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...kin/Unit 5 Finite-Difference Approximation to Linear-Flow Equations/fd1d_linearflow.ipynb
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| { | ||
| "nbformat": 4, | ||
| "nbformat_minor": 0, | ||
| "metadata": { | ||
| "colab": { | ||
| "name": "fd1d_linearflow.ipynb", | ||
| "provenance": [], | ||
| "collapsed_sections": [], | ||
| "authorship_tag": "ABX9TyNXN1hI1PA52xiT8k/v0165", | ||
| "include_colab_link": true | ||
| }, | ||
| "kernelspec": { | ||
| "name": "python3", | ||
| "display_name": "Python 3" | ||
| } | ||
| }, | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": { | ||
| "id": "view-in-github", | ||
| "colab_type": "text" | ||
| }, | ||
| "source": [ | ||
| "<a href=\"https://colab.research.google.com/github/yohanesnuwara/reservoir-engineering/blob/master/Reservoir%20Simulation%20Ertekin/Unit%205%20Finite-Difference%20Approximation%20to%20Linear-Flow%20Equations/fd1d_linearflow.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": { | ||
| "id": "eOe4EUXrFd9G", | ||
| "colab_type": "text" | ||
| }, | ||
| "source": [ | ||
| "# **Unit 5 Finite-Difference Approximations to Linear-Flow Problems**\n", | ||
| "\n", | ||
| "## Explicit Formulation\n", | ||
| "\n", | ||
| "$$p_{i}^{n+1} = (\\frac{\\alpha_c B_l \\Delta t}{V_b \\phi c_l})_i \\cdot q_{lsc_i} + (\\frac{\\alpha_c B_l \\Delta t}{V_b \\phi c_l})_i \\cdot [T_{lx_{i+1/2}}^{n} p_{i+1}^{n}-(T_{lx_{i+1/2}}^{n} + T_{lx_{i-1/2}}^{n})p_{i}^{n}+T_{lx_{i-1/2}}p_{i-1}^{n}]$$\n", | ||
| "\n", | ||
| "In the following codes, $(\\frac{\\alpha_c B_l \\Delta t}{V_b \\phi c_l})_i$ will be written as `factor`" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "metadata": { | ||
| "id": "IJsmLh1xKz8S", | ||
| "colab_type": "code", | ||
| "colab": {} | ||
| }, | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "import matplotlib.pyplot as plt\n", | ||
| "import pandas as pd" | ||
| ], | ||
| "execution_count": 0, | ||
| "outputs": [] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "metadata": { | ||
| "id": "rJZBuBCVK6JV", | ||
| "colab_type": "code", | ||
| "colab": { | ||
| "base_uri": "https://localhost:8080/", | ||
| "height": 134 | ||
| }, | ||
| "outputId": "e871c872-7bd9-49e5-f833-63db4056e97e" | ||
| }, | ||
| "source": [ | ||
| "!git clone https://github.com/yohanesnuwara/reservoir-engineering" | ||
| ], | ||
| "execution_count": 2, | ||
| "outputs": [ | ||
| { | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "Cloning into 'reservoir-engineering'...\n", | ||
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| "remote: Compressing objects: 100% (134/134), done.\u001b[K\n", | ||
| "remote: Total 845 (delta 49), reused 0 (delta 0), pack-reused 696\u001b[K\n", | ||
| "Receiving objects: 100% (845/845), 4.95 MiB | 30.33 MiB/s, done.\n", | ||
| "Resolving deltas: 100% (347/347), done.\n" | ||
| ], | ||
| "name": "stdout" | ||
| } | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": { | ||
| "id": "N-NT2lf1GKb3", | ||
| "colab_type": "text" | ||
| }, | ||
| "source": [ | ||
| "## Example 5.8 \n", | ||
| "\n", | ||
| "" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "metadata": { | ||
| "id": "dLVKK7xd7fGK", | ||
| "colab_type": "code", | ||
| "colab": {} | ||
| }, | ||
| "source": [ | ||
| "\"Task. determine pressure distribution during first year of production with timestep 10 days\"\n", | ||
| "\n", | ||
| "# known\n", | ||
| "pi = 6000 # initial pressure, in psia\n", | ||
| "delta_x = 1000 # ft\n", | ||
| "delta_y = 1000\n", | ||
| "delta_z = 75\n", | ||
| "B = 1 # phase FVF, assumed constant over pressure, rb/stb\n", | ||
| "c = 3.5E-06 # phase compressibility, psi^-1\n", | ||
| "k_x = 15 # perm in x direction, md\n", | ||
| "poro = 0.18\n", | ||
| "mu = 10 # phase viscosity, cp\n", | ||
| "\n", | ||
| "delta_t = 10 # days\n", | ||
| "qsc = -150 # minus means production, stb/d\n", | ||
| "\n", | ||
| "# calculate " | ||
| ], | ||
| "execution_count": 0, | ||
| "outputs": [] | ||
| } | ||
| ] | ||
| } |