Oil Field Models, Decline Rates and Convolution

This post is by Dennis Coyne

The eventual peak and decline of light tight oil (LTO) output in the Bakken/ Three Forks play of North Dakota and Montana and the Eagle Ford play of Texas are topics of much conversation at the Peak Oil Barrel and elsewhere.

The decline rates of individual wells are very steep, especially early in the life of the well (as much as 75% in the first year for the average Eagle Ford well), though the decline rates become lower over time and eventually stabilize at around 6 to 7% per year in the Bakken.

What is not obvious is that for the entire field (or play), the decline rates are not as steep as the decline rate for individual wells. I will present a couple of simple model to illustrate this concept.

Much of the presentation is a review of ideas that I have learned from Rune Likvern and Paul Pukite (aka Webhubbletelescope), though any errors in the analysis are mine.

A key idea underlying the analysis is that of convolution. I will attempt an explanation of the concept which many people find difficult.

At Wikipedia there is a fairly mathematical presentation of the concepts which often confuses people.  There are a couple of nice visuals to convey the concept as well see this page.

In the visual below a function f (in blue) is convolved with a function g (in red) to produce a third function (in black) which we could call h where h=f*g and the asterisk represents convolution, just as a + symbol is used to represent addition.

Convolution of box signal with itself2.gif
Convolution of box signal with itself2” by Convolution_of_box_signal_with_itself.gif: Brian Amberg
derivative work: Tinos (talk) – Convolution_of_box_signal_with_itself.gif. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

I think the best way to present convolution is with pictures. Chart A below shows a relationship between oil output (in barrels per month) and months from the first oil output for the average well in an unspecified LTO play.

This relationship is a simple hyperbola of the form q=a/(1+kt), where a and k are constants of 13,000 and 0.25 respectively, t is time in months, and q is oil output.

Chart A is often referred to as a well profile. The values for the constants were chosen to make the well profile fairly similar to an Eagle Ford average well profile. EUR30 is the estimated ultimate recovery from this average well over a 30 year well life.


Chart B shows the relationship between the number of new wells that begin producing each month and the months from the start of production for the entire field.


The convolution of the relationship shown in chart A and the relationship shown in chart B results in a third relationship shown in Chart C below, oil output vs. months from start of field output. Output has been converted to kb/d from barrels per month.


It is indeed strange that two very different shapes (a hyperbola and a trapezoid) would combine to form the shape shown in chart C.   A spreadsheet can be downloaded here, with the scenario above laid out.
What was surprising to me when I first tried this analysis was that a combination of the average well profile with the number of wells added each month reproduced the oil output data fairly closely.

To clarify this further, I have created a simple model. As before, we have a hyperbolic well profile in chart 1 (slightly different than chart A above) and the number of new wells added each month in chart 2, but in chart 2 this is over a short 6 month period. After that time no more new wells are added.



In the chart below I show the output for each group of wells that begins production in successive months. The output from all wells starting production in month 1 are labelled “month 1 wells”, there are 6 of these groups up to “month 6 wells”. The number of wells added each month is shown as a dashed line read off the right axis. Remember that 30 wells are added each month from month 1 to month 6 so output for “month x wells” will be 30 times month 1 of the well profile in month x and 30 times month 2 of the well profile in month x+1, etc.


The convolution of Chart 1 and Chart 2 results in Simple oil model 1 shown below.


This model is very simple in order to present how the principle works in a clear manner. When the annual decline rate for the “field” is compared to the average well’s annual decline rate, they are very similar for this simple 6 month model. More realistic models are presented later for comparison.

Note that month zero in the chart below is the month of maximum annual decline rate, for the average well the maximum annual decline rate happens in month 13 and for the field it occurs in month 18, the curves have been shifted to the left by 13 and 18 months so that the maximum decline rates match up at month zero for easy comparison.


The spreadsheet for simple model 1 can be downloaded here.

A second simple model with the number of wells added each month rising from 5 new wells per month to 30 new wells per month over 6 months and then falling back to no wells added by month 12 is shown below.




Note that the “month 7 wells” output curve is the same as the “month 5 wells“ output curve, but shifted 2 months to the right. Likewise month 8 is month 4 shifted 4 months to the right and this same symmetry is true for months 9 and 3(6 month shift right), months 10 and 2, and months 11 and 1 where the shift right in the curve is equal to the difference in the month when the well started production (8 months and 10 months for the last two cases respectively).

When all of these 11 curves are added up for each month (the convolution of the “well output of the average new well” chart and the “number of new wells added per month” chart) we get the Simple Oil Model 2 chart below.


Simple model 2 can be downloaded here.

I now present a different model with a higher EUR well profile (than in chart A) and a lower rate of addition of new wells (than in chart B). This model’s well profile is similar to the average North Dakota Bakken well profile.



The convolution of the two charts above results in the field output shown below.


How does the annual field decline rate compare to the average new well annual decline rate in this case? In the chart below we see that a slower decrease in the rate that new wells are added causes the annual field decline rate to be only 22% at most, about 3 times lower than the maximum annual well decline rate.


The spreadsheet for the model above can be downloaded here.

As this result is rather counterintuitive, I will try another modification to the model. The well profile remains unchanged, but there is a steeper reduction in the rate that new wells are added to field production.

Such a scenario could occur if there was a steep drop in oil prices as in the early 1980s. It will also occur if there is a decrease in new well productivity which will reduce profits and the incentive to add more wells.
The well profile chart is unchanged, the other two charts are as follows:



Even in this case the maximum annual field decline rates are less than half the maximum well decline rate. This is because we have almost 15,000 wells added over an 11 year period and their decline behavior in the aggregate is much different than that of an individual well. See chart below.


Note that the field decline rate is very high, close to a 30% maximum rate in this scenario. If the rate that new wells are added drops to zero over a 1 to 2 year period and no further wells are added, we would expect the field decline to behave like the gray curve in the chart above.  Spreadsheet for the 5.6 Gb scenario can be downloaded here.

Earlier I mentioned that when I first tried this method I was surprised that such a simple model could accurately match output from the Bakken or Eagle Ford fields.

Using data from the North Dakota Industrial Commission(NDIC) on oil output, the number of new wells added per month, and individual well data(from Rune Likvern initially and lately from Enno Peters) I attempted to match scenarios initially presented by Rune Likvern at the Oil Drum.

Below I present the well profile and number of new wells added each month.



When the two charts above are combined (convolved) we get the output curve below.


Note that the sharp drop off in the number of producing wells added each month is not very realistic and is an artifact of the way I set up these simple models for illustration (they end at 130 months so the number of producing wells had to be ramped down very quickly).

Such a scenario would be more likely if there was a sharp rise in well costs, or a sharp drop in oil prices or new well productivity (EUR). The field decline rate is somewhat similar to the previous scenario, rising quickly to a 28% annual decline rate which falls to 10% after 5 years and to 7% in 8 years.


This simple Bakken model can be downloaded here.

A fairly realistic scenario for the North Dakota Bakken (it is a little on the low end of likely scenarios) is presented now for comparison to the model above. This scenario has an ERR (economically recoverable resource) of 5.3 Gb where the more likely range is 7 to 9 Gb, based on USGS estimates. The average well profile and number of new wells added each month are below.



When we convolve the two charts above the following model output results. The match to the data is surprisingly good.


The annual field decline rate and well decline rate are shown below. In this case the maximum annual field decline is about 16% in 2021 and falls to 8% by 2026 and to 5% in 2031, the maximum annual well decline rate is 61%, the well decline rate is shown for a well starting production in Dec 2013.


The spreadsheet with this more realistic model is quite large (18 MB) so those with limited bandwidth may want to skip it.  The realistic Bakken model can be downloaded here.

For the Eagle Ford play I was able to collect data on single well leases from the Railroad Commission of Texas, data on the number of producing wells in the play and output data. I developed an average well profile (shown below) and combined it with the number of new wells added each month to produce an output chart.

Note that the output chart is for crude only and does not include condensate.



The two charts above are combined (or convolved) to give the output chart below.


Note that there is about 20% of Eagle Ford output that is condensate, when this condensate is added to the URR above for crude only we get a URR of 5.1 Gb of C+C.

As in the case of the North Dakota Bakken/Three Forks the match between the model and data is surprisingly good considering the simplicity of the model and the complexity of the real world.


Oil field output can be simulated with the convolution of the average well profile of newly added wells and the number of new wells added each month. I presented several simple models to demonstrate this concept.  An obvious weakness for any attempt at forecasting is that the future average well profile may change over time and the number of new wells added in any future month is unknown.

The decline rate of a field of wells will tend to be considerably lower than the decline rate of the individual well. The field decline rate depends on several factors: the decline rate of individual wells, the total number of wells in the field, the period of time over which these older wells were added (whether the period was long or short), and finally the rate at which the number of new wells added decreases as the field begins to decline.

Several models were presented showing how the field decline rate might vary under differing circumstances.

The concepts presented were applied to scenarios which simulated both the North Dakota Bakken and Eagle Ford shale plays with fairly good precision.

In a future post I plan to show how the convolution of two mathematical functions is used to develop the Oil Shock Model.

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188 Responses to Oil Field Models, Decline Rates and Convolution

  1. aws. says:

    Producers wait for herd rebuild

    PETER KOSTOS, Stock & Land, 26 Jun, 2014 04:00 AM

    HAVING observed the Pakenham trade cattle sale on Monday, I was left wondering when the market will improve.

    If you follow Meat & Livestock Australia’s (MLA) reports on overseas trends one could rightfully expect prices to be quite a bit higher.

    US cattle prices continue to remain at high levels, which in theory should at least create stronger demand for our grinding beef.

    Why are we not seeing much benefit from the US grinding beef market?

    The main reason is the extended drought in northern Australia, which is continuing the extraordinary slaughter of adult female cattle.

    This scenario has been going for 22 months and while it is not unheard of, other years in 1972, 1974, 1989, 1997-98 and more recently 2006-07, evoke strong memories of poor prices.

    Those previous years were oversupply here, coupled with oversupply overseas, but that is not the case this time.

    Winter rainfall in the north will continue to be sparse, according to the Bureau of Meteorology, which only sustains the high female cattle slaughter.

    Methane emissions from cattle likely in decline with diminished herds.

  2. B says:

    Goldman Says Shale Gas Boom Driving Fear From Market

    Gone will be the near tripling of costs to $15.78 as in 2005 as traders remain confident the fuel will be there when needed. Natural gas will trade “largely” at $4 to $5 per million British thermal units for the next 20 years, says Goldman Sachs. Societe Generale SA sees prices at $5 through 2019. Bank of America Corp. forecasts $5.50 for 2017, while BlackRock Inc. projects $4 to $5 for the next decade.

    Prices were four times more volatile in 2009 than they are today as production grows for the ninth straight year and new pipelines deliver the fuel to customers. Gas for use next winter costs 3.2 percent more than now, the smallest premium for the peak-demand period since 2000. Stockpiles will start the heating season at the lowest levels since 2008.

    “The market is rightfully not that worried because you have so much supply that is coming online,” Jeffrey Currie, head of commodities research at Goldman Sachs in New York, said in a June 23 telephone interview. “We have enough flexibility in the supply system.”…

    The U.S. Energy Information Administration forecasts natural gas prices will average below $5 through 2023 and less than $6 until 2030. The fuel will average less than $5 through 2017, based on analyst estimates compiled by Bloomberg.

    Fears of gas shortages have dissipated since 2005, when hurricanes Katrina and Rita damaged Gulf of Mexico production platforms. Offshore gas accounted for 5 percent of U.S. supplies last year, dropping from 17 percent in 2005, as shale-gas output, boosted by hydraulic fracturing, or fracking, surged from Pennsylvania to Texas.

    U.S. output will increase 4 percent in 2014 to a record for the fourth consecutive year, according to the EIA, the Energy Department’s statistical arm.

  3. B says:

    You’re paying more for gasoline, and here’s why

    Here’s the explanation for the stubbornly high prices: Fear has gripped oil trading markets, after the Islamic State of Iraq and Syria, known as ISIS, seized the Iraqi city of Mosul on June 10 and Fallujah soon afterward.

    Financial traders fear a collapse of the Iraqi state that could suck Iran and Saudi Arabia into a regional conflict that threatens oil supplies. And those financial players far outnumber actual end users of oil in the markets where contracts for future barrels of oil are traded.

    Iraq is a becoming a more important Middle East exporter over the past five years and is now the second largest producer in the Organization of Petroleum Exporting Countries. But OPEC Secretary General Abdalla El-Badri said this week that there is no oil supply shortage in Iraq and blamed the recent increase in oil prices on speculative trading in the markets.

    Right now the market is very well supplied,” he told reporters in Brussels on Wednesday. He pledged that OPEC could increase production if there is a disruption.

    Iraq’s main oilfields are deep in the Shiite Muslim South, an area that is hostile to the Sunni Muslim ISIS. The global energy consulting firm IHS said the fields are protected by government forces as well as Shiite militias, and that an ISIS offensive against them would require substantial fuel and be difficult to sustain for long.

    Despite the fears in financial markets, ISIS is unlikely to disrupt Iraqi oil exports, said IHS senior director Jamie Webster, a position widely shared among experts.

    Robert McNally, an energy consultant and founder of the Rapidan Group in Washington, suggested that Iraq’s semiautonomous Kurdish region might be able to actually increase oil exports from northern Iraq after seizing the city of Kirkuk in the midst of the crisis.

    There have been reports the Kurds already are starting to export oil independently while the central Iraqi government based in Baghdad is in turmoil.

    While reports out of Iraq suggest production and export are, for now, unaffected, big global oil companies won’t discuss their production there.

    “We don’t have any comment,” said Richard D. Keil, a spokesman for ExxonMobil in Irving, Texas.

    There’s little incentive for Keil to discuss production, since the fear gripping financial markets is tantamount to free money for the oil companies. ExxonMobil and other large players reap a windfall from higher oil prices and suffer if prices collapse, as they did during the Great Recession.

    What’s particularly galling for many Americans is that the energy industry and its allies in Congress, when pushing for the rights to expand domestic drilling of oil and natural gas, insisted this new production would amount to energy independence and insulate U.S. consumers from events in the faraway Middle East.

    John Felmy, chief economist of the American Petroleum Institute, said the Iraq crisis comes at a time when the oil markets already have lost expected supplies of crude from other troubled areas of the globe. He pointed to sanctions against Iran and lost production as a result of problems in South Sudan and Libya.

    “It’s not just Iraq, of course. We’ve lost a couple of million barrels per day of capacity . . . at the same time you’ve had growth in world demand . . . about 1.3 million (barrels per day),” Felmy said. “It’s a tighter market, and if not from the increased U.S. production, it would be even tighter.”

    • Watcher says:

      As already shown, shut in oil totals of today are small in comparison to historical norms of the past 40 yrs.

      And let’s also note that WTI was logging in well north of $100 long before we’d ever heard of ISIS, or before Kiev ever appeared on any headlines.

      The really ominous thing? It was doing this in Q1, as the US was doing -2.9% GDP activity, and as we all know, GDP growth is defined by oil consumption.

      So that price was there as consumption had to be down, and prior to any geopolitics fears. So, yes, there is a supply problem, but it ain’t from war fears.

      • Old farmer mac says:

        People have incredibly short memories- probably some animals have better ones. My old Daddy says that he never caught a fox back in his younger days when he did a lot of trapping for fun and profit at a spot where a fox escaped a trap- not even years later.

        In less than a decade, we have as a society almost totally forgotten that oil used to sell for twenty bucks or so a barrel no more than fifteen years ago and that before that five and ten dollar oil was common.

        If any other commodity had gone up so fast the people in that industry would never let us forget it -not for a single minute would they quit bragging about how much money they have made by predicting short supplies and increasing demand.

        A decade or two is only a yawn in terms of history although big events can turn that yawn into a scream and change the course of history thereafter.

        The people who are insisting we are well supplied with oil are counting on us having a collective memory not much better than a chicken.

        And sad to say, they are safe in making that assumption.

        Noboby has ever gone broke overestimating the gullibility of the general public.

        But even chickens can learn a little given repeated opportunities.In another decade or so the public is finally going to gain a glimmer of understanding of depleting natural resources with oil and water being at the top of the list.

        IF I were younger and a technocopian optimist I would sell my little farm and invest every dime in Tesla.

        I believe Elon Musk is one of the best thinkers in the entire history of industry when it comes to understanding the big picture. Right now my estimation of his strategy is that it is the same as that of Microsoft. To hell with the computer itself,Bill Gates made his money by owning the dominant software.Musk will own the dominant technology in electric vehicles and be licensing out tons of it later at affordable rates to other manufacturers.

        Suppose he gets a hundred bucks a car for two million cars a year ten years now.That is a very very conservative estimate of the possibilities in my opinion.That two hundred million would be in addition to whatever he earns on his own cars and most likely by then light trucks too.

        A lot of countries are going to enforce the sale of battery electric vehicles by taxing the hell out of imported fuel and imported gasoline and diesel burning personal vehicles. Direct electric vehicle subsidies will not be necessary in a two hundred bucks a barrel oil market in any country that imports both vehicles and oil.

        The last people to get it will be the conventional economists of course.

        And paradoxically I believe they would be proven right in their faith in human ingenuity if only business as usual could persist for another half a century or a century or so.I do believe that given time enough we could solve almost any sort of problem in terms of maintaining a wealthy industrial society.But ” time enough ” means a LONG time in human terms.

        But the oil fueled ambulance that is hauling society to the techno hospital is going to run out of diesel before it makes it to the E R ramp.

  4. Toolpush says:


    An article giving the go ahead for tight gas in shale, with the “F” word attached,ie Fraccinf, in Australia.
    The interesting line I thought was ” Each frack is predicted to extend up to 100 m vertically and 300m horizontally”. So I am not sure how indicative these distances are of other locations, but it is the first time I have seen anybody quote actual numbers. So just to convert, 330 ft x 990ft.
    We maybe could use these number to work out the total number of wells able to be drilled in the Bakken, assuming a horizontal section of approx 2 miles.
    Also the max number of wells from a pad, assuming the max deviation of 30 deg at 10,000ft gives 7500 ft displacement from centre. So potentially 7 wells drilled north and 7 drilled south, would mean a max of 14 wells per pad per zone.
    It sounds like there is some way to go to intensify pad drilling as it stands at the moment.

    • BW Hill says:

      Hi ToolPusher,

      The distance that a fracture will propagate is dependent on several factors. The density of the stone, the intervening natural fractures, and the grain of the stone. Almost all stones are anisotropic, that is, they are stronger in one direction than they are in the other. Structural slate deposits, for example, may be 20 to 50% stronger “across the grain” than they are “on the grain”. Fracture mechanics is a science all of its own. The best place to get additional information is the Colorado School of Mines. They have a huge library of research information on the subject. You’ll probably have to pay for most of it, but their prices are reasonable. The internet is the only place where people expect to get something for nothing, and the quality of much of it is dubious at best.

      Maximum fracture propagation of 1000 feet sounds about right for a shale/slate like formation. That is, if the grain of the stone is perpendicular to the bedding planes. Early frac’ing technology was limited to less than 100 feet, and was done with black powder. If the grain of this Ausi formation lies across the bedding planes 330 feet vertically sounds quite unlikely unless this is a very unusual formation; that is, very weak grained with few intervening natural fractures. 50 to 100 feet would be more likely. Hope this helps a little.


  5. Michael Lynch has another Peak Oil Denier Forbes article up this morning.

    Peak Oil 3: Has Production Peaked?

    The remnants of the peak oil community cling avidly to the belief that oil production has already peaked and that high prices prove this. “Look at the data” seems to have become a catechism amongst them, and it can be hard to dissuade them otherwise, especially by considering more than one variable as explaining oil supply and price.

    Most anyone can understand that high oil prices are no more an indicator of resource scarcity than the occasional spike in coffee, pork or orange juice prices.

    That is about the dumbest thing I have ever heard in my life. High prices are almost always an indicator of resource scarcity.

    Things happen that can cause prices to rise for a period before supply and demand can re-equilibrate, with oil particularly vulnerable to political disruptions–witness developments in Iraq, Iran, Libya, Nigeria to name the primary ones.

    Those things are all examples of causes of resource scarcity just as a hard freeze can cause resource scarcity, and high prices, for orange juice. Just because something caused it does not mean that is resource scarcity.

    Well Brent has been above $100 a barrel for about three and one half years now. It is about time it re-equilibrated.

    • Jeffrey J. Brown says:

      He has to argue that high prices don’t matter, because oil prices have not been at the low levels that he predicted, for years, that we would see.

      Michael C. Lynch (August, 2009:
      Peak Oil’ Is a Waste of Energy

      Oil remains abundant, and the price will likely come down closer to the historical level of $30 a barrel as new supplies come forward in the deep waters off West Africa and Latin America, in East Africa, and perhaps in the Bakken oil shale fields of Montana and North Dakota. But that may not keep the Chicken Littles from convincing policymakers in Washington and elsewhere that oil, being finite, must increase in price.

      • Dennis Coyne says:

        Hi Jeff and Ron,

        Although I disagree with most of what Lynch has to say, he is correct that oil has not peaked. One way to counter the “all liquids” argument is to track all liquids, but discount the NGL and biofuels according to their energy content relative to crude.

        It is a painful process to do this, but in rough terms if we take 70% of the barrels of ethanol and NGL, that gets us pretty close to a “barrel of oil equivalent” (boe). Chart below was done a while ago, data through June 2013 from the EIA.

        • Jeffrey J. Brown says:

          My usual argument.

          Substitution is always a factor, at least incrementally.

          However, in my opinion it is very likely that actual global crude oil production (45 or lower API gravity crude oil) peaked in 2005, while global natural gas production and associated liquids (condensates & natural gas liquids) have so far continued to increase.

          As I have periodically noted, when we ask for the price of oil, we get the price of 45 or lower API gravity crude oil, but when we ask for the volume of oil, we get some combination of crude oil + condensate + NGL (Natural Gas Liquids) + biofuels + refinery gains.

          Shouldn’t the price of an item relate to the quantity of the item being priced, and not the quantity of the item + the quantity of (partial) substitutes?

          In any case, a key question is the ratio of global condensate to Crude + Condensate (C+C) production. Unfortunately, we don’t appear to have any global data on the Condensate/(C+C) Ratio. Insofar as I know, the only complete Condensate/(C+C) data base, from one agency, is the Texas RRC data base for Texas, which is shown below for 2005 and 2012:


          Condensate: 0.12 mbpd
          C+C: 1.08 mbpd

          Condensate/(C+C) Ratio: 11.1%


          0.30 mbpd
          C+C: 1.95 mbpd

          Condensate/(C+C) Ratio: 15.4%

          The 2013 Ratio (more subject to revision than the 2012 data) shows that the ratio fell, down to 14.7%, which probably reflects more focus on the crude oil prone areas in the Eagle Ford.

          The EIA shows that Texas marketed gas production increased at 5%/year from 2005 to 2012, versus a 13%/year rate of increase in Condensate production. So, Texas condensate production increased 2.6 times faster than Texas marketed gas production increased, from 2005 to 2012.

          The EIA shows that global dry gas production increased at 2.8%/year from 2005 to 2012, a 22% increase in seven years. What we don’t know is by what percentage that global condensate production increased from 2005 to 2012. What we do know is that global C+C production increased at only 0.4%/year from 2005 to 2012. In my opinion, the only reasonable conclusion is that rising condensate production accounted for virtually all of the increase in global C+C production from 2005 to 2012, which implies that actual global crude oil production was flat to down from 2005 to 2012, as annual Brent crude oil prices doubled from $55 in 2005 to $112 in 2012.

          Normalized global gas, NGL and C+C production from 2002 to 2012 (2005 values = 100%):


          Estimated* normalized global condensate and crude oil production from 2002 to 2012 (2005 values = 100%):


          *I’m assuming that the global Condensate/(C+C) Ratio was about 10% for 2002 to 2005 (versus 11% for Texas in 2005), and then I (conservatively) assume that condensate increased at the same rate as global gas production from 2005 to 2012, which is a much lower rate of increase in condensate (relative to the increase in gas production) than what we saw in Texas from 2005 to 2012.

          • Dennis Coyne says:

            Hi Jeff,

            My point was not to disagree with your point. Just another line of attack.

            All liquids increased about 5% since 2005, C+C increased about 3%, maybe crude didn’t increase at all, though for a long time the World has combined crude plus condensate when accounting for oil, so as I have said before focusing on crude plus condensate is best in my opinion.

      • Watcher says:

        That link should be sent to Forbes, so they can think more carefully about who they fund.

  6. Enno says:

    Mike, you mentioned “Dennis, I think produced water will be the single biggest threat to predicted EURs from tight oil resources.”

    Until thus far I ignored the water data in the NDIC reports, but it is available. I don’t know the accuracy, but just glancing at the data there don’t seem to be major errors in it.
    Below I post 3 graphs:
    1) Cumulative oil production per starting year. The same graph I posted before, showing the average oil production for wells starting production in a certain year.
    2) Cumulative water production per starting year. This graph is exactly the same as 1), except that it shows the average cumulative water production, instead of oil production.
    3) Total water production in North Dakota. This shows that quite some water was already produced with the old wells in North Dakota, until recently. Water production initially slowly increased with the new oil production, but as also can be seen from graph 2), newer wells are producing more water.

    I hope Mike or someone else can chime in with thoughts on this average well/overall water production.

    • Enno says:

      The last graph was slightly incorrect, here the update.

      • Dennis Coyne says:

        Hi Enno,

        Very interesting thanks.

        I think the water becomes more important toward the end of the wells life. So the ratio of oil to water and how it changes from year 3 to year 7 of the well’s life (as we only have about 7 years of data for Bakken wells).

        At this point we just don’t know, but Mike’s intuition is likely correct when these horizontal fracked wells get down to 7 b/d (or possibly even 10 b/d if costs rise faster than oil prices) the wells will be capped. The question then becomes how quickly do we get down to 10 b/d, I am doubtful that the terminal decline rate (exponential tail of well profile) is any larger than 10%. If that is correct the 10 b/d level is reached at about 20 years and the new well EUR decreases by about 7%. Those last 10 years from 20 to 30 years are very low output so it does not really change thing very much.

        • Watcher says:

          NoDak needs to think about this in the context of Mike’s comment.

          When flow gets low, the big company wants to sell it. They will sell the well to some newly formed LLC that will collect money for a year or so as it flows 7 bpd and then 6 and then 5 and then 4 — at which point, being an LLC with no other assets, they walk away.

          And there is the well, unplugged and leaking residual radioactive stage markers onto the surface.

          NoDak should refuse to allow purchase of wells by LLCs without plug and abandon escrow.

          • Mike says:

            Watcher, in Texas all operators must now post a bond with the Texas Railroad Commission to cover the cost of plugging abandoned wells. Several years ago the cost of drilling permits was raised significantly and those additional funds were earmarked for plugging orphaned wells in Texas. Also, it is next to impossible to assign, or convey, plugging liability from one operator to another without bonds being in place at the time of conveyance.

            I suspect that N.D. has, like most of the world, taken the TRRC’s lead in this regard, as well as most regulatory matters. I hope so, anyway.


        • Mike says:

          Hi, Enno, that’s some good work; thank you. Cleary the oil to water ratio for North Dakota wells began to increase at the time the Bakken was ramping up and that makes perfect sense to me given the enormous number of wells drilled and that few of those wells make water initially, other than small amounts of induced frac water. Dennis is correct, typically produced water begins to increase as reservoir depletion occurs.

          I guess for all the ranting I’ve done about the costs of water production and the effects of water on late-life well economics, it occurs to me that these tight oil wells do not produce from conventional reservoirs that often are associated with structural traps and that often contain underlying connate water. In other words, each tight oil well produces only that oil in place around the wellbore, within the frac radius, that it created for itself. Each shale well more or less makes a space for itself in dense shale, drains that space, and that’s that. Its hard to think of the Bakken as one vast, homogenous reservoir, like for instance, Ghawar where an ocean of oil use to sit on an ocean of water. The big question to me is how much interstitial water there is bound in the shale matrix that will begin to increase over time and reduce OWR. I don’t know, others surely do.

          In Texas we do not report water production each month from individual wells. I would not expect a public company needing desperately to sell stock and raise investment capital to want to volunteer something as ominous as increasing produced water rates. So water is like a 4 letter word in the shale patch and it seldom gets uttered. As I drive up and down S. Texas highways, however, the vacuum truck traffic hauling water to disposal systems is enormous and growing. There are waiting lines going into disposal facilities, 24/7. Not all of that is flowback frac water, I guarantee.

          If N.D, on the other hand, does require monthly water production on a well by well, or unit by unit basis, it would be fascinating to see if, and to what extent, the OWR is declining on individual tight oil wells over time.

          • Enno says:

            Thanks Mike & others for your comments, very interesting.

            • Dennis Coyne says:

              Hi Mike,

              I really appreciate your comments I have learned a lot from what you have said. Please continue to point out any mistakes I make.

              I am no oil man and can learn much from people who actually produce oil.

              • Mike says:

                Thanks, Dennis. We’ll learn together, all of us. So we can take the message of peak production rates to the street.

          • Jeffrey J. Brown says:

            There is also a question as to often and to what extent that the massive frac jobs break into water bearing zones, and as pressure depletion continues around the fractures, water encroachment from water bearing zones increases.

            • Mike says:

              Westexas, goodonya. Along the EF trend, updip from the shelf margin, there are lots of growth faults associated with sediment slumping towards the basin. These faults often have lots of displacement and grow with depth. In the overlying Austin Chalk carbonate, these growth faults can be connected to the underlying Edwards ocean, so to speak, and lots of very, very salty water was produced from the Chalk when wells were frac’d too close to these big faults. Now and then we’ll hear of a shale well in the EF that is frac’d and makes no hydrocarbons and mucho 150,000 ppm chlorides water…from the Edwards. It is a very good point you bring up.

    • SuddenDebt says:

      That is some excellent charts and information.

      To me there are two observations worth noticing;
      1) Looking at wells by vintage it appears as water production has grown faster than oil production.
      2) It could be interesting to see how the water oil ratio (or its inverse) developed with time. Water to oil ratio appears to be growing with time.

      I do not know about the chemical composition from the produced water, but somehow the produced water is disposed of.
      Water normally flows more willingly than oil.

    • Enno says:

      The chart below shows the ratio of the water produced vs oil produced, using the same data. The strange peaks/drops at the end of the tails are indeed in the data. I can’t really explain it, except that the number of wells at the last 12 points in each tail is dropping, because wells from those years did not reach that age yet, and therefore the last point only contains the January wells from that year, which can cause some erratic behavior (low denominator).

      • SuddenDebt says:

        Thanks a lot for your work and sharing!

        From your chart(s) there appear to be one trend (barring any noise in the data); the water to oil ratio has increased with time both for the “older” legacy wells, but also for the newer wells.
        Water, oil and natural gas flows co-mingled in the wells and looking at your charts it appears as with time, total liquid flow for “newer” wells has increased and so has the water to oil ratio.

      • Dennis Coyne says:

        Thanks Enno.

        Great stuff. Seems like it leveled off in 2013 (similar level to 2012), 2014 probably too early to tell.

      • Mike says:

        Yikes, Enno. I don’t like what I see in your data.

        I wonder; I said in Texas we do not report water production per well every month and that is true. We do, however, estimate, loosely, water production per well each annual quarter. I wonder if N.D. does not do the same thing?

  7. Old farmer mac says:

    The inestimable Mr Lynch is still explaining why guys who majored in the sciences and have spent their life working in the sciences are ignorant of the realities of oil over at Forbes whereas the economists know all about it.

    My maternal grand father once had a beautiful 62 Chevy two door hardtop that really was driven only to church and the doctors office. He bought it new after retiring and it had only a few thousand miles on it in the mid eighties when he decided to park it under an old shade tree instead of the carport as usual.We all tried to explain that the tree was rotten and just about dead and thus in danger of falling on the car but the old fellow got more stubborn by the day being close on to a hundred and would not listen.If we had not said anything he would probably have put it back in the carport.

    He reminds me of the cornucopian element of businessmen who do not believe something that comes out of a hole in the ground will ever run short.

  8. Dean F. says:


    “The Railroad Commission of Texas’ estimated final production for April 2014 is 72,632,766 barrels of crude oil”, which means 2421092 bbl/day.

    My corrected model gave (reported in the comments of the previous post):
    2455818 bbl/day using the correction with absolute numbers
    2461750 bbl/day using the correction with percentages

    Not bad… I am quite close ^_^ !

    • Dean F. says:

      P.S. these numbers are for oil only, no condensate (RRC does not give final estimates for condensate)

    • Dennis Coyne says:

      Hi Dean,

      I think if you look back at older reports, you will find that the RRC usually underpredicts even with the adjustment factor.

      • Dean F. says:

        Thanks. I will have a look at them

      • Dean F. says:

        I considered for curiosity the data before September 2013 because, for those data, the EIA data and my corrected data show a difference which is smaller than 1%. I found that for 2013 data, the adjusted RRC data are usually underestimated with respect to EIA and my corrected data of an amount close to 5%. For 2012 data, the underestimation ranged between 5% and 10%. However, the level of underestimation tends to decrease over time (I suppose because the oil growth in Texas is decreasing and oil production will probably reach a maximum at the end of 2014 / beginning of 2015).

  9. robert wilson says:

    Fun at Forbes——excerpts

    …Michael Lynch, 2 days ago
    We don’t plant petroleum but we explore for it.

    Rob Rob 2 days ago

    And, as you showed in the graph in Peak Oil 1 – discoveries from exploration peaked in the 1960′s and have declined each decade since. Does that not demonstrate that oil is not “effectively infinite” as some economists have postulated?

    Michael Lynch, 1 day ago
    That graph is one of the problems: ‘discoveries’ actually means ‘currently estimated discoveries’. Thus, the amount of oil discovered shown is underestimated. Reserves have not declined because of upward revisions to field size.


    Robert Wilson 2 hours ago
    Nature planted the petroleum as noted in Hartmann’s book “The Last Hours of Ancient Sunlight”.——

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