Appendix B, Problem 22 - Gas solubility in, and compressibility and FVF of brines.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defined seperator conditions\n",
    "import math\n",
    "pr = 4050 #psia\n",
    "tr = 255 #deg F\n",
    "cgr = 13 #stb/mmscf\n",
    "cond_api = 69 #deg API\n",
    "salinity = 36200 #ppm TDS\n",
    "psep = 1000 #psia\n",
    "tsep = 80 #deg F\n",
    "gamma_sep = 0.7 #From Problem 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A1: 1151.8 , A2: 1.63 , A3: -0.00024633 , Rs_plus: 1462.5\n",
      "Avg surface sep gas gravity: 0.711 sg, rel to air = 1.0\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Need to first estimate amount and sg of gas from separator at 1,000psia and 80 deg F\n",
    "A1 = ((psep/18.2+1.4)*10**(0.0125*cond_api-0.00091*tsep))**1.205 # Eq 3.61b\n",
    "A2 = 0.25 + 0.02 * cond_api # Note, worked  equation has 0.2, it should actually be 0.02 per original in chapter 3\n",
    "A3 = -3.57e-6 * cond_api\n",
    "\n",
    "Rsplus =  (A1*A2)/(1-(A1*A3)) # Eq 3.63, Additional gas expected to be released from 1st stage separator oil\n",
    "# **Note: Not sure what happens here, as the constituent A1, A2 & A3 match with worked answers, but the Rs+ is much different\n",
    "# ** Checking consistency with equations 3.61a and 3.62, it appears that the worked solution is incorrect\n",
    "# ** Eq 3.61a: A1 * SG+ = 1,152 * 0.985 = 1,134 which does not equal 2,620 scf/stb\n",
    "\n",
    "gamma_g_plus = A2 + A3 * Rsplus #Eq 3.62, Gas gravity of the expected solution gas to be released from the condensate\n",
    "\n",
    "Rs1 = 1/(cgr*1e-6) # scf/stb from separator\n",
    "Rp = 1/(Rs1 + Rsplus) # Eq 3.60, Total producing OGR (including gas from 1st stage sep + gas expected from 1st stage condensate)\n",
    "sg_avg = (gamma_sep*Rs1 + gamma_g_plus*Rsplus)/(Rs1 + Rsplus) # Eq 3.64, Avg separator gas gravity \n",
    "\n",
    "print('A1:', round(A1,1), ', A2:', round(A2,2), ', A3:', A3, ', Rs_plus:',round(Rsplus,1))\n",
    "print('Avg surface sep gas gravity:', round(sg_avg,3), 'sg, rel to air = 1.0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dissolved gas in brine: 14.9 scf gas / stb brine\n"
     ]
    }
   ],
   "source": [
    "# Brine dissolved gas content\n",
    "Rsw0 = 17.5 #scf gas / stb fresh water, Assumed by interpolating Figures 9.1 / 9.2 with Sg = 0.711\n",
    "ks = 0.1813 - 7.692e-4*tr + 2.6614e-6*tr**2 - 2.612e-9*tr**3 # Salting out coefficient, Eq 9.10 for methane/NaCl\n",
    "Rs = Rsw0 * 10**(-17.1e-6*ks*salinity) # scf gas / stb brine Eq 9.9\n",
    "print('Dissolved gas in brine:', round(Rs,1), 'scf gas / stb brine')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Brine density at standard conditions: 1.02504 g/cm3\n",
      "Brine density at reservoir temperature: 0.96488 g/cm3\n"
     ]
    }
   ],
   "source": [
    "# Brine density\n",
    "tsc = 60 #deg F\n",
    "tsc_K = (tsc-32)/1.8 + 273 # Standard temp in degrees Kelvin - required for Eq 9.14\n",
    "\n",
    "A0 = 5.91635 - 0.01035794*tsc_K + 0.9270048e-5*tsc_K**2 - 1127.522/tsc_K + 100674.1/(tsc_K**2)\n",
    "A1 = -2.5166 + 0.0111766*tsc_K - 0.170552e-4*tsc_K**2\n",
    "A2 = 2.84851 - 0.0154305*tsc_K + 0.223982e-4*tsc_K**2\n",
    "ws = salinity * 1e-6\n",
    "vw = A0 + A1 * ws + A2 * ws**2 # cm3/g, Eq 9.14\n",
    "rhow = 1/vw # g/cm3 **Note, the example has a misprint insofar that it has identical vw and rhow, which only makes sense when = 1\n",
    "\n",
    "tr_K = (tr-32)/1.8 + 273\n",
    "A0 = 5.91635 - 0.01035794*tr_K + 0.9270048e-5*tr_K**2 - 1127.522/tr_K + 100674.1/(tr_K**2)\n",
    "A1 = -2.5166 + 0.0111766*tr_K - 0.170552e-4*tr_K**2\n",
    "A2 = 2.84851 - 0.0154305*tr_K + 0.223982e-4*tr_K**2\n",
    "vw0 = A0 + A1 * ws + A2 * ws**2 # Eq 9.14\n",
    "rhow0 = 1/vw0\n",
    "\n",
    "print('Brine density at standard conditions:', round(rhow,5), 'g/cm3')\n",
    "print('Brine density at reservoir temperature:', round(rhow0,5), 'g/cm3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Brine FVF: 1.0561 rb/stb\n",
      "Brine Compressibility: 3.56 e-06 psi-1\n"
     ]
    }
   ],
   "source": [
    "# Compressibility - start with gas-free Cw*\n",
    "A0 =1e6*(0.314 + 0.58*ws + 1.9e-4*tr - 1.45e-6*tr**2)\n",
    "A1 = 8 + 50*ws - 0.125*ws*tr \n",
    "cw_star = 1/(A0 + A1 * pr)\n",
    "\n",
    "#Bw without dissolved gas\n",
    "Bw0 = rhow / rhow0 # FVF of brine at reservoir temperature, but atmospheric pressure\n",
    "Bw_star = Bw0 * (1 + (A1/A0)*pr)**(-1/A1) # Eq 9.18, FVF of brine at reservoir temp AND reservoir pressure\n",
    "# ** Note: Example has a minus in the exponent, which is not present in the original equation\n",
    "# ** Checking independat correlation, I believe that the example representation is correct, and the equation requires the minus\n",
    "\n",
    "# Note below correlations are against pure water, hence we use Rsw0\n",
    "Bw = Bw_star * (1 + 0.0001 * Rsw0**1.5) #Eq 9.19\n",
    "Cw = cw_star * (1 + 0.00877*Rsw0) # Eq 9.20\n",
    "\n",
    "print('Brine FVF:', round(Bw,4), 'rb/stb')\n",
    "print('Brine Compressibility:', round(Cw*1e6,2), 'e-06 psi-1')\n",
    "\n",
    "# Note: Comments in Chapter 9 suggest that Eq 9.19 and 9.20 are only valid for undersaturated oil/water systems, which raises\n",
    "# suspicion that not entirely appropriate to use here, suggesting instead application of Eq 9.21\n",
    "# I would further point out that using the correlations suggested by McCain, Spivey & Len in 'Petreoleum reservoir Fluid Properties'\n",
    "# I get higher compressibilities for this saturated brine, being 4.96 x 10^-6 psi-1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}