Bo and Solution GOR Calculator: Standing Correlations for Black Oil PVT

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Black Oil PVT Studio: Standing Correlations

Solution gas oil ratio, bubble point pressure, oil formation volume factor and reservoir oil density from the Standing correlations, with the saturated and undersaturated branches handled separately and the bubble point verified two independent ways.

Fluid properties
Saturation state
Two charts against pressure for a 30 API oil at 200 degrees Fahrenheit, showing solution gas oil ratio rising to a plateau at the bubble point and oil formation volume factor rising to a peak at the bubble point then falling as the undersaturated oil compresses
Solution gas rises with pressure until the bubble point and is constant above it. The formation volume factor peaks at the bubble point, the largest the oil ever gets in the reservoir.

One barrel in the tank is not one barrel in the ground

A barrel of oil measured in a stock tank at the surface occupied more space in the reservoir than it does in the tank, because down there it had gas dissolved in it and it was hot. The formation volume factor is the ratio of those two volumes, and the solution gas oil ratio is how much gas was dissolved. Get these wrong and every volumetric number downstream is wrong with them, because oil in place divides by Bo and production forecasts multiply by it.

The right way to get these numbers is a laboratory PVT report on a properly collected bottomhole sample. The common situation is that you do not have one, or you have one from a well four miles away in a different fault block, and you still need numbers today. That is what correlations are for, and Standing published the ones still most widely used in 1947, fitted to California crudes.

What Standing actually gives you

Three expressions do most of the work. Solution gas oil ratio comes from gas gravity times the quantity pressure over 18.2 plus 1.4, times 10 raised to 0.0125 times API minus 0.00091 times temperature, all raised to the power 1.2048. Bubble point pressure is the same relationship rearranged. Formation volume factor is 0.9759 plus 0.000120 times the quantity Rs times the square root of gas gravity over oil gravity, plus 1.25 times temperature, raised to 1.2.

Those constants look arbitrary because they are: they are regression coefficients, not physics. What matters is the shape they produce. More gas dissolved means a larger Bo. Hotter oil means a larger Bo. Lighter oil, meaning higher API, dissolves more gas at a given pressure and therefore swells more. All three behaviours are visible by changing one input in the tool and watching the curves move.

The two published forms are not exact inverses

Here is something worth knowing that most calculators quietly hide. If you take a solution gas oil ratio of 350 scf/STB for a 30 API oil at 200 degrees Fahrenheit with 0.70 gas gravity, Standing published bubble point expression returns 2003.21 psia. If you instead take the published Rs expression and solve it numerically for the pressure that produces exactly 350 scf/STB, you get 2003.38 psia.

The gap is 0.17 psi, or 0.0084 percent. It is not a bug in either equation and it is not a rounding error in the arithmetic. Standing published the two expressions separately, each with its own rounded coefficients, so they are near inverses rather than exact ones. The tool computes both and reports the difference in the status line rather than picking one and hoping you do not notice. In practice the discrepancy is far smaller than the uncertainty in the correlation itself, which is several percent. It matters only if you build a loop that converts back and forth repeatedly, where it can slowly drift.

The same effect shows up if you switch the tool from entering solution gas to entering bubble point pressure and back. Entering 350 scf/STB gives a bubble point of 2003.21 psia, and feeding that pressure back gives 349.97 scf/STB rather than 350.00. Now you know why.

Above and below the bubble point are different worlds

The bubble point is where the first bubble of gas comes out of solution. Above it the oil is undersaturated: all the gas is dissolved, and lowering the pressure simply lets the oil expand slightly, so Bo rises as pressure falls. Below it the oil is saturated: gas is leaving solution, and each cubic foot that leaves takes volume out of the oil phase, so Bo falls as pressure falls.

That is why the Bo curve has a peak rather than a slope, and the peak sits exactly at the bubble point. It is the largest the oil ever is inside the reservoir. Standing covers the saturated side. For the undersaturated side this tool uses the Vasquez and Beggs isothermal compressibility, applying Bo equals Bo at the bubble point times the exponential of minus compressibility times the pressure difference. The two branches are joined at the bubble point, and you can see in the table that the crossover is smooth.

A worked example

Take the defaults: 30 API oil, gas gravity 0.70, reservoir temperature 200 degrees Fahrenheit, solution gas at the bubble point of 350 scf/STB, and a current reservoir pressure of 2000 psia.

  1. Oil specific gravity is 141.5 divided by 161.5, which is 0.87616.
  2. Bubble point from Standing is 2003.21 psia. The reservoir at 2000 psia is therefore just barely saturated, essentially sitting on its bubble point.
  3. Formation volume factor at the bubble point is 0.9759 plus 0.000120 times the quantity 350 times the square root of 0.70 over 0.87616, plus 250, raised to 1.2. That comes to 1.21559 rb/STB.
  4. At 2000 psia the solution gas has fallen very slightly to 349.30 scf/STB and Bo to 1.21527 rb/STB.
  5. Reservoir oil density: one stock tank barrel carries 62.4 times 0.87616 pounds of oil, which is 54.67 lb, plus 0.0136 times 349.30 times 0.70 pounds of dissolved gas, which is 3.33 lb, a total of 58.00 lb. Dividing by Bo gives 47.72 lb/ft3.

That last step is a genuine check rather than a restatement. The density card is computed from the standard density expression, and the mass balance above arrives at the same number from the separate quantities of oil and gas. If those two disagreed, something in the chain would be wrong. They agree exactly, which is why the tool shows the working.

Note how close the reservoir pressure is to the bubble point in this example. That is an uncomfortable place for a field to be. A small drawdown puts the near wellbore region below bubble point, gas comes out of solution, relative permeability to oil falls, and productivity drops before any material depletion has occurred.

Knowing when not to trust the answer

  • Standing was fitted to California crudes. On waxy, aromatic or unusual fluids the error can reach ten percent or more.
  • Condensates are outside the range. Above roughly 60 API the black oil model itself is the wrong description, not just the coefficients.
  • Non hydrocarbon gas breaks it. Significant carbon dioxide, nitrogen or hydrogen sulphide changes the solution behaviour and Standing has no term for it.
  • Separator conditions matter. Solution GOR depends on how the fluid was separated at surface, so a reported GOR from a different separator train is not directly comparable.
  • Gas gravity is often guessed. It has a strong influence on both bubble point and Bo, so a casual 0.65 typed in place of a measured 0.80 moves the answer more than most people expect.
  • Use laboratory data when it exists. A correlation is a stand in, and the tool exists to give a defensible estimate, not to replace a PVT report.

Using the tool

Enter oil gravity, gas gravity, reservoir temperature and the pressure you care about. Then tell the tool which saturation quantity you actually know: solution gas oil ratio at the bubble point, or the bubble point pressure itself. It computes the other one and everything downstream.

The two plots show solution gas and formation volume factor against pressure with the bubble point marked and your chosen pressure highlighted as a point on the curve. The table gives the full pressure walk with the saturation state labelled row by row, and the step listing reproduces the arithmetic including both routes to the bubble point and the density mass balance. The export row will download the plots as an image, the table as a CSV file, or print the panel.

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