OGPSS - California oil and Hubbert Linearization

Last week, when I was writing about the heavy oil fields of California I used a plot from Jean Laherrère to illustrate the potential ultimate production from the Kern River oilfield as a way to illustrate its potential future. Jean has written, via Luis de Sousa, to point out that the curves that I used are out of date, and was kind enough to send along the more up to date curves, not only for the Kern River, but also for the Midway-Sunset field which, as I noted, is the largest remaining field. It seems to be to good an opportunity to miss to also take this opportunity to briefly discuss the basis on which these projections are made, since they allow an estimate of the ultimate oil recovery from a field, and a projection, as the following figures show, of when the field will effectively run out of oil. Let me start by putting up his figures for Kern River to facilitate the discussion, and then I will explain, and add the Midway-Sunset plots at the end. Jean has (since the initial post went up) written to point out that it is important to note that, despite oil price increases and more wells, the field has steadily declined in production, at a rate of about 5% pa, since 1998.

Figure 1. Past and projected future production from the Kern River oilfield in California (Jean Laherrère).

This projection of field decline involves an estimate of ultimate recovery from the field which is derived from this curve.

Figure 2. Kern River production decline and total estimate of production (Jean Laherrère)

So how are these plots derived?

This is a topic that has been covered almost since the time that The Oil Drum was founded (back in March 2005), since it was in May of that year that Jean published a paper describing how to “Forecast Production from Discovery.” (His pioneering work, internationally recognized in this field, did not start with this. For example, he co-authored with Colin Campbell the Scientific American article on “The End of Cheap Oil” in 1998.)

Within the pages of TOD Stuart Staniford had briefly explained it while comparing different methods of estimating future production back in September 2005, with a follow-on post looking at specific examples where it might be applied.

The technique derives from a process known as Hubbert Linearization (after King Hubbert, who is largely remembered for predicting the date of peak oil production in the US before it happened). Examining the data from oil production over time, Dr Hubbert postulated that it followed a logistic curve, which as Stuart pointed out, is an accepted model of how exponential growth occurs in a system that is of a certain finite size. It has been used since its original discovery in 1838.

The mathematics of the equation are fairly straightforward, and for consistency I am going to quote Stuart’s explanation:

In terms of oil production, the differential equation looks like this:

dQ/dt = kQ(1-Q)

Here, Q is the cumulative production as a proportion of the ultimately recovered resource, t is time, and k is a constant that sets the width of the peak.

The solution Q(t) to this equation is a sigmoid function, and the derivative is the famous Hubbert peak. The idea behind the equation is that early on, the oil industry grows exponentially - the annual increase in production is proportional to the total amount of knowledge of resources, oil field equipment, and skilled personnel, all of which are proportional to the size of the industry. Thus dQ/dt is proportional to Q.

Later, however, the system begins to run into the finiteness of the resource - it gets harder and harder to get the last oil from the bottom of the depressurized fields, two miles down in the ocean, etc, etc. The Hubbert model assumes that all of this complexity just comes down to that annual production gets an extra proportionality term of (1-Q) - the amount still to produce.

Now, there's a nice trick which I learned about from Deffeye's book "Beyond Oil", but I don't know if he thought of it or got it from somewhere else. The idea is that if we plot dQ/dt / Q versus Q, the above equation says that it should be a straight line, since

dQ/dt / Q = k(1-Q)

So we plot the ratio of annual production to cumulative production to that date, versus cumulative production. In his book, Deffeyes does this on p37 for US oil production. In the beginning, the data are crazy, but after about 1958, they settle down into pretty much a linear regime (with a little noise) that has held good ever since. The nice thing about this method is that you do not need to input an estimate for the URR. Instead, you extrapolate the straight line, and it tells you the URR.

You will note that Figure 2 shows this for the Kern River field, with the extrapolated out to an Ultimate Resource Recovery (URR) of around 2700 Mb of crude. One can then project out the decline in current production (Jean notes that it remains at around 5%) with an estimate of how long the field will last. (Figure 1).

The technique has some limitations in fields that are produced under political control, or due to other external forces where production can be shut off for significant periods (one thinks of Saudi Arabia, Iraq and now Libya as examples) however when political constraints are removed (such as for example in Texas) then the decline does assume a linear trend.

It does not, however, always apply, and Robert Rapier has explained, in two posts (here, and here) why he has concerns about using the technique. But in terms of giving a ballpark for production (and recognizing that there are always new discoveries and inventions that can be, as they say, game changers) the technique has considerable support. And the consistency with which the Californian fields are following the predictions provide evidence for such an opinion.

Figure 3. Midway-Sunset production decline and total estimate of production (Jean Laherrère)

Figure 4. Past and projected future production from the Midway-Sunset oilfield in California (Jean Laherrère).

I am deeply indebted to Jean for making this updated information available, as well as his indefatigable work in examining the remaining oil reserves in the oilfields of the world.

P.S. Jean has also discussed results from this region in other material, such as, for example, here.

OGPSS - The heavier oils of California's Kern Valley

The Kern River field was first found by a wood cutter and his son, after being asked to drill a well on the Means property, who began digging with a 3-inch auger, below a seep on the Kern River shore; they found oil at a depth of 13-ft. They then dug out a larger hole, using a pick and shovel to create a larger access from higher up the river bank down to that oil level, and then drilled down an additional 30-ft after having fixed the auger to the end of a section of connected pipes. (This was done by manually turning the auger). The well then started flowing, filling the excavation at around three bd. That oil was then taken and used as boiler fuel to power a more conventional drill that, nineteen days later, reached another producing horizon at a depth of 256 ft. and became the first commercial well in the field. By 1904 the field was producing 17.5 million bbl/a year, at which it peaked.

It is important to distinguish the different fields in the region, since there are many fields around Bakersfield, each having different histories and projections for the future. The Kern River field, for example, has produced roughly 2 billion barrels of oil since that first well, with about 476 million barrels estimated as being still available.

Oil Fields in the Kern Valley around Bakersfield, CA with the Kern River field (the first) and the Midway- Sunset (the largest) further identified. (CA Conservation )

The Kern Valley as a region rapidly became the largest oil producing region in the state, particularly since the arrival of the railroad in 1902 made it possible to develop the adjacent Midway-Sunset field, which remains the largest oilfield in the State. As a result of this, by 1904, California was producing more oil than Texas. Times have changed a bit since then, and while the Midway-Sunset claims to remain the largest oil producing field within the lower 48 states (not that this doesn’t include the offshore Gulf), the largest operator in the field now only produces some 29,000 bd.

Gail Tverberg visited the production facilities at the Kern River field back in February 2009 and gave a more detailed description of the field and the work Chevron is doing than I plan to cover today. (There is no point in trying to compete with her excellent report, though the reference to the video of the tour is now here, and the API picture record of her visit seems to have vanished. The oil in the field is heavy, and so steam has been injected through one set of wells, in an increasingly refined operation, to heat the oil in place, so that it will flow more easily to other collection wells where it can be pumped to the surface.

Kern River production process (from Chevron via Gail Tverberg )

The impact of the steam flood on production was dramatic, and has become the main method of production since it was introduced

Impact of steam flood on oilfield performance (Chevron via Gail Tverberg )

Gail also then posted a comment by Jean Laherrère on his estimate of future production from the field, showing its future decline, even with an increased number of wells , to a final estimate of production for the field.

Cumulative oil production estimate (Jean Laherrere )

My own visit to Bakersfield looked at a different way of producing the oil. The Bureau of Mines (as then was) brought large borehole mining equipment to Bakersfield and used pressurized jets of water to mine the oil and sand from around a well in the McKittrick field at a depth of 350 ft, bringing the mix to the surface, where the oil was removed, and the sand then re-injected back into the cavity. (This process was also successfully applied in mining small pods of uranium ore in Wyoming). The method has the advantage of getting all the oil from the formation section that was mined, with relatively little environmental impact, but the closure of the Bureau shut down this program. (Though I retain slides of the operation).

Some of the sand is even closer to the surface, as the initial well showed, so that strip mining of the region to produce the oil in the same way as in Alberta may be economic for the upper layers of some of the fields, were it not from the emissions that would come from the exposed oil and have a negative impact on local air quality.

The continued search for more efficient methods to extract a greater proportion of the remaining oil in place continue through the present. Methods have been proposed where the steam is generated using solar power to heat the steam. A small pilot plant was opened at the beginning of this year to demonstrate the feasibility of the technique, though as yet on too small a scale to produce a significant amount of oil. Higher temperature steam has been generated at other power plants using the same technological concept and so there may be a path forward for this development.

In the same way there are some experiments to use the injection of oxygen and steam as a way of increasing production. The process is claimed to be able to work below the 2,000 ft limitation of conventional steam flooding to a depth of perhaps 3,500 ft. The claim is also that the costs are down at $4/bbl capital cost and $15/bbl operating cost to achieve this enhanced recovery. The process sounds a little too good to be true in the simple form in which it has been presented to date, but it illustrates the possible potential for improving absolute recovery levels above those

Unfortunately the research budgets for finding enhanced ways of producing fossil fuels are not seen as having the critical importance that they may well have. The greater emphasis on advancing renewable forms of energy, and Washington power struggles have meant that energy research is not the hot topic it once was and the interest in developing new techniques to obtain more oil from existing fields is often subsumed by the desire in companies to grow reserves, even if only by purchase instead of discovery or development.

The debate over energy supply and the environmental impact of different sources of power continues to make it difficult to find satisfactory ways to supply California with the energy that its population needs. With the confines within which the oil and gas industry currently work in the state it is hard to see any future gains in production over the levels of today, and the greater likelihood of declining production.