11_two_dimensional_filtration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Неявное решение уравнения фильтрации однофазной жидкости в двухмерном пласте\n",
    "\n",
    "Муравцев Александр. Вариант 16\n",
    "\n",
    "В данной Jupyter-тетради допушены ошибки в рассуждениях и решении. Основная ошибка: проницаемость в уравнении пьезопроводности вынесена из производной по координате, но в данной задаче это недопустимо, ведь проницаемость зависит от координаты.\n",
    "\n",
    "Верное решение (с составлением матриц проницаемости и проводимости) представлено по ссылке: [Неявное решение однофазной 2D фильтрации](https://github.com/mualal/notebooks-source/blob/master/12_two_dimensional_filtration.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.matrices import Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Задание значений входных параметров и перевод единиц измерения в СИ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesh_x_count = 4  # количество ячеек по пространству в направлении оси Ox\n",
    "mesh_y_count = 4  # количество ячеек по пространству в направлении оси Oy\n",
    "mesh_t_count = 5  # количество шагов по времени"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 10  # сут, временной шаг\n",
    "dt *= 24 * 60 * 60  # с, временной шаг\n",
    "\n",
    "m = 0.18  # пористость\n",
    "\n",
    "mu = 4  # мПа*с, вязкость жидкости\n",
    "mu *= 1e-3  # Па*с, вязкость жидкости\n",
    "\n",
    "k = np.array([\n",
    "    [30.0, 30.0, 30.0, 30.0],\n",
    "    [30.0, 40.0, 40.0, 40.0],\n",
    "    [30.0, 40.0, 40.0, 50.0],\n",
    "    [30.0, 40.0, 50.0, 40.0]\n",
    "])  # мД, проницаемость\n",
    "k *= 1e-3 * (1e-6) ** 2  # м^2, проницаемость\n",
    "\n",
    "dx = 100  # м, ширина ячейки по оси Ox\n",
    "dy = 100  # м, ширина ячейки по оси Oy\n",
    "\n",
    "h = 50  # м, толщина пласта\n",
    "\n",
    "b_liq = 1  # м^3/м^3, объёмный коэффициент жидкости\n",
    "\n",
    "compr = 2.2e-9  # Па^(-1), общая сжимаемость\n",
    "\n",
    "p_initial = 20  # МПа, начальное пластовое давление\n",
    "p_initial *= 1e6  # Па, начальное пластовое давление\n",
    "\n",
    "q_inj = 40  # м^3/сут, расход нагнетательной скважины в поверхностных условиях\n",
    "q_inj /= (24 * 60 * 60)  # м^3/с, расход нагнетательной скважины в поверхностных условиях\n",
    "\n",
    "q_prod = 40  # м^3/сут, дебит добывающей скважины в поверхностных условиях\n",
    "q_prod /= (24 * 60 * 60)  # м^3/с, дебит добывающей скважины в поверхностных условиях"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# безразмерные множители, входящие в формулы неяного метода\n",
    "gamma = (m * mu * compr / k) * (dx ** 2 / dt)\n",
    "beta = (dx / dy) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Запись конечно-разностного уравнения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Конечно-разностное уравнение 2D-фильтрации:\n",
    "\n",
    "$$\\frac{P_{i+1,j}^{t+\\Delta t}-2P_{i,j}^{t+\\Delta t}+P_{i-1,j}^{t+\\Delta t}}{\\left(\\Delta x\\right)^2}+\\frac{P_{i, j+1}^{t+\\Delta t}-2P_{i,j}^{t+\\Delta t}+P_{i,j-1}^{t+\\Delta t}}{\\left(\\Delta y\\right)^2}=\\left(\\frac{m\\mu c}{k_{i,j}}\\right)\\frac{P_{i,j}^{t+\\Delta t}-P_{i,j}^{t}}{\\Delta t}$$\n",
    "\n",
    "Приведём подобные и перепишем в следующем виде:\n",
    "\n",
    "$$e_{i,j}P_{i,j-1}^{t+\\Delta t}+a_{i,j}P_{i-1,j}^{t+\\Delta t}+b_{i,j}P_{i,j}^{t+\\Delta t}+c_{i,j}P_{i+1,j}^{t+\\Delta t}+f_{i,j}P_{i,j+1}^{t+\\Delta t}=d_{i,j},$$\n",
    "\n",
    "где $e_{i,j}=\\beta$; $a_{i,j}=1$; $b_{i,j}=-2-2\\beta-\\gamma_{i,j}$; $c_{i,j}=1$; $f_{i,j}=\\beta$; $d_{i,j}=-\\gamma_{i,j} P_{i,j}^t$; \n",
    "\n",
    "$\\beta=\\left(\\dfrac{\\Delta x}{\\Delta y}\\right)^2$; $\\gamma_{i,j}=\\left(\\dfrac{m\\mu c}{k_{i,j}}\\right)\\dfrac{\\left(\\Delta x\\right)^2}{\\Delta t}$\n",
    "\n",
    "Коэффициенты получены для всех ячеек за исключением граничных ячеек и за исключением ячеек со скважинами."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Матрица системы и левые части уравнений в символьном виде"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Нумерация ячеек пласта:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 2 & 3\\\\4 & 5 & 6 & 7\\\\8 & 9 & 10 & 11\\\\12 & 13 & 14 & 15\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 0,  1,  2,  3],\n",
       "[ 4,  5,  6,  7],\n",
       "[ 8,  9, 10, 11],\n",
       "[12, 13, 14, 15]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Матрица СЛАУ:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{array}{cccccccccccccccc}b_{00} & f_{00} & 0 & 0 & c_{00} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\e_{01} & b_{01} & f_{01} & 0 & 0 & c_{01} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & e_{02} & b_{02} & f_{02} & 0 & 0 & c_{02} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & e_{03} & b_{03} & f_{03} & 0 & 0 & c_{03} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\a_{10} & 0 & 0 & e_{10} & b_{10} & f_{10} & 0 & 0 & c_{10} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & a_{11} & 0 & 0 & e_{11} & b_{11} & f_{11} & 0 & 0 & c_{11} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & a_{12} & 0 & 0 & e_{12} & b_{12} & f_{12} & 0 & 0 & c_{12} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & a_{13} & 0 & 0 & e_{13} & b_{13} & f_{13} & 0 & 0 & c_{13} & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & a_{20} & 0 & 0 & e_{20} & b_{20} & f_{20} & 0 & 0 & c_{20} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & a_{21} & 0 & 0 & e_{21} & b_{21} & f_{21} & 0 & 0 & c_{21} & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & a_{22} & 0 & 0 & e_{22} & b_{22} & f_{22} & 0 & 0 & c_{22} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & a_{23} & 0 & 0 & e_{23} & b_{23} & f_{23} & 0 & 0 & c_{23}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & a_{30} & 0 & 0 & e_{30} & b_{30} & f_{30} & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & a_{31} & 0 & 0 & e_{31} & b_{31} & f_{31} & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & a_{32} & 0 & 0 & e_{32} & b_{32} & f_{32}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & a_{33} & 0 & 0 & e_{33} & b_{33}\\end{array}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[b_00, f_00,    0,    0, c_00,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0],\n",
       "[e_01, b_01, f_01,    0,    0, c_01,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0],\n",
       "[   0, e_02, b_02, f_02,    0,    0, c_02,    0,    0,    0,    0,    0,    0,    0,    0,    0],\n",
       "[   0,    0, e_03, b_03, f_03,    0,    0, c_03,    0,    0,    0,    0,    0,    0,    0,    0],\n",
       "[a_10,    0,    0, e_10, b_10, f_10,    0,    0, c_10,    0,    0,    0,    0,    0,    0,    0],\n",
       "[   0, a_11,    0,    0, e_11, b_11, f_11,    0,    0, c_11,    0,    0,    0,    0,    0,    0],\n",
       "[   0,    0, a_12,    0,    0, e_12, b_12, f_12,    0,    0, c_12,    0,    0,    0,    0,    0],\n",
       "[   0,    0,    0, a_13,    0,    0, e_13, b_13, f_13,    0,    0, c_13,    0,    0,    0,    0],\n",
       "[   0,    0,    0,    0, a_20,    0,    0, e_20, b_20, f_20,    0,    0, c_20,    0,    0,    0],\n",
       "[   0,    0,    0,    0,    0, a_21,    0,    0, e_21, b_21, f_21,    0,    0, c_21,    0,    0],\n",
       "[   0,    0,    0,    0,    0,    0, a_22,    0,    0, e_22, b_22, f_22,    0,    0, c_22,    0],\n",
       "[   0,    0,    0,    0,    0,    0,    0, a_23,    0,    0, e_23, b_23, f_23,    0,    0, c_23],\n",
       "[   0,    0,    0,    0,    0,    0,    0,    0, a_30,    0,    0, e_30, b_30, f_30,    0,    0],\n",
       "[   0,    0,    0,    0,    0,    0,    0,    0,    0, a_31,    0,    0, e_31, b_31, f_31,    0],\n",
       "[   0,    0,    0,    0,    0,    0,    0,    0,    0,    0, a_32,    0,    0, e_32, b_32, f_32],\n",
       "[   0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0, a_33,    0,    0, e_33, b_33]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Левая часть СЛАУ (после перемножения матрицы на столбец):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}P_{00} b_{00} + P_{01} f_{00} + P_{10} c_{00}\\\\P_{00} e_{01} + P_{01} b_{01} + P_{02} f_{01} + P_{11} c_{01}\\\\P_{01} e_{02} + P_{02} b_{02} + P_{03} f_{02} + P_{12} c_{02}\\\\P_{02} e_{03} + P_{03} b_{03} + P_{10} f_{03} + P_{13} c_{03}\\\\P_{00} a_{10} + P_{03} e_{10} + P_{10} b_{10} + P_{11} f_{10} + P_{20} c_{10}\\\\P_{01} a_{11} + P_{10} e_{11} + P_{11} b_{11} + P_{12} f_{11} + P_{21} c_{11}\\\\P_{02} a_{12} + P_{11} e_{12} + P_{12} b_{12} + P_{13} f_{12} + P_{22} c_{12}\\\\P_{03} a_{13} + P_{12} e_{13} + P_{13} b_{13} + P_{20} f_{13} + P_{23} c_{13}\\\\P_{10} a_{20} + P_{13} e_{20} + P_{20} b_{20} + P_{21} f_{20} + P_{30} c_{20}\\\\P_{11} a_{21} + P_{20} e_{21} + P_{21} b_{21} + P_{22} f_{21} + P_{31} c_{21}\\\\P_{12} a_{22} + P_{21} e_{22} + P_{22} b_{22} + P_{23} f_{22} + P_{32} c_{22}\\\\P_{13} a_{23} + P_{22} e_{23} + P_{23} b_{23} + P_{30} f_{23} + P_{33} c_{23}\\\\P_{20} a_{30} + P_{23} e_{30} + P_{30} b_{30} + P_{31} f_{30}\\\\P_{21} a_{31} + P_{30} e_{31} + P_{31} b_{31} + P_{32} f_{31}\\\\P_{22} a_{32} + P_{31} e_{32} + P_{32} b_{32} + P_{33} f_{32}\\\\P_{23} a_{33} + P_{32} e_{33} + P_{33} b_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                        P_00*b_00 + P_01*f_00 + P_10*c_00],\n",
       "[            P_00*e_01 + P_01*b_01 + P_02*f_01 + P_11*c_01],\n",
       "[            P_01*e_02 + P_02*b_02 + P_03*f_02 + P_12*c_02],\n",
       "[            P_02*e_03 + P_03*b_03 + P_10*f_03 + P_13*c_03],\n",
       "[P_00*a_10 + P_03*e_10 + P_10*b_10 + P_11*f_10 + P_20*c_10],\n",
       "[P_01*a_11 + P_10*e_11 + P_11*b_11 + P_12*f_11 + P_21*c_11],\n",
       "[P_02*a_12 + P_11*e_12 + P_12*b_12 + P_13*f_12 + P_22*c_12],\n",
       "[P_03*a_13 + P_12*e_13 + P_13*b_13 + P_20*f_13 + P_23*c_13],\n",
       "[P_10*a_20 + P_13*e_20 + P_20*b_20 + P_21*f_20 + P_30*c_20],\n",
       "[P_11*a_21 + P_20*e_21 + P_21*b_21 + P_22*f_21 + P_31*c_21],\n",
       "[P_12*a_22 + P_21*e_22 + P_22*b_22 + P_23*f_22 + P_32*c_22],\n",
       "[P_13*a_23 + P_22*e_23 + P_23*b_23 + P_30*f_23 + P_33*c_23],\n",
       "[            P_20*a_30 + P_23*e_30 + P_30*b_30 + P_31*f_30],\n",
       "[            P_21*a_31 + P_30*e_31 + P_31*b_31 + P_32*f_31],\n",
       "[            P_22*a_32 + P_31*e_32 + P_32*b_32 + P_33*f_32],\n",
       "[                        P_23*a_33 + P_32*e_33 + P_33*b_33]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cells_numbering = Matrix([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]])\n",
    "\n",
    "\n",
    "square_matrix = Matrix(\n",
    "    [['b_00', 'f_00', 0, 0, 'c_00', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "     ['e_01', 'b_01', 'f_01', 0, 0, 'c_01', 0, 0 ,0 ,0 ,0 ,0 ,0 ,0, 0, 0],\n",
    "     [0, 'e_02', 'b_02', 'f_02', 0, 0, 'c_02', 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "     [0 ,0, 'e_03', 'b_03', 'f_03', 0, 0, 'c_03', 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "     ['a_10', 0, 0, 'e_10', 'b_10', 'f_10', 0, 0, 'c_10', 0, 0, 0, 0, 0, 0, 0],\n",
    "     [0, 'a_11', 0, 0, 'e_11', 'b_11', 'f_11', 0, 0, 'c_11', 0, 0, 0, 0, 0, 0],\n",
    "     [0, 0, 'a_12', 0, 0, 'e_12', 'b_12', 'f_12', 0, 0, 'c_12', 0, 0, 0, 0, 0],\n",
    "     [0, 0, 0, 'a_13', 0, 0, 'e_13', 'b_13', 'f_13', 0, 0, 'c_13', 0, 0, 0, 0],\n",
    "     [0, 0, 0, 0, 'a_20', 0, 0, 'e_20', 'b_20', 'f_20', 0, 0, 'c_20', 0, 0, 0],\n",
    "     [0, 0, 0, 0, 0, 'a_21', 0, 0, 'e_21', 'b_21', 'f_21', 0, 0, 'c_21', 0, 0],\n",
    "     [0 ,0, 0, 0, 0, 0, 'a_22', 0, 0, 'e_22', 'b_22', 'f_22', 0, 0, 'c_22', 0],\n",
    "     [0, 0, 0, 0, 0, 0, 0, 'a_23', 0, 0, 'e_23', 'b_23', 'f_23', 0, 0, 'c_23'],\n",
    "     [0, 0, 0, 0, 0, 0, 0, 0, 'a_30', 0, 0, 'e_30', 'b_30', 'f_30', 0, 0],\n",
    "     [0, 0, 0, 0, 0, 0, 0, 0, 0, 'a_31', 0, 0, 'e_31', 'b_31', 'f_31', 0],\n",
    "     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 'a_32', 0, 0, 'e_32', 'b_32', 'f_32'],\n",
    "     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 'a_33', 0, 0, 'e_33', 'b_33'],\n",
    "     ]\n",
    ")\n",
    "        \n",
    "pressures_vector = Matrix(\n",
    "    [['P_00'], ['P_01'], ['P_02'], ['P_03'],\n",
    "     ['P_10'], ['P_11'], ['P_12'], ['P_13'],\n",
    "     ['P_20'], ['P_21'], ['P_22'], ['P_23'],\n",
    "     ['P_30'], ['P_31'], ['P_32'], ['P_33']]\n",
    ")\n",
    "\n",
    "print('Нумерация ячеек пласта:')\n",
    "display(cells_numbering)\n",
    "print('Матрица СЛАУ:')\n",
    "display(square_matrix)\n",
    "print('Левая часть СЛАУ (после перемножения матрицы на столбец):')\n",
    "display(square_matrix * pressures_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Запись граничных условий на скважинах"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для добывающей скважины:\n",
    "\n",
    "$$\\frac{P_{0,2}^{t+\\Delta t}-P_{0,3}^{t+\\Delta t}}{\\left(\\Delta x\\right)^2}+\\frac{P_{1,3}^{t+\\Delta t}-P_{0,3}^{t+\\Delta t}}{\\left(\\Delta y\\right)^2}-Q_{prod}\\frac{\\mu}{\\Delta x\\cdot A\\cdot k_{0,3}}=\\left(\\dfrac{m\\mu c}{k_{0,3}}\\right)\\frac{P_{0,3}^{t+\\Delta t}-P_{0,3}^{t}}{\\Delta t}$$\n",
    "\n",
    "домножим на $\\left(\\Delta x\\right)^2$:\n",
    "\n",
    "$$P_{0,2}^{t+\\Delta t}-P_{0,3}^{t+\\Delta t}+\\beta\\left(P_{1,3}^{t+\\Delta t}-P_{0,3}^{t+\\Delta t}\\right)-Q_{prod}\\frac{\\mu}{h\\cdot k_{0,3}}=\\gamma_{0,3}\\left(P_{0,3}^{t+\\Delta t}-P_{0,3}^{t}\\right)$$\n",
    "\n",
    "Таким образом, $e_{0,3}=1$; $a_{0,3}=0$; $b_{0,3}=-1-\\beta-\\gamma_{0,3}$; $c_{0,3}=\\beta$; $f_{0,3}=0$; $d_{0,3}=-\\gamma_{0,3}P_{0,3}^{t}+Q_{prod}\\dfrac{\\mu}{h\\cdot k_{0,3}}$\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для нагнетательной скважины:\n",
    "\n",
    "$$\\frac{P_{3,1}^{t+\\Delta t}-P_{3,0}^{t+\\Delta t}}{\\left(\\Delta x\\right)^2}+\\frac{P_{2,0}^{t+\\Delta t}-P_{3,0}^{t+\\Delta t}}{\\left(\\Delta y\\right)^2}+Q_{inj}\\frac{\\mu}{\\Delta x\\cdot A\\cdot k_{3,0}}=\\left(\\dfrac{m\\mu c}{k_{3,0}}\\right)\\frac{P_{3,0}^{t+\\Delta t}-P_{3,0}^{t}}{\\Delta t}$$\n",
    "\n",
    "домножим на $\\left(\\Delta x\\right)^2$:\n",
    "\n",
    "$$P_{3,1}^{t+\\Delta t}-P_{3,0}^{t+\\Delta t}+\\beta\\left(P_{2,0}^{t+\\Delta t}-P_{3,0}^{t+\\Delta t}\\right)+Q_{inj}\\frac{\\mu}{h\\cdot k_{3,0}}=\\gamma_{3,0}\\left(P_{3,0}^{t+\\Delta t}-P_{3,0}^{t}\\right)$$\n",
    "\n",
    "Таким образом, $e_{3,0}=0$; $a_{3,0}=\\beta$; $b_{3,0}=-1-\\beta-\\gamma_{3,0}$; $c_{3,0}=0$; $f_{3,0}=1$; $d_{3,0}=-\\gamma_{3,0}P_{3,0}^{t}-Q_{inj}\\dfrac{\\mu}{h\\cdot k_{3,0}}$\n",
    "\n",
    "---\n",
    "\n",
    "Далее эти коэффициенты будут прописаны в коде (в ячейках с соответствующими скважинами)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Задание начальных и граничных условий. Решение системы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# список, в который будут добавляться поля давлений на каждом временном шаге\n",
    "p = []\n",
    "p.append(np.full((mesh_x_count, mesh_y_count), p_initial))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "for time_step in range(mesh_t_count):\n",
    "    \n",
    "    system_matrix = np.zeros((mesh_x_count * mesh_y_count, mesh_x_count * mesh_y_count))\n",
    "    d = np.zeros(mesh_x_count * mesh_y_count)\n",
    "\n",
    "    # базовые условия из уравнения пьезопроводности, записанном в конечно-разностном виде\n",
    "    for i in range(mesh_x_count):\n",
    "        for j in range(mesh_x_count):\n",
    "            system_matrix[i * mesh_x_count + j, i * mesh_x_count + j] = -2 - 2 * beta - gamma[i, j]\n",
    "            d[i * mesh_x_count + j] = -gamma[i, j] * p[-1][i, j] \n",
    "    system_matrix += np.diag([beta] * (mesh_x_count * mesh_y_count - 1), k=-1)\n",
    "    system_matrix += np.diag([beta] * (mesh_x_count * mesh_y_count - 1), k=1)\n",
    "    system_matrix += np.diag([1] * (mesh_y_count * mesh_x_count - mesh_x_count), k=mesh_x_count)\n",
    "    system_matrix += np.diag([1] * (mesh_y_count * mesh_x_count - mesh_x_count), k=-mesh_x_count)\n",
    "\n",
    "    # условия, устраняющие связь последних ячеек в ряду с первой ячейкой в следующем ряду\n",
    "    system_matrix[3, 4] = 0\n",
    "    system_matrix[4, 3] = 0\n",
    "    system_matrix[7, 8] = 0\n",
    "    system_matrix[8, 7] = 0\n",
    "    system_matrix[11, 12] = 0\n",
    "    system_matrix[12, 11] = 0\n",
    "\n",
    "    # ГУ в ячейке 3 (добывающая скважина) -- при нумерации ячеек с нуля\n",
    "    system_matrix[3, 2] = 1\n",
    "    system_matrix[3, 3] = -1 - beta - gamma[0, 3]\n",
    "    system_matrix[3, 7] = beta\n",
    "    system_matrix[3, 4] = 0\n",
    "    d[3] = -gamma[0, 3] * p[-1][0, 3] + q_prod * mu / (h * k[0, 3])\n",
    "\n",
    "    # ГУ в ячейке 12 (нагнетательная скважина) -- при нумерации ячеек с нуля\n",
    "    system_matrix[12, 11] = 0\n",
    "    system_matrix[12, 8] = 1\n",
    "    system_matrix[12, 12] = -1 - beta - gamma[3, 0]\n",
    "    system_matrix[12, 13] = beta\n",
    "    d[12] = -gamma[3, 0] * p[-1][3, 0] - q_inj * mu / (h * k[3, 0])\n",
    "\n",
    "    # решение системы\n",
    "    p.append(np.linalg.solve(system_matrix, d).reshape(mesh_x_count, mesh_y_count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Вывод результатов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, field in enumerate(p):\n",
    "    plt.figure()\n",
    "    plt.title(f'Шаг по времени: {i}')\n",
    "    plt.imshow(field / 1e6)\n",
    "    plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Неудавшаяся попытка поставить условия неперетока"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qKN+I6ANtXhYT27cBT4+T5ATgChfuBPYd6dWJiMHX0DPASTdZzwBnAes69ofKYxtGJ5S0iKKWyLT9thnyFxF9xojhAZ0QdbJK3a3u2/XfA9tLbM+zPW/annvu4GJFRBNcces3k1UDHALmdOzPBtZPUt4RsSN5cOcDnKwa4FLg42Vv8Hzg2ZGxfRGxExjQKmAjNUBJVwMLKAY6DwFfBaYD2F4MLKN4X2ct8Bvgk03kGxH9YVBrgI0EQNsn9zhv4Iwm8oqI/mJgeLjFATAiWsxAm2uAEdFu/fiOXxUJgBFRXwJgRLRTf47zrSIBMCLqSw0wIlrJ4PQCR0R7JQBGRFulCRwRrZUAGBGtlBehI6LN8iJ0RLRXeoEjoq2UGmBEtFKfzvVXRQJgRNSkdIJERIulBhgRrTU81QXYPgmAEVHPAL8H2MiiSJIulbRR0gNjnF8g6VlJq8rtK03kGxH9Qa62jXsPaY6kWyStkbRa0pnl8f0lLZf0SPnZdcFwScdKeljSWklnVyl3U6vCXQYc2yPNT2y/s9y+3lC+EdEPmlkVbgvwedtvAeYDZ0h6K3A2cLPtucDN5f4rSJoGfBs4DngrcHJ57bgaCYC2bwOebuJeEdFOtjfYXll+fw5YA8wCTgAuL5NdDny4y+VHAGttP2r7JeC75XXjmqx1gQGOlHSvpBslvW2sRJIWSVohacXW55+fxOJFxPaaQBN4xsjf73Jb1PV+0iHA4cBdwEEj64iXnwd2uWQWsK5jf6g8Nq7J6gRZCbze9mZJC4HvA3O7JbS9BFgCsPucOQPauR7RImYiQ+GetD1vvASS9gKuA86yvUmqdO9uiXrGj0mpAdreZHtz+X0ZMF3SjMnIOyImQTPPAJE0nSL4XWX7+vLwE5JmludnAhu7XDoEzOnYnw2s75XfpARASa9VGcYlHVHm+9Rk5B0RO15DvcACLgHW2D6v49RS4NTy+6nAD7pcfjcwV9IbJO0GnFReN65GmsCSrgYWULTvh4CvAtMBbC8GPgp8WtIW4AXgJHtQJ9CJiG0087f5KOAU4H5Jq8pj5wDnAtdIOg14HDgRQNLBwMW2F9reIukzwE3ANOBS26t7ZdhIALR9co/zFwIXNpFXRPShBgKg7dsZe3GRo7ukXw8s7NhfBiybSJ4ZCRIRtVRp3varBMCIqC8TokZEW6UGGBHtlQAYEa2UZ4AR0WoJgBHRVhrQCVEnczKEiIi+khpgRNSXJnBEtFI6QSKi1RIAI6K1EgAjoo3E4PYCJwBGRD15BhgRrZYAGBGtlQAYEW2VJnBEtNeABsDaQ+EkzZF0i6Q1klZLOrNLGkm6QNJaSfdJelfdfCOiT7joBa6y9ZsmaoBbgM/bXilpb+AeScttP9iR5jiKdYDnAu8GLio/I2Jn0NYaoO0NtleW358D1rDtiuwnAFe4cCew78g6nxEx+JpYFnMqNDobjKRDgMOBu0admgWs69gfYtsgOXKPRZJWSFqx9fnnmyxeROwoDS2MPtkaC4CS9qJY0f0s25tGn+5ySdc/DttLbM+zPW/anns2VbyI2FGqBr8+DIBNLYw+nSL4XWX7+i5JhoA5HfuzgfVN5B0RU0v0Z/O2iiZ6gQVcAqyxfd4YyZYCHy97g+cDz9reUDfviOgPg/oMsIka4FHAKcD9klaVx84BXgdgezHFau0LgbXAb4BPNpBvRPSLPgxuVdQOgLZvp/szvs40Bs6om1dE9KkBDYBZEyQi6qnY/K3SBJZ0qaSNkh7oOHaYpDsk3S/ph5L2GePaz5WDMR6QdLWkPXrllwAYEfU11wt8GXDsqGMXA2fbfgfwPeCLoy+SNAv4M2Ce7bcD04CTemWWABgRtTU1FM72bcDTow4fCtxWfl8OfGSMy3cFXiVpV+DVVHjTJAEwImqbQBN4xshAh3JbVOH2DwAfKr+fyCtfqQPA9i+AbwKPAxso3jT5371unAAYEfVM7EXoJ0cGOpTbkgo5fAo4Q9I9wN7AS6MTSNqPYsjtG4CDgT0lfazXjRMAI6K+HTgSxPZDtt9v+/eBq4F/6pLsGOCfbf/K9svA9cC/7XXvBMCIqGVkJMiOehFa0oHl5y7Al4HFXZI9DsyX9OpycMbRFBOzjCsBMCJq07ArbT3vI10N3AEcKmlI0mnAyZJ+DjxE0bHxnTLtwZKWAdi+C7gWWAncTxHbejavMyN0RNTT4EQHtk8e49T5XdKupxhhNrL/VeCrE8kvATAiauvHcb5VJABGRH0JgBHRVqkBRkR7JQBGRCu5P1d8qyIBMCJqGeQZoRMAI6I+D2YETACMiNpSA4yIdurTFd+qaGJRpDmSbpG0ppyN9cwuaRZIelbSqnL7St18I6J/NDUf4GRroga4Bfi87ZWS9gbukbTc9oOj0v3E9vEN5BcRfaYfg1sVTSyKtIFiAkJsPydpDTALGB0AI2JnZNIJAiDpEOBw4K4up4+UdC/FbA5fsL16jHssAhYBvG7WrvzTSd1mvhls/+q7p091ESIaNaidII1NhyVpL+A64Czbm0adXgm83vZhwN8B3x/rPraXjMwWe8DvTWuqeBGxI+3ACVF3pEYCoKTpFMHvKtvXjz5ve5PtzeX3ZcB0STOayDsiptaOnhB1R6rdBC5nX70EWGP7vDHSvBZ4wrYlHUEReJ+qm3dE9AFXm+y0HzXxDPAo4BTgfkmrymPnAK8DsL0Y+CjwaUlbgBeAk+wBfWoaEdsa0L/NTfQC305RCx4vzYXAhXXzioj+1I/N2yoyEiQi6jHQ4iZwRLTdYMa/BMCIqC9N4IhorTb3AkdEm/XpS85VJABGRC3Fi9CDGQETACOivrbOBhMRMag1wMYmQ4iIlqo6EUKFGCnpUkkbJT3QcewwSXdIul/SDyXtM8a1+0q6VtJD5QTNR/bKLwEwImoqxgJX2Sq4DDh21LGLgbNtvwP4HvDFMa49H/iR7X8NHAas6ZVZAmBE1GdX23rexrcBT486fChwW/l9OfCR0deVtcL3UEzMgu2XbD/TK78EwIioxxNaE2SGpBUd26IKOTwAfKj8fiIwp0uaNwK/Ar4j6WeSLpa0Z68bJwBGRH3Va4BPjkx4XG5LKtz9U8AZku4B9gZe6pJmV+BdwEW2DweeB87udeP0AkdEfTuwE9j2Q8D7ASS9Gfhgl2RDwJDtkeU4rqVCAEwNMCJq0/BwpW277i0dWH7uAnwZ2GahINu/BNZJOrQ8dDQVFmZLAIyIekzxInSVrQdJVwN3AIdKGpJ0GnCypJ8DD1EsqvadMu3BkpZ1XP5Z4CpJ9wHvBL7RK780gSOiFuHGXoS2ffIYp87vknY9sLBjfxUwbyL5JQBGRH1tHQkiaQ9JP5V0r6TVkr7WJY0kXSBpraT7JL2rbr4R0Ucaeg9wsjVRA3wReK/tzeXymLdLutH2nR1pjgPmltu7gYvKz4gYdCPPAAdQE4siGdhc7k4vt9Gh/gTgijLtneWYvZm2N9TNPyKm3vb28E61phZGn1YuibkRWN7xLs6IWcC6jv2h8lhEDLyKzd8+bAI3EgBtb7X9TmA2cISkt49K0m3ZzK5/GpIWjQyT+dVTW5soXkTsSKbdAXBEOfj4VradzWGIV47fm03xPk+3eywZGSZzwO9Na7J4EbGjNPQe4GRrohf4AEn7lt9fBRxD8cJip6XAx8ve4PnAs3n+F7HzkF1p6zdN9ALPBC6XNI0ioF5j+wZJpwPYXgwso3hhcS3wG+CTDeQbEf2iD4NbFU30At8HHN7l+OKO7wbOqJtXRPQhG7b2Yfu2gowEiYj62loDjIhIAIyIdjJQbb2PvpMAGBE1GZxngBHRRiadIBHRYnkGGBGtlQAYEe3Un+N8q0gAjIh6DAzodFgJgBFRX2qAEdFOGQoXEW1lcN4DjIjWykiQiGitPAOMiFay0wscES2WGmBEtJPx1sFcwKzRRZEiooVGpsOqsvUg6VJJGyU90HHsMEl3SLpf0g8l7TPO9dMk/UzSDVWKngAYEfV5uNrW22Vsu6rkxcDZtt8BfA/44jjXnwmsqVrsJlaF20PSTyXdK2m1pK91SbNA0rOSVpXbV+rmGxH9wYCHXWnreS/7NuDpUYcPBW4rvy8HPtLtWkmzgQ9SBMxKmngG+CLwXtubJU0Hbpd0o+07R6X7ie3jG8gvIvqJJzQh6gxJKzr2l9he0uOaB4APAT8ATuSVa4x3+hbw58DeVQvTxKpwBjaXu9PLbTC7hCJiu0ygE+RJ2/MmePtPAReULcelwEujE0g6Htho+x5JC6reuJFe4HJN4HuANwHftn1Xl2RHSroXWA98wfbqMe61CFhU7m6eNnPtw02UsYIZwJOTk9UXJiebwiT+rkm1s/4umNzf9vq6N3iOX9/0Y187o2LyCf8u2w8B7weQ9GaKZu5oRwEfkrQQ2APYR9KVtj823r3lBt/fkbQvxUPKz9ru7MXZBxgum8kLgfNtz20s4wZIWrEd/zL1vfyuwbMz/7YqJB0C3GD77eX+gbY3StqFopPkVtuXjnP9AopKVs9Hbo32Att+BriVUb04tjfZ3lx+XwZMl1T1X4yIaAlJVwN3AIdKGpJ0GnCypJ8DD1G0IL9Tpj1Y0rI6+dVuAks6AHjZ9jOSXgUcA/z1qDSvBZ6wbUlHUATep+rmHRE7F9snj3Hq/C5p1wMLuxy/laIi1lMTzwBnApeXzwF3Aa6xfYOk08vCLAY+Cnxa0hbgBeAkN9n2bkavnqhBld81eHbm39ZXGn0GGBExSDISJCJaKwEwIlqr9QFQ0rGSHpa0VtLZU12epnQbVL4zkDRH0i2S1pRDL8+c6jI1ocqQ0mheq58Blh03PwfeBwwBdwMn235wSgvWAEnvoRihc8XI+1Q7A0kzgZm2V0ram+IF/A8P+n8zSQL27BxSCpzZZUhpNKjtNcAjgLW2H7X9EvBd4IQpLlMjxhhUPvBsb7C9svz+HMXMH7OmtlT1uZAhpZOs7QFwFrCuY3+IneAvU1uUIwYOB7oNvRw45Vx2q4CNwPIxhpRGg9oeANXlWP7VHQCS9gKuA86yvWmqy9ME21ttvxOYDRwhaad5dNGv2h4Ah3jl1DqzKYbaRB8rn5FdB1xl+/qpLk/TxhpSGs1rewC8G5gr6Q2SdgNOophuJ/pU2VlwCbDG9nlTXZ6mSDqgnEyEjiGlD01poVqg1QHQ9hbgM8BNFA/Trxlrmq5BM8ag8p3BUcApwHs7ZhjfZjzoAJoJ3CLpPop/mJfbrrSuRWy/Vr8GExHt1uoaYES0WwJgRLRWAmBEtFYCYES0VgJgRLRWAmBEtFYCYES01v8HGObE2UJ4IA0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lMuWA7Ua8RESfMWLbgE6IOlGl7lX37fnvge3FtufYnjNl7713crEiogmuuPWbiaoBDgGzOvZnAusnKO+I2JkaagSZDBNVA1wGfESFecDTw0NbImIXMKBVwKa6wVwLzKcY5zcEXABMBbC9CFhO0Vy9lqIbzMeayDci+sOg1gAbCYC2Tx3jvIGzmsgrIvqLgW3bWhwAI6LFDLS5BhgR7daPffyqSACMiPoSACOinSpNdNCXEgAjor7UACOilQxOK3BEtFcCYES0VR6BI6K1EgAjopXSEToi2iwdoSOivdIKHBFtpdQAI6KV+nSuvyoSACOiJqURJCJaLDXAiGitbZNdgB2TABgR9QxwP8BGFkWSdIWkjZIeHOH8fElPS1pVbl9qIt+I6A9ytW3Ue0izJN0iaY2k1ZLOLo+/WtIKSQ+XP3suGC7peEk/l7RW0nlVyt3UqnBXAsePkebHto8st680lG9E9INmVoXbApxr+43APOAsSW8CzgNutj0buLncfxlJU4BvAicAbwJOLa8dVSMB0PZtwJNN3Csi2sn2Btsry8/PAGuAGcBJwNIy2VLg/T0unwustf2I7ReBb5fXjWoi3wG+Q9J9FAuif9b26l6JJC0EFgJMOaBnTTf62WC+ChrbgLZyjqmh7zWOjtDTJN3Tsb/Y9uLt7icdBhwF3AUcPLyOuO0Nkg7qcd8ZwLqO/SHg7WMVZqIC4ErgtbaflbQA+B4wu1fC8g9jMcCes2btqv/bRew6zHiGwm2yPWe0BJL2Aa4HzrG9Wap0716JxowfTb0DHJXtzbafLT8vB6ZKmjYReUfEBGjmHSCSplIEv2ts31AeflzS9PL8dGBjj0uHgFkd+zMpnjZHNSEBUNIhKsO4pLllvk9MRN4RsfM11Aos4HJgje2LOk4tA04vP58OfL/H5XcDsyW9TtIewCnldaNq5BFY0rXAfIrn+yHgAmAqgO1FwAeBT0raAjwPnGIP6gQ6EbGdZn6bjwZOAx6QtKo8dj5wIXCdpDOAx4CTASQdCiyxvcD2FkmfAm4CpgBXjNTO0KmRAGj71DHOXwpc2kReEdGHGgiAtm9n5Ga0Y3qkXw8s6NhfDiwfT54ZCRIRtVR5vO1XCYARUV8mRI2ItkoNMCLaKwEwIlop7wAjotUSACOirTSgE6JOyEiQiIh+lBpgRNSXR+CIaKU0gkREqyUARkRrJQBGRBuJwW0FTgCMiHryDjAiWi0BMCJaKwEwItoqj8AR0V4DGgBrD4WTNEvSLZLWSFot6eweaSTpEklrJd0v6W11842IPuGiFbjK1m+aqAFuAc61vVLSvsC9klbY/llHmhMo1gGeTbFY8WVUWLQ4IgZEW2uAtjfYXll+fgZYQ7FKe6eTgKtcuBPYf3idz4gYfE0sizkZGp0NRtJhwFHAXV2nZgDrOvaH2D5IDt9joaR7JN2z9bnnmixeROwsDS2MPtEaC4CS9qFY0f0c25u7T/e4pOcfh+3FtufYnjNl772bKl5E7CxVg18fBsCmFkafShH8rrF9Q48kQ8Csjv2ZwPom8o6IySX68/G2iiZagQVcDqyxfdEIyZYBHylbg+cBT9veUDfviOgPg/oOsIka4NHAacADklaVx84HXgNgexHFau0LgLXAb4CPNZBvRPSLPgxuVdQOgLZvp/c7vs40Bs6qm1dE9KmGAqCkK4ATgY2231IeOwJYBOwDPAp8qEc7A5I+A3yiLM0DwMds/8to+WVNkIiop+Ljb8VH4CuB47uOLQHOs/1W4LvA57ovkjQD+GNgThk4pwCnjJVZAmBE1NdQK7Dt24Anuw4fDtxWfl4BfGCEy3cHXiFpd+CVVGhoTQCMiNrGMRRu2nA/33JbWOH2DwLvKz+fzMt7lABg+5+BrwOPARsoGlr/91g3TgCMiNrG8Qi8abifb7ktrnD7jwNnSboX2Bd4cbv8pQMoRpy9DjgU2FvSh8e6cQJgRNSzkztC237I9rtt/x5wLfAPPZIdC/yj7V/Zfgm4Afj9se6dABgR9e3EACjpoPLnbsAXKVqEuz0GzJP0yrJv8jEU8xKMKgEwImoZHgnSRCuwpGuBO4DDJQ1JOgM4VdIvgIcoGja+VaY9VNJyANt3Ad8BVlJ0gdkNGPPxOhOiRkRt2tZMR0Dbp45w6uIeaddTDLAY3r8AuGA8+SUARkQ9fTrRQRUJgBFRWz+O860iATAi6ksAjIi2Sg0wItorATAiWsn9ueJbFQmAEVHLIM8InQAYEfV5MCNgAmBE1JYaYES00wB3hG5iUaRZkm6RtEbSakln90gzX9LTklaV25fq5hsR/WMc8wH2lSZqgFuAc22vlLQvcK+kFbZ/1pXux7ZPbCC/iOgz/RjcqmhiUaQNFDOwYvsZSWuAGUB3AIyIXZFJIwiApMOAo4C7epx+h6T7KKaz+azt1SPcYyGwEOA1M3bnH07pNfXXYPtX3z5zsosQ4zXquocDrKHvNaiNII3NByhpH+B64JweS9atBF5r+wjgr4HvjXQf24uHp8s+8HemNFW8iNiZduKEqDtTIwFQ0lSK4HeN7Ru6z9vebPvZ8vNyYKqkaU3kHRGTq8kJUSda7Ufgcvrpy4E1ti8aIc0hwOO2LWkuReB9om7eEdEH7MYmRJ1oTbwDPBo4DXhA0qry2PnAawBsLwI+CHxS0hbgeeAUe0DfmkbE9gb0t7mJVuDbGeNVqu1LgUvr5hUR/akfH2+ryEiQiKjHQIsfgSOi7QYz/iUARkR9eQSOiNZqcytwRLRZn3ZyriIBMCJqKTpCD2YETACMiPraOhtMRMSg1gAbmwwhIlqq6kQIFWKkpCskbZT0YMexIyTdIekBSX8rab8Rrt1f0nckPVRO0PyOsfJLAIyImoqxwFW2Cq4Eju86tgQ4z/Zbge8Cnxvh2ouBH9r+18ARwJqxMksAjIj67GrbmLfxbcCTXYcPB24rP68APtB9XVkrfCfFxCzYftH2U2PllwAYEfV4XGuCTJN0T8e2sEIODwLvKz+fDMzqkeZ3gV8B35L0U0lLJO091o0TACOivuo1wE3DEx6X2+IKd/84cJake4F9gRd7pNkdeBtwme2jgOeA88a6cVqBI6K+ndgIbPsh4N0Akt4AvLdHsiFgyPbwchzfoUIATA0wImrTtm2Vth26t3RQ+XM34IvAdgsF2f4lsE7S4eWhY6iwMFsCYETUY4qO0FW2MUi6FrgDOFzSkKQzgFMl/QJ4iGJRtW+VaQ+VtLzj8k8D10i6HzgS+NpY+eUROCJqEW6sI7TtU0c4dXGPtOuBBR37q4A548kvATAi6mvrSBBJe0n6iaT7JK2W9OUeaSTpEklrJd0v6W11842IPtJQP8CJ1kQN8AXgXbafLZfHvF3SD2zf2ZHmBGB2ub0duKz8GRGDbvgd4ABqYlEkA8+Wu1PLrTvUnwRcVaa9sxyzN932hrr5R8Tk29EW3snW1MLoU8olMTcCKzr64gybAazr2B8qj0XEwKv4+NuHj8CNBEDbW20fCcwE5kp6S1eSXstm9vzTkLRweJjMr57Y2kTxImJnMu0OgMPKwce3sv1sDkO8fPzeTIr+PL3usXh4mMyBvzOlyeJFxM7SUD/AidZEK/CBkvYvP78COJaiw2KnZcBHytbgecDTef8XseuQXWnrN020Ak8HlkqaQhFQr7N9o6QzAWwvApZTdFhcC/wG+FgD+UZEv+jD4FZFE63A9wNH9Ti+qOOzgbPq5hURfciGrX34fFtBRoJERH1trQFGRCQARkQ7Gai23kffSQCMiJoMzjvAiGgjk0aQiGixvAOMiNZKAIyIdurPcb5VJABGRD0GBnQ6rATAiKgvNcCIaKcMhYuItjI4/QAjorUyEiQiWivvACOiley0AkdEiw1oDbDRNUEioo2Mt26ttI1F0hWSNkp6sOPYEZLukPSApL+VtN8o10+R9FNJN1YpeQJgRNQzPB1WlW1sV7L9ompLgPNsvxX4LvC5Ua4/G1hTtegJgBFRn7dV28a6jX0b8GTX4cOB28rPK4AP9LpW0kzgvRQBs5ImVoXbS9JPJN0nabWkL/dIM1/S05JWlduX6uYbEf3BgLe50gZMG173u9wWVsjiQeB95eeTefkSu52+AfwJ41iAs4lGkBeAd9l+VtJU4HZJP7B9Z1e6H9s+sYH8IqKfeFwTom6yPWecOXwcuKSsOC0DXuxOIOlEYKPteyXNr3rjJlaFM/BsuTu13AazSSgidkiVBo4dvrf9EPBuAElvoHjM7XY08D5JC4C9gP0kXW37w6PdW26g+bpcE/he4PXAN21/vuv8fOB6YAhYD3zW9uoR7rUQGK4WHw78vHYBq5kGbJqgvCZSvtfgmcjv9lrbB9a5gaQfUpS5ik22uxs5uu93GHCj7beU+wfZ3ihpN4pGklttXzHK9fMpYsyYT5yNBMCOjPenaKX5tO3OZuz9gG3lY/IC4GLbsxvLuAGS7tmBqnnfy/caPLvydxuLpGuB+RQB9XHgAmAf/v+64jcAX7BtSYcCS2wv6LrHfCYjAJaZXwA8Z/vro6R5FJhju2/+Bd9V/6fL9xo8u/J36zdNtAIfWNb8kPQK4Fjgoa40h0hS+Xlume8TdfOOiKijiVbg6cDS8j3gbsB1tm+UdCaA7UXAB4FPStoCPA+c4qarnvUtnuwC7CT5XoNnV/5ufaXxR+CIiEGRkSAR0VoJgBHRWq0PgJKOl/RzSWslnTfZ5WlKr1k1dgWSZkm6RdKacujl2ZNdpiZUGVIazWv1O8Cy4eYXwHEUnbTvBk61/bNJLVgDJL2TYoTOVcMdSncFkqYD022vlLQvRQf89w/631nZS2LvziGlwNk9hpRGg9peA5wLrLX9iO0XgW8DJ01ymRoxwqwaA8/2Btsry8/PUEx9NGNyS1WfCxlSOsHaHgBnAOs69ofYBX6Z2qIcMnUUcNckF6UR5WSeq4CNwArbu8T36mdtD4DqcSz/6g4ASftQjC8/x/bmyS5PE2xvtX0kMBOYK2mXeXXRr9oeAId4+dxiMykma4g+Vr4jux64xvYNk12eptl+CriV7WdGjoa1PQDeDcyW9DpJewCnUMw3Fn2qbCy4HFhj+6LJLk9Tqgwpjea1OgDa3gJ8CriJ4mX6dSNN0zVoylk17gAOlzQk6YzJLlNDjgZOA97VMcP4grEuGgDTgVsk3U/xD/MK25UW9okd1+puMBHRbq2uAUZEuyUARkRrJQBGRGslAEZEayUARkRrJQBGRGslAEZEa/0/WTbZcoM/L6QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# список, в который будут добавляться поля давлений на каждом временном шаге\n",
    "p = []\n",
    "p.append(np.full((mesh_x_count, mesh_y_count), p_initial))\n",
    "\n",
    "\n",
    "for time_step in range(mesh_t_count):\n",
    "    \n",
    "    system_matrix = np.zeros((mesh_x_count * mesh_y_count, mesh_x_count * mesh_y_count))\n",
    "    d = np.zeros(mesh_x_count * mesh_y_count)\n",
    "\n",
    "    # базовые условия из уравнения пьезопроводности, записанном в конечно-разностном виде\n",
    "    for i in range(mesh_x_count):\n",
    "        for j in range(mesh_x_count):\n",
    "            system_matrix[i * mesh_x_count + j, i * mesh_x_count + j] = -2 - 2 * beta - gamma[i, j]\n",
    "            d[i * mesh_x_count + j] = -gamma[i, j] * p[-1][i, j] \n",
    "    system_matrix += np.diag([beta] * (mesh_x_count * mesh_y_count - 1), k=-1)\n",
    "    system_matrix += np.diag([beta] * (mesh_x_count * mesh_y_count - 1), k=1)\n",
    "    system_matrix += np.diag([1] * (mesh_y_count * mesh_x_count - mesh_x_count), k=mesh_x_count)\n",
    "    system_matrix += np.diag([1] * (mesh_y_count * mesh_x_count - mesh_x_count), k=-mesh_x_count)\n",
    "\n",
    "    # условия, устраняющие связь последних ячеек в ряду с первой ячейкой в следующем ряду\n",
    "    system_matrix[3, 4] = 0\n",
    "    system_matrix[4, 3] = 0\n",
    "    system_matrix[7, 8] = 0\n",
    "    system_matrix[8, 7] = 0\n",
    "    system_matrix[11, 12] = 0\n",
    "    system_matrix[12, 11] = 0\n",
    "\n",
    "    # ГУ в ячейке 3 (добывающая скважина) -- при нумерации ячеек с нуля\n",
    "    system_matrix[3, 2] = 1\n",
    "    system_matrix[3, 3] = -1 - beta - gamma[0, 3]\n",
    "    system_matrix[3, 7] = beta\n",
    "    system_matrix[3, 4] = 0\n",
    "    d[3] = -gamma[0, 3] * p[-1][0, 3] + q_prod * mu / (h * k[0, 3])\n",
    "\n",
    "    # ГУ в ячейке 12 (нагнетательная скважина) -- при нумерации ячеек с нуля\n",
    "    system_matrix[12, 11] = 0\n",
    "    system_matrix[12, 8] = 1\n",
    "    system_matrix[12, 12] = -1 - beta - gamma[3, 0]\n",
    "    system_matrix[12, 13] = beta\n",
    "    d[12] = -gamma[3, 0] * p[-1][3, 0] - q_inj * mu / (h * k[3, 0])\n",
    "\n",
    "    \n",
    "    # ГУ в ячейке 1 (условие неперетока)\n",
    "    system_matrix[1, 0] = 0\n",
    "    system_matrix[1, 1] = -1 - gamma[0, 1]\n",
    "    system_matrix[1, 5] = 1\n",
    "    system_matrix[1, 2] = 0\n",
    "\n",
    "    # ГУ в ячейке 2 (условие неперетока)\n",
    "    system_matrix[2, 1] = 0\n",
    "    system_matrix[2, 2] = -1 - gamma[0, 2]\n",
    "    system_matrix[2, 6] = 1\n",
    "    system_matrix[2, 3] = 0\n",
    "\n",
    "    # ГУ в ячейке 13 (условие неперетока)\n",
    "    system_matrix[13, 12] = 0\n",
    "    system_matrix[13, 9] = 1\n",
    "    system_matrix[13, 13] = -1 - gamma[3, 1]\n",
    "    system_matrix[13, 14] = 0\n",
    "\n",
    "    # ГУ в ячейке 14 (условие неперетока)\n",
    "    system_matrix[14, 13] = 0\n",
    "    system_matrix[14, 10] = 1\n",
    "    system_matrix[14, 14] = -1 - gamma[3, 2]\n",
    "    system_matrix[14, 15] = 0\n",
    "\n",
    "    # ГУ в ячейке 0 (условие неперетока)\n",
    "    system_matrix[0, 0] = -1 - beta - gamma[0, 0]\n",
    "    system_matrix[0, 4] = 1\n",
    "    system_matrix[0, 1] = beta\n",
    "\n",
    "    # ГУ в ячейке 15 (условие неперетока)\n",
    "    system_matrix[15, 14] = beta\n",
    "    system_matrix[15, 11] = 1\n",
    "    system_matrix[15, 15] = -1 - beta - gamma[3, 3]\n",
    "\n",
    "    # ГУ в ячейке 4 (условие неперетока)\n",
    "    system_matrix[4, 3] = 0\n",
    "    system_matrix[4, 0] = 0\n",
    "    system_matrix[4, 4] = -1 - gamma[1, 0] / beta\n",
    "    system_matrix[4, 8] = 0\n",
    "    system_matrix[4, 5] = 1\n",
    "\n",
    "    # ГУ в ячейке 8 (условие неперетока)\n",
    "    system_matrix[8, 7] = 0\n",
    "    system_matrix[8, 4] = 0\n",
    "    system_matrix[8, 8] = -1 - gamma[2, 0] / beta\n",
    "    system_matrix[8, 12] = 0\n",
    "    system_matrix[8, 9] = 1\n",
    "\n",
    "    # ГУ в ячейке 7 (условие неперетока)\n",
    "    system_matrix[7, 6] = 1\n",
    "    system_matrix[7, 3] = 0\n",
    "    system_matrix[7, 7] = -1 - gamma[1, 3] / beta\n",
    "    system_matrix[7, 11] = 0\n",
    "    system_matrix[7, 8] = 0\n",
    "\n",
    "    # ГУ в ячейке 11 (условие неперетока)\n",
    "    system_matrix[11, 10] = 1\n",
    "    system_matrix[11, 7] = 0\n",
    "    system_matrix[11, 11] = -1 - gamma[2, 3] / beta\n",
    "    system_matrix[11, 15] = 0\n",
    "    system_matrix[11, 12] = 0\n",
    "    \n",
    "    # решение системы\n",
    "    p.append(np.linalg.solve(system_matrix, d).reshape(mesh_x_count, mesh_y_count))\n",
    "\n",
    "for i, field in enumerate(p):\n",
    "    plt.figure()\n",
    "    plt.title(f'Шаг по времени: {i}')\n",
    "    plt.imshow(field / 1e6)\n",
    "    plt.colorbar()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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