The Monte Carlo method is attractive when it is infeasible or impossible to compute an exact result with a deterministic algorithm.
Excel can handle common probability distributions, and can thus serve as a Monte Carlo simulator.
Quantitative estimation of uncertainty allows one to determine where time / money is most effectively spent, and to further avoid the trap of being misled as a result of a previous bad experience with a poorly defined parameter
The importance of the various input parameters will change, according to the various magnitudes. There is a linkage in that one parameter becomes more or less important as another parameter value is changed, so the simulation must be executed for locally specific conditions.
Additional Details as a Text Document The Statistical Approach
To modify spreadsheet to accommodate a different three parameter simulation, simply re-title the various attributes and adjust the individual calculations as required. This worksheet models the Wang & Lucia Dual Porosity “m” Exponent
As a QC device, the distribution of Excel random numbers used to drive the Monte Carlo simulation, are ‘binned’ from zero to one
With 2000 simulation performed, we expect to find Frequency ~ 200 in each of the ten bins
The Excel Random() function has approached the ideal distribution
QC the Monte Carlo
Monte Carlo Simulation of Sw(Archie) Sw(Archie) Uncertainty
One issue of interest is the dependence of Sw upon individual attribute values / uncertainties
With the specifications at right
Sw(mean) = 0.357
(Sw) = 0.038
There is a 95% likelihood that Sw is contained within + / - 2
(0.357 – 0.076) < Sw < (0.357 + 0.076)
0.28 < Sw < 0.433
Be aware of how Excel ‘bins’ data
Monte Carlo Simulation of Sw(Archie) Excel Bins
The Freq of a specific Bin is not a centered value
Sw_Bin=0.25 0.225 .LT. Sw .LE. .25
Sw_Bin=0.275 0.25 .LT. Sw .LE. .275
Sw_Bin=0.30 0.275 .LT. Sw .LE. .30
Sw_Bin=0.325 0.30 .LT. Sw .LE. .325
Sw(Mean)=0.357 but Bin Freq, and associated graphic, peaks to the high side of this value
Bin Values are shifted with respect to actual distribution
Be aware of how Excel ‘bins’ data
Nonlinear relationship affects probability distributions. Oilfield Review. Autumn 2002. Ian Bryant, Alberto Malinverno, Michael Prange, Mauro Gonfalini, James Moffat, Dennis Swager, Philippe Theys, Francesca Verga.
The Archie relationship for a given formation, with constant “a”, “m”, “n” and Rt results in a hyperbolic relationship of Sw to porosity (blue)
This relationship distorts the frequency distributions , which are shown along the axes
A normal uncertainty distribution about a given porosity ( green ) becomes a log-normal distribution for the resulting Sw uncertainty (red)
The mean value ( dashed yellow ) and three sigma points ( dashed purple ) show the skewed Sw distribution
Sw distributions determined with Monte Carlo modeling are distorted at high values, since Sw cannot exceed 100%.
A change in one can cause another to become more, or less, important
Concepts (and spreadsheet) applicable to many common oilfield issues
Allow us to focus time and budget in the most efficient manner
Comments by Carlos Torres-Verdin, University of Texas
Phillipe Theys has a book which addresses this issue, as does Darwin.
The book by Darwin especially considers the effects on porosity (also of the shaly-sand case). He was the first to perform a similar analysis .
One should be sure to recognize that resistivity logs are affected by invasion and shoulder-bed effects
This can cause significant errors in the estimation of Sw because Rt is not representative . The latter effects can be more significant that the ones you have explicitly addressed.
Electrical anisotropy effects could have a significant impact on Rt in deviated and horizontal wells .
The most significant example is that of thinly-bedded sequences , where nuclear and resistivity logs are significantly biased (in addition to the clay effect) because of shoulder-bed and invasion effects.
Carlos Torres-Verdin: Be sure to recognize that logs are affected by various issues Ozark Mtns Road Cut, SW Missouri
Quantifying Petrophysical Uncertainties S J Adams 2005 Asia Pacific Oil & Gas Conference, Jakarta, Indonesia, 5 - 7 April 2005
Quantitative uncertainty definition is more than just using Monte Carlo simulation to vary the inputs to the interpretation model
The largest source of uncertainty may be the interpretation model itself
In graphic at right, (Rhob) is calculated with , and without , light hydrocarbon corrections
(D-N) and (Dt) are not LHC corrected
Accounting for LHC effects shifts (D) to over-lay the core distribution
We appreciate the unidentified LSU faculty who posted their material (located via Google) to http://www.enrg.lsu.edu/pttc/ Additional Considerations
How can I simulate values of a discrete random variable ?
How can I simulate values of a normal random variable ?
You can download the sample files that relate to excerpts from Microsoft Excel Data Analysis and Business Modeling from Microsoft Office Online. This article uses the files RandDemo.xls, Discretesim.xls, NormalSim.xls, and Valentine.xls.
Early morning carbonate bluffs along Steel Creek, Arkansas Thank you for your Time and Interest
R. E. (Gene) Ballay’s 32 years in petrophysics include research and operations assignments in Houston (Shell Research), Texas; Anchorage (ARCO), Alaska; Dallas (Arco Research), Texas; Jakarta (Huffco), Indonesia; Bakersfield (ARCO), California; and Dhahran, Saudi Arabia. His carbonate experience ranges from individual Niagaran reefs in Michigan to the Lisburne in Alaska to Ghawar, Saudi Arabia (the largest oilfield in the world). He holds a PhD in Theoretical Physics with double minors in Electrical Engineering & Mathematics , has taught physics in two universities , mentored Nationals in Indonesia and Saudi Arabia, published numerous technical articles and been designated co-inventor on both American and European patents . At retirement from the Saudi Arabian Oil Company he was the senior technical petrophysicist in the Reservoir Description Division and had represented petrophysics in three multi-discipline teams bringing on-line three (one clastic, two carbonate) multi-billion barrel increments. Subsequent to retirement from Saudi Aramco he established Robert E Ballay LLC, which provides physics - petrophysics training & consulting services. He served in the U.S. Army as a Microwave Repairman and in the U.S. Navy as an Electronics Technician, and he is a USPA Parachutist and a PADI Dive Master. Chattanooga shale Mississippian limestone