menu_book Chapter 8PVTStandingCorrelations

PVT Black-Oil Property Builder

Generate a full fluid-property table from a few field numbers when you have no lab PVT — the input that feeds material balance and simulation.

What it does

From oil gravity, gas gravity, temperature and solution GOR, computes the bubble-point pressure and builds solution GOR, oil formation volume factor and oil viscosity versus pressure using the Standing and Beggs-Robinson correlations.

How it works

1Bubble-point pressure from the Standing correlation.
2Solution GOR vs. pressure, held constant above the bubble point.
3Oil FVF from Standing, shrinking above the bubble point via compressibility.
4Oil viscosity from Beggs-Robinson (saturated) and Vasquez-Beggs (undersaturated).
5Plot Rs, Bo and viscosity vs. pressure — change API, GOR or temperature and re-run.

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Run it live

Runs entirely in your browser — no install. Edit any value and press Run to see the result change. This is the whole project; read it top to bottom.

pvt-property-builder.pystarting Python…

import numpy as np
import matplotlib.pyplot as plt

# ── Field inputs — tweak these and re-run ───────────────────────────────
API   = 35.0      # oil gravity, degrees API
gas_g = 0.75      # gas specific gravity (air = 1)
T     = 180.0     # reservoir temperature, degF
Rsb   = 650.0     # solution GOR at the bubble point, scf/STB
gamma_o = 141.5 / (131.5 + API)                 # oil specific gravity

# ── Bubble-point pressure (Standing) ────────────────────────────────────
Pb = 18.2 * ((Rsb / gas_g)**0.83 * 10**(0.00091*T - 0.0125*API) - 1.4)

# ── Black-oil property correlations ─────────────────────────────────────
def Rs(P):    # Standing solution GOR (scf/STB), held at Rsb above Pb
    r = gas_g * ((P/18.2 + 1.4) * 10**(0.0125*API - 0.00091*T))**(1/0.83)
    return np.minimum(r, Rsb)

def Bo(P):    # Standing oil FVF (rb/STB); shrinks above Pb via compressibility
    F   = Rs(P) * (gas_g/gamma_o)**0.5 + 1.25*T
    bo  = 0.9759 + 0.00012 * F**1.2
    bob = 0.9759 + 0.00012 * (Rsb*(gas_g/gamma_o)**0.5 + 1.25*T)**1.2
    co  = 1e-5
    return np.where(P <= Pb, bo, bob*np.exp(-co*(P - Pb)))

def mu_o(P):  # Beggs-Robinson (saturated) + Vasquez-Beggs (undersaturated), cp
    mu_od = 10**(10**(3.0324 - 0.02023*API) * T**-1.163) - 1     # dead oil
    A = 10.715*(Rs(P) + 100)**-0.515
    Bexp = 5.44*(Rs(P) + 150)**-0.338
    mu_ob = A * mu_od**Bexp
    M = 2.6 * P**1.187 * np.exp(-11.513 - 8.98e-5*P)
    return np.where(P <= Pb, mu_ob, mu_ob*(P/Pb)**M)

# ── Build the PVT table over pressure ───────────────────────────────────
P = np.linspace(200, max(Pb*1.6, 4000), 80)
print(f"Bubble point Pb : {Pb:6.0f} psia")
print(f"At Pb  ->  Rs = {float(Rs(Pb)):4.0f} scf/STB   "
      f"Bo = {float(Bo(np.array([Pb]))[0]):.3f} rb/STB   "
      f"mu_o = {float(mu_o(np.array([Pb]))[0]):.2f} cp")

# ── Plot Rs, Bo, mu_o vs pressure ───────────────────────────────────────
fig, ax = plt.subplots(1, 3, figsize=(10, 4))
for a_, y, lbl, c in [(ax[0], Rs(P), "Rs (scf/STB)", "green"),
                      (ax[1], Bo(P), "Bo (rb/STB)", "navy"),
                      (ax[2], mu_o(P), "mu_o (cp)", "firebrick")]:
    a_.plot(P, y, color=c, lw=2); a_.axvline(Pb, ls="--", c="0.6")
    a_.set_xlabel("Pressure (psia)"); a_.set_title(lbl); a_.grid(alpha=0.3)
fig.suptitle("Black-oil PVT from field data (Standing / Beggs-Robinson)", fontweight="bold")
plt.tight_layout(); plt.show()

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