15 October 2010

Is Your "b exponent" Hyperbolic or Exponential?

In the FT yesterday, John Dizard explains an important debate over the future of natural gas, with far reaching implications for investors, governments and you and me.  Like many debates of relevance to policy, the debate over production decline curves in natural gas wells from shale gas formations hinges on expectations of the future that can only partially be addressed via scientific predictions.  Uncertainties and ignorance are fundamental.  The market has been rife with optimism that there is plentiful, recoverable natural gas available via new technologies for drilling.  But not everyone agrees.  Dizard explains the debate:
[R]right now in the US and European energy world, there is one number that does tell you the story. It’s just not a number most investors, and the policy tribes, ever heard of, let alone used as a guide to action.

I’m speaking of the “b exponent”. You are much safer questioning the occupation of a gas promoter’s mother than doubting the “b exponent” of his wells. After all, the former is only about the past; the latter tells his future. And your future, since you’re paying for his future.

The b exponent is a term in the equations that define curves on a chart that describe the rate at which the production of gas or oil wells declines over time.

These equations have been tweaked and elaborated over the past 60 years, incorporating the slow increase in geological science, along with the cyclical requirements of gas and oil promoters.

The decline curve equations all incorporate terms for initial production rate, the initial rate of production decline, and the degree to which that initial decline rate flattens out over time.

The b exponent is a way of getting the curve generated by the equation to fit that rate of flattening.
He explains the debate over the "b exponent" in terms of two views on how it will play out in the context of shale gas:
The debate, which is turning into an argument, over the potential for shale gas development turns on that rate of flattening. The two schools of thought are the “hyperbolic decline” people and the “exponential decline” people, referring to two curve shapes.

The hyperbolics believe that decline curves for shale gas flatten out over time, much like conventional, vertical wells drilled into sandstone or carbonate formations. For them, the b exponents of their wells would be 1 or greater. They can take the high initial production rate of shale wells, or “IP”, and show financiers how this translates into high recoverable reserves or “EUR”.

The exponentials, a so-far smaller group, say that shale wells decline quickly after their initial high production, so the b exponents would be, say, 0.5. On hearing this, the hyperbolics will break a long neck beer bottle on the bar, and a fight will start.
Why does this debate matter?
If the hyperbolics are right, then shale gas wells in Louisiana or, prospectively, Poland will produce gas at a reasonably high rate and low cost over a long period of time.

That is what has been sold to Wall Street and is being used as a negotiating position with Russian gas officials. Up to now, the hyperbolic argument has worked with Wall Street. Unfortunately for Europe, the Russians think the production and unit cost numbers are an empty bluff.

I have seen very smart exploration and production people using the best available science and data make large losing bets on the size and location of hydrocarbon deposits. Unlike Wall Street or political people, they eventually face the facts, admit when they’re wrong, and use the information from the failures to do better next time.

If this were only an insider industry debate, then the rest of us could ignore it, or buy some popcorn and watch the show.

But it isn’t. The US, Europe, and now China are making huge investments in switching from coal-fired power to gas-fired power, and if there isn’t enough gas at a low enough price, they have a problem.

For example, if the pessimists/exponentials are right, then the ultimately recovered gas reserves from, say, the Haynesville deposits in Louisiana and Texas could be closer to 2bn cu ft for the average well, rather than the 6 bcf some operators project. If so, then the wells on most of their land would need a gas price that is at least twice, and perhaps three times, what is on offer in the spot and futures markets.
Keep your eye on the evolution of knowledge of the "b exponent" -- this is not a debate that will be settled via theoretical arguments, but through actual experience in natural gas recovery.  Stay tuned.


  1. Great information in this post. In the energy/environment/economy nexus, there is no more important single issue to clarify than natural gas reserves.

    That said, on a worldwide basis, the enormous reserves in the Middle East and former USSR will provide plenty of energy going forward. The consequences for global security, economic development, and the environment remain to be seen. The other key point to keep in mind is EROI on the depleting resource.


  2. I wonder how this might apply to Bangladesh, which relies on its natural gas deposits for over 70 percent of its energy supply, both for electricity generation and for transport (replacing gasoline with CNG in Dhaka city's rickshaws was a large factor in reducing urban air pollution). The proved reserves are anticipated to run out in around 25 years at current trends in consumption, and this is a big concern in the country, which has one of the faster growing third-world economies.

    Currently, disputes between Bangladesh and Burma over offshore gas deposits are a large diplomatic issue.

    Understanding what can be recovered from a reserve will be crucial there.

  3. For me, it's pretty scary for us who live in the neighborhood of cheap coal to tie our future to the unknown future prices of natural gas. First we have to pay for building the new plants, then our power bills will be unknown based on all these unknowns. And I don't know that the utility regulators are really looking at the risks to the people who can least afford what amounts to public utilities gambling on the future costs of gas.

  4. There are other problems with hydraulic fracturing to recover gas from tight shale formations. It's not just a matter of pumping water under very high pressure into the well. There are chemicals added to the water.

    "...changes to the Clean Water Act made in the 2005 Energy Policy Act exempt natural gas explorers from disclosing what chemicals they use in hydraulic fracturing, allowing those explorers to avoid costly regulatory oversight."


    I have heard second hand that the solution pumped into the well is strongly caustic so that the cracks are widened by dissolution of the shale. When the solution is pumped back out of the well, it will likely have to be treated as hazardous waste. But it's all trade-offs. Is it better or worse than coal mining and burning?

  5. Exactly why we should be building nuclear powered plants and developing thorium power plants.
    My cynical view is that if Wall St.- the same bunch that screwed up the mortgage market- is all in on gentle depletion curves, then I will bet against them.

  6. DeWitt otheres who are in interested in shale plays, check this out. it is a conference on the subject sponsored by U of Colorado Law School.

  7. Sharon F. said... 3

    "For me, it's pretty scary for us who live in the neighborhood of cheap coal to tie our future to the unknown future prices of natural gas."

    For me the scary part is that most of us heat our homes with natural gas, if there is a big switch to natural gas for electricity generation and the estimates of future supply are wrong we could end up living in the dark without heat.

    If I have to chose between living in the dark or freezing to death I will choose the dark.

  8. Harrywr2-

    But when people in our part of the country find fuel prices to be too high, we buy woodstoves. So it might be more smoky or not(don't know the comparison of woodstoves to coal plants with current technology on both)but we won't be freezing.

  9. So why is our current experience insufficient to determine the correct "b exponent"?

  10. I don't know about b-exponents, but certainly a large part of climate change debate is hyperbolic. ;)

  11. bernie #9,

    Because hydrofracing shale is new technology and there hasn't been a field producing long enough to get a good estimate. It may also be dependent on the local geology.

  12. Sharon F. said... 8

    "But when people in our part of the country find fuel prices to be too high, we buy woodstoves."

    We have air quality burn bans which occur periodically mostly in the winter months. No burning wood of any kind in any device unless it is your only available source of heat.

    Interestingly enough, the weather conditions that create an air quality burn ban, an extended period without wind will probably create the conditions where large segments of the population can qualify for the exception as most modern furnaces require electricity to operate and our growing dependence on windmills for electricity will insure we don't have enough electricity during an air quality burn.

  13. here's the CDPHE website on the Denver Metro area.http://www.cdphe.state.co.us/ap/woodhome.html

    "The graphic above shows expected air quality conditions for the Denver metro area. During the winter high pollution season (November through March) the graphic indicates whether an air quality Action Day is currently in effect. During an air quality Action Day, residential burning is restricted in the seven-county Denver-metro area, including Denver, Boulder, Broomfield, Douglas, Jefferson, and areas west of Kiowa Creek in Adams and Arapahoe counties. The only exceptions to the residential burning restrictions are for people living above 7,000 feet; those who use Colorado Phase III (Phase II EPA) certified stoves, Colorado approved pellet stoves, approved masonry heaters or those whose stoves or fireplaces are their primary source of heat. For more information on residential burning restrictions follow the links below."

    Here's EPAs list of some places with restrictions:
    Looking lower down on this webpage we find:
    The state of Montana offers an Alternative Energy Systems Credit against income tax liability for the cost of purchasing and installing an energy system in a Montana resident’s principal home that uses " . . . a low emission wood or biomass combustion device such as a pellet or wood stove."

    If gas prices are high enough, we may be able to afford the certified or pellet stoves where restrictions currently exist.

  14. Producing gas from fractured shale is a fairly new concept but producing gas (and oil) from fractured low permeability reservoirs in general is not. It's well understood that fractured reservoirs initially produce at very high rates as the gas or oil is drained from the natural fracture network. The sometimes specacular fracture production depletes rapidly and is followed by a long period of relatively low-rate, slowly declining production as gas or oil oozes out of the solid rock.

    Companies have been sucking in unsophisticated investors by hyping IP's from horizontal wells in fractured reservoirs for a long time. See also, Austin Chalk and Chesapeake Energy back in the 90's.

    The problems with trying to predict the shape of the "long tail" from early production numbers are not new, although they may have been newly discovered by a fresh batch of investors known generically as "New York Doctors" in the industry.

    In a similar vein, hydrofracking of shale gas reservoirs is relatively new technology but hydrofracking has been widely used in other reservoirs for decades. It's been done tens (hundreds?) of thousands of times in oil and gas wells all over the world. Widespread claims that it will destroy the planet have emerged only in a few recently developed shale gas plays. A cynic might observe that the worst effects of fracking seem to occur in coal mining states.

    It has the earmarks of a controversy using sketchy scientific data to push an underlying political agenda, not that that has ever happened before.

  15. Working with a lot of people who estimate reserves, I have a simpler explanation. People who use exponential curves instead of hyperbolic have an audience that finds the latters' math too hard. Of course you're not going to have a nice exponential curve when you're doing things like blowing up the formation and pumping fluid to get liquids out as quickly as possible.