Thursday, January 3, 2013

Playing With a Simple Depletion Model

Shale oil plays are a hot topic these days.  James Hamilton at Econbrowser points at a variety of presentations made recently at the American Geophysical Union meeting.  Some analyses are optimistic: Citigroup forecasts that by 2020 the US will be producing almost four million barrels per day of shale oil, with almost a million barrels per day from the Bakken Shale in North Dakota and Montana alone.  Others are much more pessimistic: David Hughes asserts that a more complete analysis suggests that Bakken production will indeed reach almost a million barrels per day in about 2017, but will then decline rapidly to only 50,000 barrels per day by 2025.

Several factors go into such analyses; most of those that appear to account for the difference between the optimists and pessimists are based on the depletion rate for production from the wells in a shale oil reservoir.  Production from any specific oil well declines over time.  The depletion rate is a measure of how rapid the decline is.  It is typically expressed as a percentage: production declines at x% per year, or at y% per month.  If the depletion rate is 10% per year, and the well is producing 100 barrels per day today, a year from now it will produce 90 barrels per day, two years from now it will produce 81 barrels per day, in three years about 73 barrels per day, and so on.  The experience so far is that wells in shale oil plays have very high depletion rates, in some cases in excess of 50% per year [1].

The rest of this discussion is based on the graph shown above, produced from a simple depletion model.  The vertical axis is total production from many wells [2], in barrels per day.  The horizontal axis is months from a time zero, when drilling is assumed to begin.  The red curve is for a hypothetical baseline case that assumes conditions typical of what we are currently experiencing: 125 new wells drilled per month, initial production of 500 barrels per day per well, and a decline rate of 3% per month.  Starting from zero, production climbs steadily, flattening out at about two million barrels per day after 180 months (15 years).  At that point, the production from 125 new wells per month simply offsets the decline in production from the wells that have already been drilled.

The "collapse" shown after 180 months represents what happens to production if you were to stop drilling new wells at that time: an exponential decline of 3% per month.  For example, for a particular field, that exponential decline kicks in when you run out of places to drill.  Some experts believe that a decline rate of 3% per month is too optimistic.  The green curve shows what happens if the rate is 4% per month instead.  Maximum production tops out at only 1.5 million barrels per day, and the decline if/when drilling is stopped is noticeably steeper.

One can make the argument that oil companies will choose the best sites for their initial wells, and that over time the quality will decline.  The blue curve shows what happens if, in addition to using a 4% per month decline rate, the initial production from new wells also declines at 2% per year.  That is, during the first year new wells start producing at 500 barrels per day; in the second year new wells produce at 490 barrels per day; and so on.  In this case, production peaks after about seven years at 1.37 million barrels per day and begins to decline slowly.  New, lower-quality wells don't completely offset the decline of existing wells.

A final argument made by the pessimists is that as the quality of the wells declines, the rate at which wells are drilled will also decline.  That is, some investors who will pay to drill a well that delivers an initial production of 500 barrels per day won't pay for a well that produces only 400 barrels per day.  The violet curve adds a decline rate for new drilling of 2% per year.  Now production peaks after about five years at 1.27 million barrels per day, and after 15 years has dropped below a million barrels per day.

Different assumptions, very different predictions.

[1] If production from the well is throttled to less than its potential, the depletion rate may be zero for a considerable amount of time.  Eventually, though, production will still decline.

[2] The code for the model drops wells once their production drops below a barrel per day.

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