Saturday, December 15, 2012

Quick update to tight oil models

I have extended both the Bakken and Eagle Ford Shale models out to 2040.  I have assumed no other significant tight oil plays are developed in the US besides these two, this is a somewhat pessimistic assumption, though most other assumptions are relatively optimistic.  These may balance out in the long run.

As the Bakken becomes fully drilled up at about 40,000 wells (around the end of 2024) it is assumed that drilling rigs are moved to Texas from North Dakota to work the Eagle Ford play and that there is a ramp up in the number of wells drilled there per month as a result.

In this current scenario, the tight oil output comes close to matching the EIA 2013 outlook (red diamonds in figure below) from 2018 to 2028, but the output is lower both before and after that period.


Eagle Ford:

US Tight Oil:



Sunday, December 2, 2012

Update on Bakken Model using hyperbolic decline

The recent World Energy Outlook (WEO) published by the International Energy Agency (IEA) predicts that US unconventional output will rise to 5 million barrels per day (Mb/d) in 2020.  This increased crude plus condensate (C+C) output will primarily come from tight oil in the Bakken trend in North Dakota and the Eagle Ford trend in Texas.

I decided to update my model of the Bakken based on information learned while attempting to model the Eagle Ford trend in Texas.  One thing I discovered in my modelling of the Eagle Ford was that the hyperbolic decline model seems to give a better approximation of the Eagle Ford then the Dispersive Discovery Model that I used in my previous Bakken Model.  For this reason I used a hyperbolic decline model for my updated Bakken Model.

The early wells from 2004 to 2007 have a lower well profile with cumulative output about half that of wells starting production between 2008 and 2012.  My previous model had decreases in well productivity of 1 % each month from 2013 to 2019 with new wells starting production in Dec 2019 producing 45 % less cumulative oil than those beginning production in Dec 2012. 

I decided that this was too large a decrease in well productivity to be realistic.  For the updated model, wells starting production in Feb 2013 produce a cumulative output about 0.5 % less than those which started producing the previous month.  Each year the well productivity profile decreases by about 6 % compared to new wells from 1 year earlier.  By Dec 2019 new well productivity has decreased by 66 % compared to new wells from Jan 2013.  The chart above only shows 3 cumulative output curves with one curve (Jun-16) between the Jan 2008 to Dec 2012 cumulative and the
Dec-2019 cumulative curves.  In fact there are 94 curves between the Jan-13 cumulative curve and the Dec-19 cumulative curve one for each month.

The data for C+C output in barrels per day and number of producing wells can be found here. 

In order to forecast future output we assume the average well profile remains unchanged for new wells from Jan 2008 until Jan 2013 and then declines for each month from Feb 2013 to Dec 2019 by 0.5 % as discussed above. 

To estimate the number of producing wells in Oct 2012 we use the average of the change in the number of producing wells (delta # of wells) for the previous 7 months which is 162.  This number is added to the 4629 wells producing in Sept 2012, thereafter the delta # of wells producing is assumed to increase by 3 each month up to Dec 2013 (162, 165, .... , 201, 204) to a total of 7374 producing wells. Note that between Jan 2010 and Sept 2012 the trend in the increase in delta # of wells was 4 per month. So the increase in the delta # of wells producing of 3 represents a decrease from the previous trend. 

This rate of increase of delta # of wells is decreased further to 2 each month from Jan 2014 to Dec 2015 to reach a total # of producing wells of 12870.  The rate of increase of the delta # of wells producing decreases again to 1 per month from Jan 2016 to Dec 2017 and producing wells increase to 19218.  From Jan 2018 to Dec 2019 the delta # of wells producing stays steady at 276 with the total number of wells reaching 25842.  

The model by James Mason suggests 40000 wells would be the saturation point for the Bakken with little room for any further increase in producing wells.  In the chart below notice the rapid dropoff in output after Dec 2019 when new wells are no longer added.  If wells continue to be added at 276 new wells per month then 40000 wells are reached in April 2024, at that point (if Mason's model and my model are both correct) we would see a rapid drop in oil production.

Output peaks at 1.35 Mb/d in early 2019 and then remains on plateau until Dec 2019, this is an example of Rune Likvern's "Red Queen" effect.

I hope to publish a post on the Eagle Ford soon.  For some flavor of this, consider this chart:

The Texas RRC database was used to develop the average well profile.  Note that data is estimated from a combination of Texas RRC data and EIA data.  The Texas data was used to estimate the  percentage of all Texas oil coming from the Eagle Ford trend, then this percentage was multiplied by EIA Texas output to estimate Eagle Ford oil output.

Based on these models I think the upper limit to tight oil output from the Bakken and Eagle Ford in 2020 is about 2.7 Mb/d rather than the 5 Mb/d predicted by the IEA.  Note that these estimates are quite optimistic and should be thought of as an upper bound to what may be attainable. This is an increase of about 1.6 Mb/d over current US tight oil output of about 1.14 Mb/d.  A more realistic scenario might be a doubling of output to 2.3 Mb/d in 2020.


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.


Wednesday, August 29, 2012

World Natural Gas and Natural Gas Liquids

   In order to model World Oil Production, we need to consider other liquid fuel besides crude plus condensate(C+C).  One of the largest additions to Total Petroleum Supply besides C+C is Natural Gas Liquids(NGL).  A paper by Jean Laherrere points to a stable relationship between NGL and Natural Gas production (see figure 1 in the paper linked above.) A post by Rune Likvern also investigates future NGL output and suggests that the output of NGL per unit volume of natural gas will likely decline in the future.

Despite the work by Likvern, so far through 2011 the world trend has been either stable (1996 to 2011) or positive (1980 to 2011) based on data from the 2012 BP Statistical Review of World Energy for Natural Gas and the US EIA for NGL.  I am also attempting to create optimistic scenarios to reduce the possibility of underestimating the length of a possible continued plateau in oil output.

Two scenarios for NGL output have been created.  The first (low case) assumes that the world production of NGL per unit volume of Natural Gas output remains at the average level of 1994 to 2011 (27.5 barrels per million cubic feet(b/mcf) of natural gas).  The second (high case) scenario assumes that the slow rise in NGL per unit volume of natural gas continues (using the linear trend from 1980 to 2011) until the world level reaches the average US level from 1983 to 2011 (34.5 b/mcf of natural gas.)

The chart below is for the world:

In order to forecast natural gas output, I used a Shock Model for Natural Gas (fallow, build, and mature periods 10 years).  This model was based on discovery data from Jean Laherrere and the middle (best guess) case in Steve Mohr's thesis for natural gas URR=16730 trillion cubic feet (tcf).  A dispersive discovery model (see Oil Conundrum)
was used to fill in discovery data after 2005.  The BP outlook (xls file) was used as a basis for natural gas production from 2015 to 2030 in developing this model (the data points for 2015 to 2030 are from this forecast).

This scenario for world natural gas is likely to be optimistic, a more realistic scenario would limit the rise in extraction rate to about 7 %.  A lower case which matches Steve Mohr's dynamic scenario (case 2) is presented below:

The higher natural gas case is used for a high NGL scenario and the low natural gas case is used as the basis for a low NGL scenario.  Both are presented in the chart below.  Note that the NGL is in barrels of oil equivalent which accounts for the lower energy content of NGL (70 % based on EIA heat content data).

Using these scenarios for NGL (low case URR=313 Gb, high case URR=359 Gb) scenarios for C+C+NGL can be developed.  Stay tuned...

Excel speadsheet named worldgasmedngl1 at this link


Monday, August 27, 2012

Extraction Rates and Developed Reserves

  If there are a given amount of developed oil reserves, let's say 900 billion barrels and the extraction rate is 3 % then 27 billion barrels of oil per year (bb/a) will be produced.  If the reserves fall to 800 billion barrels and the extraction rate is unchanged, output falls to 24 bb/a.  Consider a rise in extraction rates to attempt to maintain output at 27 bb/a as reserves deplete.  If extraction rates could be increased to 3.375 %, we would remain at 27 bb/a.

In reality, the extraction rate will rise and fall based on economic conditions, oil prices and the resulting level of oil demand.  As we reach the eventual peak in oil output, we will likely see a rise in extraction rate while developed reserves are declining (because we are producing oil at a higher rate than we can develop oil reserves).  

For a while the increased extraction rate could counteract the smaller level of reserves and enable either a plateau in output (like C+C since 2005) or possibly a slow rise in output.  Eventually we will be unable to maintain a plateau or increase output further because there is some limit to how high extraction rates can rise.  Eventually developed reserves will fall from the near plateau they have been on since 2004.  Consider the following model:

From the reserves and extraction rate above we get the C+C output below:

If extraction rates are limited to 4.5 %, the plateau would end in 2035 and a limit of 4 % would mean the plateau would end in 2030 for the scenario where the URR for C+C (including oil sands at 350 Gb and Orinoco belt at 250 Gb) is 2800 Gb.  See posts below for more conservative estimates.


Wednesday, August 22, 2012

Update to Crude plus Condensate Models

I noticed that compared to a model by webhubbletelescope, that my shock model extraction rates were very high (around 13 % vs. 5.5 % in 1973).  This was due to using different discovery data that had not been backdated.  I have updated the model using better discovery data based on data from ASPO and Jean Laherrere, as well as from the most recent shock model presented on the Oil Conundrum.

Laherrere uses 2200 Gb for his URR for conventional oil + deep water.  If we add oil sands at 170 Gb and Orinoco belt reserves at 220 Gb (390 Gb total) we get a URR of 2590 Gb. An optimistic Canadian geologist might guess that the oil sands could yield as much as 340 Gb, and an optimistic Venezuelan might suggest 260 Gb of URR from the Orinoco Belt.  This combination of oil sands and Orinoco belt oil I call extra heavy oil and will have a URR from 300 to 600 Gb in total.  This is the basis of a C+C URR between 2500 and 2800 Gb.

The new models are below, they use discovery data similar to that presented at the following link:


Note that the forecast "data" is from the 2012 BP Outlook (2015-2030), but this outlook has been scaled back by my estimate of future NGL output, which is based on the BP Outlook for natural gas and continued increase in NGL per unit of natural gas to US levels worldwide.  This will be presented in greater detail in a future post.  Also note that NGL only has 70 % of the energy content per barrel compared to crude plus condensate.  I always present NGL on this energy equivalent basis.

The extraction rate profile for the larger URR of 2800 Gb is similar to the 2500 Gb case and ranges from 3 % on the low end to 5.2 % in 1973 and 2042 (for the plateau case).

For URR=2500 Gb scenarios:

The low case extends the increased extraction rate over the period 2002-2011 at the same linear rate of increase out to 2070, the medium case increases the extraction rate linearly from 2011 to 2050 up to the 1973 rate of 5.45 %.  The plateau case increases the extraction rate enough to maintain a plateau without exceeding the 1973 rate.  The BP outlook case attempts to match the forecast in the 2012 BP Outlook (after deducting my estimate of future NGL output) out to 2030 without exceeding the 1973 extraction rate.

For the 2800 Gb scenarios:

The low case extends the increased extraction rate over the period 2002-2011 at the same linear rate of increase out to 2070.  The medium case follows a linear rate of increase up to 2020 which if continued would reach the 1973 rate of 5.2 % by 2050, after 2020 the extraction rate is increased to maintain a plateau at the 2020 output level until the 5.2 % extraction rate is reached.  The plateau case simply maintains the 2011 level of output by increasing the extraction rate as necessary until the 1973 extraction level is reached.  The BP outlook case tries to match the BP outlook (after deducting NGL) to 2030 and then maintains the 2030 level until the 5.2 %  extraction rate is reached in 2035.

Note that there may be a technical limit to how high the extraction rates can rise, I have assumed that today's technology may enable us to match the level achieved in 1973.  The problem is that we do not have the young Middle eastern Giant fields today and the technical challenges of ultra deep water oil, polar oil, tight oil, and extra heavy oil are much greater today than they were 40 years ago.

For the 2500 Gb case, if the technical extraction rate limit is 4.2 %, then the plateau would end in 2020, for a limit of 4.5 % the plateau ends in 2025.  In the 2800 Gb case, 4.2 % extraction rate limit would end the plateau in 2032 and a 4.5 % limit would end it at 2036.


Wednesday, July 25, 2012

Further modeling for world crude plus condensate

Based on suggestions from WebHubbleTelescope that a World URR (ultimate recoverable reserves) of 2800 Gb (billion barrels) for C+C(crude oil plus condensate) is too high (but maybe appropriate for C+C+NGL), I created a different model. The first model was done in early May 2012 and the second a few weeks later.

The second model used a URR of 2560 Gb for C+C based on a Hubbert Linearization (HL) of US EIA(Energy Information Administration) World Data for C+C from 1993 to 2011 (annual data). Many people have commented that the HL method is unreliable and I agree, but I am using it as a ballpark estimate and I recognize that it has tended to underestimate the World C+C URR in the past.
To try to nail down some of this uncertainty over the URR for C+C, I did several HL regressions on the EIA data from 1993 to different end years, to see how the estimate has changed since 2005:

URR (Gb) lower 95 % upper 95% R squared
1993-2011 2580 2292 2924 0.97
1993-2010 2594 2272 2988 0.97
1993-2009 2601 2239 3057 0.96
1993-2008 2669 2270 3184 0.95
1993-2007 2689 2230 3304 0.94
1993-2006 2725 2193 3479 0.93
1993-2005 2689 2096 3578 0.92
1993-2002 2452 1783 3583 0.91
avg 05-11 2650 2228 3216

From 2005 to 2008 the HL method points to a URR of about 2700 Gb, the URR drops to about 2600 from 2009 to 2011. This may simply be an artifact of the slower world economic growth over the period from 2009 to 2011. Also note that the 95% confidence interval becomes narrower as more data is included (not unexpected), these intervals assume a normal distribution which may not be valid, so the confidence interval is in fact unknown.

The second model is below:

Compared to the first model the low case has lower extraction rates after 2060 (they are similar from 1860 to 2060), the high case has extraction rates similar to the medium case of the earlier model, and the medium case is between the low and medium cases of the first model. The high case of the first model was thrown out due to lack of realism where extraction rates similar to the highs of 1973 are achieved over a 30 year period which is highly unlikely.

Two different plateau scenarios are presented. The two are identical up to 2023, after that year the first follows the medium scenario and the second attempts to extend the plateau as far as possible. The model uses the same fallow, build, and maturation (6, 8, and, 10 years) characteristics of the first model.

The low case peaks in 2011, medium in 2018, and high in 2019 at 74, 76, and 79 mb/d respectively, and the plateaus end at 2025 and 2028 for the 2 plateau scenarios.

The two models can be compared on the same chart to give a low and high peak and plateau scenario. Two peak models “low 2560” (the low scenario from the chart above in today’s post) and “med 2795” (the medium scenario from my July 20 post) are presented and two plateau models (I used the plateau2 model from the chart above for the “plateau 2560” case (see chart below).

A future where crude oil peaks over a short period (less than 10 years) is likely to fall somewhere between the low 2560 curve and the higher med 2795 curve. A future where the current 7 year plateau (the so-called "undulating plateau" scenario) continues for 19 to 24 more years would fall between the two plateau scenarios illustrated above.


The chart above attempts to present most of the scenarios presented so far (only one plateau scenario has been omitted) on a single chart. It is interesting that there is only a minor change in output up to 2022 for the peak scenarios when the URR increases by 235 Gb. This is not surprising because the increased URR is due to larger future discoveries in the 2795 Gb URR model vs the 2560 Gb URR model.

Further modeling will consider C+C+NGL.

The Excel spreadsheet "world2560plat.xls" for this model can be found at:


Friday, July 20, 2012

An early scenario for world crude oil

Above is a model for world output using Webhubbletelescope’s oil shock model and dispersive discovery

Actual discoveries from 1900 to 2009 were used for the discovery curve with a dispersive discovery model used to fill in discoveries before 1900 and after 2009 where the actual data is unknown (this is essentially a statistical guess using a maximum entropy estimator.)

URR for the scenarios is about 2800 GB for crude + condensate, a Hubbert Curve is also presented based on a Hubbert linearization from 1993 to 2011 using EIA annual C+C data this model has a URR of 2560 Gb.

For future years beyond 2011 four scenarios were created low, medium, high and plateau. All of these have the same URR of 2790 Gb. The difference lies in different rates of extraction from mature reserves, shown  below:

The low scenario matches the hubbert curve rather closely from 2011 to 2035.  The most likely scenarios are the plateau, medium, and low scenarios. 

The high scenario attempts to ramp extraction rates to 1973 levels over a 30 year time frame, this seems quite unrealistic when considering that Saudi Arabia and other middle east OPEC members were aggressively ramping up production from 1960 to 1973 at the some of largest oil fields discovered to date. 

I doubt that such world wide extraction rates will be seen in the future, but included it to illustrate that even if it were accomplished the peak would only move by a few years (to 2021 from 2019 in the medium scenario).  Even the medium scenario is somewhat unrealistic as it ramps to 1990 extraction rates over just a 5 year period, the reality is likely to fall between the plateau and medium scenarios.

I chose 2800 Gb as a rather optimistic URR for crude plus condensate.

WebHubbleTelescope offered helpful advice, suggesting that a URR of 2800 Gb is more appropriate for c+c+ngl rather than just crude plus condensate.  His comment led to further modelling which I will discuss later.