Technology and oil production

[Surlethe]

I was thinking this evening about peak oil, naturally, and was wondering how to quantify the effect technology has on oil extraction. Qualitatively, it should bring the peak back and make it higher, but that doesn't tell us too much. So, here're the assumptions:

• technology advances exponentially with respect to time
• oil production is proportional to technological advance.

Mathematically, I can make this a little clearer. The basic model of oil production is the logistic curve -- simply, with cumulative production P and total reserves T, we have dP/dt = P(1-P/T). It's pretty common knowledge that this solves to P = [TCexp{t}]/[1+Cexp{t}]. If we want to take into account technology, let's try putting dP/dt = exp{at}P(1-P/T). This solves to P=[TCexp{exp{at}/a}]/[1+Cexp{exp{at}/a}]. A quick differentiation checks that this is indeed a solution of the equation.

Are the assumptions okay? What can this tell us quantitatively?

[Alyrium Denryle]

Technology probably does not increase on an exponential curve. Eventually, the technology we can actually apply to a given problem will level off.

your second premise is also false, precisely because oil production is limited by the actual amount of oil. If anything increasing the technology base would make the peak come faster, and be at the same point. Assuming you mean total oil, and not just oil locked in technologically easy sources (IE. if you are including shale oil and the like in the initial oil reserve)

[Duckie]

However, the second premise is true if you say "Oil Production is proportional to a logistic growth model where technology is substituted for time", possibly.

[bobalot]

* technology advances exponentially with respect to time
* oil production is proportional to technological advance.

The first one is is an unjustifiable assumption. We have advanced technologically exponentially in the past, this does not mean that it will happen in future.

Extracting oil depends on a lot of physical attributes such as geology. No matter how much technology advances there are going to be certain physical limits. We can only make things so efficient. For example, there are limits to how efficient a combustion engine or wind turbine can be.

The 2nd statement is true to an extent. As we improve our extraction techniques we will increase production. I think when a lot of the public hear this, they believe that oil won't run out or decline in supply. It is a incorrect assumption. Better extraction techniques simply mover the peak closer. Production will increase but then will have a much sharper drop then originally expected when it hits the peak. Texas and the North Sea have had little restrictions (relatively) on drilling and have had the best private companies investing in new technologies. Production is still collapsing.

Off the topic , I think as a society we have become a bit irresponsible. We simply assume there can be technological fixes around every corner to solve all our problems.

I find this a strange thing about America, where there is a healthy suspicion of science (which has lead to ridiculous debates about Evolution, Climate change etc.), while at the same time there is 'faith' there is a technological fix to every problem, and the 'market' will find a way. Scientists and Engineers are derided but then expected to fix the nations problems. Truly strange.

[SirNitram]

It's worth noting many technologies are now geared towards synthesizing oil, instead of extracting it. However, none have yet been proven on the large scale, and many are net-energy-negative. Final problem, polluting as hell.

We will ultimately see synthetic petroleum replace drilled petroleum. It will likely not be common as a fuel source, but as a source for things like plastics.

[Surlethe]

Technology probably does not increase on an exponential curve. Eventually, the technology we can actually apply to a given problem will level off.

True -- so should we assume that technology follows a logistic curve instead? That makes the math a bit more complicated.

your second premise is also false, precisely because oil production is limited by the actual amount of oil. If anything increasing the technology base would make the peak come faster, and be at the same point. Assuming you mean total oil, and not just oil locked in technologically easy sources (IE. if you are including shale oil and the like in the initial oil reserve)

Right; I thought it would be more clearly communicated in the math. That's why I set dP/dt = exp{at}P(1-P/T).

[Surlethe]

* technology advances exponentially with respect to time
* oil production is proportional to technological advance.

The first one is is an unjustifiable assumption. We have advanced technologically exponentially in the past, this does not mean that it will happen in future.

So should it be a logistic curve instead?

Extracting oil depends on a lot of physical attributes such as geology. No matter how much technology advances there are going to be certain physical limits. We can only make things so efficient. For example, there are limits to how efficient a combustion engine or wind turbine can be.

The 2nd statement is true to an extent. As we improve our extraction techniques we will increase production. I think when a lot of the public hear this, they believe that oil won't run out or decline in supply. It is a incorrect assumption. Better extraction techniques simply mover the peak closer. Production will increase but then will have a much sharper drop then originally expected when it hits the peak. Texas and the North Sea have had little restrictions (relatively) on drilling and have had the best private companies investing in new technologies. Production is still collapsing.

That's what I'm trying to model. If we assume technology increases extraction ability exponentially, what are the mathematical consequences when we factor in the geological constraints?

[Vehrec]

So should it be a logistic curve instead?

While technological advances overall compound exponentially, in any one field it becomes a matter of diminishing returns after a while. For instance, the original ICE was ten feet tall and totally immobile. Within 40 years it had shrunk to a car engine. In the hundred years since, we've gotten more power and efficiency, but the last ten years have not netted great gains in these areas. We aren't even close to extracting all the energy in a gallon of gasoline to power our cars, but the rewards of our efforts get smaller and smaller with every advance we make. Research is dependent on a lot of factors, so I would hesitate to ascribe simply a Logistic or a Exponential curve to such a complex process. However, the overall average might look somewhat logistic.

Your oil production numbers look alright to me, but I'm terrible with calculus and should not be allowed within ten feet of a derivative.

[The Duchess of Zeon]

The problem is that some of the technology developed is basically going to give us a plateau, rather than a nice peak in the curve, or more precisely, an undulating plateau, because the technology is explicitly designed to increase the rate of extraction--while reducing the overall recoverable reserves from that deposit as a consequence. Saline injection is a good example. This throws most of the curve calculations right to hell and requires something far more complex.

[Paolo]

your second premise is also false, precisely because oil production is limited by the actual amount of oil.

That assumption is captured by the logistic map Surlethe's multiplying the exponential function against.

[Paolo]

So should [a model of technological advance] be a logistic curve instead?

That's about as conservative as you can get with a continuous function.