Computer Programs and Code

Matlab function for F-test

James A. Conder — Thu, 10 Mar 2011 11:10:09 PST

A supplemental Matlab function “ftest” is included with the manuscript

Anderson and Conder, 2011, Discussion of Multicyclic Hubbert modeling as a method for forecasting future petroleum production, Energy and Fuels, dx.doi.org/10.1021/ef1012648.

This function uses a statistical F-test to determine the likelihood that an observed improvement of a fit to data warrants the use of additional parameters. The function was written in Matlab ver. R2010b (Mac). The “.txt” extension is for ease of distribution and should be removed for use.

Usage:

>> [ p ] = ftest(n,np1,np2,chi1,chi2)

The function requires five inputs: n is the number of data to be fit. np1 & np2 are the numbers of free parameters used in the two models. chi1 and chi2 are (normalized) sums of the squares of the misfits to the data for the two models.

One output, p, is returned. p is the probability (between 0 and 1) that the improvement of the fit is due to chance. Therefore a small value of p means a high confidence that the additional parameters are warranted.

Caveat emptor.

March 10, 2011

James Conder

Matlab function for Multicycle Hubbert curve fitting

James A. Conder — Fri, 21 Jan 2011 12:50:16 PST

A supplemental Matlab function “fit_multicycle” is included with the manuscript “Discussion of Multicyclic Hubbert modeling as a method for forecasting future petroleum production”, by Anderson and Conder. This function fits a production time series to a desired number of Hubbert cycles (derivatives of logistic curves). The function was written in Matlab ver. R2010b (Mac). The “.txt” extension is for ease of distribution and should be removed for use.

Usage:

>> [Ppred params rmse] = fit_multicycle(time,prod,nk,nseeds)

The function requires four inputs: time, prod, nk, nseeds. prod and time are vectors of production and associated time stamps. nk is the number of desired curves. nseeds is the number of random seed trials. The greater number of trials, the more likely the program will find a global minimum, but at the expense of time. More curves will generally require a non-linearly increasing number of seeds.

Three outputs are returned: 1) Ppred: predicted production having the same number of data as actual production. Predicted production is the sum of the curves. 2) params: nk x 3 matrix containing the best fitting parameters, tmax (col.1), pmax (col.2), and a (col.3), for each curve. 3) rmse: root mean square error for the model production curve relative to the actual production.

Note: It is not only possible but, quite likely for physically unrealistic parameters (e.g., negative production) to arise when asking for more curves than the data warrant.

For a quick comparison of actual and model production:

>> plot(time,prod,time,Ppre)

Caveat emptor. James Conder

Excel Interface for the Kansas Geological Survey Slug Test Model

Steven P. Esling — Thu, 29 Jan 2009 08:55:27 PST

The Kansas Geological Survey (KGS) developed a semi-analytical solution for slug tests that incorporates the effects of partial penetration, anisotropy, and the presence of variable conductivity well skins. The solution can simulate either confined or unconfined conditions. The original model, written in FORTRAN, has a text-based interface with rigid input requirements and limited output options. We recreated the main routine for the KGS model as a Visual Basic macro that runs in most versions of Microsoft Excel and built a simple-to-use Excel spreadsheet interface that automatically displays the graphical results of the test. A comparison of the output from the original FORTRAN code to that of the new Excel spreadsheet version for three cases produced identical results.