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Mark Anthony, is an IT professional and who had a scientific research background before joining the information revolution. Visit his blog: Stockology (
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  • A Mathematical Model Of Shale Gas Well Production Decline 11 comments

    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:

    (click to enlarge)

    Assuming the production rate is a function of time, P(NYSE: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:

    (click to enlarge)

    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.

    (click to enlarge)

    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:

    (click to enlarge)

    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:

    (click to enlarge)

    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 (NYSEARCA:UNG), ProShares Ultra DJ-UBS Natural Gas (NYSEARCA:BOIL), ProShares UltraShort DJ-UBS Natural Gas (NYSEARCA:KOLD), Market Vectors Coal ETF (NYSEARCA: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 (NASDAQ:ARLP), Cloud Peak Energy Inc. (NYSE:CLD), Cliffs Natural Resources Inc. (NYSE:CLF), Consol Energy Corp. (NYSE:CNX), Natural Resource Partners (NYSE:NRP), Penn Virginia Resource Partners LP (NYSE:PVR) and last but not least, Walter Energy Inc. (NYSE:WLT).

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

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

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Comments (11)
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  • Mark Anthony
    , contributor
    Comments (3595) | Send Message
    Author’s reply » The official web page to get Barnett shale gas well statistics:


    Barnett shale well statistics:


    The chart:
    30 Apr 2012, 01:32 PM Reply Like
  • Dryspell
    , contributor
    Comments (15) | Send Message
    Congrats - you derived an equation that has already been in use in the oil industry for 70 years. What else have you discovered?
    30 Apr 2012, 02:40 PM Reply Like
  • Mark Anthony
    , contributor
    Comments (3595) | Send Message
    Author’s reply » Dryspell:


    I am not trying to win a Nobel Prize. I am trying to find out some facts. Good you agree the formula works. That's all I ever care. Now get back to the question.


    The question is how much can a typical shale gas well produce and whether it can be profitable. Since my formula correctly projected Barnett Shale's production over the years, based on merely knowing the new wells added each year, it proves my formula works.


    And it predicts very low ultimate yields of the shale gas wells. Way much lower than the shale gas industry projected. That's the point!
    30 Apr 2012, 04:05 PM Reply Like
  • Justin M. Hall
    , contributor
    Comments (748) | Send Message
    Thanks Mark! No need to explain yourself. I appreciate your insight.


    2 May 2012, 02:17 PM Reply Like
  • Mark Anthony
    , contributor
    Comments (3595) | Send Message
    Author’s reply » The point I want to make is the math formula I used is pretty flexible. It can describe both quick decline and slow decline case.


    I tried quick decline paramaters, and then tried the slow decline one. It does not make a huge different on the ultimate recoverable gas volume, which is always some where below 2 BCF. So the conclusion is always that shale gas producers can not make money no matter what.
    2 May 2012, 03:30 PM Reply Like
  • dnpvd51
    , contributor
    Comments (2492) | Send Message


    Jeff E. Wojahn


    I have one piece of information. In the Haynesville for the long lateral wells, we’ve drilled long lateral 7,500-foot horizontal wells in the $12 million to $13 million range. So that's something that we demonstrated to ourselves that we know we can do in a resource play hub manner, and that would clearly be one of the steps that we'll be looking at is to take those learnings from the Haynesville and apply them to the Tuscaloosa.


    One contract of NG has 10,000 X 1,000 Cubic feet or ten million cubic feet of NG. 10 million cubic feet is worth about 22-23 thousand dollars at spot. So the well is worth (2 billion cubic feet divided 10 million cubic feet equals 200) times 23 thousand or 4.6 million dollars.


    OK, these NG producers must be losing a fortune if this math is right.
    2 May 2012, 04:14 PM Reply Like
  • minorman
    , contributor
    Comments (245) | Send Message
    Indeed. It doesn't matter which shale play you choose. If you do the math you see that gas sales cover (at best) 75% of opex - in some places its more like 25%. These guys are "burning" money at incredible rates fracking gas plays. Surely that's way drilling rates in the dry plays are falling off a cliff.


    There may or may not be "plenty" of nat. gas to be had, but it sure as hell won't be profitable until it sells about $6/mmBTU (and probably the broader break-even is more like $8/mmBTU).


    US. Natural gas is a bubble in search of a pin. It is the most obvious bubble in the entire financial horizon IMHO.


    If you are willing to risk the nasty contango that continued madness in the nat. gas market brings, a properly timed position in Henry Hub futures will make you very, very rich.
    3 May 2012, 11:21 AM Reply Like
  • Mark Anthony
    , contributor
    Comments (3595) | Send Message
    Author’s reply » Here is a link to shale well cost estimate:


    What is the Cost of Shale Well Play


    It was an interview of David Brown on Arthur Berman himself. Published on AAPG Explorer in the April, 2011 issue.
    4 May 2012, 02:10 PM Reply Like
  • Mihal
    , contributor
    Comments (11) | Send Message
    Thanks Mark for your well researched & well presented articles. Don't be put off by the detractors - keep up the good work.
    7 May 2012, 06:19 PM Reply Like
  • brond
    , contributor
    Comments (12) | Send Message
    can you publish the fit of your formula to individual well production and what range of betas that gives? I'm concerned that fitting aggregate production over the time period given is leaving you insensitive to the long time part of the formula, since the well count is also apparently growing almost exponentially. Fitting 100 individual wells over 10-15 years would be less vulnerable to this. (On the other hand that would discount any learning that has taken place over that time to increase yield on recent wells, but it would be a valuable alternate viewpoint.)
    thanks for the article.
    19 May 2012, 01:16 PM Reply Like
  • Mark Anthony
    , contributor
    Comments (3595) | Send Message
    Author’s reply » Brond:


    I wish I have access to individual well data for research. But those are well guarded secret of the industry. But you are right, the long term part of the formula is the important part. Based on basic physics, the long term shoudl see an exponential decay, not hyperbolic decline as suggested by the industry experts.
    29 May 2012, 01:07 PM Reply Like
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