Hyperbolic and Exponential Decline Curves

The Arps Hyperbolic Decline curves are generally used to predict oil or gas production after the first couple of weeks of production. They use past performance of the well to predict future performance. We will see that predicting performance is sensitive to the value of b selected.

  Hyperbolic Curves take the form Qt = qib/(1-b)Di*(qi1-b-q1-b). Where Qt=Cumulative Oil Production at time t; qi=Production Rate at time t; q=Production Rate; Di=Initial Decline as a fraction of production rate; b is a value between 0<b<1. The median value of b is 0.5.

We will now show several examples .

Assuming rate at abandonment is 20 BOPD, the cumulative oil at abandonment is 13,000 Bbl.

Assuming rate at abandonment is 20 BOPD, the cumulative oil at abandonment is 12,000 Bbl.

Assuming rate at abandonment is 20 BOPD, the cumulative oil at abandonment is 15,000 Bbl.

Generating these Hyperbolic trendlines is discussed in the following linkwww.dofusdaddy.com/Decline-Curve-Analysis/Hyperbolic-Curves-Analysis.htm . It involves using Excel VBA programming in conjunction with the Excel Solver. If you want a simpler method of generating Rate Cumulative Curves use the Exponential  trendline that comes with Excel and check the following link www.dofusdaddy.com/Decline-Curve-Analysis/Decline-Curve-Analysis.htm .

 

Assuming rate at abandonment is 20 BOPD, the cumulative oil at abandonment is 18,000 Bbl.

Assuming rate at abandonment is 20 BOPD, the cumulative oil at abandonment is 32,000 Bbl. Here we have omitted the first two early points on the graph to make sure we are dealing with pseudo steady state flow.

You will need the following books. Excel Scientific and Engineering Cookbook and Microsoft Excel 2010 Bible. You can order them on http://www.amazon.com . I also suggest articles by Arps and Fetkovich available at the Society for Petroleum Engineers. One of the most comprehensive sources on line is http://www.fekete.com/software/rta/media/webhelp/c-te-analysis.htm .

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