PVT correlations for oil and gas condensate

Quick refresher

A correlation is a formula fitted to laboratory data, of the form $p_b = f(R_{sb}, \gamma_g, \gamma_o, T)$ , together with related formulas for $R_s$ and $B_o$ . It carries over the experience of the oils it was built on. Outside their range, and for oils of another type, the error grows.
The relationships make physical sense. More dissolved gas and a higher temperature mean a higher bubble point pressure. A heavier gas and a lighter oil mean that the gas dissolves more easily, so the bubble point pressure is lower. $B_o$ grows with the solution gas–oil ratio and with temperature.
The classical correlations were built in oilfield units: psia, °F, scf/STB, °API, with gas at 60 °F. It matters which gas specific gravity the correlation needs: that of the total separator gas, or that of the first-stage gas.
Correlations usually give the bubble point pressure with an error of 5–15% and the formation volume factor with an error of 1–3%. For one and the same oil, different correlations can disagree by more than each of them errs on its own database.
We describe the error on our own data by the average relative error (the bias) and the average absolute relative error (the overall level of errors). Tuning to a measured point removes the bias. It does not remove the scatter.
Below the bubble point pressure a correlation describes a family of different oils, each at its own bubble point pressure, and not the degassing of one oil. Take the $R_s(p)$ and $B_o(p)$ curves below the bubble point pressure from experiment.

Key relationships

p_b = 18.2\left[\left(\frac{R_{sb}}{\gamma_g}\right)^{0.83}10^{\,0.00091\,T - 0.0125\,\mathrm{API}} - 1.4\right]

Standing correlation: psia, scf/STB, °F

e_i = \frac{x_i^{\text{corr}} - x_i^{\text{lab}}}{x_i^{\text{lab}}},\qquad \bar e = \frac{1}{n}\sum e_i,\qquad \overline{|e|} = \frac{1}{n}\sum |e_i|

relative error, bias and average absolute error

p_b^{*} = k\,p_b^{\text{corr}},\qquad k = \frac{p_b^{\text{lab}}}{p_b^{\text{corr}}}

tuning to a single measured point

B_{gc} = (R + GE)\,B_g

reservoir gas per 1 m³ of stable condensate

Common pitfalls

Putting a solution gas–oil ratio in m³/m³ and a pressure in MPa into a formula built in scf/STB and psia.
Taking the specific gravity of the first-stage gas where the correlation needs the total separator gas, and the other way round.
Taking the producing gas–oil ratio of a test when the bottomhole pressure was below the bubble point pressure. It contains free gas, and the bubble point pressure will come out too high.
Applying a correlation outside its data: to a volatile or heavy oil, or to an oil with a large content of carbon dioxide, nitrogen or hydrogen sulfide.
Treating tuning to a single point as a cure for everything. It removes the bias, but not the scatter, and not an error in the shape of the curve below the bubble point pressure.

After this lesson you can

explain what a PVT correlation is, what it is based on and why it is reliable only for its own set of oils
prepare the input data: convert the solution gas–oil ratio, pressure, temperature and oil density to oilfield units and choose the right gas specific gravity
calculate the bubble point pressure, solution gas–oil ratio and oil formation volume factor with the Standing correlation and compare the result with other correlations
estimate the error of correlations from laboratory data, using the average relative error and the average absolute relative error, and choose a correlation for a field
tune a correlation to a single measured bubble point pressure and understand what such tuning corrects and what it does not
name the cases in which correlations cannot be trusted, and estimate the formation volume factor of a gas condensate (a gas that gives a light liquid when its pressure falls) from surface production

What a PVT correlation is

The properties of reservoir oil depend on its composition, pressure and temperature. Before samples are taken, there is no full composition. But there are indirect indicators that we measure at the very first well test: how much gas there is per cubic metre of oil, how heavy this gas is, what the density of the stock-tank oil is, and what the reservoir temperature is. A correlation links these indicators to the bubble point pressure, the solution gas–oil ratio and the formation volume factor (Black oil model: solution gas–oil ratio and formation volume factors).

A correlation is built like this. We collect laboratory reports for a group of oils, from one region or from all over the world. We choose the form of the formula and fit the coefficients so that the formula reproduces the measurements as well as possible. The first correlations were nomograms (charts for reading off a result), and they were later written as equations. A correlation is a compact record of its own database. For similar oils, and within its ranges, it works well. For dissimilar oils it transfers someone else's experience.

Input data of correlations and where to get them

Quantity: $R_{sb}$ — solution gas–oil ratio at the bubble point pressure
Where it comes from: producing gas–oil ratio of the test: all the separator and stock-tank gas per 1 m³ of stock-tank oil
What to watch for: the bottomhole pressure during the test must be above the bubble point pressure, otherwise the producing gas–oil ratio includes free gas

Quantity: $\gamma_g$ — gas specific gravity
Where it comes from: analysis of the separator and stock-tank gas; the average weighted by volume
What to watch for: some correlations need the total separator gas, others need the gas of the first stage

Quantity: $\gamma_o$ , °API — stock-tank oil density
Where it comes from: density measured in the tank or in the laboratory
What to watch for: converted to 60 °F (15.6 °C); °API comes from the formula $141.5/\gamma_o - 131.5$

Quantity: $T$ — reservoir temperature
Where it comes from: measurements in wells (Reservoir pressure and temperature)
What to watch for: in correlations, °F or °R

Quantity	Where it comes from	What to watch for
$R_{sb}$ — solution gas–oil ratio at the bubble point pressure	producing gas–oil ratio of the test: all the separator and stock-tank gas per 1 m³ of stock-tank oil	the bottomhole pressure during the test must be above the bubble point pressure, otherwise the producing gas–oil ratio includes free gas
$\gamma_g$ — gas specific gravity	analysis of the separator and stock-tank gas; the average weighted by volume	some correlations need the total separator gas, others need the gas of the first stage
$\gamma_o$ , °API — stock-tank oil density	density measured in the tank or in the laboratory	converted to 60 °F (15.6 °C); °API comes from the formula $141.5/\gamma_o - 131.5$
$T$ — reservoir temperature	measurements in wells (Reservoir pressure and temperature)	in correlations, °F or °R

We use correlations while there are no samples. They give a first estimate of hydrocarbons in place and of the reservoir drive (the natural energy that pushes oil to the wells). They help us choose the sampling conditions (Reservoir fluid sampling). And they serve neighbouring accumulations of the same petroleum system. Once laboratory data are available, correlations serve to check them. If the bubble point pressure of a sample differs strongly from all the correlations (by a third, say), check the sample first. Correlations also sit behind the calculation options in inflow and lift programs (software for well inflow and for lifting fluid up the well). They are also used to prepare data for reservoir simulation models when there is no laboratory table yet.

The Standing correlation

The best-known correlation is the Standing correlation. It was built in the 1940s from 105 measurements on 22 California oils, and it was first presented as nomograms. The equations below are their form in oilfield units. The bubble point pressure is linked to the solution gas–oil ratio through $R_{sb}/\gamma_g$ . The effect of temperature and oil density enters as the factor $10^{\,0.00091T - 0.0125\,\mathrm{API}}$ .

Standing correlation for the bubble point pressure

p_b = 18.2\left[\left(\frac{R_{sb}}{\gamma_g}\right)^{0.83}10^{\,0.00091\,T - 0.0125\,\mathrm{API}} - 1.4\right]

where:

$p_b$ bubble point pressure, absolute, psia
$R_{sb}$ solution gas–oil ratio at the bubble point pressure: all the separator gas per barrel of stock-tank oil, gas at 60 °F, scf/STB
$\gamma_g$ specific gravity (relative to air) of the total separator gas, —
$T$ reservoir temperature, °F
$\mathrm{API}$ API gravity of the stock-tank oil, °API

Units: oilfield units: psia, scf/STB, °F, °API. To get MPa, multiply the result by 0.006895

Holds when

The data behind the correlation: bubble point pressure 130–7000 psia (0.9–48 MPa), temperature 100–258 °F (38–126 °C), $R_{sb}$ 20–1425 scf/STB (4–258 m³/m³), 16.5–63.8 °API, $\gamma_g$ 0.59–0.95.
The gas came from two-stage separation (first stage 265–465 psia at 100 °F). With another scheme $R_{sb}$ and $\gamma_g$ are different, and the result shifts.
The oil has no appreciable admixture of carbon dioxide, nitrogen and hydrogen sulfide.

If we solve the equation for the solution gas–oil ratio, we get the $R_s$ of oil saturated at pressure $p$ . This is the next equation. We use it to build the $R_s(p)$ curve below the bubble point pressure, but with the caveat given in the section on the limits of applicability.

Standing correlation for the solution gas–oil ratio of saturated oil

R_s = \gamma_g\left[\left(\frac{p}{18.2} + 1.4\right)10^{\,0.0125\,\mathrm{API} - 0.00091\,T}\right]^{1.2048}

where:

$R_s$ solution gas–oil ratio of oil saturated at pressure $p$ , scf/STB
$p$ pressure, not above the bubble point pressure of the oil, psia
$\gamma_g,\ T,\ \mathrm{API}$ as in the equation above, —, °F, °API

Units: oilfield units

Holds when

The same data as for the bubble point pressure equation. The exponent 1.2048 = 1/0.83.

At $p = p_b$ the formula gives $R_{sb}$ . Above the bubble point pressure the solution gas–oil ratio does not grow: $R_s = R_{sb}$ .

Standing correlation for the formation volume factor of saturated oil

B_o = 0.9759 + 0.000120\left[R_s\left(\frac{\gamma_g}{\gamma_o}\right)^{0.5} + 1.25\,T\right]^{1.2}

where:

$B_o$ oil formation volume factor at or below the bubble point pressure, rb/STB = m³/m³
$R_s$ solution gas–oil ratio, scf/STB
$\gamma_o$ specific gravity of the stock-tank oil at 60 °F relative to water, —
$\gamma_g,\ T$ as above, —, °F

Units: oilfield units; $B_o$ is a dimensionless ratio of volumes

Holds when

The oil is saturated ( $p \le p_b$ ). The data have $B_{ob}$ of 1.024–2.15 and the same ranges as above.
Above the bubble point pressure, $B_o = B_{ob}\,\e^{-c_o(p - p_b)}$ with the oil compressibility (Density and compressibility of reservoir oil).

The expression in square brackets combines two contributions to the volume: the dissolved gas (the term with $R_s$ , weighted by the ratio of the gas and oil densities) and thermal expansion (the term with $T$ ). With no gas and at 60 °F the formula gives $B_o \approx 0.997$ , which is almost 1, as it should be.

Worked exampleBubble point pressure and formation volume factor from the Standing correlation

Given (assumed data)

Oil: the same as in the topic Laboratory PVT tests: $R_{sb} = 110$ m³/m³ with two-stage separation, gas at 20 °C
Separator gas: $\gamma_g = 0.80$ , the average of both stages
Stock-tank oil: 850 kg/m³ at 20 °C; thermal expansion $8\cdot 10^{-4}$ 1/°C (assumed)
Reservoir: 85 °C
Laboratory: $p_b = 18.0$ MPa, $B_{ob} = 1.350$ m³/m³

Solution

Solution gas–oil ratio: $110\cdot 5.615\cdot 0.985 = 608$ scf/STB. The factor 0.985 converts the gas from 20 °C to 60 °F (288.7/293.15). We neglect the 0.35% change in the volume of the oil. This understates $R_{sb}$ and the bubble point pressure by a few tenths of a per cent.
Oil: at 15.6 °C the density is $850\cdot(1 + 8\cdot 10^{-4}\cdot 4.4) = 853$ kg/m³, so $\gamma_o = 853/999.0 = 0.854$ and $\mathrm{API} = 141.5/0.854 - 131.5 = 34.2$ . Temperature: $85\cdot 1.8 + 32 = 185$ °F.
The temperature factor is $10^{\,0.00091\cdot 185 - 0.0125\cdot 34.2} = 10^{-0.25915} = 0.5506$ . The gas term is $(608/0.80)^{0.83} = 246.1$ .
$p_b = 18.2\,(246.1\cdot 0.5506 - 1.4) = 2441$ psia $= 2441\cdot 0.006895 = 16.83$ MPa, which is 6.5% below the laboratory value.
$B_{ob} = 0.9759 + 0.000120\,[608\,(0.80/0.854)^{0.5} + 1.25\cdot 185]^{1.2} = 0.9759 + 0.000120\cdot 819.7^{1.2} = 1.352$ m³/m³, which is 0.1% above the laboratory value.

Answer: The Standing correlation gives

p_b = 16.83

MPa (laboratory: 18.0) and

B_{ob} = 1.352

m³/m³ (laboratory: 1.350).

What it means. The formation volume factor agrees with the experiment to within 0.1%, while the bubble point pressure is too low by 6.5%, which is about 1.2 MPa. This is the typical picture. The volume of the oil depends mainly on the amount of dissolved gas, and hardly on the fine details of composition. The bubble point pressure is sensitive to composition. For an estimate of hydrocarbons in place such a correlation is enough. For choosing the sampling conditions it is already risky, because an error of 1.2 MPa is comparable to the margin above the bubble point pressure that we keep while conditioning the well before sampling (Reservoir fluid sampling). The data in this example are assumed for illustration.

Other correlations and the oils they were built on

Dozens of correlations have been proposed. Each new one was built from a new database, often a regional one, and in its own region it is usually more accurate than the ones before it. The most commonly used ones for oils are in the table. Their equations are in the advanced section of the lesson.

Correlations for the bubble point pressure, solution gas–oil ratio and formation volume factor

Correlation: Standing
Oils it was built on: 22 California oils
$R_{sb}$ , m³/m³: 4–258
°API: 16.5–63.8

Correlation: Lasater
Oils it was built on: 137 oils of Canada, the United States and South America
$R_{sb}$ , m³/m³: 0.5–525
°API: 17.9–51.1

Correlation: Vasquez–Beggs
Oils it was built on: about 6,000 measurements, about 600 studies from all over the world
$R_{sb}$ , m³/m³: 0–398
°API: 15.3–59.5

Correlation: Glasø
Oils it was built on: 45 North Sea oils
$R_{sb}$ , m³/m³: 16–477
°API: 22.3–48.1

Correlation: Al-Marhoun
Oils it was built on: 69 Middle East oils
$R_{sb}$ , m³/m³: 5–290
°API: 19.4–44.6

Correlation: Petrosky–Farshad
Oils it was built on: Gulf of Mexico oils
$R_{sb}$ , m³/m³: 39–254
°API: 16.3–45.0

Correlation	Oils it was built on	$R_{sb}$ , m³/m³	°API
Standing	22 California oils	4–258	16.5–63.8
Lasater	137 oils of Canada, the United States and South America	0.5–525	17.9–51.1
Vasquez–Beggs	about 6,000 measurements, about 600 studies from all over the world	0–398	15.3–59.5
Glasø	45 North Sea oils	16–477	22.3–48.1
Al-Marhoun	69 Middle East oils	5–290	19.4–44.6
Petrosky–Farshad	Gulf of Mexico oils	39–254	16.3–45.0

The solution gas–oil ratio is converted from scf/STB at 60 °F by dividing by 5.53. Different reviews give slightly different limits for the same correlations. The ranges of bubble point pressure, temperature and gas specific gravity are given next to the equations of the correlations.

Lasater works through the mole fraction of gas in the reservoir oil (the share of gas molecules among all the molecules). It gives a generalised “bubble point pressure factor” $p_b\gamma_g/T$ . The molar mass of the oil is estimated from its density.
Vasquez–Beggs has two groups of coefficients, for oils heavier and lighter than 30 °API. The gas specific gravity is converted to a first separator stage at 100 psig (0.79 MPa absolute), because the gas gravity depends on the separation conditions.
Glasø was built on North Sea oils. Corrections have been proposed for oils with a different paraffin content (waxiness) and for gas containing carbon dioxide, nitrogen or hydrogen sulfide.
Al-Marhoun and Petrosky–Farshad are regional: the first is for Middle East oils, and the second is for Gulf of Mexico oils. As their authors report, in their own regions they are more accurate than general correlations.

Worked exampleFive correlations for one oil

Given (assumed data)

Oil of the example above: 608 scf/STB, $\gamma_g = 0.80$ , $\gamma_o = 0.854$ (34.2 °API), 185 °F (644.7 °R)
First separator stage: 0.7 MPa (101.5 psia), 30 °C (86 °F); first-stage gas 0.745
Laboratory: $p_b = 18.0$ MPa, $B_{ob} = 1.350$ m³/m³

Solution

Standing (the example above): $p_b = 16.83$ MPa, $B_{ob} = 1.352$ .
Vasquez–Beggs needs the first-stage gas converted to 100 psig: $0.745\,[1 + 5.912\cdot 10^{-5}\cdot 34.2\cdot 86\cdot\lg(101.5/114.7)] = 0.738$ . With it, $p_b = 20.16$ MPa and $B_{ob} = 1.352$ .
Glasø: $p_b = 19.40$ MPa and $B_{ob} = 1.327$ . Al-Marhoun: $p_b = 17.92$ MPa. Petrosky–Farshad: $p_b = 19.37$ MPa.
Deviations of the bubble point pressure from the laboratory value: −6.5; 12.0; 7.8; −0.4; 7.6%. The correlations range from 16.83 to 20.16 MPa, which is a spread of 3.33 MPa.
Suppose we put the average gas of both stages into the Vasquez–Beggs correlation by mistake, instead of the first-stage gas (0.80; 0.793 after conversion to 100 psig). Then $p_b = 18.97$ MPa, which is 1.19 MPa lower.

Answer: The five correlations give a bubble point pressure from 16.83 to 20.16 MPa, against 18.0 in the laboratory. Three of them give a formation volume factor from 1.327 to 1.352, against 1.350 in the laboratory.

What it means. For this oil the Al-Marhoun correlation is closest to the experiment. But we cannot choose a correlation from a single sample, because the agreement may be a coincidence (next section). The example also shows the price of wrong input data. A different gas specific gravity shifts the bubble point pressure by 1.19 MPa, about 7%. This input error is comparable to the error of the correlations themselves. All three correlations give the formation volume factor to within 2%. The data in this example are assumed for illustration.

CalculatedBubble point pressure of the lesson oil from five correlations (dots) and from the experiment (vertical line, 18.0 MPa). Each segment is the deviation of the correlation from the experiment.

Correlation error and tuning to a measurement

To see how well a correlation suits the oils of a field, we check it against the laboratory data of the samples that we already have. For each sample we calculate the relative error. Then, over all the samples, we calculate two statistics. The average error shows the systematic bias. The average absolute error shows the overall level of errors, including the scatter.

Relative error of a correlation and its statistics

e_i = \frac{x_i^{\text{corr}} - x_i^{\text{lab}}}{x_i^{\text{lab}}}\cdot 100\,\%,\qquad \bar e = \frac{1}{n}\sum_{i=1}^{n} e_i,\qquad \overline{|e|} = \frac{1}{n}\sum_{i=1}^{n} |e_i|

where:

$x_i^{\text{corr}},\ x_i^{\text{lab}}$ value from the correlation and laboratory value for the $i$ -th sample — bubble point pressure, $B_{ob}$ and so on, units of the quantity
$e_i$ relative error for the $i$ -th sample, %
$\bar e$ average relative error — the bias, %
$\overline{|e|}$ average absolute relative error (AARE), %
$n$ number of samples, —

Units: per cent

Holds when

The samples are representative and were studied in one laboratory or by one method.
There are enough samples for the statistics to mean something. With three or four samples the conclusions are preliminary.

If $\overline{|e|} \approx |\bar e|$ , the errors all have one sign. The correlation systematically overestimates or underestimates, and we can correct this. If $\overline{|e|}$ is noticeably larger than $|\bar e|$ , the errors have different signs. This is scatter, and tuning will not remove it. To measure the scatter, people sometimes add the standard deviation of the errors.

Tuning to a single measured point corrects the bias. The simplest way is to multiply the result of the correlation by a correction factor $k = p_b^{\text{lab}}/p_b^{\text{corr}}$ , found from one sample. Then apply it to other oils of the same system: neighbouring wells and blocks, and oils with a different producing gas–oil ratio in the same accumulation. We treat the formation volume factor in the same way: we shift the correlation by the difference at the bubble point pressure. The factor transfers to new oils only the part of the error that they share. That is why we check a tuned correlation with a second sample.

Tuning a bubble point pressure correlation to a single sample

p_b^{*}(R_{sb}, \gamma_g, \gamma_o, T) = k\,p_b^{\text{corr}}(R_{sb}, \gamma_g, \gamma_o, T),\qquad k = \frac{p_{b,1}^{\text{lab}}}{p_{b,1}^{\text{corr}}}

where:

$p_b^{*}$ tuned estimate of the bubble point pressure, MPa
$p_b^{\text{corr}}$ bubble point pressure from the original correlation, MPa
$k$ correction factor from sample 1, —
$p_{b,1}^{\text{lab}},\ p_{b,1}^{\text{corr}}$ laboratory and calculated bubble point pressure of sample 1, MPa

Units: any pressure units; the factor is dimensionless

Holds when

The oils belong to one system: a common source and a similar composition of the gas and the heavy fraction. For an oil of another type the factor does not transfer.
The input data of the new oil lie within the range of the correlation and are close to those of sample 1.

This is the simplest tuning. We can also fit the constants of the correlation to several samples. The more samples we have, the more reliable the factor is, and the better we can see whether the error has a scatter.

Worked exampleChoosing and tuning a correlation with the samples of a field

Given (assumed data)

Well 1: 110 m³/m³ (608 scf/STB); $\gamma_g = 0.80$ ; $\gamma_o = 0.854$ (34.2 °API); 85 °C (185 °F); $p_b = 18.0$ MPa
Well 2: 82 m³/m³ (453 scf/STB); $\gamma_g = 0.78$ ; $\gamma_o = 0.862$ (32.7 °API); 78 °C (172.4 °F); $p_b = 14.9$ MPa
Well 3: 138 m³/m³ (763 scf/STB); $\gamma_g = 0.82$ ; $\gamma_o = 0.846$ (35.8 °API); 92 °C (197.6 °F); $p_b = 20.7$ MPa
Well 4: 64 m³/m³ (354 scf/STB); $\gamma_g = 0.76$ ; $\gamma_o = 0.870$ (31.1 °API); 72 °C (161.6 °F); $p_b = 12.7$ MPa

Solution

Standing correlation: 16.83; 13.66; 19.55; 11.61 MPa. Errors: −6.5; −8.3; −5.6; −8.6%. Average error −7.2%, average absolute error 7.2%. All the errors have the same sign.
Al-Marhoun correlation: 17.92; 15.28; 20.05; 13.53 MPa. Errors: −0.4; 2.6; −3.1; 6.5%. Average error 1.4%, average absolute error 3.2%. The bias is small, but the errors have different signs.
We tune Standing to well 1: $k = 18.0/16.83 = 1.0695$ . For wells 2–4 the tuned values are 14.61; 20.91; 12.42 MPa, with errors of −1.9; 1.0; −2.2%.
On the same wells 2–4, the average absolute error is 1.7% for the tuned Standing correlation and 4.1% for the Al-Marhoun correlation.

Answer: The Standing correlation tuned to one sample predicts the bubble point pressure of the other three wells with an average absolute error of 1.7%, against 4.1% for the best untuned correlation.

What it means. The Al-Marhoun correlation is on average closer to the experiment, but its errors have different signs, and tuning will not remove them. The Standing correlation systematically understates the bubble point pressure of the oils of this system by about 7%, and one good sample removes this bias. The conclusion rests on only four samples. Before you rely on a tuned correlation, check it with the next sample, and do not apply it to oils outside the range of the samples. The data in this example are assumed for illustration.

When correlations cannot be trusted

Outside the range of the data. Beyond the solution gas–oil ratios, densities and temperatures on which the correlation was built, the formula continues smoothly, but nobody has checked it.
Volatile oils and near-critical fluids. Black oil correlations were built on oils with a moderate gas content. Volatile oils (light oils with a lot of dissolved gas) and near-critical fluids (fluids close to the critical point, where liquid and gas become alike) need a laboratory study and an equation of state. So do gas condensates (Types of reservoir fluids).
Heavy and high-viscosity oils. There are separate correlations for them. General formulas built on average oils make larger errors.
Non-hydrocarbon gases. Carbon dioxide, nitrogen and hydrogen sulfide noticeably change the gas solubility and the bubble point pressure. Some correlations have corrections. But for the oils of the subsalt fields of the Pre-Caspian Basin (fields below a thick salt layer), whose gas contains a lot of hydrogen sulfide, you cannot do without laboratory data.
An unusual composition of the heavy fraction. A correlation “knows” the oil only by its density. Highly paraffinic oils (waxy oils), such as those of Mangyshlak, have a different composition at the same density. For them we check the general correlations against samples.
Wrong input data. These include a producing gas–oil ratio that contains free gas, the gas specific gravity of the wrong stage, the oil density at 20 °C instead of 60 °F, and gauge pressure instead of absolute. An input error is often larger than the error of the correlation itself.
Mixing correlations. A bubble point pressure from one formula and a formation volume factor from another may be inconsistent with each other. In calculations, take the properties from one set and check them for consistency.

There is one more trap: the solution gas–oil ratio below the bubble point pressure. The Standing correlation, solved for $R_s$ , answers this question: how much gas is dissolved in an oil with such $\gamma_g$ and °API if its bubble point pressure is $p$ ? That describes a family of different oils, each at its own bubble point pressure. The degassing of one oil goes differently. With each step, both the composition of the freed gas and the oil itself change. So the $R_s(p)$ curve from the correlation may differ noticeably from the experiment, and tuning to the bubble point pressure does not correct its shape.

Worked exampleSolution gas–oil ratio below the bubble point pressure: correlation against experiment

Given (assumed data)

Oil: the same; from the laboratory data converted to separator conditions (the conversion example), $R_s = 76.3$ m³/m³ at 12 MPa and 41.0 m³/m³ at 6 MPa
Correlation: Standing, with the input data of the examples above; the correction factor $k = 1.0695$ from the tuning example

Solution

12 MPa $= 12/0.006895 = 1740.4$ psia. Then $R_s = 0.80\,[(1740.4/18.2 + 1.4)\cdot 10^{\,0.0125\cdot 34.2 - 0.00091\cdot 185}]^{1.2048} = 406.6$ scf/STB, or $406.6/5.53 = 73.5$ m³/m³. The error is −3.7%.
6 MPa: $R_s = 32.5$ m³/m³. The error is −20.7%.
With tuning, we divide the bubble point pressure by $k$ . At 12 MPa we put $1740.4/1.0695 = 1627.3$ psia into the formula, and get $R_s = 67.9$ m³/m³ (−11.0%). At 6 MPa we get 30.0 m³/m³ (−26.8%).

Answer: Below the bubble point pressure the correlation understates the solution gas–oil ratio of this oil by 3.7% at 12 MPa and by 21% at 6 MPa. Tuning to the bubble point pressure does not reduce the error.

What it means. In this oil the gas comes out more evenly as the pressure falls than in the “average” oil of the correlation's database, so the shape of the curve is different. Tuning shifted the whole curve downward. This moved it closer to the experiment at the bubble point pressure, but further from it below. That is why, for solution gas drive, the material balance and the reservoir simulation model, we take $R_s(p)$ and $B_o(p)$ below the bubble point pressure from differential liberation converted to separator conditions. The data in this example are assumed for illustration.

CalculatedSolution gas–oil ratio of the lesson oil: from laboratory data (solid line) and from the Standing correlation with the same

R_{sb}

= 110 m³/m³ (dashed). By the correlation the oil is saturated already at 16.8 MPa, not at 18. Below about 14 MPa the correlation gives less gas than the experiment: at 6 MPa, 32 against 41 m³/m³.

Gas condensate: what can be estimated from surface production

Black oil correlations do not suit gas condensate. In the reservoir it is a gas, and the liquid comes out at the surface. Correlations estimate the dew point (the pressure at which liquid first drops out of the gas) only roughly, so we measure it in the laboratory (gas condensate experiments). But from surface measurements we can estimate the properties of the reservoir gas above the dew point: the specific gravity of the whole stream, the gas deviation factor (from the curve for gas condensate mixtures), and the gas condensate formation volume factor. This factor is how much reservoir gas is needed to get a cubic metre of stable condensate (condensate with its dissolved gas removed).

Specific gravity of the reservoir gas and the gas condensate formation volume factor

\gamma_w = \frac{R\,\gamma_g + \rho_c/\rho_{\text{air}}}{R + GE},\qquad B_{gc} = (R + GE)\,B_g(p, T, Z_w)

where:

$\gamma_w$ specific gravity (relative to air) of the reservoir gas (the whole well stream), —
$R$ separator and stock-tank gas per 1 m³ of stable condensate, gas at 20 °C, m³/m³
$\gamma_g$ specific gravity of this gas, —
$\rho_c,\ \rho_{\text{air}}$ density of the condensate and of air at standard conditions (1.204 kg/m³ at 20 °C), kg/m³
$GE$ gas equivalent of the condensate (the volume of gas that a cubic metre of liquid condensate would make if it turned into gas), $V_m\rho_c/M_c$ , m³/m³
$B_{gc}$ gas condensate formation volume factor: reservoir gas per 1 m³ of stable condensate, m³/m³ (rb/STB)
$B_g,\ Z_w$ formation volume factor and gas deviation factor of the reservoir gas at $p$ and $T$ , m³/m³, —

Units: gas at 0.101325 MPa and 20 °C; $B_g = p_{\text{sc}}Z_wT/(pT_{\text{sc}})$

Holds when

The reservoir pressure is above the dew point, so the reservoir mixture is single-phase, and all the production came from the reservoir as gas.
The producing gas–oil ratio was measured at steady-state conditions, and the condensate droplets carried in the gas are counted (Reservoir fluid sampling).

The mass of reservoir gas per cubic metre of condensate is the mass of the separator gas plus the mass of the condensate itself. The amount of substance is $(R + GE)/V_m$ . From these we get $\gamma_w$ . The inverse, $1/B_{gc}$ , shows how much stable condensate is contained in a cubic metre of reservoir gas, that is, of the pore volume occupied by gas.

Worked exampleHow much reservoir gas per cubic metre of condensate

Given (assumed data)

Test: separator gas 1800 m³ per 1 m³ of stable condensate, $\gamma_g = 0.72$
Condensate: 760 kg/m³, molar mass 130 kg/kmol
Reservoir: 40 MPa, 105 °C (378.15 K), above the dew point

Solution

Gas equivalent: $GE = 24.055\cdot 760/130 = 140.6$ m³/m³ (24.055 m³/kmol is the molar volume of gas at 0.101325 MPa and 20 °C).
Reservoir gas: $\gamma_w = (1800\cdot 0.72 + 760/1.204)/(1800 + 140.6) = 0.993$ . This is noticeably heavier than the separator gas.
Pseudo-critical properties from the curve for gas condensate mixtures: $T_{pc} = 187 + 330\cdot 0.993 - 71.5\cdot 0.993^2 = 444.2$ °R $= 246.8$ K, and $p_{pc} = 706 - 51.7\cdot 0.993 - 11.1\cdot 0.993^2 = 643.7$ psia $= 4.438$ MPa.
Pseudo-reduced properties: $T_{pr} = 378.15/246.8 = 1.532$ and $p_{pr} = 40/4.438 = 9.01$ . From the equation fitted to the generalised chart (the topic on real gas), $Z = 1.061$ .
$B_g = \dfrac{0.101325\cdot 1.061\cdot 378.15}{40\cdot 293.15} = 0.003467$ m³/m³, and $B_{gc} = (1800 + 140.6)\cdot 0.003467 = 6.73$ m³/m³.

Answer: To get 1 m³ of stable condensate, we must withdraw 6.73 m³ of reservoir gas from the reservoir. A cubic metre of pore volume occupied by gas contains 0.149 m³ of condensate and 268 m³ of separator gas.

What it means. With $B_{gc}$ we convert the pore volume occupied by gas directly into condensate in place. To get separator gas, we multiply by the producing gas–oil ratio. The estimate holds while the pressure is above the dew point. Below it, part of the condensate drops out in the reservoir, and the condensate yield per cubic metre of gas falls. The constant-volume depletion experiment shows this. $Z$ from the curve for gas condensate mixtures is also a correlation. For rich mixtures we refine it with a calculation from the composition. The data in this example are assumed for illustration.

Terms and symbols

PVT correlation: An empirical formula that links the bubble point pressure, solution gas–oil ratio or formation volume factor to the producing gas–oil ratio, the gas and oil densities and the temperature. It is fitted to the laboratory data of a particular set of oils.
Range of a correlation: The intervals of solution gas–oil ratio, densities, temperature and pressure covered by the database of the correlation. Outside it the formula has not been checked.
Average relative error $\bar e$: The mean of the relative errors, with their signs. It shows the systematic bias of the correlation.
Average absolute relative error (AARE): The mean of the absolute values of the relative errors. It shows the overall level of errors.
Correlation tuning: Correcting a correlation with measurements, for example by multiplying it by a correction factor found from one sample.
Gas condensate formation volume factor $B_{gc}$: The volume of reservoir gas from which we get 1 m³ of stable condensate at the surface.

Common mistakes and misconceptions

Wrong

“Let us put 110 m³/m³ and 18 MPa straight into Standing's formula.”

In fact

The correlation was built in scf/STB, psia and °F. Convert the solution gas–oil ratio with a factor of about 5.53 (which includes a correction for the standard temperature of the gas), convert the pressure by dividing by 0.006895, and convert the temperature to degrees Fahrenheit.

Wrong

“A correlation that agreed with the laboratory on one sample is the best one for the field.”

In fact

The agreement may be a coincidence. Choose a correlation using several samples, and look at both the bias and the scatter of the errors. Tuning can remove the bias, but not the scatter.

Wrong

“If the bubble point pressure from the correlation has been tuned, the solution gas–oil ratio curve below it is correct too.”

In fact

Tuning corrects the level, not the shape. Below the bubble point pressure the correlation describes other oils, each at its own bubble point pressure. Take $R_s(p)$ below the bubble point pressure from the experiment.

Wrong

“The producing gas–oil ratio of the test is the solution gas–oil ratio of the reservoir oil.”

In fact

Only if the bottomhole pressure during the test was above the bubble point pressure and the flow had stabilised. Otherwise the producing gas–oil ratio contains free gas, and the bubble point pressure from the correlation comes out too high.

In depth: advanced detail

Equations of other correlations

Below are the equations of the correlations from the comparison in the lesson. They use oilfield units: pressure in psia, temperature in °F (in the Al-Marhoun correlation, °R, $T_R = T + 459.67$ ), and solution gas–oil ratio in scf/STB. $\lg$ is the base-10 logarithm. Do not put metric quantities into them.

Vasquez–Beggs correlation

R_s = C_1\,\gamma_{g100}\,p^{C_2}\exp\!\left(\frac{C_3\,\mathrm{API}}{T + 459.67}\right),\qquad \gamma_{g100} = \gamma_{g1}\left[1 + 5.912\cdot 10^{-5}\,\mathrm{API}\,T_1\,\lg\frac{p_1}{114.7}\right]

where:

$R_s,\ p$ solution gas–oil ratio of oil saturated at pressure $p$ ; at $p = p_b$ it is $R_{sb}$ (which gives $p_b$ ), scf/STB, psia
$\gamma_{g1},\ p_1,\ T_1$ specific gravity of the first-stage separator gas, and the pressure and temperature of that stage, —, psia, °F
$\gamma_{g100}$ gas specific gravity converted to a first stage at 114.7 psia (100 psig), —
$C_1,\ C_2,\ C_3$ 0.0362; 1.0937; 25.724 for oils of up to 30 °API and 0.0178; 1.1870; 23.931 for oils lighter than 30 °API, —

Units: oilfield units; $T$ is the reservoir temperature, °F

Holds when

The data: $R_s$ 0–2199 scf/STB, 15.3–59.5 °API. Different reviews give slightly different limits.
The formation volume factor of saturated oil: $B_o = 1 + A_1R_s + (T - 60)\,(\mathrm{API}/\gamma_{g100})\,(A_2 + A_3R_s)$ with $A_1 = 4.677\cdot 10^{-4}$ , $A_2 = 1.751\cdot 10^{-5}$ , $A_3 = -1.811\cdot 10^{-8}$ (up to 30 °API) and $4.670\cdot 10^{-4}$ , $1.100\cdot 10^{-5}$ , $1.337\cdot 10^{-9}$ (lighter oils).

To get the bubble point pressure, solve the equation for $p$ at $R_s = R_{sb}$ .

Glasø correlation

\lg p_b = 1.7669 + 1.7447\lg p_b^{*} - 0.30218\,(\lg p_b^{*})^2,\qquad p_b^{*} = \left(\frac{R_{sb}}{\gamma_g}\right)^{0.816}\frac{T^{0.172}}{\mathrm{API}^{0.989}}

where:

$p_b$ bubble point pressure, psia
$p_b^{*}$ auxiliary number of the correlation, —
$R_{sb},\ \gamma_g,\ T,\ \mathrm{API}$ solution gas–oil ratio, specific gravity of the total separator gas, temperature, °API, scf/STB, —, °F, °API

Units: oilfield units

Holds when

The data: bubble point pressure 165–7142 psia (1.1–49 MPa), 80–280 °F (27–138 °C), $R_{sb}$ 90–2637 scf/STB, 22.3–48.1 °API, $\gamma_g$ 0.65–1.276.
Formation volume factor: $\lg(B_{ob} - 1) = -6.58511 + 2.91329\lg B^{*} - 0.27683\,(\lg B^{*})^2$ , $B^{*} = R_{sb}(\gamma_g/\gamma_o)^{0.526} + 0.968\,T$ .

The squared logarithm lets the formula follow the curvature of the dependence over a wide range of pressures.

Al-Marhoun correlation for the bubble point pressure

p_b = 5.38088\cdot 10^{-3}\,R_{sb}^{0.715082}\,\gamma_g^{-1.87784}\,\gamma_o^{3.1437}\,T_R^{1.32657}

where:

$p_b$ bubble point pressure, psia
$R_{sb},\ \gamma_g,\ \gamma_o$ solution gas–oil ratio, specific gravities of the total separator gas and of the stock-tank oil, scf/STB, —, —
$T_R$ reservoir temperature in degrees Rankine, °R

Units: oilfield units

Holds when

The data: bubble point pressure 130–3573 psia (0.9–24.6 MPa), 74–240 °F (23–116 °C), $R_{sb}$ 26–1602 scf/STB, 19.4–44.6 °API, $\gamma_g$ 0.752–1.367.

This is a power-law form. Each input enters with its own exponent, found by regression (fitting) on Middle East oils.

Petrosky–Farshad correlation for the bubble point pressure

p_b = 112.727\left(\frac{R_{sb}^{0.5774}}{\gamma_g^{0.8439}}\,10^{x} - 12.34\right),\qquad x = 4.561\cdot 10^{-5}\,T^{1.3911} - 7.916\cdot 10^{-4}\,\mathrm{API}^{1.541}

where:

$p_b$ bubble point pressure, psia
$R_{sb},\ \gamma_g,\ T,\ \mathrm{API}$ as in the Standing correlation, scf/STB, —, °F, °API

Units: oilfield units

Holds when

The data: bubble point pressure 1574–6523 psia (10.9–45 MPa), 114–288 °F (46–142 °C), $R_{sb}$ 217–1406 scf/STB, 16.3–45.0 °API, $\gamma_g$ 0.578–0.852.

The form is the same as Standing's, but each variable has its own multiplier and exponent. The coefficients were fitted to Gulf of Mexico oils.

Your own correlation for a field or region

When many laboratory reports have accumulated for a region, we can build a correlation of our own. We take the form of one of the known correlations, for example $p_b = a\,(R_{sb}/\gamma_g)^{b}\,10^{\,cT - d\,\mathrm{API}}$ . We take logarithms and fit the constants by least squares (the method that makes the squared errors as small as possible). We set some of the reports aside for checking. The correlation should predict them no worse than the reports it was built on. Otherwise it has memorised the noise of the sample instead of the pattern.

A correlation of our own inherits the shortcomings of its data. If the sample contains no volatile oils or high temperatures, the correlation knows nothing about them. So we state its ranges and error statistics alongside it, as for published correlations. For accumulations with complex fluids, we tune an equation of state to all the samples instead of using correlations (Cubic equations of state).

Connections to other topics

Black oil model: solution gas–oil ratio and formation volume factors — what the solution gas–oil ratio and the formation volume factor are and how they are used.
Laboratory PVT tests — the laboratory data against which correlations are checked and tuned.
Ideal and real gas: the gas deviation factor (Z) — correlations for the gas deviation factor and for gas condensate mixtures.
Oil viscosity and interfacial tension — correlations for oil viscosity and interfacial tension.
Density and compressibility of reservoir oil — oil density in the reservoir and compressibility above the bubble point pressure.
Types of reservoir fluids — which fluids black oil correlations suit and which they do not.
Material balance for gas reservoirs — the gas equivalent of condensate in the balance of a gas condensate accumulation.

Check yourself

1
Which oil, other things being equal, will have the higher bubble point pressure?
1. A.The one with the higher reservoir temperature
2. B.The one with the lower solution gas–oil ratio
3. C.The one with the higher API gravity
4. D.The one whose dissolved gas is heavier
Show the answer
Correct answer: A. The one with the higher reservoir temperature
As temperature rises, the solubility of gas in oil falls, and a higher pressure is needed to hold the same amount of gas. A heavy gas and a light oil (higher °API), on the contrary, make dissolving easier and lower the bubble point pressure. Less gas also means a lower bubble point pressure.
2
Estimate the bubble point pressure with the Standing correlation: $R_{sb} = 95$ m³/m³ (gas at 20 °C), $\gamma_g = 0.72$ , oil 32 °API, reservoir 70 °C.
Show the answer
$R_{sb} = 95\cdot 5.53 = 525$ scf/STB, and $T = 70\cdot 1.8 + 32 = 158$ °F. The temperature factor is $10^{\,0.00091\cdot 158 - 0.0125\cdot 32} = 10^{-0.256} = 0.555$ , and the gas term is $(525/0.72)^{0.83} = 729^{0.83} \approx 238$ . So $p_b = 18.2\,(238\cdot 0.555 - 1.4) \approx 2380$ psia $\approx 16.4$ MPa.
3
For three samples a correlation was in error by +4, −6 and +2%. Find the average and the average absolute relative error. Will tuning help?
Show the answer
The average error is $(4 - 6 + 2)/3 = 0$ %, and the average absolute error is $(4 + 6 + 2)/3 = 4$ %. There is no bias. Errors of different signs are scatter, and a factor will not remove it. To understand the cause of the scatter, you need a different correlation, laboratory data for each object, or more samples.
4
A correlation gave a bubble point pressure 8% below the laboratory value for the first sample of a field. What is sensible to do for neighbouring wells of the same accumulation?
1. A.Switch to another correlation that matches this sample
2. B.Multiply the result of the correlation by 1/0.92 ≈ 1.087 for oils of the same system and check this with the next sample
3. C.Add 8% of the solution gas–oil ratio to all the results
4. D.Nothing: 8% is the usual accuracy of correlations
Show the answer
Correct answer: B. Multiply the result of the correlation by 1/0.92 ≈ 1.087 for oils of the same system and check this with the next sample
If the oils belong to one system, the bias of the correlation is most likely common to them, and the factor $k = 1/0.92$ removes it. Checking with the next sample is essential: one sample cannot tell a bias from a random error. Choosing a correlation by its agreement with one sample is the same mistake.
5
Why can we not use the producing gas–oil ratio of a test run at a bottomhole pressure below the bubble point pressure to estimate the solution gas–oil ratio of the reservoir oil?
Show the answer
Gas came out of the oil near the bottomhole. When this gas is mobile, it reaches the well faster than the oil, so the producing gas–oil ratio is greater than the solution gas–oil ratio of the reservoir oil. A correlation with such an $R_{sb}$ will give a bubble point pressure that is too high. You need the producing gas–oil ratio at a flow rate where the bottomhole pressure is above the bubble point pressure (Reservoir fluid sampling).
6
Which quantity for a gas condensate do black oil correlations and surface measurements not give reliably?
1. A.The gas equivalent of the condensate
2. B.The specific gravity of the reservoir gas
3. C.The dew point pressure
4. D.The gas condensate formation volume factor above the dew point
Show the answer
Correct answer: C. The dew point pressure
The specific gravity of the reservoir gas and $B_{gc}$ above the dew point come from the producing gas–oil ratio and the properties of the condensate and the gas. The gas equivalent comes from the density and molar mass of the condensate. Only a laboratory can find the dew point reliably, in a cell with a window.

Updated: 16 October 2026