Only expert needed

Test Data

In class problems:

1. At p = 2800 psig, determine: Bo, Rs.

2. At p = pb = 2620 psig, determine: Bob, Rsb.

3. At p = 1850 psig, determine: Bo, Rs.

Homework problems:

4. At p = 4500 psig, determine: Bo, Rs.

5. At p = pb = 2620 psig, determine: Bob, Rsb.

6. At p = 23500 psig, determine: Bo, Rs.

7. Determine the oil compressibility (co) between the bubble point pressure (pb = 2620) and p = 3500 psi.

Answers: 1. Bo = 1.4687 RVB/STB; Rs = 768 SCF/STB. 2,5. Bo = 1.474 RVB/STB; Rs = 768 SCF/STB.

3. Bo = 1.3625 RVB/STB; Rs = 545 SCF/STB. 4. Bo = 1.4302 RVB/STB; Rs = 768 SCF/STB.

6. Bo = 1.4316 RVB/STB; Rs = 684.17 SCF/STB 7. 0.0000176 1/psi

A. Informational Questions on Black Oil, Correlations and the Regression Process

1. What is a correlation? Give one example for gas and two for oil.

2. Regression is a process that involves several steps: (a) Determine which variables are significant; (b) Determine a functional form; (b) Determine constants for that function to minimize error.

For black oil correlations, which three quantities appear in all correlations as the basic three variables?

Give three example functional forms:

3. Explain a “black oil” model for reservoir fluid properties. How is it a simplification of the “true” or “actual” fluid properties?

4. What is the best source of fluid data for a given field? Give two ways to sample a reservoir fluid.

5. When must you use fluid correlations?

6. How do you choose an oil correlation? (Give three considerations.)

7. Which pressure is the most important point at which to determine a fluid’s properties? How is this value found in a lab PVT cell?

8. If you or your company prefers to use a particular fluid correlation but it is slightly off on known bubble point fluid properties for a particular reservoir, can you still use this correlation? How? What must you be careful about?

B. Basic Black Oil Calculations using Standing and Vasquez/Beggs Correlations (See correlation equations in the accompanying handout)

Use this basic data for all calculations:

Basic three input variables:

Gas Gravity g = 0.86

Oil Gravity o = 0.94 = 19.03 °API (check this!)

Reservoir Temperature, TR = 150 °F

Additional input variables (depends on case):

Pressure, p = pb = 5200 psi

Solution Gas Oil Ratio, Rs = 940 SCF/STB

8. If Rsb = 940 SCF/STB, determine the bubble point pressure of this oil system, using:

(a) Standing [Answer = 4769.2 psi ];

(b) Vasquez and Beggs [Answer = 5990.3 psi ]

9. If pb = 5200 psi, determine the solution GOR (Rs) of this oil system, using:

(a) Standing [Answer = 1043.8 SCF/STB ];

(b) Vasquez and Beggs [Answer = 805.4 SCF/STB ]

10. If pb = 5200 psi and Rsb = 940 SCF/STB, determine the oil FVF (Bob) of this oil system, using:

(a) Standing [Answer = 1.515 RVB/STB ];

(b) Vasquez and Beggs [Answer = 1.441 RVB/STB]

11. If pb = 5200 psi and Rsb = 940 SCF/STB, determine the oil compressibility (co) of this oil system at pb, using Vasquez and Beggs. [Answer: co = 9.754∙10-6 1/psi]

12. If pb = 5200 psi and Bob = 1.515 RVB/STB, determine the oil FVF (Bo) of this oil system at p = 6000 psi. (Use the co from problem 11). [Answer: Bo = 1.5032 RVB/STB]

1. Draw a p-V diagram for a pure component with one isotherm. Label the liquid, two-phase, and vapor regions. Explain how the concept of compressibility (both for liquid and vapor) is represented in that picture.

2. Give four examples of volume changes that occur in an oil/free gas/water reservoir as pressure drops.

3. Draw a Bo vs. p curve. Explain which part of the curve illustrates isothermal compressibility. What is the slope of this part of the curve? What feature on this picture illustrates thermal expansion (volume change due to temperature change)?

4. At bubble point pressure pBP = 4450 psi, B0BP = 1.5 RVB/STB, and co = 8.8·10-6 psi-1. Find Bo at p = 5000 psi using (a) Eqn. (4) and (b) Eqn. (5). (c) Draw the Bo vs. p curve for this oil. [ Bo = 1.49 RVB/STB ]

5. Equations (4) and (5) look different but give essentially the same answer. Why?

6. Is co constant for an oil above its bubble point?

7. An oil reservoir (with a fluid filled pore volume of 85 million bbls) is discovered at an initial average pressure pi = 6000 psi. Fluid tests indicate that the oil has a bubble point of 4860 psi. The averaged compressibility of both the connate water and the oil present is c = 8.8·10-6 psi-1. Assume the rock and formation pore volume remains constant. As oil is produced from the reservoir, assume that pressure changes occur instantly over the entire reservoir. (Not true, since pressures will be lower near wells.) When the average pressure in this reservoir has dropped to the bubble point (4860 psi), how many RVB of oil have been removed from the reservoir? If Bo = 1.30 RVB/STB and Rs = 800SCF/STB for this oil, how many STB of oil have been removed? How many MCF of gas has been produced at the surface? (Hint: Use Eqn. (6)) [ RVB produced = 852.7·103 RVB oil; Np = 655.9·103 STB; Gp = 524.75 MMCF gas ]

1. Define the following: (a) Dead Oil; (b) Live Oil

2. Sketch a graph of o vs. p. Why does o increase above the bubble point?

3. For a 32 °API oil at TR = 160° F, with Rs = 800 SCF/STB, please determine: (a) od; (b) o .Perform the calculations on another page (show your work), and write answers in the chart below: Check your calculations with the Excel viscosity project I sent you. Do not just write in numbers below from the Excel project.

4. Let the same oil as in Problem 3 (32 °API oil at TR = 160 °F, with Rsb = 800 SCF/STB) be at its bubble point pressure (pb = 3500 psi). (Use ob from the Beggs and Robinson equations above.) Please determine o at p = 4000 psi using Vasquez and Beggs, (a) Graph; (b) Equations.

1. Give an approximate viscosity at reservoir conditions (T = 140 F, p = 5000 psi) for the following fluids:

(First pick numbers from your head. I hope your intuition is right. Then, look at your correlation charts and/or plug basic numbers into the Excel calculations to get a more firm idea. For both oils, consider moderate values of Rs of 600-800 SCF/STB.)

2. How does reservoir water viscosity vary with temperature? Pressure? Salinity? (Sketch three small graphs of w vs. T, w vs. Pressure (p), and w vs. Salinity (S).)

3. Water viscosity: Determine the viscosity of a formation water with these properties: (p = 6000 psi, T = 180 F, and Salinity S = 4 wt % salinity) Use the McClain charts, check with Excel.

4. Gas viscosity (Lee, Gonzalez and Eakin): For a gas with gravity  = 0.9, at p = 5000 psi and T = 160 F, please determine: (a) AMW; (b) Gas Density, g ; (c) Gas viscosity, g . (Use Z from Excel. Show your calculations on another piece of paper.)

5. Sketch a graph of how gas viscosity varies with pressure, p.

1. Look at the graph of the Hall data. (a) From the graph, read the cf for  = 10%.

(b) From Hall’s equation (1) which takes  as a percent, calculate cf for  = 10%.

(c) From Hall’s equation (2) which takes as a fraction, calculate cf for  = 10%. How close are these three values?

2. Give four examples of volume changes that occur in an oil/free gas/water reservoir as pressure drops.

3. Look at the Newman Consolidated Sandstone graph. (a) From the graph, read the cf for  = 10%.

(b) From Newman’s SS equation (3), calculate cf for  = 10%. How close are these two values?

4. Look at the Newman Limestone graph. (a) From the graph, read the cf for  = 15%.

(b) From Newman’s LS equation (4), calculate cf for  = 15%. How close are these two values?

5. A reservoir with an initial pressure of p1 = 7800 psi has a porosity 1 = 17.0%. If the reservoir has a formation compressibility of cf = 8·10-6 1/psi, determine the porosity 2 of the formation after the average pressure has declined to 6500 psi. Use both the “exact” equation and the equation using the truncated series approximation for ex. [Answers: 16.823% and 16.823%]

6. Below is a graph of measured values of cf for friable sandstones. Does the Hall correlation fit this data? Would any correlation fit this data set? Why is this data so scattered?

From Newman’s paper: Measured values of cf for friable sandstones.

Petr 241: Formation Compressibility Correlations

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