m.C1 = pyo.Constraint(rule=constraint1)\n", + " \n", + " def constraint2(m):\n", + " # Add your solution here\n", + "\n", + " m.C2 = pyo.Constraint(rule=constraint2)\n", + " \n", + " return m" ] }, { - "cell_type": "markdown", - "metadata": { - "id": "ZuOBPYd5d-fT" - }, + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ - "### 3c. Visualize Solution " + "rho = 0.0008\n", + "model1 = create_model(rho,R_avg_tolist,Cov_list)\n", + "\n", + "#Solve Pyomo in the method learned in Class 11\n", + "\n", + "# Add your solution here" ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 357 - }, - "executionInfo": { - "elapsed": 1668, - "status": "ok", - "timestamp": 1664677559084, - "user": { - "displayName": "Alexander Dowling", - "userId": "00988067626794866502" - }, - "user_tz": 240 - }, - "id": "qLQGM8Urd-fT", - "outputId": "751136c4-d2eb-4edc-c183-e30b80d82128" - }, + "metadata": {}, "outputs": [], "source": [ - "# Extract indices\n", - "x = sorted(m.x)\n", - "t = sorted(m.t)\n", + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3e. Volatility and Expected Return Tradeoff\n", "\n", - "# Create numpy arrays to hold the solution\n", - "xgrid = np.zeros((len(t), len(x)))\n", - "# Hint: define tgrid and Tgrid the same way\n", - "# Add your solution here\n", + "We will now perform sensitivity analysis of the optimization problem in 3d to characterize the tradeoff between return and risk.\n", "\n", - "# Loop over time\n", - "for i in range(0, len(t)):\n", - " # Loop over space\n", - " for j in range(0, len(x)):\n", - " # Copy values\n", - " xgrid[i,j] = x[j]\n", - " tgrid[i,j] = t[i]\n", - " # Hint: how to access values from Pyomo variable m.T?\n", - " # Add your solution here\n", + "Write Python code to:\n", + "1. Solve the optimization problem for many values of $\\rho$ between min($\\bar{r}$) and max($\\bar{r}$) and save the results. Use the Pyomo function created in 3d.\n", + "2. Plot $\\rho$ versus $\\sqrt{z}$ (using the saved results).\n", + "3. Write at least one sentence to interpret and discuss your plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho_vals = np.arange(0.0005,0.0038,0.0001)\n", + "std_dev = []\n", "\n", - "# Create a 3D wireframe plot of the solution\n", - "# Hint: consult the matplotlib documentation\n", - "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Plot\n", "\n", "# Add your solution here" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Discussion**:" + ] + }, { "cell_type": "markdown", "metadata": { "id": "X1GR0jYZd-e9" }, "source": [ - "**Submission Instructions and Tips:**\n", + "## Submission Instructions and Tips\n", + "\n", "1. Answer discussion questions in this notebook.\n", "2. When asked to store a solution in a specific variable, please also print that variable.\n", "3. Turn in this notebook via Gradescope.\n", @@ -1399,6 +1461,11 @@ "5. Even if you are not required to turn in pseudocode, you should always write pseudocode. It takes only a few minutes and can save you *hours* of time.\n", "6. For this assignment especially, read the problem statements twice. They contain important information and tips that are easy to miss on the first read." ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { diff --git a/notebooks/assignments/ProblemSet4_F23.ipynb b/notebooks/assignments/ProblemSet4_F23.ipynb new file mode 100644 index 00000000..f2330c0c --- /dev/null +++ b/notebooks/assignments/ProblemSet4_F23.ipynb @@ -0,0 +1,321 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Set 4\n", + "\n", + "CBE 60258, University of Notre Dame. © Prof. Alexander Dowling, 2023\n", + "\n", + "You may not distribution the solutions without written permissions from Prof. Alexander Dowling.\n", + "\n", + "**Your Name and Email:**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import Libraries" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Measuring Acceleration Two Ways\n", + "\n", + "You and a classmate want to measure the acceleration of a cart rolling down an incline plane, but disagree on the best approach. The cart starts at rest and travels distance $l = 1.0$ m. The location of the finish line is measured with negligible uncertainty. You (student 1) measure the instantaneous velocity $v = 3.2 \\pm 0.1 $ m/s at the finish line. Your classmate (student 2) instead measures the elapsed time $t = 0.63 \\pm 0.01$s." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1a. Approach 1\n", + "\n", + "Calculate the acceleration for approach 1,\n", + "\\begin{equation}\n", + "\ta_1 = \\frac{v^2}{2l} ~,\n", + "\\end{equation}\n", + "\n", + "and estimate the associated uncertainty. Round your answer to the correct number of significant digits and store your answers in variables `A1` for acceleration and `U_A1` for the uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-a", + "locked": true, + "points": "0.4", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1b. Approach 2\n", + "\n", + "Calculate the acceleration for approach 2,\n", + "\\begin{equation}\n", + "\ta_2 = \\frac{2 l}{t^2}~,\n", + "\\end{equation}\n", + "\n", + "and estimate the associated uncertainty. Round your answer to the correct number of significant digits and store your answers in variables `A2` for acceleration and `U_A2` for the uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-b", + "locked": true, + "points": "0.4", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1c. Weighted Average\n", + "\n", + "A third classmate suggests to use a weighted average of your two calculations:\n", + "\n", + "$$\n", + "\ta_{3} = w a_1 + (1-w) a_2\n", + "$$\n", + "\n", + "where $0 \\leq w \\leq 1$ is the weight you place on the approach 1 calculation calculations. Determine the value of $w$ that minimizes the uncertainty in $a_3$. Do the following steps: \n", + "1. Make a plot to graphically determine this value of $w$ and from the plot, read the minimum value for $w$ and save it as the variable `weight`. Submit your plot via **Gradescope**.\n", + "2. Then calculate the acceleration and uncertainty from the above equation. Round your answer for acceleration and corresponding uncertainty to the correct number of significant digits and store your answers in variables `A3` for acceleration and `U_A3` for the uncertainty. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here\n", + "\n", + "print(\"weight =\",weight)\n", + "print(\"A3 =\",A3)\n", + "print(\"U_A3 =\",U_A3)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-c", + "locked": true, + "points": "0.3", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1d. Analysis\n", + "\n", + "Write one or two sentences (each) to answer the following questions:\n", + "\n", + "1. If restricted to use only $a_1$ or $a_2$, which would you choose? Why?\n", + "2. How can a weighted average reduce the uncertainty? Why does this make sense?\n", + "3. Why does the uncertainty in $a_3$ depend on $w$?\n", + "\n", + "Record your answers below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Q1:\n", + " \n", + "Q2:\n", + " \n", + "Q3:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Calorimetry for Food Analysis\n", + "\n", + "As an intern at Tasty Foods, Inc., you are asked to estimate the caloric content (kilo-calories per gram) of mayo: You burn a $0.40 \\pm 0.01$ gram sample of mayo in a calorimeter and measure a 2.75 $\\pm$ 0.02 $^\\circ{}$C temperature increase. You then calculate caloric content $C$:\n", + "\n", + "\\begin{equation}\n", + "\tC = \\frac{c ~ H ~ \\Delta T}{m} \n", + "\\end{equation}\n", + "\n", + "where $c = 0.2390$ kcal/kJ is a conversion factor. Assume the calorimeter heat capacity $H = 4.0$ kJ/$^\\circ{}$ C is known with negligible uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2b. Relative Uncertainty\n", + "\n", + "Find the relative uncertainty in $C$ by doing the following:\n", + "\n", + "1. Set $\\sigma_m = 0.01 m$ and $\\sigma_{\\Delta T} = 0$ and recalculate $\\sigma_C$. This tells us the impact of 1% uncertainty in $m$. Store your answer as variable `U_C_mass`.\n", + "2. Set $\\sigma_m = 0$ and $\\sigma_{\\Delta T} = 0.01 \\Delta T$ and recalculate $\\sigma_C$. This tells us the impact of 1% uncertainty in $\\Delta T$. Store your answer as variable `U_C_temperature`.\n", + "\n", + "*Hint*: Use the $m$ and $\\Delta T$ data reported above.\n", + "\n", + "Remember to store your answer using the correct number of significant digits." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2c. Which is better?\n", + "\n", + "Which would provide a greater reduction in $\\sigma_C$: i) reducing the uncertainty in $m$ to 0.005 g OR ii) reducing the uncertainty in $\\Delta T$ to 0.001 $^\\circ{}$C? Do the following steps:\n", + "1. Calculate the uncertainty for each scenario, storing your variables as i) `Reduce_mass` and ii) `Reduce_temperature`. \n", + "2. After determining which method would provide a greater reduction in $\\sigma_C$, set the variable `method` equal to either 1, for reducing the uncertainty in mass, or 2, for reducing the uncertainty in temperature, to save which method you found would more significantly reduce $\\sigma_C$.\n", + "\n", + "Remember to use the correct number of significant digits." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/contrib-dev/McCabe_Thiele_Steven_Final.ipynb b/notebooks/contrib-dev/McCabe_Thiele_Steven_Final.ipynb new file mode 100644 index 00000000..ef9487dc --- /dev/null +++ b/notebooks/contrib-dev/McCabe_Thiele_Steven_Final.ipynb @@ -0,0 +1,1665 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "2wgBEY7p6-9B" + }, + "source": [ + "# **Plotting McCabe-Thiele diagram through computational methods**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "GpAjVy8DS_P-" + }, + "source": [ + "Prepared by:\n", + "\n", + "Zeping Chen - zchen23@nd.edu\n", + "\n", + "Suporna Paul - spaul2@nd.edu\n", + "\n", + "Steven Yeo - syeo@nd.edu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XtXFNP0z6ccg" + }, + "source": [ + "## **1. Introduction**\n", + "\n", + "Do you ever find yourself frustrated with the painstaking process of manually sketching McCabe-Thiele diagrams? Have you ever questioned whether there's a more efficient and precise approach, especially when dealing with the intricacies of the operating line and stepping lines? We will embark on a journey that combines data science and chemical engineering to improve separation processes! In this notebook, we'll delve into harnessing the power of Python to streamline the McCabe-Thiele diagram plotting process, making it not only simpler but also more data-centric and accurate, whilst giving special attention to the construction of the operating line and stepping lines." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LB88rTwE6n8H" + }, + "source": [ + "## 1.1 Target audience and learning objectives\n", + "\n", + "\n", + "This notebook is intended for Chemical Engineering students (both undergraduates and graduate students) who have completed or are currently enrolled in a Chemical Engineering Separations Process class.\n", + "\n", + "After studying this notebook, completing the activities, and asking questions in class, you should be able to:\n", + "\n", + "* Use numpy to solve system of linear equations\n", + "* Use pandas to read csv\n", + "* Produce \"publication ready\" plots\n", + "* Graph the McCabe-Thiele diagram using computational techniques\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "soxKSlO669DC" + }, + "source": [ + "## 1.2 Relevant notebooks from the class:\n", + "\n", + "\n", + "1.15. [Preparing Publication Quality Figures in Python](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html)\n", + "\n", + "1.3. [Modeling Systems of Linear Equations](https://ndcbe.github.io/data-and-computing/notebooks/01/Python-Basics-III-Lists-Dictionaries-Enumeration.html)\n", + "\n", + "1.5.[Functions and Scope](https://ndcbe.github.io/data-and-computing/notebooks/01/Functions-and-Scope.html)\n", + "\n", + "4.1. [Python Basics II: Loopy Logic](https://ndcbe.github.io/data-and-computing/notebooks/01/Flow-control.html)\n", + "\n", + "14.7. [Multivariate Linear Regression](https://ndcbe.github.io/data-and-computing/notebooks/14/Multivariate-Linear-Regression.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uvxlvi_gIaQ3" + }, + "source": [ + "## 1.3 References:\n", + "1. McCabe-Thiele Plot | Neutrium. https://neutrium.net/unit-operations/distillation/mccabe-thiele-plot/ (accessed 2022-10-15\n", + "\n", + "\n", + "2. Vapor-Liquid Equilibrium (VLE) Model for vapor mole frac methanol and liquid mole frac methanol. https://raw.githubusercontent.com/chennieXD/McCabe-Thiele/main/LiquidVaporEquil.csv (accessed 2022-10-15).\n", + "\n", + "3. Stichlmair, G.; Klein, H.; Rehfeldt, S. Distillation: Principles and Practice, 2nd ed.; Wiley, 2021.\n", + "\n", + "4. Gorak, A.; Sorensen, E. Distillation: Fundamentals and Principles (Handbooks in Separation Science), 1st ed.; Academic Press, 2014." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KaVgvFRXDqLH" + }, + "source": [ + "## 1.4 Background information\n", + "\n", + "### Distillation\n", + "Distillation is a widely used separation technique that exploits the differences in the boiling points of components within a liquid mixture. The process involves heating a liquid mixture to create vapor, and then cooling that vapor to condense it back into a liquid, separating the components in the process. Distillation can be used to separate two or more components from a mixture based on their volatility, which is determined by their boiling points." + ] + }, + { + "cell_type": "markdown", + "source": [ + "###Components of a Distillation Column:\n", + "\n", + "A distillation column is a tall vertical vessel. Consists of several components\n", + "\n", + "1. **Reboiler**: Where the liquid feed is heated to create vapor. This is in the bottom of the column\n", + "2. **Distillation Trays or packing**: Stages inside the column. This is designed to facilitate contact between vapor and liquid\n", + "3. **Condenser**: Cools the vapor to condense back to liquid at the top of the tower" + ], + "metadata": { + "id": "rzy5Fb4pIzDl" + } + }, + { + "cell_type": "markdown", + "source": [ + "Key Operating Parameters:\n", + "\n", + "1. **Temperature**: Temperature gradient allows for components with different boiling point to separate\n", + "2. **Pressure**: Changes along the column's height. In this problem, we assume that it's constant\n", + "3. **Vapor and Liquid flow Rates**: Flow rate of vapor and liquid in the columns\n", + "4. **Reflux Ratio**: The portion of the condensed liquid returned to the column as liquid" + ], + "metadata": { + "id": "HD7iWk5mJ3F_" + } + }, + { + "cell_type": "markdown", + "source": [ + "![](../../media/Distillation_column.png)\n", + "\n", + "(Gunawan et al. (2021))" + ], + "metadata": { + "id": "NEDDdEdGfcz2" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "CiAHPqhIMJhl" + }, + "source": [ + "## **2. Solving distillation column using McCabe-Thiele method**" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "26k7Oq1lc8QF" + }, + "outputs": [], + "source": [ + "# libraries used\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cYiBIRTOWE81" + }, + "source": [ + "### **Problem description**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QP4UfEimWCgg" + }, + "source": [ + "A student is trying to calculate the number of stages in a distillation column. Since there is insulation installed to improve the efficiency of the column, he can not just count the number of stages physically. To figure out the number of stages, he is feeding a methanol-water mixture into the column to observe how the column performs. Using a hydrometer, the student is able to measure the specific gravity of the feed: 0.887, distillate: 0.815 and bottoms: 0.990. He is also able to measure the reflux ratio to be 1.25 and the feed has a liquid mole fraction of 0.36.\n", + "\n", + "Using the above information:\n", + "1. Calculate the mole fraction of each stream from specific gravity\n", + "2. Plot the vapor liquid equilibrium line and 45 degree line.\n", + "3. Plot the McCabe-Thiele diagram for a total reflux run for the mixture and calculate the number of stages.\n", + "4. Plot the McCabe-Thiele diagram for a feed run for the mixture and calculate the number of stages.\n", + "5. Discuss what the McCabe-Thiele diagram tells you about the feed condiiton\n", + "6. Discuss how a McCabe-Thiele plot with 100% efficiency is unrealistic.\n", + "\n", + "**Note:** This problem is developed by Zeping Chen and Suporna Paul. Here, we demonstrated a step-by-step process of using this python notebook to solve for distillation column parameters.\n", + "\n", + "For further information, readers are encouraged to read these following text books which contains similar math problems.\n", + "\n", + "**References:**\n", + "\n", + "1. Stichlmair, G.; Klein, H.; Rehfeldt, S. Distillation: Principles and Practice, 2nd ed.; Wiley, 2021.\n", + "2. Gorak, A.; Sorensen, E. Distillation: Fundamentals and Principles (Handbooks in Separation Science), 1st ed.; Academic Press, 2014.\n", + "3. Gunawan, P., Kwan, J., Cai, Y., & Yang, R. (2021). Augmented reality application for Chemical Engineering Unit Operations. Virtual and Augmented Reality, Simulation and Serious Games for Education, 29–43. https://doi.org/10.1007/978-981-16-1361-6_4\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cDaMW2X3XOak" + }, + "source": [ + "## 2.1. Solve for mole fraction of each stream" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "M0uJ9fiFmQPe" + }, + "source": [ + "We can rearrange the definition of specific gravity (SG) to get the density of mixture in each stream:\n", + "\n", + "\n", + "\\begin{align}\n", + " SG = \\frac{density \\ of \\ mixture}{density \\ of \\ water}\n", + " \\end{align}\n", + "\n", + "We also know that the density (ρ) of a mixture can be calculated by summing the mole fraction (X) of each component by that component's density.\n", + "\n", + "\\begin{align}\n", + " ρ_t = ρ_a X_a + ρ_b X_b\n", + " \\end{align}\n", + "\n", + "\n", + "From these information, we can write a system of linear equations to calculate the mole fraction of methanol and water in each stream:\n", + "\n", + "\n", + "\\begin{align}\n", + " 1 = X_W + X_M\n", + " \\end{align}\n", + " \n", + "\\begin{align}\n", + " ρ_t = ρ_M X_M + ρ_W X_W\n", + " \\end{align}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Co3E5xSUALY0" + }, + "source": [ + "## 2.1.a. Obtaining density of mixture through specific gravity\n", + "\n", + "The density of each component is given as below:\n", + "* Water: 997 kg/m$^3$\n", + "* Methanol: 792 kg/m$^3$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "o4rndH2QgnAi" + }, + "outputs": [], + "source": [ + "# Density of each species\n", + "\n", + "# Water\n", + "rho_water = 997 # kg/m^3\n", + "# Methanol\n", + "rho_methanol = 792 # kg/m^3" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "q6PdrxgweFCQ" + }, + "source": [ + "## 2.1.b. Create a function to solve Linear System\n", + "\n", + "An easier method to calculate the mole fraciton of Methanol in each stream is to use linear algebra.\n", + "\n", + "Matrix form:\n", + "$$\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "ρ_W & ρ_M\\\\\n", + "1 & 1\n", + "\\end{bmatrix} \\cdot\n", + "\\begin{bmatrix}\n", + "\tX_W \\\\\n", + "\tX_M\n", + "\\end{bmatrix} =\n", + "\\begin{bmatrix}\n", + "\tρ_t \\\\\n", + "\t1\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "$$\n", + "\n", + "\n", + "Now let's write a function that will solve the linear system of equations to obtain the mole fraction of Methanol in each stream **using Python**." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "2jmiPXBfdZW4" + }, + "outputs": [], + "source": [ + "def conc_solver(SG):\n", + " ### BEGIN SOLUTIONS\n", + "\n", + " \"\"\"calculates the mole fraction of Methanol in the stream by solving one variable in one equation\n", + "\n", + " Arguments:\n", + " SG: specfic gravity\n", + "\n", + " Returns:\n", + " x: molar fraction of Methanol\n", + " \"\"\"\n", + "\n", + " # the left matrix above\n", + " a = np.array([[rho_water, rho_methanol], [1, 1]])\n", + "\n", + " # the right matrix above\n", + " b = np.array([SG * rho_water, 1])\n", + "\n", + " #mole fraction for each component\n", + " x = np.linalg.solve(a, b)\n", + "\n", + " #mole fraction of metanol\n", + " x_methanol = x[1]\n", + "\n", + " return x_methanol\n", + "\n", + " ### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qZDUyGUpM1CA" + }, + "source": [ + "The specific gravity of each stream (Feed, Distillate, Bottoms) is given as below:\n", + "* $SG_Z$ = 0.887\n", + "* $SG_D$ = 0.815\n", + "* $SG_B$ = 0.990" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "aNJxVaIcf3i_" + }, + "outputs": [], + "source": [ + "# Specify the Specific Gravity of each stream\n", + "\n", + "### BEGIN SOLUTIONS\n", + "\n", + "# Specific Gravity of feed\n", + "SG_Z = 0.887\n", + "\n", + "# Specific Gravity of distillate\n", + "SG_D = 0.815\n", + "\n", + "# Specific Gravity of bottoms\n", + "SG_B = 0.990\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "OmdZMkxneBPA" + }, + "source": [ + "## 2.1.c. Solve for the mole fraction of Methanol in each stream\n", + "\n", + "Using the function created previously to calculate and print the mole fraction of Methanol in each stream:\n", + "\n", + "Use **$x_D$** for the distillate stream\n", + "\n", + "Use **$x_B$** for the bottom stream\n", + "\n", + "Use **$x_Z$** for the feed stream" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "JeOQpz4kgWIc", + "outputId": "fa878419-23cc-4b3a-e6c7-bdefb83db9a0" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The molar fraction of Methanol in the distillate stream is: 0.900\n", + "The molar fraction of Methanol in the bottoms stream is: 0.049\n", + "The molar fraction of Methanol in the feed stream is: 0.550\n" + ] + } + ], + "source": [ + "# calculate the molar fraction of each stream\n", + "### BEGIN SOLUTIONS\n", + "\n", + "# Mole fraction of Feed\n", + "xZ = float(conc_solver(SG_Z))\n", + "\n", + "# Mole fraction of Distillate\n", + "xD = float(conc_solver(SG_D))\n", + "\n", + "# Mole fraction of Bottoms\n", + "xB = float(conc_solver(SG_B))\n", + "\n", + "\n", + "print(\"The molar fraction of Methanol in the distillate stream is: %1.3f\" % xD)\n", + "print(\"The molar fraction of Methanol in the bottoms stream is: %1.3f\" % xB)\n", + "print(\"The molar fraction of Methanol in the feed stream is: %1.3f\" % xZ)\n", + "\n", + "\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "De31VcuNfeFt" + }, + "source": [ + "## **3. Vapor-liquid equilibrium (VLE) model**\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FuGr8o9l-dqR" + }, + "source": [ + "## 3.1. Fit the VLE data points to create a best fit line\n", + "\n", + "Using the points of VLE obtained from Aspen Plus to generate a best fit line to model VLE. **Hint:** Use Excel or Python." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "04W1iERGHTxO", + "outputId": "00590f3f-6c0d-481b-a055-8773532c73de" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " vapor mole frac methanol liquid mole frac methanol\n", + "0 1.000000 1.00\n", + "1 0.991953 0.98\n", + "2 0.983907 0.96\n", + "3 0.975858 0.94\n", + "4 0.967805 0.92\n", + "5 0.959746 0.90\n", + "6 0.951678 0.88\n", + "7 0.943597 0.86\n", + "8 0.935500 0.84\n", + "9 0.927383 0.82\n", + "10 0.919242 0.80\n", + "11 0.911073 0.78\n", + "12 0.902868 0.76\n", + "13 0.894623 0.74\n", + "14 0.886331 0.72\n", + "15 0.877983 0.70\n", + "16 0.869572 0.68\n", + "17 0.861087 0.66\n", + "18 0.852518 0.64\n", + "19 0.843852 0.62\n", + "20 0.835076 0.60\n", + "21 0.826174 0.58\n", + "22 0.817129 0.56\n", + "23 0.807920 0.54\n", + "24 0.798526 0.52\n", + "25 0.788920 0.50\n", + "26 0.779072 0.48\n", + "27 0.768950 0.46\n", + "28 0.758514 0.44\n", + "29 0.747718 0.42\n", + "30 0.736511 0.40\n", + "31 0.724832 0.38\n", + "32 0.712610 0.36\n", + "33 0.699758 0.34\n", + "34 0.686178 0.32\n", + "35 0.671750 0.30\n", + "36 0.656326 0.28\n", + "37 0.639734 0.26\n", + "38 0.621753 0.24\n", + "39 0.602116 0.22\n", + "40 0.580482 0.20\n", + "41 0.556419 0.18\n", + "42 0.529364 0.16\n", + "43 0.498575 0.14\n", + "44 0.463048 0.12\n", + "45 0.421395 0.10\n", + "46 0.371637 0.08\n", + "47 0.310848 0.06\n", + "48 0.234504 0.04\n", + "49 0.135217 0.02\n", + "50 0.000000 0.00\n" + ] + } + ], + "source": [ + "# imports the csv data into python\n", + "url = \"https://raw.githubusercontent.com/chennieXD/McCabe-Thiele/main/LiquidVaporEquil.csv\"\n", + "liq_vap_data = pd.read_csv(url)\n", + "print(liq_vap_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WyG_uHyiYLQr" + }, + "source": [ + "## 3.2. Vapor-liquid equilibrium of methanol\n", + "\n", + "Plot the VLE of methanol using the model generated from linear regression using the format $a+bx+cx^2+dx^3+ex^4+fx^5+gx^6$ and define the equation in the function \"VLE_Eq\" Plot the 45 degree line on the same plot.\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "We will do a linear regression fitting of VLE data to a 6th degree polynomial:\n", + "\n", + "\\begin{equation}\n", + "VLE(x) = a + bx + cx^2 + dx^3 + ex^4 + fx^5 + gx^6\n", + "\\end{equation}\n", + "\n", + "where:\n", + "\\begin{align*}\n", + "x & : \\text{Mole Fraction of Methanol} \\in [0, 1] \\\\\n", + "VLE(x) & : \\text{Mole Fraction of Methanol in Vapor} \\\\\n", + "a, b, c, d, e, f, g & : \\text{Coefficients to be determined}\n", + "\\end{align*}\n", + "\n", + "The goal is to obtain the coefficients $a, b, c, d, e, f, g$ that best fit the VLE data. The model is fitted using linear regression in matrix form, following these equations:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{X}^T = \\text{np.transpose}(X)\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{XX}^{-1} = \\text{np.linalg.inv}(\\mathbf{X}^T \\cdot X)\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{X}^T \\mathbf{Y} = \\mathbf{X}^T \\cdot Y\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\text{coefficients} = \\mathbf{XX}^{-1} \\cdot (\\mathbf{X}^T \\cdot Y)\n", + "\\end{equation}\n", + "\n", + "\n" + ], + "metadata": { + "id": "l5jgZIR5MW5s" + } + }, + { + "cell_type": "code", + "source": [ + "# Function for matrix operations\n", + "\n", + "def calculate_regression_coefficients(X, Y):\n", + " \"\"\"solving for the coefficients of the 6th degree polynomials\n", + "\n", + " Arguments:\n", + " X = the polynomial we are trying to fit, based on the liquid vapor fraction\n", + " Y = feature of the data, in this case the vapor fraction\n", + "\n", + " Returns:\n", + " Coefficient of each term of the polynomials\n", + "\n", + " \"\"\"\n", + " ### BEGIN SOLUTION\n", + "\n", + " XT = np.transpose(X)\n", + " XXinv = np.linalg.inv(XT.dot(X))\n", + " XTy = XT.dot(Y)\n", + " return XXinv.dot(XTy)\n", + "\n", + " ### END SOLUTION" + ], + "metadata": { + "id": "ykIL9J_IeWjk" + }, + "execution_count": 7, + "outputs": [] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 556 + }, + "id": "4djK6hGuh-f1", + "outputId": "17fcdc58-4046-4925-eb82-f02ca638930b" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "liqvapy = liq_vap_data[\"vapor mole frac methanol\"]\n", + "liqvapx = liq_vap_data[\"liquid mole frac methanol\"]\n", + "\n", + "# Feature matrix (store in 'X')\n", + "X = np.column_stack([np.ones(len(liqvapx))] + [liqvapx**i for i in range(1, 7)])\n", + "Y = np.array(liqvapy)\n", + "\n", + "# Calculate regression coefficients\n", + "beta_hat = calculate_regression_coefficients(X, Y)\n", + "\n", + "# Separate data preparation from plotting\n", + "x = liqvapx\n", + "y = X.dot(beta_hat)\n", + "\n", + "# create empty lists to store x and y coordinates for the VLE equilibrium graph\n", + "x = liqvapx\n", + "liqvapy = liqvapy\n", + "\n", + "def VLE_eq(x):\n", + " \"\"\"plot the \"stair case\" line of the McCabe-Thiele diagram\n", + "\n", + " Arguments:\n", + " x: x value on the VLE diagram\n", + "\n", + " Returns:\n", + " liqvap: y value on the VLE diagram\n", + "\n", + " \"\"\"\n", + " liqvap = (\n", + " beta_hat[0]\n", + " + beta_hat[1] * x\n", + " + beta_hat[2] * x**2\n", + " + beta_hat[3] * x**3\n", + " + beta_hat[4] * x**4\n", + " + beta_hat[5] * x**5\n", + " + beta_hat[6] * x**6\n", + " )\n", + " return liqvap\n", + "\n", + "\n", + "y = VLE_eq(x)\n", + "\n", + "# Plot the VLE line\n", + "fig = plt.figure(figsize=(6, 6))\n", + "plt.plot(liqvapx, liqvapy, \"o\", label=\"Data Points\")\n", + "plt.plot(x, y, color=\"black\", label=\"Modeled Equation VLE Line\")\n", + "plt.plot([0, 1], [0, 1], color=\"orange\", linestyle=\":\", label=\"45° Line\")\n", + "plt.xlabel(\"Liquid Mole Fraction of Methanol\", fontsize=10)\n", + "plt.ylabel(\"Vapor Mole Fraction of Methanol\", fontsize=10)\n", + "plt.xticks(fontsize=10)\n", + "plt.yticks(fontsize=10)\n", + "plt.tick_params(direction=\"in\", top=True, right=True)\n", + "plt.title(\"VLE Equilibrium of Methanol\", fontsize=10)\n", + "plt.legend(fontsize=10, bbox_to_anchor=(1.0, 0.15), borderaxespad=0)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xpHXH5xD-6as" + }, + "source": [ + "## 3.3. Plot the McCabe-Thiele for a Total Reflux Run" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZiG2JcDWfyPn" + }, + "source": [ + "## 3.3.a. Stepping line\n", + "\n", + "The stepping line connects the points that represent the mole fraction of Methanol in each stage of the distillation column. It starts at the bottom mole fraction of Methanol on the 45 degree line and ends after reaching the mole fraction of Methanol in the distillate on the 45 degree line.\n", + "\n", + "![](../../media/MCabe_thiele_stepping_line.png)\n", + "\n", + "Create a function that is able to generate the points requried to plot the stepping line." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "id": "mioHfOn4ht0G" + }, + "outputs": [], + "source": [ + "def stair(slope, y_intercept, x_start, y_start, y_end, Efficiency=1):\n", + "\n", + " \"\"\"plot the \"stair case\" line of the McCabe-Thiele diagram\n", + "\n", + " Arguments:\n", + " slope: slope of the line compared to the vapor-liquid equilibrium line\n", + " y_intercept: y_intercept of the line compared to the vapor-liquid equilibrium line\n", + " x_start: the bottom mole fraction of Methanol\n", + " y_start: the mole fraction of the Methanol\n", + " y_end: the distillate mole fraction of the mixture\n", + "\n", + " Returns:\n", + " xplot: x cordinates of the stair case\n", + " yplot: y cordinates of the stair case\n", + " n: number of stages in the distillation column\n", + "\n", + " \"\"\"\n", + " # establish arrays for the \"stair case\"\n", + " xplot = []\n", + " yplot = []\n", + "\n", + " # first point on 45 line\n", + " x = x_start\n", + " y = y_start\n", + " xplot.append(x)\n", + " yplot.append(y)\n", + "\n", + " # initial number of stages\n", + " n = 0\n", + "\n", + " ### BEGIN SOLUTIONS\n", + "\n", + " # while the mole fraction is less than the distillate product\n", + " while y < y_end:\n", + " xplot.append(x)\n", + " # create the equation from slope and y-intercept of equation\n", + " equation = slope * x + y_intercept\n", + " y = ((VLE_eq(x)) - equation) * Efficiency + equation\n", + " yplot.append(y)\n", + " x = (y - y_intercept) / slope\n", + " # sol=solve(Equation)\n", + " # x=sol[0]\n", + "\n", + " # append points to list\n", + " xplot.append(x)\n", + " yplot.append(y)\n", + "\n", + " # counts the number of stages\n", + " n += 1\n", + " return (xplot, yplot, n)\n", + " ### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PxYdeMPXiJ1h" + }, + "source": [ + "## 3.3.b. McCabe-Thiele for a total reflux run\n", + "\n", + "In a total reflux run, there are no feed entering the column and no product leaving the column. The distillate is all refluxed back into the top of the column. The stepping line is plotted along the 45 degree line and the vapor-liquid equilibrium line." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 459 + }, + "id": "K9ogeBGqP8rS", + "outputId": "fa9461ea-1bce-4bb6-91b7-59d408e94393" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The number of total theoretical stage is 4\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "### BEGIN SOLUTIONS\n", + "\n", + "# slope and y-intercept of the 45 degree line\n", + "slope = 1\n", + "y_intercept = 0\n", + "Efficiency = 1\n", + "\n", + "# call stair funciton to generate the points needed to plot\n", + "complete_reflux = stair(slope=1, y_intercept=0, x_start=xB, y_start=xB, y_end=xD)\n", + "# extract x and y points for the plot\n", + "xplot = complete_reflux[0]\n", + "yplot = complete_reflux[1]\n", + "total_stage = complete_reflux[2]\n", + "print(\"The number of total theoretical stage is \", total_stage)\n", + "\n", + "# McCabe-Thiele diagram\n", + "fig = plt.figure(figsize=(4, 4))\n", + "# plot the LVE line\n", + "plt.plot(liqvapx, liqvapy)\n", + "# plot the 45 degree line\n", + "plt.plot([0, 1], [0, 1], color=\"orange\", linestyle=\":\")\n", + "# plot the VLE line\n", + "plt.plot(xplot, yplot, color=\"red\")\n", + "plt.xlabel(\"Liquid Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.ylabel(\"Vapor Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.xticks(fontsize=15)\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\", top=True, right=True)\n", + "plt.title(\"McCabe-Thiele of a total \\n reflux system\", fontsize=10)\n", + "plt.legend(\n", + " labels=(\"LVE line\", \"45 line\", \"step line\"),\n", + " fontsize=10,\n", + " bbox_to_anchor=(1.0, 0.23),\n", + " borderaxespad=0,\n", + ")\n", + "plt.show()\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zp6Kin33_jBE" + }, + "source": [ + "## **4. Plot the McCabe-Thiele diagram of a feed run**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "OVURADZKkp3v" + }, + "source": [ + "In a more realistic sense, there will be mixture feed entering the column to be separated. As a result, there will also be a distillate stream and a bottoms stream. When there are feed entering the column and product leaving the column, the McCabe-Thiele diagram will have the feed condition (q) line, rectifying line, and stripping line. The rectifying starts at the distillate mole fraction of Methanol and comes down until it crosses the q-line. The q-line starts at the feed mole fraction of Methanol and meets the stripping and rectifying line. The stripping line starts at the bottom mole fraction of Methanol and meets the q-line and rectifying line. \n", + "\n", + "![](../../media/MCabe_thiele_diagram.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mwsK8bEMhVPf" + }, + "source": [ + "## 4.1. Solve for the slope of the q and rectifying line\n", + "\n", + "Using the relationship below, calculate the slope of the q and rectifying line. q is the mole fraction of liquid in the feed stream and R is the reflux ratio. Store the slope of q-line as **m_q** and slope of rectifying operating line as **m_rec**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1ZbzkD_6hySQ" + }, + "source": [ + "\\begin{align}\n", + " m_{feed} = \\frac{q}{ q - 1 }\n", + " \\end{align}\n", + "\n", + "\\begin{align}\n", + " m_{rec} = \\frac{R}{ R + 1 } \n", + " \\end{align}\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "id": "UMuh1VJ5l1-o" + }, + "outputs": [], + "source": [ + "# Mole fraction of liquid in feed\n", + "q = 0.3\n", + "# Reflux Ratio\n", + "R = 1\n", + "\n", + "### BEGIN SOLUTIONS\n", + "\n", + "# slope of rectifying opearting line\n", + "m_rec = R / (R + 1)\n", + "# slope of feed condition line (q-line)\n", + "m_q = q / (q - 1)\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wzlsXB8UjNSj" + }, + "source": [ + "## 4.2. Intercept of the q-line and the rectifying line, and calculate the slope and y-intercept of the stripping line\n", + "\n", + "To find the intercept of the q-line and the rectifying line, the point-slope equation of the q-line and the rectifying line can be turned into slope-interecept form and made into a system of linear equations.\n", + "\n", + "\\begin{equation}\n", + " y-y_q = m_q(x-x_q)\n", + "\\end{equation}\n", + "\n", + "\\begin{align}\n", + " y-y_{rec} = m_{rec}(x-x_{rec})\n", + "\\end{align}\n", + "\n", + "\n", + "Matrix form:\n", + "\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "m_{rec} & -1\\\\\n", + "m_{q} & -1\n", + "\\end{bmatrix} \\cdot\n", + "\\begin{bmatrix}\n", + "\tx \\\\\n", + "\ty\n", + "\\end{bmatrix} =\n", + "\\begin{bmatrix}\n", + "\tm_{rec}*x_{rec} - y_{rec} \\\\\n", + "\tm_{q} *x_q - y_q\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "After calculating the intercept, we have two points of the stripping line to calculate the slope and y-intercept to get the slope-intercept form of the equation." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "id": "ogUO2OzdtfSD" + }, + "outputs": [], + "source": [ + "### BEGIN SOLUTIONS\n", + "\n", + "# solve for the intercept of the rectifying line and q-line\n", + "a = np.array([[m_rec, -1], [m_q, -1]])\n", + "b = np.array([m_rec * xD - xD, m_q * xZ - xZ])\n", + "intercept = np.linalg.solve(a, b)\n", + "\n", + "# solve for stripping operating line slope and y-intercept\n", + "m_strip = (intercept[1] - xB) / (intercept[0] - xB)\n", + "y_intercept_strip = xB * (1 - m_strip)\n", + "\n", + "# y-intercept of the rectifying opearting line\n", + "y_intercept_rec = xD * (1 - m_rec)\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "0dD5nKV6jjaD" + }, + "source": [ + "## 4.3. Generate the points needed to plot the stepping line, plot the McCabe-Thiele diagram, and calculate the number of stages\n", + "\n", + "Think where you want the \"stair\" to stop on your plot when you enter the y_start and y_end for the function. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "id": "FAIXZi5YVJwf" + }, + "outputs": [], + "source": [ + "### BEGIN SOLUTIONS\n", + "\n", + "# McCabe-Thiele of a feed run\n", + "# stripping portion of stepping line generation\n", + "stripping_line = stair(\n", + " slope=m_strip,\n", + " y_intercept=y_intercept_strip,\n", + " x_start=xB,\n", + " y_start=xB,\n", + " y_end=intercept[1],\n", + ")\n", + "xplot_stripping = stripping_line[0]\n", + "yplot_stripping = stripping_line[1]\n", + "\n", + "# rectifying portion of stepping line generation\n", + "rectifying_line = stair(\n", + " slope=m_rec,\n", + " y_intercept=y_intercept_rec,\n", + " x_start=(yplot_stripping[-1] - y_intercept_rec) / m_rec,\n", + " y_start=yplot_stripping[-1],\n", + " y_end=xD,\n", + ")\n", + "xplot_rectifying = rectifying_line[0]\n", + "yplot_rectifying = rectifying_line[1]\n", + "\n", + "# complie the x and y points to respective lists\n", + "xplot = xplot_stripping + xplot_rectifying\n", + "yplot = yplot_stripping + yplot_rectifying\n", + "\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "code", + "source": [ + "### BEGIN SOLUTIONS\n", + "\n", + "# McCabe-Thiele diagram\n", + "fig = plt.figure(figsize=(4, 4))\n", + "# plot the LVE line\n", + "plt.plot(liqvapx, liqvapy)\n", + "# plot the 45 degree line\n", + "plt.plot([0, 1], [0, 1], color=\"orange\", linestyle=\":\")\n", + "# plot the step line\n", + "plt.plot(xplot, yplot, color=\"red\")\n", + "# plot the SOP\n", + "plt.plot([xB, intercept[0]], [xB, intercept[1]], color=\"purple\")\n", + "# plot the ROP\n", + "plt.plot([xD, intercept[0]], [xD, intercept[1]], color=\"green\")\n", + "# plot the q-line\n", + "plt.plot([xZ, intercept[0]], [xZ, intercept[1]], color=\"grey\")\n", + "# Formating the plot\n", + "plt.xlabel(\"Liquid Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.ylabel(\"Vapor Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.xticks(fontsize=15)\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\", top=True, right=True)\n", + "plt.title(\"McCabe-Thiele of a \\n feed system\", fontsize=10)\n", + "plt.legend(\n", + " labels=(\"LVE line\", \"45 line\", \"step line\", \"SOP\", \"ROP\", \"q-line\"),\n", + " fontsize=10,\n", + " bbox_to_anchor=(1.01, 0.43),\n", + " borderaxespad=0,\n", + ")\n", + "plt.show()\n", + "total_stage = stripping_line[2] + rectifying_line[2]\n", + "print(\"The number of total theoretical stage is \", total_stage)\n", + "\n", + "### END SOLUTIONS" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 459 + }, + "id": "JsQlY8ycS6jI", + "outputId": "d8edee15-3f20-4b6b-c9b1-36af2c4a516d" + }, + "execution_count": 14, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The number of total theoretical stage is 6\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "OJBs_kYcdD4j" + }, + "source": [ + "## **5. Discussion Question 1**\n", + "From the McCabe-Thiele diagram plotted above what can we say about the phase of the feed stream? **Hint: Look at the slope of the q-line.**\n", + "\n", + "![](../../media/MCabe_thiele_q1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LoP3LjSNMsOf" + }, + "source": [ + "**Your Answer:**\n", + "\n", + "Since the q-line slope is between 0 and -1, it tells us that the feed stream is mostly a vapor feed. This conclusion is in line with the problem statement where q, the mole fraction of liquid, is 0.36, which means the feed is mostly vapor." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "R8BY1lHjR36P", + "outputId": "9726ce20-231a-42d4-9f5e-7c6d03867f03" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " \n" + ] + } + ], + "source": [ + "### BEGIN SOLUTIONS\n", + "\"\"\"\n", + "Since the q-line slope is between 0 and -1, it tells us that the feed stream is mostly a vapor feed.\n", + "This conclusion is in line with the problem statement where q, the mole fraction of liquid, is 0.36, which means the feed is mostly vapor.\n", + "\"\"\"\n", + "print(\" \")\n", + "### END SOLUTIONS" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BmdDtWrDNMdF" + }, + "source": [ + "## **6. Discussion Question 2**\n", + "\n", + "Why is the McCabe-Thiele diagram plotted above is unrealistic in the real world? What would you change to make the plot more realistic. Plot the modified plot and talk about how the number of stages changed. **Hint: Think efficiency. Is there ever 100% efficiency in the real world? A distillation column typically have a efficiency of 60%.**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TlPtqtgHV1Wq" + }, + "source": [ + "**Your Answer:**" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h_aWc3gSR36Q", + "outputId": "f4994c33-7cc3-4887-ebe9-c0319e3b922d" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\n" + ] + } + ], + "source": [ + "### BEGIN SOLUTION\n", + "\"\"\" The diagram plotted above uses 100% efficiency in the column.\n", + "Since 100% efficiency is not possible in the real world, it makes the plot above unrealistic.\n", + "A more realistic plot would use a efficiency of around 60% like the one plotted below.\n", + "The number of stages increased from 5 to 9, which makes sense because less efficiency means more stages are required.\n", + "\"\"\"\n", + "print()\n", + "### END SOLUTION" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + }, + "id": "6wmItV90cjwc", + "outputId": "8c89be05-05c5-4c4d-f55d-0dda0c8881df" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The number of total theoretical stage is 11\n" + ] + } + ], + "source": [ + "# Efficency\n", + "\n", + "### BEGIN SOLUTIONS\n", + "efficiency = 0.6\n", + "### END SOLUTIONS\n", + "\n", + "# McCabe-Thiele of a feed run\n", + "# stripping portion of stepping line generation\n", + "stripping_line = stair(\n", + " slope=m_strip,\n", + " y_intercept=y_intercept_strip,\n", + " x_start=xB,\n", + " y_start=xB,\n", + " y_end=intercept[1],\n", + " Efficiency=efficiency,\n", + ")\n", + "xplot_stripping = stripping_line[0]\n", + "yplot_stripping = stripping_line[1]\n", + "\n", + "# rectifying portion of stepping line generation\n", + "rectifying_line = stair(\n", + " slope=m_rec,\n", + " y_intercept=y_intercept_rec,\n", + " x_start=(yplot_stripping[-1] - y_intercept_rec) / m_rec,\n", + " y_start=yplot_stripping[-1],\n", + " y_end=xD,\n", + " Efficiency=efficiency,\n", + ")\n", + "xplot_rectifying = rectifying_line[0]\n", + "yplot_rectifying = rectifying_line[1]\n", + "\n", + "# complie the x and y points to respective liststogether\n", + "xplot = xplot_stripping + xplot_rectifying\n", + "yplot = yplot_stripping + yplot_rectifying\n", + "\n", + "\n", + "# McCabe-Thiele diagram\n", + "fig = plt.figure(figsize=(4, 4))\n", + "# plot the LVE line\n", + "plt.plot(liqvapx, liqvapy)\n", + "# plot the 45 degree line\n", + "plt.plot([0, 1], [0, 1], color=\"orange\", linestyle=\":\")\n", + "# plot the step line\n", + "plt.plot(xplot, yplot, color=\"red\")\n", + "# plot the SOP\n", + "plt.plot([xB, intercept[0]], [xB, intercept[1]], color=\"purple\")\n", + "# plot the ROP\n", + "plt.plot([xD, intercept[0]], [xD, intercept[1]], color=\"green\")\n", + "# plot the q-line\n", + "plt.plot([xZ, intercept[0]], [xZ, intercept[1]], color=\"grey\")\n", + "# Formating the plot\n", + "plt.xlabel(\"Liquid Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.ylabel(\"Vapor Mole Fraction \\n of Methanol\", fontsize=10)\n", + "plt.xticks(fontsize=7)\n", + "plt.yticks(fontsize=7)\n", + "plt.tick_params(direction=\"in\", top=True, right=True)\n", + "plt.title(\"McCabe-Thiele of a \\n feed system\", fontsize=10)\n", + "plt.legend(\n", + " labels=(\"LVE line\", \"45 line\", \"step line\", \"SOP\", \"ROP\", \"q-line\"),\n", + " fontsize=10,\n", + " bbox_to_anchor=(1.0, 0.43),\n", + " borderaxespad=0,\n", + ")\n", + "plt.show()\n", + "total_stage = stripping_line[2] + rectifying_line[2]\n", + "print(\"The number of total theoretical stage is \", total_stage)" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **7. Discussion Question 3: Evaluating the minimum reflux rate of the system (Graphical)**" + ], + "metadata": { + "id": "HtyCIZXTqodc" + } + }, + { + "cell_type": "markdown", + "source": [ + "Under the conditions given by the problem statement, what is the theoretical minimum reflux of the system? And describe how you would find this. Hint: At the minimum reflux rate, it would require infinite number of stage to achieve separation. **Do this by hand and submit**\n", + "\n", + "---\n", + "\n" + ], + "metadata": { + "id": "QAAt5d64qtJB" + } + }, + { + "cell_type": "code", + "source": [ + "# Mole fraction of Feed\n", + "xZ = float(conc_solver(SG_Z))\n", + "\n", + "# Mole fraction of Distillate\n", + "xD = float(conc_solver(SG_D))\n", + "\n", + "# Mole fraction of Bottoms\n", + "xB = float(conc_solver(SG_B))\n", + "\n", + "##BEGIN SOLUTION\n", + "\n", + "# Mole fraction of liquid in feed\n", + "q = 0.3\n", + "# Reflux Ratio\n", + "R = 0.65\n", + "\n", + "\"\"\" The total reflux gives out the maximum number of reflux that can be theoretically achieved for a given system; this was discussed in discussion 5.\n", + "The minimum reflux is the opposite, as the reflux rate gets smaller, the q-line and the operating line gets closer to the VLE line. Therefore, N gets larger as it requires more stepping to reach xD\n", + "Graphically, this is where the q-line intersects with the VLE line given a specified q.\n", + "In traditional chemical engineering term, this is called a \"Pinch\"\n", + "\"\"\"\n", + "\n", + "###END SOLUTION\n", + "\n", + "# slope of rectifying opearting line\n", + "m_rec = R / (R + 1)\n", + "# slope of feed condition line (q-line)\n", + "m_q = q / (q - 1)\n", + "\n", + "\n", + "# solve for the intercept of the rectifying line and q-line\n", + "a = np.array([[m_rec, -1], [m_q, -1]])\n", + "b = np.array([m_rec * xD - xD, m_q * xZ - xZ])\n", + "intercept = np.linalg.solve(a, b)\n", + "# solve for stripping operating line slope and y-intercept\n", + "m_strip = (intercept[1] - xB) / (intercept[0] - xB)\n", + "y_intercept_strip = xB * (1 - m_strip)\n", + "\n", + "# y-intercept of the rectifying opearting line\n", + "y_intercept_rec = xD * (1 - m_rec)\n", + "\n", + "# McCabe-Thiele diagram\n", + "fig = plt.figure(figsize=(4, 4))\n", + "\n", + "# plot the LVE line\n", + "plt.plot(liqvapx, liqvapy)\n", + "\n", + "# plot the 45 degree line\n", + "plt.plot([0, 1], [0, 1], color=\"orange\", linestyle=\":\")\n", + "\n", + "# plot the SOP\n", + "plt.plot([xB, intercept[0]], [xB, intercept[1]], color=\"purple\")\n", + "# plot the ROP\n", + "plt.plot([xD, intercept[0]], [xD, intercept[1]], color=\"green\")\n", + "# plot the q-line\n", + "plt.plot([xZ, intercept[0]], [xZ, intercept[1]], color=\"grey\")\n", + "\n", + "# Add points for xD and xB\n", + "plt.scatter(xD, xD, color=\"blue\", label=\"xD\")\n", + "plt.scatter(xB, xB, color=\"red\", label=\"xB\")\n", + "\n", + "# Formating the plot\n", + "plt.xlabel(\"Liquid Mole Fraction of Methanol\", fontsize=10)\n", + "plt.ylabel(\"Vapor Mole Fraction of Methanol\", fontsize=10)\n", + "plt.xticks(fontsize=15)\n", + "plt.yticks(fontsize=15)\n", + "plt.tick_params(direction=\"in\", top=True, right=True)\n", + "plt.title(\"McCabe-Thiele of a feed system\", fontsize=10)\n", + "plt.legend(\n", + " labels=(\"LVE line\", \"45 line\", \"SOP\", \"ROP\", \"q-line\", \"xD\", \"xB\"),\n", + " fontsize=10,\n", + " bbox_to_anchor=(1.0, 0.43),\n", + " borderaxespad=0,\n", + ")\n", + "plt.show()\n", + "\n", + "# print(intercept)\n", + "# print(m_q)\n", + "\n", + "# print(xB)\n", + "# print(xD)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 408 + }, + "id": "JAW0SaIlT5Yz", + "outputId": "615471da-3247-456f-d923-92665c46a682" + }, + "execution_count": 18, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "##8. **Discussion Question 4: Evaluating the minimum reflux of the system (Newton's method)**" + ], + "metadata": { + "id": "VRE59ad9bSqM" + } + }, + { + "cell_type": "markdown", + "source": [ + "Now that we have graphically identified the location of the pinch, we can employ our data science skills to precisely pinpoint this critical point. As previously mentioned, the pinch occurs at the intersection of the q-line and the VLE line. At this intersection, we can determine the minimum reflux ratio, R_min, by finding the slope of the ROP line.\n", + "\n", + "To approach this problem computationally, we can use numerical methods, such as Newton's method, to find the solution where the VLE line and the q-line intersect. The goal is to determine the composition at this intersection point, which corresponds to the exact location of the pinch and allows us to calculate R_min" + ], + "metadata": { + "id": "7v24FezT0mV-" + } + }, + { + "cell_type": "markdown", + "source": [ + "1. Define the VLE curve equation\n", + "\n", + "2. Define the q-line equation\n", + "\n", + "3. Implement Newton's method to find the intersection point of the VLE curve and the q-line. This intersection point corresponds to the pinch location. (Solution of a 6th degree polynomial to a line)\n", + "\n", + "4. Once the intersection point is found, calculate R_min\n", + " \n" + ], + "metadata": { + "id": "E3pOTtzq38Rt" + } + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "\n", + "###BEGIN SOLUTION\n", + "\n", + "#defining the VLE-line\n", + "def polynomial(x):\n", + "\n", + " liqvap = (\n", + " beta_hat[0]\n", + " + beta_hat[1] * x\n", + " + beta_hat[2] * x**2\n", + " + beta_hat[3] * x**3\n", + " + beta_hat[4] * x**4\n", + " + beta_hat[5] * x**5\n", + " + beta_hat[6] * x**6\n", + " )\n", + " return liqvap\n", + "\n", + "# Define the equation of the q-line\n", + "def line(x):\n", + " return m_q*x + xZ/(1-q)\n", + "\n", + "# Define the derivative of the polynomial function\n", + "def polynomial_derivative(x):\n", + " \"\"\"Calculate the derivative of the polynomial function.\n", + "\n", + " Arguments:\n", + " x: x value on the VLE diagram\n", + "\n", + " Returns:\n", + " liqvap_derivative: Derivative of the polynomial at x\n", + " \"\"\"\n", + "\n", + " liqvap_derivative = (\n", + " beta_hat[1]\n", + " + 2 * beta_hat[2] * x\n", + " + 3 * beta_hat[3] * x**2\n", + " + 4 * beta_hat[4] * x**3\n", + " + 5 * beta_hat[5] * x**4\n", + " + 6 * beta_hat[6] * x**5\n", + " )\n", + "\n", + " return liqvap_derivative\n", + "\n", + "# Initial guess for the intersection point\n", + "x0 = 0.0\n", + "\n", + "# Set a tolerance level for the approximation\n", + "tolerance = 1e-6\n", + "\n", + "# Maximum number of iterations\n", + "max_iterations = 100\n", + "\n", + "# Newton's method to find the intersection\n", + "\n", + "for i in range(max_iterations):\n", + " f_x0 = polynomial(x0) - line(x0)\n", + " if abs(f_x0) < tolerance:\n", + " break\n", + " x0 = x0 - f_x0 / polynomial_derivative(x0)\n", + "\n", + "# Check if the maximum number of iterations is reached\n", + "if i == max_iterations - 1:\n", + " print(\"Maximum iterations reached without convergence.\")\n", + "else:\n", + " print(\"Approximate intersection point:\", x0)\n", + " print(\"Approximate y-coordinate:\", line(x0))\n", + "\n", + "# Plot the polynomial\n", + "x_values = np.linspace(0, 1, 100) # Adjust the range and number of points as needed\n", + "polynomial_values = [polynomial(x) for x in x_values]\n", + "\n", + "#plotting the line\n", + "plt.plot(x_values, polynomial_values, label=\"VLE\")\n", + "x_values_line = np.linspace(x0,xZ,100)\n", + "line_values = [line(x) for x in x_values_line]\n", + "plt.plot(x_values_line, line_values, label=\"q-line\")\n", + "\n", + "\n", + "plt.scatter(x0, line(x0), color=\"red\", label=\"Pinch at Rmin\", marker=\"o\")\n", + "\n", + "\n", + "\n", + "# Add a 45-degree line\n", + "fortyfive_deg_line = [x for x in x_values]\n", + "\n", + "#plot of the 45 degree line\n", + "plt.plot(x_values, fortyfive_deg_line, label=\"45-degree Line\", linestyle=\"--\")\n", + "\n", + "#plot of xD point\n", + "plt.scatter(xD, xD, color=\"blue\", label=\"xD\")\n", + "\n", + "#plot of xB point\n", + "plt.scatter(xB, xB, color=\"red\", label=\"xB\")\n", + "\n", + "#plotting SOP line\n", + "plt.plot([xB,x0],[xB,line(x0)],label=\"SOP\")\n", + "\n", + "#plotting ROP line\n", + "plt.plot([xD,x0],[xD,line(x0)], label=\"ROP\")\n", + "\n", + "#labelling\n", + "plt.xlabel(\"Liquid fraction of methanol\")\n", + "plt.ylabel(\"Vapor fraction of methanol\")\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()\n", + "\n", + "R_min = (xD - line(x0))/(line(x0) - x0)\n", + "\n", + "print(\"R_min is: \",R_min)\n", + "\n", + "###END SOLUTION" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 503 + }, + "id": "cyADEW_ZUSg9", + "outputId": "6d69b372-71f9-48e6-e2ef-b4cf5eaebd42" + }, + "execution_count": 21, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Approximate intersection point: 0.2890625846948517\n", + "Approximate y-coordinate: 0.6612101117858299\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "R_min is: 0.6409329047427269\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "LTNaey22j1Br" + }, + "execution_count": 19, + "outputs": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file