import pandas as pd import numpy as np import matplotlib.pyplot as plt from scipy.interpolate import make_interp_spline

# Productivity Index (darcy law) def j_darcy(ko, h, bo, uo, re, rw, s, flow_regime = 'seudocontinuo'): if flow_regime == 'seudocontinuo': J_darcy = ko * h / (141.2 * bo * uo * (np.log(re / rw) - 0.75 + s)) elif flow_regime == 'continuo': J_darcy = ko * h / (141.2 * bo * uo * (np.log(re / rw) + s)) return J_darcy

# Índice de Productividad def j(q_test, pwf_test, pr, pb, ef=1, ef2=None): if ef == 1: if pwf_test >= pb: J = q_test / (pr - pwf_test) else: J = q_test / ((pr - pb) + (pb / 1.8) * \ (1 - 0.2 * (pwf_test / pb) - 0.8 * (pwf_test / pb)**2)) elif ef != 1 and ef2 is None: if pwf_test >= pb: J = q_test / (pr - pwf_test) else: J = q_test / ((pr - pb) + (pb / 1.8) * \ (1.8 * (1 - pwf_test / pb) - 0.8 * ef * (1 - pwf_test / pb)**2)) elif ef !=1 and ef2 is not None: if pwf_test >= pb: J = (q_test / (pr - pwf_test) / ef) * ef2 else: J = (q_test / ((pr - pb) + (pb / 1.8) * \ (1.8 * (1 - pwf_test / pb) - 0.8 * ef * \ (1 - pwf_test / pb)**2)) / ef) * ef2 return J

# Q(bpd) @ Pb def Qb(q_test, pwf_test, pr, pb, ef=1, ef2=None): qb = j(q_test, pwf_test, pr, pb, ef, ef2) * (pr - pb) return qb

# AOF(bpd) def aof(q_test, pwf_test, pr, pb, ef=1, ef2=None): if (ef == 1 and ef2 is None): if pr > pb: # Yac. subsaturado if pwf_test >= pb: AOF = j(q_test, pwf_test, pr, pb) * pr elif pwf_test < pb: AOF = Qb(q_test, pwf_test, pr, pb, ef=1) + ((j(q_test, pwf_test, pr, pb) * pb) / (1.8)) elif pr <= pb: # Yac. Saturado AOF = q_test / (1 - 0.2 * (pwf_test / pr) - 0.8 * (pwf_test / pr)**2) elif (ef < 1 and ef2 is None): if pr > pb: if pwf_test >= pb: AOF = j(q_test, pwf_test, pr, pb, ef) * pr elif pwf_test < pb: AOF = Qb(q_test, pwf_test, pr, pb, ef) + ((j(q_test, pwf_test, pr, pb, ef) * pb) / (1.8)) * (1.8 - 0.8 * ef) elif pr <= pb: AOF = q_test / (1.8 * ef * (1 - pwf_test/pr) - 0.8 * ef**2 * (1 - pwf_test/pr)**2) * (1.8 * ef - 0.8 * ef**2) elif (ef > 1 and ef2 is None): if pr > pb: if pwf_test >= pb: AOF = j(q_test, pwf_test, pr, pb, ef) * pr elif pwf_test < pb: AOF = Qb(q_test, pwf_test, pr, pb, ef) + ((j(q_test, pwf_test, pr, pb, ef) * pb) / (1.8)) * (0.624 + 0.376 * ef) elif pr <= pb: AOF = q_test / (1.8 * ef * (1 - pwf_test/pr) - 0.8 * ef**2 * (1 - pwf_test/pr)**2) * (0.624 + 0.376 * ef) elif (ef < 1 and ef2 >= 1): if pr > pb: if pwf_test >= pb: AOF = j(q_test, pwf_test, pr, pb, ef, ef2) * pr elif pwf_test < pb: AOF = Qb(q_test, pwf_test, pr, pb, ef, ef2) + ((j(q_test, pwf_test, pr, pb, ef, ef2) * pb) / (1.8)) * (0.624 + 0.376 * ef2) elif pr <= pb: AOF = q_test / (1.8 * ef * (1 - pwf_test/pr) - 0.8 * ef**2 * (1 - pwf_test/pr)**2) * (0.624 + 0.376 * ef2) elif (ef > 1 and ef2 <= 1): if pr > pb: if pwf_test >= pb: AOF = j(q_test, pwf_test, pr, pb, ef, ef2) * pr elif pwf_test < pb: AOF = Qb(q_test, pwf_test, pr, pb, ef, ef2) + (j(q_test, pwf_test, pr, pb, ef, ef2) * pb / 1.8) * (1.8 - 0.8 * ef2) elif pr <= pb: AOF = q_test / (1.8 * ef * (1 - pwf_test/pr) - 0.8 * ef**2 * (1 - pwf_test/pr)**2) * (1.8 * ef - 0.8 * ef2**2) return AOF

# Qo (bpd) @ Darcy Conditions def qo_darcy(q_test, pwf_test, pr, pwf, pb): qo = j(q_test, pwf_test, pr, pb) * (pr - pwf) return qo

#Qo(bpd) @ vogel conditions def qo_vogel(q_test, pwf_test, pr, pwf, pb): if pr <= pb: # Yac. Saturado qo = aof(q_test, pwf_test, pr, pb) * \ (1 - 0.2 * (pwf / pr) - 0.8 * ( pwf / pr)**2) return qo

#Qo(bpd) @ vogel conditions def qo_ipr_compuesto(q_test, pwf_test, pr, pwf, pb): if pr > pb: # Yac. subsaturado if pwf >= pb: qo = qo_darcy(q_test, pwf_test, pr, pwf, pb) elif pwf < pb: qo = Qb(q_test, pwf_test, pr, pb) + \ ((j(q_test, pwf_test, pr, pb) * pb) / (1.8)) * \ (1 - 0.2 * (pwf / pb) - 0.8 * ( pwf / pb)**2) elif pr <= pb: # Yac. Saturado qo = aof(q_test, pwf_test, pr, pb) * \ (1 - 0.2 * (pwf / pr) - 0.8 * ( pwf / pr)**2) return qo

# Datos de un yacimiento saturado pr = 2400 #psia pb = 2500 #psia pwf = 1000 #psia q_test = 100 #stb/d pwf_test = 1800 #psia

# Crear Dataframe df = pd.DataFrame() df['Pwf(psia)'] = np.array([2400, 2000, 1500, 1000, 500, 0]) df['Qo(bpd)'] = df['Pwf(psia)'].apply(lambda x: qo_vogel(q_test, pwf_test, pr, x, pb))

# Plot fig, ax = plt.subplots(figsize=(20, 10)) x = df['Qo(bpd)'] y = df['Pwf(psia)'] X_Y_Spline = make_interp_spline(x, y) # This step is used to smooth the curve X_ = np.linspace(x.min(), x.max(), 500) Y_ = X_Y_Spline(X_) ax.plot(X_, Y_, c='g') ax.set_xlabel('Qo(bpd)') ax.set_ylabel('Pwf(psia)') ax.set_title('IPR') ax.set(xlim=(0, df['Qo(bpd)'].max() + 10), ylim=(0, df['Pwf(psia)'][0] + 100)) ax.grid() plt.show()

# IPR Curve def IPR_curve(q_test, pwf_test, pr, pwf:list, pb): # Creating Dataframe df = pd.DataFrame() df['Pwf(psia)'] = pwf df['Qo(bpd)'] = df['Pwf(psia)'].apply(lambda x: qo_ipr_compuesto(q_test, pwf_test, pr, x, pb)) fig, ax = plt.subplots(figsize=(20, 10)) x = df['Qo(bpd)'] y = df['Pwf(psia)'] # The following steps are used to smooth the curve X_Y_Spline = make_interp_spline(x, y) X_ = np.linspace(x.min(), x.max(), 500) Y_ = X_Y_Spline(X_) #Build the curve ax.plot(X_, Y_, c='g') ax.set_xlabel('Qo(bpd)') ax.set_ylabel('Pwf(psia)') ax.set_title('IPR') ax.set(xlim=(0, df['Qo(bpd)'].max() + 10), ylim=(0, df['Pwf(psia)'][0] + 100)) # Arrow and Annotations plt.annotate( 'Bubble Point', xy=(Qb(q_test, pwf_test, pr, pb), pb),xytext=(Qb(q_test, pwf_test, pr, pb) + 100, pb + 100) , arrowprops=dict(arrowstyle='->',lw=1) ) # Horizontal and Vertical lines at bubble point plt.axhline(y=pb, color='r', linestyle='--') plt.axvline(x=Qb(q_test, pwf_test, pr, pb), color='r', linestyle='--') ax.grid() plt.show()

# Datos pr = 4000 #psi pb = 3000 #psi q_test = 600 #bpd pwf_test = 2000 #bpd pwf = np.array([4000, 3500, 3000, 2500, 1000, 0])

IPR_curve(q_test, pwf_test, pr, pwf, pb)

# IPR Curve def IPR_curve_methods(q_test, pwf_test, pr, pwf:list, pb, method, ef=1, ef2=None): # Creating Dataframe fig, ax = plt.subplots(figsize=(20, 10)) df = pd.DataFrame() df['Pwf(psia)'] = pwf if method == 'Darcy': df['Qo(bpd)'] = df['Pwf(psia)'].apply(lambda x: qo_darcy(q_test, pwf_test, pr, x, pb)) elif method == 'Vogel': df['Qo(bpd)'] = df['Pwf(psia)'].apply(lambda x: qo_vogel(q_test, pwf_test, pr, x, pb)) elif method == 'IPR_compuesto': df['Qo(bpd)'] = df['Pwf(psia)'].apply(lambda x: qo_ipr_compuesto(q_test, pwf_test, pr, x, pb)) # Stand the axis of the IPR plot x = df['Qo(bpd)'] y = df['Pwf(psia)'] # The following steps are used to smooth the curve X_Y_Spline = make_interp_spline(x, y) X_ = np.linspace(x.min(), x.max(), 500) Y_ = X_Y_Spline(X_) #Build the curve ax.plot(X_, Y_, c='g') ax.set_xlabel('Qo(bpd)') ax.set_ylabel('Pwf(psia)') ax.set_title('IPR') ax.set(xlim=(0, df['Qo(bpd)'].max() + 10), ylim=(0, df['Pwf(psia)'].max() + 100)) # Arrow and Annotations plt.annotate( 'Bubble Point', xy=(Qb(q_test, pwf_test, pr, pb), pb),xytext=(Qb(q_test, pwf_test, pr, pb) + 100, pb + 100) , arrowprops=dict(arrowstyle='->',lw=1) ) # Horizontal and Vertical lines at bubble point plt.axhline(y=pb, color='r', linestyle='--') plt.axvline(x=Qb(q_test, pwf_test, pr, pb), color='r', linestyle='--') ax.grid() plt.show()

IPR_curve_methods(q_test, pwf_test, pr, pwf, pb, 'Darcy')

IPR_curve_methods(q_test, pwf_test, pr, pwf, pb, 'IPR_compuesto')

# Datos de un yacimiento saturado pr = 2400 #psia pb = 2500 #psia pwf = np.array([2400, 2000, 1500, 1000, 0]) #psia q_test = 100 #stb/d pwf_test = 1800 #psia

IPR_curve_methods(q_test, pwf_test, pr, pwf, pb, 'Vogel')

# Datos pr = 120 #bar pb = 65 #bar q_test = 400 #m3/d pwf_test = 100 #bar

# Datos pr = 4000 #psi pb = 3000 #psi q_test = 600 #bpd pwf_test = 2000 #bpd pwf = np.array([4000, 3500, 3000, 2500, 1000, 0])

# Datos pr = 3000 #psig pb = 2130 #psig q_test = 631 #stb/d pwf_test = 1700 #psig pwf = np.array([3000, 2500, 2000, 1000, 0])