1 Engineering hw
Jim_Ak
hw_19_homework.docx1. Give an approximate viscosity at reservoir conditions (T = 140 F, p = 5000 psi) for the following fluids:
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Type of Fluid |
Your Intuition |
Quick Check of Chart and/or Excel Calcs |
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(a) Reservoir water: |
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(b) Light oil (API 35-40) |
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(c) Heavy oil (API 15-20): |
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(c) Gas |
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(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.
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Method |
w1 |
(w/w1) |
w |
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Chart |
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Excel |
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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.)
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Excel |
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AMW |
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Z |
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g |
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g |
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5. Sketch a graph of how gas viscosity varies with pressure, p.
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Formation Compressibility Equations |
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(Thermodynamic) Definition of Isothermal Compressibility [Eqn (1)] (units are 1/pressure; for petroleum engineers, usually 1/psi) |
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In terms of ordinary derivative (understanding that T = const) [Eqn (2)] |
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In terms of V and p….(this is a(n) (useful) approximation) [Eqn (3)] |
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Integrated form of Eqn (2) [Eqns (4a) and (4b)] |
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Truncated series approximations to Eqns (4) [Eqn (5a) and (5b)] |
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Reduction (V) of pore volume V in a reservoir which has undergone an average p (over the entire volume V) (rearranged Eqn (3)) [Eqn (6)] |
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Series representation of ex….. |
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6. 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?
7. Give four examples of volume changes that occur in an oil/free gas/water reservoir as pressure drops.
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Formation Compressibility Correlations |
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1. Hall Correlation (porosity as a PERCENT) (in other words, if = 16%, use 16, not 0.16)
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2. Newman Correlation for Consolidated Sandstones: (porosity as a fraction)
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3. Newman Correlation for Limestones: (porosity as a fraction)
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8. 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?
9. 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?
10. 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%]
From Newman’s paper: Measured values of cf for friable sandstones.
Petr 241: Formation Compressibility Correlations
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1. Hall Correlation (porosity as a PERCENT) (in other words, if = 16%, use 16, not 0.16)
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2. Hall Correlation (porosity as a fraction) (in other words, if = 16%, use 0.16)
(I do not know the origin of this version of Hall’s. Most books give the first version of Hall’s. Both give fairly similar results (but not identical). Note: The Hall correlations are based on only 12 rock data points! Sandstones and limestones. This is a very limited set of data. |
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3. Newman Correlation for Consolidated Sandstones: (porosity as a fraction)
This was based on data for 79 SS samples, ranging in porosities from 2-23%. The average error of the correlation is 2.6%. Note that this equation (and the one below) are of the general hyperbolic form:
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4. Newman Correlation for Limestones: (porosity as a fraction)
This was based on data for LS samples (not sure the number) ranging in porosities from 2-33%, with average error of 11.8%. (A poorer correlation for LS.)
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