Unformatted text preview: 2 cp∆p 2.00E02 1.50E02
1.00E02
5.00E03 0.00E+00
1.80E+07 1.90E+07 2.00E+07 2.10E+07 2.20E+07 Pressure (Pa) The maximum value occurs at the extremes with a value of 0.0273 (unitless)
Formula Explanation/Derivation
Formula for pore compressibility: But , therefore: Assuming bulk volume is a constant: Rearranging and simplifying to single differentials: This is a first order separable ODE. If does not depend on pressure we find: 6 2.30E+07 2.40E+07 ENGI 9114 – Advanced Reservoir Engineering
Assignment # 1 Solutions – Winter 2011 Or: A Taylor series expansion yields: It is normally adequate in solid and liquids to neglect the second order or higher terms since
. Therefore: Now we must show the validity of the second formula. Note that: Therefore: May be rewritten as: Now completing a Taylor Series expansion: Again, neglecting second order or higher terms leads to: Therefore showing both formula to be valid.
NOTE: THERE IS NO SOLUTION TO PART C – IT WAS ONLY A HINT. 7 ENGI 9114 – Advanced Reservoir Engineering
Assignment # 1 Solutions – Winter 2011
Part D
Information given: Bulk volume reduced by 0.1% when pore pressure drops 1 bar
o when o is measured in bar
when is measured in Pa Porosity reduced by 0.3% when pore pressure drops 1 bar
o
o when is measured in bar
when is measured in Pa We have to fine the pore compressibility: But , therefore: Differentiating: Filling in our values: 8 ENGI 9114 – Advanced Reservoir Engineering
Assignment # 1 Solutions – Winter 2011
Part E
For a real gas: Since we know: Filling in for : Canceling constant terms: Rearranging: Differentiating: This is the formula for a real gas. For an ideal gas, , simplifying to: 9 ENGI 911...
View
Full Document
 Winter '11
 DrJohansen
 Advanced Reservoir Engineering

Click to edit the document details