Wednesday, October 3, 2012

Using a Dispersive Diffusion Model for Bakken Oil Scenarios

There is a great deal of excitement about the increased oil output from the Bakken Oil field in North Dakota.  A recent post by Rune Likvern at the Oil Drum sparked my interest in this topic.  The EIA estimates that under an optimistic high technically recoverable resource (TRR) case that the Bakken might produce as much as 1 Mb/d by 2021 and then remain at that level until 2035.  A paper by James Mason presents a scenario where Bakken output rises to 1.5 Mb/d by 2020 and remains at this level out to 2045.

At the Oil Conundrum, Webhubbletelescope (WHT) presents a dispersive diffusion model to model Bakken output, based on the data presented in Mason's paper.  He tells us that P-naught(P0) is 2.6 million barrels, but he leaves it to the reader to determine D-naught(D0).

P(t)= P0/(1+1/(sqrt(D0*t))

is the equation describing the model and its derivation is presented at the Oil ConunDRUM (link is above).

By trial and error we find D0=0.0023, for month 1 we get a different value from the 580 b/d in the chart above (it should be 1166 b/d), other than that the model agrees.

The North Dakota Department of Mineral Resources estimates the Bakken original oil in place (ooip)at 167 Gb,  Mason suggests total development will lead to 40,000 wells producing which suggests 4.175 Mb of ooip per well.  I chose P0=4.175 Mb and D0=0.00045 (high model) in order to model the Bakken oil data from the North Dakota government.  A low model was also created with P0=4.175 Mb and D0=0.0001.

The models (high, low, and 2.6) are below(2.6 is WHT's original model):

In order to create this model I made a number of simplifying assumptions.  We have the number of wells producing oil for every month from Dec 1953 to July 2012 and the number of barrels produced each of those months.  We are particularly interested in the recent increase in output which began in January 2005.

Using the Bakken Production Model developed by WHT and assuming that the average well follows this model we can create our model in a spreadsheet.  We first find the change in the number of producing wells each month and then assume any increase in the number of producing wells is due to new wells being brought online. We also assume all wells are average wells and we know what the output for every future month will be from those new wells (because we assume they behave as the model predicts.)  Keep in mind that the only input to the model is the change in the number of wells producing each month and two parameters P0=4,175,000 barrels and D0=0.00045, in the equation derived by WHT (see above.)

The first cut is below:

The model matches the data quite well from Jan 2010 to July 2012.  The early part of the data from Jan 2005 to Dec 2007 may not be modelled properly by the "high" model.  The differences are more apparent in the following semi-log plot.  (The plot beyond July 2012 is a future scenario discussed below.)

In order to improve the early (before 2010) part of the model I created a "low" model where output per well is about half the level of the "high" model.  This low model was used for wells which started production between Dec 2004 and Dec 2007.

The fit is improved for 2007, 2008, and 2009.  From Jan 2007 to July 2012 the number of producing wells increased at about 4.1 % each month.  To create a future scenario I assumed the "high" model would continue to describe the average well.  This assumption may be problematic as sweet spots become saturated with wells, in the future the low model or some "medium" model may be more appropriate.  The rate of increase of new wells was assumed to decrease by 2.3% each month( so we multiply last month's rate of increase by 0.977 for every future month).  We assume August 2012 will be a 4 % increase in # of wells, Sept 2012 would be 4 times 0.977=3.908%.  We continue in this manner from Aug 2012 to Dec 2017.  The following x-y plot is easier for reading the data:


Under these assumptions we see that future output from the Bakken would roughly double by Dec 2017 to 1.3 Mb/d.  This scenario is about midway between the EIA's optimistic scenario of 1 Mb/d by 2021 and Mason's middle scenario of 1.5 Mb/d by 2020, though it reaches the plateau 3 to 4 years earlier than those other scenarios.

The following chart shows contributions to output from various years:

Further modelling could guess at future production models which would likely fall between the high and low models presented here.

Edit 10-4-2012

In response to a question at the Oil Drum, I have decided to do a crude approximation of falling well productivity in future years.  I did this by assuming the "high" well profile remains valid until Dec 2014.  Abruptly in Jan 2015 all new wells follow the "low"  well profile as presented above.  The rate that new wells are added also increases to compensate for the fall in well productivity.  Clearly in the real world these changes would happen gradually, but this is a rough approximation of reality.

I also have added two more years to Dec 2019 to this model and I show how output would decline if new wells are no longer added.  If this model approximates reality (a rather large if), the plateau could be maintained until April 2023.  At that point we reach 40000 wells and if Mason's analysis is correct,  no more wells would be added in the North Dakota Bakken and decline would begin.  The decline would be a little flatter than shown above due to the extra 9500 wells.

Another update:

In response to further comments at the Oil Drum, I have attempted to make the model more realistic by creating several average well profiles that decrease by 10 % each year from 2013 to 2019, I also interpolated between the yearly profiles on a monthly basis to make the transition to lower output somewhat smoother.  The rate of increase in wells falls from 4 % to 1 % from Aug 2012 to Dec 2019.



  1. Your well drilling presumptions are likely bogus.
    You are increasing well count on a % basis, not a fixed number of new wells drilled per month -- which is the correct model for a fixed (or decreasing) number of rigs in existence (rig count is falling in the Bakken).
    And where is your dry hole model? Even in established geological trends, you reach endpoints of porosity in the rock and drill a hole that is dry -- spending $10 million to tell you not to drill in that direction (north, east, south or west) anymore. You don't have that.

  2. Although my future scenarios for the number of producing wells may be incorrect (most future scenarios are incorrect). Note that the number of producing wells shown in my charts over the period from January 2005 to July 2012 are data from the North Dakota Dept of Mineral Resources.

    I have no dry hole model, nor have I ever seen one. Keep in mind that my "number of wells" refers to the number of producing wells as reported by a North Dakota government agency. I am not attempting to model all wells drilled, it may be possible, but it is beyond my abilities. I would be very interested if you know of a better model you could point me to.



  3. Facinating work, thank you.

    In the Eagle Ford shale in S. Texas we are essentially in our fourth year of growth; my very fundamental production research is bewildering as to the economic viability of the play. Eight million dollar wells require 145,000 BO to payout based on 55.00 dollar net oil prices (after royalty, severance and property taxes, and incremental lift costs). Half the wells I look at on will not come close to 285,000 BO EUR. It simply cannot be working. I look forward to you and WHT and others having sufficent data to do the same sort of studies as you have done in the Bakken down here in the brush.


    1. Mike,

      Thanks for the comment. I have looked briefly at some of the data for the Eagle Ford Shale. It was not as easy to get a handle on the data from the TRRC as it was from the North Dakota Dept of Mineral Resources.
      Many of the plays seem to be condensate only, is that true of all of the EFS plays? I will look at, a complete rollup of all the EFS oil data would help.


    2. DC, admittedly the TRRC data is difficult to come by (slow) and liquids not very distinguishable. It is however mostly an oil play, the most recent activity anyway. Some of the orignal stuff done, perhaps what you were looking at, in DeWitt County for instance, is in a liquids-rich gas condensate leg. These very high GOR wells are the best in the play.

      I think we are just going to have to be patient for the data; the Bakken is 7-8 years old(?), the EF maybe 3-4. I am told now, by service companies, that just about all the players are caught up on frac'ing and more and more IP's and production data is going to become available. Some of these companies, by the way, are stacking pump trucks and letting some hands go, I am told. DI's field summaries for decline and EUR is pretty neat o burito.

      The industry, my industry, and everyone from dishwashers at the local Dairy Queens to Chamber of Commerces are in a promotional feeding frenzy: 40,000 wells, 40 years, 4 million more barrels per day of domestic production. I don't see it.

      Thanks again for your work.


    3. Mike,

      I am not from Texas and don't have a good handle on where the Eagle Ford Shale is located. There is somewhat more detailed production data by House District at the TRRC Website. Which House districts would coincide with the Eagle Ford Shale? Also which counties are most relavent to the EFS? North Dakota separates Bakken production from the rest of the state making my job fairly easy. With a little guidance from you I might be able to put something together for the EFS. Thanks.


    4. Got to go the field today but this link might help begin to delineate for you various Texas counties and the up dip limits of the play versus the oil to gas contact where 85% of the activity is now in due to natgas prices. This shale play coincides with NE to SW deposition of sediments typical to the Gulf Coast basin. In this map "file" there are TRRC maps outlining Districts. The TRRC also delineates oil and/or gas production by field designations and by producing reservoir, for instance Eagleville (Eagleford-2) Field, Karnes County, District 2. This is where will really help you as field decline, type curves, all kinds of cool stuff can be dug up. Go to Gonzales County, District 1, and look at EOG's stuff. Its amazing, good and bad. The problem, as I believe WHT has already pointed out, on 1100 acre proration units multiple wells can be drilled in that unit, for instance the Hootowl 1H to 5H and production is reported per unit, not per well.

      The real deal on unconventional shale plays is vital to our country's energy future. Americans are getting spoon fed a lot of stuff about energy independence from these shale plays and worries about rising gasoline prices are getting left at the SUV dealership parking lot. A true understanding of the Eagle Ford, just like the Bakken, is paramount.

      We have shale wells here in Texas, that are chaning the landscape forever, but we don't have Brook trout.

    5. I haven't been able to access I was able to find some information on production for the EFS play at TRRC. What I cannot find is the number of producing wells in the EFS on a monthly basis. If you have any insight as to how that information could be obtained, that would be great. If not I could just make some guesses based on the Bakken.


  4. I think my comment was misunderstood. The well count is *projected* on a % basis, and obviously based on NDak govt past numbers. Unless I have your projection wrong, you seem to draw lines forward based on % growth of well count. The past had rig counts grow. That should be something that can be modeled by knowing the rigs in the state. If they are falling, then only X wells can be drilled, regardless of if the total already drilled increases. It's not properly a % issue.

    As for dry hole models, it seems an easy thing to do based on annual reports of the relevant companies and how much they spend on drilling, the number of wells drilled with that money and how much oil flowed from each lease/well (which I do believe is in the NDak data). In other words, parenthetically, perhaps the single most important parameter that could emerge from the work would be an increase in dry holes as the sweet spots get scarce.

  5. Hi Owen,

    I don't have historic information on rig counts, only the number of producing wells.

    From the article at the address above:

    "Leaseholders have a set number of years to start producing on a property or surrender the lease, and that pressure created a frenzy of drilling activity. North Dakota has become the No. 2 oil-producing U.S. state after Texas.

    "The whole industry has been frantically trying to hold a lot of the acreage, hold it by production, and get the wells drilled," Continental Chief Operating Officer Rick Bott said, describing how a shift to drilling more from one site had cut its drilling time per well by more than a third this year.

    "That's allowed us to essentially do quite a lot more with a lot less."

    Many other companies in the region, with stakes secured, are turning to sinking more wells from single spots, known as pad drilling.

    "Your efficiencies can get a whole lot better once you get away from drilling a well just to hold a section," Magnum Hunter Resources Corp (MHR.N) Chief Executive Gary Evans said at a conference hosted last week by the Independent Producers of America Association (IPAA)."

    The number of wells drilled per rig can change when companies start to switch to pad drilling rather than having to scramble to drill in order to hold leased areas. Less time is spent moving rigs around. So your assumption that a reduction of # of rigs should lead to reduced number of new wells drilled seems valid at first, this second effect of more wells drilled per rig due to less travel time for rigs would counteract the first effect.

    It may seem easy to you to dig up the information on 4000 producing wells and the other "dry holes" drilled (I have no idea what that number would be.) I have neither the time nor the inclination to attempt such a model. I agree however that a dry hole model would be useful.

    You are correct that the forward projection for well counts was on a percentage basis. Over the period from Jan 2007 to July 2012 the number of producing wells had increased exponentially at a 4.1 % per month rate. I assumed this rate of increase would slow down from 4% to 1% a fairly substantial slow down.

    We start at about 4 % in Aug 2012, decrease gradually to 3 % by Aug 2013, to 2.5 % by Aug 2014, 1.95 % by Aug 2015. At this point producing wells are increasing at about 233 wells per month (starting from 174 in Aug 2012) and from that point the increase is almost linear increasing by only 3 wells to 236 by Aug 2018 and to an increase of 242 wells in Dec 2019 at the end of the projection period.

    As I stated earlier these projections are likely incorrect, your idea of using rig counts is excellent, I will use that if I can dig up rig counts in the Bakken or ND as a whole.

    Thanks again for your input.


  6. "By trial and error we find D0=0.0023, for month 1 we get a different value from the 580 b/d in the chart above (it should be 1166 b/d), other than that the model agrees."

    The early part is tricky because the production flow rates show a singularity at t=0. I recall taking the values at t=0.5 and t=1.5 months and using that as the average. I may have messed that up.

    Very cool analysis. It's just a matter of time before more numbers come out.