Fluid properties for reservoir engineering

Nadia Petrov, who builds the reservoir models, sends Ethan the PVT report for the Cardium A pool: a bottomhole sample taken from the discovery well, with a constant composition expansion, a differential liberation and separator tests. 'You learned how these are measured in PET-260,' she says. 'For reservoir engineering we need them as tables: Bo, Rs, Bg and viscosity against pressure, at reservoir temperature. Every equation in this course uses them. Get them wrong and every answer is wrong in the same direction.'

This lesson reviews the fluid properties a reservoir engineer uses, how they change with pressure, and how they are estimated when laboratory data are missing. It treats the reservoir fluid with the black-oil model, the simplest description that captures gas coming out of oil, which is adequate for black oils and many light oils. Volatile oils and condensates need compositional methods, introduced in PET-260.

The black-oil model

The black-oil model treats the reservoir fluid as two surface components, stock-tank oil and surface gas, which can exist in two reservoir phases, oil and gas. Gas can dissolve in the oil phase, but oil does not vaporize into the gas phase. Three functions of pressure, at the fixed reservoir temperature, describe how the surface components distribute between the phases and how much space they take up.

The solution gas-oil ratio, Rs, is the volume of surface gas dissolved in each unit volume of stock-tank oil. Above the bubble point it is constant at its initial value Rsi, because all the gas is in solution. Below the bubble point, gas leaves solution as pressure falls, so Rs decreases. The oil formation volume factor, Bo, is the reservoir volume occupied by one stock-tank volume of oil together with its dissolved gas. Above the bubble point, Bo increases slightly as pressure falls, because the liquid expands. Below the bubble point, Bo decreases, because gas leaves solution and the oil shrinks. The gas formation volume factor, Bg, is the reservoir volume of one standard volume of free gas.

Two more combinations are useful. The total formation volume factor, Bt = Bo + Bg (Rsi − Rs), is the reservoir volume occupied by one stock-tank volume of oil and the gas originally dissolved in it, whether that gas is still in solution or now free. The undersaturated oil compressibility, co, describes how Bo changes above the bubble point.

Units and conversions

In SI practice, Rs is in standard cubic metres of gas per cubic metre of stock-tank oil (m³/m³), Bo in reservoir cubic metres per stock-tank cubic metre, and Bg in reservoir cubic metres per standard cubic metre. Many Canadian reports also quote oilfield units, so the conversions are worth memorizing: 1 m³/m³ = 5.615 scf/STB, and a Bg in rm³/sm³ is numerically the same as one in ft³/scf. A Bg in reservoir barrels per standard cubic foot is the ft³/scf value divided by 5.615.

Laboratory data: which experiment to use

PVT reports contain several experiments, and the choice matters. The constant composition expansion measures the bubble point and the compressibility above it. The differential liberation removes the gas at each pressure step, imitating, roughly, what happens in the reservoir once free gas becomes mobile and flows away from the oil. Separator tests flash the reservoir oil through the field's separator stages to stock-tank conditions, giving the Bo and Rs that match field production measurements.

Differential liberation values are not used directly, because they are referred to a residual oil at reservoir temperature rather than to stock-tank oil from the real separators. The standard practice, described in PET-260, adjusts the differential data with the separator-test Bob and Rsb to give Bo and Rs referred to stock-tank oil. Reservoir engineers should check which values a report or a simulation deck is using, because the difference in Bo can be several percent.

Correlations when data are missing

Many pools, especially small ones, have no reliable PVT sample. Engineers then use empirical correlations fitted to large laboratory datasets. Standing's correlations, from California crude oils, estimate the bubble point and Rs from gas gravity, oil API gravity and temperature, and Bo from Rs and the same properties. The Vasquez-Beggs and Glasø correlations are alternatives fitted to wider data. For viscosity, the Beggs-Robinson correlation estimates dead-oil viscosity from API gravity and temperature, then corrects it for dissolved gas.

In Standing's equations, p is in psia, T in degrees Fahrenheit, Rs in scf/STB and γg and γo are the gas and oil specific gravities. The coefficients are approximate, and correlations typically carry errors of 5 to 15 percent in bubble point and a few percent in Bo for oils like those in their datasets, and more for others. They are a starting point, to be replaced by laboratory data when it exists, and checked against field data such as the initial producing gas-oil ratio.

Gas properties: the z-factor

The z-factor corrects the ideal gas law, pV = z n R T. It depends on reduced pressure and temperature, the actual values divided by the pseudocritical values of the gas mixture, which can be estimated from the gas gravity when the composition is unknown. The Standing-Katz chart gives z against reduced pressure and temperature, and equations such as Hall-Yarborough or Dranchuk-Abou-Kassem reproduce it for computer use. Acid gases such as carbon dioxide and hydrogen sulphide need corrections such as Wichert-Aziz.

For typical reservoir gases, z falls from 1 at low pressure to a minimum of about 0.8 to 0.9 at moderate pressure, then rises again at high pressure, exceeding 1 in deep, overpressured reservoirs. This behaviour matters directly in the p/z material balance of lesson 8.

# Black-oil PVT table from Standing and Beggs-Robinson correlations (approximate), and gas z by Hall-Yarborough
import math
SI = True   
api, gg, T_F = (38.0, 0.80, 140.0) if SI else (42.0, 0.85, 240.0)
pb = 1856.0 if SI else 2600.0          # bubble point, psia (ca value is 12,800 kPa)
pi = 15300 / 6.895 if SI else 5370.0   # initial pressure, psia
co = 1.4e-5 if SI else 1.5e-5          # undersaturated oil compressibility, 1/psi (assumed)
go = 141.5 / (131.5 + api)
def rs(p):        # scf/STB, Standing; constant above pb
    p = min(p, pb)
    return gg * ((p / 18.2 + 1.4) * 10 ** (0.0125 * api - 0.00091 * T_F)) ** 1.2048
def bo(p):        # rb/STB
    b = 0.9759 + 0.00012 * (rs(p) * math.sqrt(gg / go) + 1.25 * T_F) ** 1.2
    return b * math.exp(-co * (p - pb)) if p > pb else b
def muo(p):       # cP, Beggs-Robinson dead and live oil; above pb a simple linear rise (assumed)
    x = 10 ** (3.0324 - 0.02023 * api) * T_F ** -1.163
    dead = 10 ** x - 1
    live = 10.715 * (rs(p) + 100) ** -0.515 * dead ** (5.44 * (rs(p) + 150) ** -0.338)
    return live * (1 + 0.00008 * (p - pb)) if p > pb else live
pts = [pi, pb + 0.6 * (pi - pb), pb, 0.75 * pb, 0.5 * pb, 0.25 * pb]
print("pressure      Rs           Bo        oil viscosity")
for p in pts:
    if SI: print(f"{p*6.895:7,.0f} kPa {rs(p)/5.615:6.1f} m3/m3 {bo(p):6.3f}   {muo(p):5.2f} mPa.s")
    else:  print(f"{p:6,.0f} psia {rs(p):6.0f} scf/STB {bo(p):6.3f}   {muo(p):5.2f} cP")
# Hall-Yarborough z factor for the gas pool (Sutton pseudo-criticals for gas gravity 0.65)
def z_hy(Tpr, Ppr):
    t = 1.0 / Tpr; A = 0.06125 * t * math.exp(-1.2 * (1 - t) ** 2)
    B = t * (14.76 - 9.76 * t + 4.58 * t * t); Cc = t * (90.7 - 242.2 * t + 42.4 * t * t); D = 2.18 + 2.82 * t
    y = 0.001
    for _ in range(100):
        f = -A * Ppr + (y + y*y + y**3 - y**4) / (1 - y) ** 3 - B * y * y + Cc * y ** D
        df = (1 + 4*y + 4*y*y - 4*y**3 + y**4) / (1 - y) ** 4 - 2 * B * y + Cc * D * y ** (D - 1)
        y -= f / df
    return A * Ppr / y
ggas = 0.65; Tpc = 169.2 + 349.5 * ggas - 74.0 * ggas ** 2; Ppc = 756.8 - 131.0 * ggas - 3.6 * ggas ** 2
Tg = 167 + 459.67
for p in ((3045.0, 2000.0, 1000.0) if SI else (3050.0, 2000.0, 1000.0)):
    z = z_hy(Tg / Tpc, p / Ppc)
    if SI: print(f"gas at {p*6.895:6,.0f} kPa and 75 C: z = {z:.3f}, Bg = {(101.325/(p*6.895))*(348.15/288.15)*z:.5f} rm3/sm3")
    else:  print(f"gas at {p:5,.0f} psia and 167 F: z = {z:.3f}, Bg = {0.02827*z*Tg/p:.5f} ft3/scf")

pressure      Rs           Bo        oil viscosity
 15,300 kPa   99.9 m3/m3  1.294    0.72 mPa.s
 14,299 kPa   99.9 m3/m3  1.296    0.71 mPa.s
 12,797 kPa   99.9 m3/m3  1.300    0.70 mPa.s
  9,598 kPa   71.0 m3/m3  1.217    0.86 mPa.s
  6,399 kPa   44.0 m3/m3  1.143    1.12 mPa.s
  3,199 kPa   19.7 m3/m3  1.081    1.63 mPa.s
gas at 20,995 kPa and 75 C: z = 0.876, Bg = 0.00511 rm3/sm3
gas at 13,790 kPa and 75 C: z = 0.871, Bg = 0.00773 rm3/sm3
gas at  6,895 kPa and 75 C: z = 0.917, Bg = 0.01628 rm3/sm3

The table reproduces the report closely. With 38° API oil, a gas gravity of 0.80 and 60 °C, Standing gives a bubble point of about 12,800 kPa, Rsb of about 100 m³/m³ and Bob of about 1.30. At the initial 15,300 kPa, Boi is 1.294. Below the bubble point, Rs and Bo fall and the oil viscosity rises from about 0.70 to 1.6 mPa·s at 3,200 kPa, because the light components that thin the oil have left. Nadia keeps the laboratory values for the model but notes that the correlation agrees within 2 percent.

Viscosity and water properties

Oil viscosity controls how easily oil flows, so it appears in every inflow and displacement calculation. It falls with temperature, is higher for heavier, lower-API oils, and depends strongly on dissolved gas: below the bubble point, as gas leaves solution, viscosity rises. Gas viscosity is much lower, typically 0.01 to 0.03 mPa·s or cP, and rises with pressure. The large contrast between oil and gas viscosity is why free gas, once it is mobile, flows to wells so easily.

Formation water properties are often treated as constants: Bw close to 1.0 to 1.05, water compressibility about 4 × 10⁻⁷ to 5 × 10⁻⁷ per kPa (3 × 10⁻⁶ per psi), and viscosity of about 0.3 to 1.0 mPa·s or cP depending on temperature and salinity. They matter in water-drive and waterflood calculations and in the material balance term for connate water expansion.

Checking PVT data

Before using a PVT report, reservoir engineers check that the sample is representative. Was it taken before the reservoir pressure fell below the bubble point near the well? Does the laboratory bubble point agree with field evidence such as the pressure at which the producing gas-oil ratio began to rise? Does the measured Rsb agree with the initial producing gas-oil ratio? Is the stock-tank gravity consistent with produced oil? A sample taken after free gas has formed around the well gives a gas-oil ratio that is too high and a bubble point equal to the sampling pressure, both misleading.

The Cardium A pool sample passes these checks: it was taken at the start of production, well above the bubble point, and its 100 m³/m³ matches the gas-oil ratio of the first months of production.