Engineering Hw For THADEUS

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

Type of Fluid	Your Intuition	Quick Check of Chart and/or Excel Calcs
(a) Reservoir water:
(b) Light oil (API 35-40)
(c) Heavy oil (API 15-20):
(c) Gas

(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.

Method	w1	(w/w1)	w
Chart
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.)

	Excel	Hand Calc’s
AMW
Z
g
g

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

 

 

Formation Compressibility Equations
(Thermodynamic) Definition of Isothermal Compressibility [Eqn (1)] (units are 1/pressure; for petroleum engineers, usually 1/psi)
In terms of ordinary derivative (understanding that T = const) [Eqn (2)]
In terms of V and p….(this is a(n) (useful) approximation) [Eqn (3)]
Integrated form of Eqn (2) [Eqns (4a) and (4b)]
Truncated series approximations to Eqns (4) [Eqn (5a) and (5b)]
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)]
Series representation of ex…..

 

 

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.

 

 

 

 

 

 

 

 

 

 

Formation Compressibility Correlations
1. Hall Correlation (porosity as a PERCENT) (in other words, if  = 16%, use 16, not 0.16)
2. Newman Correlation for Consolidated Sandstones: (porosity as a fraction)
3. Newman Correlation for Limestones: (porosity as a fraction)

 

 

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%]

 

 

 

 

11. 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

 

1. Hall Correlation (porosity as a PERCENT) (in other words, if  = 16%, use 16, not 0.16)
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.
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:
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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