Creates Corey relative perm curves with interactive gas relative perm parameters, and prepares tables for CMG and SLB reservoir simulators.
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#Author: Mouin Almasoodi, PhD
#Objective: 3-Phase Relative Perm Model
#%%#####################################(Tools Needed for Analysis)#################################
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
#%%#####################################(INPUTS)################################
#Saturations
Swcon = Swirr = Swcrit = 0.18
Soirw = Sorw = 0.11
Soirg = Sorg = 0.11
Sgcon = Sgc = 0
#Max Relative Perm - endpoints
krw_sgc = 0.6
krg_Swirr = Krgcl = 0.1
Krocw = Kro_swirr_ = Krogcg = 0.9
Krwiro = krw_sgc = 0.6
#Corey Exponents
now = 3
nw = 3
ng = 2
nog = 1.5
#%%#####################################(Equations Used)################################
# Krw = Krwiro * ((Sw - Swcrit)/(1.0 - Swcrit - Soirw)) ^ Nw
# Krow = Krocw * ((So - Sorw )/(1.0 - Swcon - Sorw )) ^ Now
# Krog = Krogcg * ((Sl - Sorg - Swcon)/(1.0 - Sgcon - Sorg - Swcon)) ^ Nog
# Krg = Krgcl * ((Sg - Sgcrit)/(1.0 - Sgcrit - Soirg - Swcon)) ^ Ng
#%%#####################################(Water-oil Table)################################
#Create Water-oil Table
SWT = pd.DataFrame()
#create SW column
SWT['Sw'] = (np.linspace(0.18 ,(1-Sorw), 17, endpoint=True))
#Evaluate Krw
SWT['Krw'] = Krwiro * ((SWT['Sw'] - Swcrit)/(1.0 - Swcrit - Soirw)) ** nw
#Evaluate So
So = 1-SWT['Sw']
#Evaluate Krow
SWT['Krow'] = Krocw * (( So - Sorw )/(1.0 - Swcon - Sorw )) ** now
# Hard code 0 for the last value in Krow column to avoid null and negative values
SWT['Krow'].iloc[-1] = 0
fig, ax = plt.subplots(2,1, figsize=(7,9))
plt.subplots_adjust(left=None, bottom=0.25, right=None, top=None, wspace=0.2, hspace=0.3)
ax[0].set_title('Oil-Water Table')
ax[0].plot( SWT['Sw'], SWT['Krw'], lw = 2, color = 'blue')
ax[0].plot( SWT['Sw'], SWT['Krow'], lw = 2, color = 'green')
ax[0].set_xlabel("Sw", fontsize = 12)
ax[0].set_ylabel("Krw and Krow", fontsize = 12)
ax[0].grid(which='both')
#%%#####################################(Gas-Liquid Table)################################
#Create Gas-Liquid Table
SGT = pd.DataFrame()
# saturation of liquid
SL = (np.linspace(Swirr+Sorg ,(1-Sgc), 17, endpoint=True))
#Saturation of gas
SGT['Sg'] = (np.linspace(Sgc ,(1-(Swirr+Sorg)), 17, endpoint=True))
#Evaluate Krg
SGT['Krg'] = Krgcl * ((SGT['Sg'] - Sgc)/(1.0 - Sgc - Soirg - Swcon)) ** ng
#Evaluate Krog
SGT['Krog'] = Krogcg * ((SL - Sorg - Swcon)/(1.0 - Sgcon - Sorg - Swcon)) ** nog
#Reverse Krog Values to use in SGT table
SGT['Krog'] = SGT['Krog'].values[::-1]
ax[1].set_title('Liquid-Gas Table')
#ax[1].plot( SGT['Sg'], SGT['Krg'], '--r', lw = 2)
ax[1].plot( SGT['Sg'], SGT['Krog'], lw = 2, color = 'green')
ax[1].set_xlabel("Sg", fontsize = 12)
ax[1].set_ylabel("Krg and Krog", fontsize = 12)
ax[1].grid(which='both')
#%%######## Creating Krg Interactive Plot #################################
#Define function for Krg to use in the interactive plot
def Krg(Krgcl, ng):
Krg_temp = Krgcl * ((SGT['Sg'] - Sgc)/(1.0 - Sgc - Soirg - Swcon)) ** ng
return Krg_temp
#Call the function
Krg(Krgcl, ng)
#Initial plot using the function
line0, = ax[1].plot( SGT['Sg'], Krg(Krgcl, ng), lw = 2, color = 'red')
#set the color for the slider
axis_color = 'lightgoldenrodyellow'
# Define an axes area and draw a slider in it
Krgcl_slider_ax = fig.add_axes([0.2, 0.15, 0.65, 0.03], facecolor=axis_color)
Krgcl_slider = Slider(Krgcl_slider_ax, 'Krg', 0.01, 1, valinit=krg_Swirr)
# Draw another slider
Ng_slider_ax = fig.add_axes([0.2, 0.1, 0.65, 0.03], facecolor=axis_color)
Ng_slider = Slider(Ng_slider_ax, 'ng', 1, 5, valinit=ng)
# Define an action for modifying the line when any slider's value changes
def sliders_on_changed(val):
line0.set_ydata(Krg(Krgcl_slider.val, Ng_slider.val))
fig.canvas.draw_idle()
Krgcl_slider.on_changed(sliders_on_changed)
Ng_slider.on_changed(sliders_on_changed)
###Bonus
#%%#####################################(Multiple Krg Plot)################################
fig, ax2 = plt.subplots( )
ax2.set_title('Krg Vs. Gas Saturation')
ax2.set_xlabel("Sg", fontsize = 12)
ax2.set_ylabel("Krg", fontsize = 12)
ax2.grid(which='both')
Krgcl = [0.6, 1]
ng = [1.5, 1.5]
linestyle = ['solid','dashed']
#loop to evalute and plot multiple Krg curves
for i,j,k in zip(Krgcl, ng, linestyle):
SGT['Krg'] = i * ((SGT['Sg'] - Sgc)/(1.0 - Sgc - Soirg - Swcon)) ** j
ax2.plot( SGT['Sg'], SGT['Krg'], lw = 2, color = 'red', linestyle = k)
