2022_04_23_MoC_analytical_tang.ipynb

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      "-0.1173372596253432\n",
      "0.0\n",
      "386.736\n",
      "387.8952\n",
      "113.59\n",
      "114.75\n"
     ]
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   "source": [
    "from iapws import IAPWS97\n",
    "import math\n",
    "\n",
    "times = 1e-3 ##days\n",
    "time  = times *24*3600\n",
    "\n",
    "\n",
    "\n",
    "g_G = 0.035 # K/m, geothermal gradient\n",
    "Teio = 295 # K, undisturbed ground temperature\n",
    "\n",
    "Tinj = 283.5\n",
    "Ts = 283.5\n",
    "t = 3600*24*times\n",
    "z = 3000\n",
    "\n",
    "T_ei = Teio + (g_G * z)\n",
    "\n",
    "\n",
    "'''water properties'''\n",
    "water = IAPWS97(T = 283.5, P = 2)\n",
    "rho_f = water.rho\n",
    "c_f = water.cp * 1e3\n",
    "k_f = water.k\n",
    "mu_f = water.mu\n",
    "\n",
    "\n",
    "'''rock properties'''\n",
    "# alpha_e = 1e-6\n",
    "rho_e = 1800\n",
    "c_e = 1000\n",
    "k_e = 1.8\n",
    "alpha_e = k_e / (rho_e * c_e)\n",
    "\n",
    "'''outer tubing'''\n",
    "d_in = 0.08 #Insulation outside diameter, m\n",
    "r_in = 0.5 * d_in\n",
    "d_ci = 0.13 #Casing inside diameter, m\n",
    "r_ci = 0.5 * d_ci\n",
    "d_co = 0.14 #Casing outside diameter, m\n",
    "r_co = d_co * 0.5\n",
    "d_cem = 0.24 #Cement outside diameter, m\n",
    "r_cem = 0.5 * d_cem\n",
    "r_wb = r_cem\n",
    "\n",
    "'''thermal conductivities'''\n",
    "k_c = 57 #Tubing and casing steel thermal conductivity, Wm-1K-1\n",
    "k_t = k_c\n",
    "k_cem = 2.3 #Cement thermal conductivity, Wm-1K-1\n",
    "k_in = 0.023 #Insulation thermal conductivity, Wm-1K-1\n",
    "rough_tc = 0.0003 #Tubing and casing steel absolute roughness, m\n",
    "\n",
    "\n",
    "'''Wellbore dimensions'''\n",
    "d_in = 0.08 #Insulation outside diameter, m\n",
    "r_in = 0.5 * d_in\n",
    "d_ci = 0.13 #Casing inside diameter, m\n",
    "r_ci = 0.5 * d_ci\n",
    "\n",
    "'''inner pipe'''\n",
    "'''radius/diameters'''\n",
    "r_e = 100 #formation radius, m\n",
    "d_ti = 0.06 #Inner tubing inside diameter, m\n",
    "r_ti = d_ti / 2\n",
    "d_ito = 0.07 #Inner tubing outside diameter, m\n",
    "r_ito = d_ito / 2\n",
    "r_to = r_ito\n",
    "\n",
    "d_e1 = 2 * r_ti # equivalent diameter, m\n",
    "d_e2 = 2 * math.sqrt((r_ci * r_ci) - (r_in * r_in)) # equivalent diameter, m\n",
    "\n",
    "\n",
    "'''Areas of cross-section'''\n",
    "A_i = math.pi * ((r_ci * r_ci) - (r_in * r_in)) # cross-section area of injection tubing, m2\n",
    "A_p = math.pi * r_ti * r_ti # cross-section area of production tubing, m2\n",
    "\n",
    "\n",
    "'''velocities'''\n",
    "v_fi = 0.2 # injection fluid velocity, m s-1\n",
    "w = A_i * rho_f * v_fi\n",
    "v_fp = w / (A_p * rho_f)\n",
    "\n",
    "\n",
    "'''Coefficients of heat transfer'''\n",
    "Re1 = rho_f * v_fp * d_e1 / mu_f\n",
    "Re2 = rho_f * v_fi * d_e2 / mu_f\n",
    "Pr = mu_f * c_f / k_f\n",
    "\n",
    "h_f1 = 0.023 * k_f * (Re1**0.8) * (Pr**0.4) / d_e1\n",
    "h_f2 = 0.023 * k_f * (Re2**0.8) * (Pr**0.4) / d_e2\n",
    "\n",
    "U_co = 1 / ((r_co / (r_ci * h_f2))         + ((r_co * math.log(r_co / r_ci)) / k_c)         + (((r_co * math.log(r_wb / r_co)) / k_cem)))\n",
    "\n",
    "U_to = 1 / ((r_to / (r_ti * h_f1)) + ((r_to * math.log(r_to / r_ti)) / k_t) + ((r_to * math.log(r_in / r_to)) / k_in)            + (r_to / (r_in * h_f2)))\n",
    "\n",
    "t_D = (alpha_e * time) / (r_wb * r_wb) # alpha_e is same as k_e / rho_e * c_e\n",
    "T_D = math.log((math.exp(-0.2 * t_D)) + ((1.5 - (0.3719 * math.exp(-t_D))) * math.sqrt(t_D)))\n",
    "\n",
    "\n",
    "# In[42]:\n",
    "\n",
    "\n",
    "'''defining constants'''\n",
    "\n",
    "r = (2 * math.pi*r_co*U_co*k_e * A_i*rho_f*c_f)/(k_e + r_co*U_co*T_D)\n",
    "p = v_fi\n",
    "m = v_fp\n",
    "n = (2*math.pi*r_to*U_to)/(A_p*rho_f*c_f)\n",
    "q = -n\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "'''evaluating m1 and m2'''\n",
    "\n",
    "\n",
    "m1 = -0.5*(n-q+r) + 0.5 * math.sqrt((n-q+r)**2- 4*n*r) ## note here : the sqrt term is coming out neg. rn\n",
    "m2 = -0.5*(n-q+r) - 0.5 * math.sqrt((n-q+r)**2- 4*n*r)\n",
    "\n",
    "# print(q, r, n)\n",
    "\n",
    "\n",
    "# In[30]:\n",
    "\n",
    "\n",
    "'''evaluating A and B'''\n",
    "\n",
    "B =  m1*(Tinj - Ts)/(m1-m2)\n",
    "A = -m2*(Tinj - Ts)/(m1-m2)\n",
    "\n",
    "\n",
    "# In[31]:\n",
    "\n",
    "\n",
    "'''now getting the production temperature'''\n",
    "Tp = A*math.exp(m1*t) + B*math.exp(m2*t) + Ts + g_G*(z-m*t)\n",
    "\n",
    "'''getting the injection temperature'''\n",
    "Ti = (m1/n + 1)* A * math.exp(m1*t) + (m2/n + 1) * B*math.exp(m2*t) + Ts + g_G*(z-p*t)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "h1 = (q - r)*(m1/n + 1) - q\n",
    "h2 = (m1/n + 1)*m1\n",
    "b1 = (q-r)*(m2/n + 1) - q\n",
    "b2 = (m2/n + 1)*m2\n",
    "print(h1-h2)\n",
    "print(b1-b2)\n",
    "print(Tp)\n",
    "print(Ti)\n",
    "print('%0.2f' %(Tp-273.15))\n",
    "print('%0.2f' %(Ti-273.15))"
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