A Mathematical Model Of Shale Gas Well Production Decline

I derived a simple and effective model of shale gas well production declines. I formulated that the decline rate ot shale wells can be calculated using this simple math formula:

Assuming the production rate is a function of time, P(T). Then the decline rate R(T) is defined as the negative time derivative of P(T) divided by P(T) itself:

Once R(T) is known, you can integrate it over time to know how much has the production rate dropped since the start of the well.

In fitting the projections of production with the actual Barnett Shale production numbers, I find that the IP (initial production rate) is 0.510 BCF/year. Time T is expressed in unit of months. Ri = 0.3515/month; Rf = 0.0005/month; Beta = 0.2475/months.

See the charts below how the shale gas well decline looks like:

Detailed explanations will be supplied at a later time. But my model makes precise prediction on the Barnett Shale production, based on merely the well counts. This is much better and more precise than many models proposed by the natural gas industry itself.

Please note that my projected production volumes, in orange bars, correlate to the well counts, in purple, much better than the actual production reported, the center bars.

My model even nicely matches Arthur Berman's shale gas well decline chart, which was created from actual production data:

Here is what it looks like when the cumulative production curve is super-imposed on Arthur Berman's chart. Please note Berman's chart is not a theoretical model, but actual production data:

See the curve fits right in the place!

This instablog post will be updated later with more elaboration of the model and of the details of the data. It will be linked to from one of my main Seeking Alpha articles. Please check back at a later time.

The discussion here pertains to US coal and natural gas stocks, as well as related ETFs: United Stated Natural Gas (UNG), ProShares Ultra DJ-UBS Natural Gas (BOIL), ProShares UltraShort DJ-UBS Natural Gas (KOLD), Market Vectors Coal ETF (KOL). It relates to coal as coal price is depressed partly due to record low natural gas prices. The discussion affect investors with interested in these names in the US coal sector: James River Coal Co. (JRCC), Patriot Coal Corp. (PCX), Arch Coal Inc. (ACI), Alpha Natural Resources Inc. (ANR) and Peabody Energy Corp. (BTU), Alliance Resource Partners LP (ARLP), Cloud Peak Energy Inc. (CLD), Cliffs Natural Resources Inc. (CLF), Consol Energy Corp. (CNX), Natural Resource Partners (NRP), Penn Virginia Resource Partners LP (PVR) and last but not least, Walter Energy Inc. (WLT).

And the discussion is relevant to these names in the oil and natural gas sector: Chesapeake Energy Corp. (CHK), Constellation Energy (CEP), Cabot Oil & Gas Corp. (COG), ConocoPhillips (COP), Anadarko Petroleum Corp. (APC), EOG Resources Inc (EOG), Devon Energy Corp. (DVN), Baker Hughes Inc. (BHI), Southwestern Energy Co. (SWN), Pioneer Natural Resources (PXD), Magnum Hunter Resources (MHR), Kinder Morgan Energy Partners (KMP), Enerplus Resource Fund (ERF), Carrizo Oil & Gas (CRZO), Callon Petroleum (CPE), Enterprise Products Partners LP (EPD), Goodrich Petroleum (GDP), GMX Resources (GMXR), IDT Corp (IDT), Lucas Energy (LEI), Rex Energy (REXX), Approach Resources (AREX), Natural Gas Services Grp. (NGS), Breitburn Energy Partners (BBEP), National Fuel Gas (NFG), Range Energy Resources (RRC), Petroquest Energy (PQ), Unit Corp. (UNT), Transocean Ltd. (RIG), BP plc. (BP) and Exxon Mobil Corp. (XOM).

Disclosure: I am long JRCC, PCX, ACI, ANR, BTU.