“Pg Gets Us on the Curve.”- Which Curve - Any Curve?

David Swinehart and Ted Dohmen                 02/01

Now that we’ve all been trained to consider the Pete Rose method for characterizing the economics of our prospects, we are aware that Pg is the probability of getting on the reserve distribution curve.  But does it matter which curve we are talking about?  Reacting to the question, as geologists and geophysicists might, our intuition says, “Yes, the reserve distribution and the Pg together define the prospect.”  We know the risk on a prospect with big upside is usually higher than one with small potential, but the effort to suggest an appropriate Pg becomes distorted by the process of defining the low end of the curve.  If the low end is allowed to be very small, then the Pg should be high, right?  Wrong.  The Pg is the probability of getting on this curve, not just any curve.  Both the high and low ends, not just the low end, define the curve.  This paper first examines a couple of examples of how this affects us – one from the Pete Rose school and one from our own peer review.  Then we’ll examine how to best deal with this problem and it’s consequences.

Pete Rose Classroom Example

An independent oil company at a Pete Rose school present the class the following example.
They presented a prospect based on an amplitude map made from 2D and 3D seismic data, which showed a stratigraphic trap based on a weak amplitude anomaly on monoclinal dip covering an area equivalent to the size of a Texas county!  There were only a few wells in the area that penetrated to the depth of the map. These wells encountered tight sands; however, the amplitude anomaly was not present where the drilling took place.  The reserve estimates for this prospect ranged from 1 BCF to 32 TCF for the P99 and P1, which resulted in a mean reserves estimate of 2.2TCF.  That’s a big prospect!


Next, they guided the class to an understanding of the Pg.  They showed that their drill location was in a bright portion of the amplitude on a well-defined, four-way structure.

They estimated their Pg for this structure to be to be about 20% - making use of the fact that it was a four-way and that it had the brightest amplitude on the map.  It seemed reasonable that 20% was a good estimate for this small, four-way structure and that 1BCF was a good estimate of its volume.

The problem is that they also used this Pg for the whole county!  They reasoned that 20% was the probability of finding their minimum case reserves, of 1BCF, and hence their probability of getting on the curve.

To put this in rough dollar teams let’s assume that all their costs can be approximated by a net profit of $1.00 per MCF.  This implies that the value of their prospect would be approximately 

$1.00 X (2.2TCF mean reserves) X (20%chance of success) =$440 million.

Pete Rose and most of the participants at the school accepted this as correct.  We feel there is a logic problem here, as did some of the class members.

The dissenters argued that if the proposed location where moved 2,000 feet in any direction, it would not test the small four-way prospect, but test the large stratigraphic prospect.  In that case, everyone in the class agreed the probability of logging pay would have to be much smaller, since it wasn’t in the brightest amplitude and wasn’t on the four-way.

The dissenters argued that there were really two prospects, not one.  The smaller one had a Pg of 20% as had been assumed, but it’s mean reserves were roughly 0.5 BCF yielding a value of 

$1 X 0.5BCF X 20% or $100 thousand.

The second prospect was the big strat trap, with a much smaller chance of success.  The probability of having up to 32 TCF stratigraphically trapped in a sand that had no permeable tests is very small.  The prospect presenters admitted it was less than 1%, since there are very few pools of this size in world.  An approximation, of the countywide prospect’s value is

$1 X 2.2TCF X 1% = $22 million.

The NPV of the two prospects drilled separately would be $100K + $22Million or $22.1 million instead of the $440 million in the first estimate.

If we persist in the single Pg approach, we feel the prospect is misrepresented.  Its Pg, mean reserves, and NPV are all too high!  This is not an attempt to suppress the advancement of large prospects.  Look at Anadarko’s Bossier Shale example.  That’s a recent stratigraphic play that may truly cover a county in Texas based on known, bypassed pay.  The issue is one of accurately representing the geology in our economics.

Gulf Coast Peer Review Example

Consider the figure at right. This is very much like a real example seen in a peer review.  The orange represents a possible salt stock, the dashed orange line is the extent of overhanging salt, and the red is an amplitude anomaly.  The two circles labeled 1 and 2 are proposed locations.  In this play, amplitude anomalies of similar quality find pay sands 80% of the time.  We understand the environment to be channel and channel-levee dominated turbidities, which are highly stratigraphic. Because of the stratigraphic nature of the sand, and without amplitude support, the probability of logging pay at the up-dip location (well 2) is very much less than at location 1, say 20%. Let’s assume that the reserve estimate for the area in red is 10 BCF, and the up-dip area under salt in the same fault block is 40 BCF.

The approach suggested by the team was to assume P90, P10 reserves of 10BCF and 50 BCF (10+40), yielding a mean of 27 BCF. And since amplitudes work 80% of the time, they said the Pg should be 80%.

In order to assign an economic value to this, we will use $1 per MCF, yielding:
                       $1 X 27BCF X 80% = $21.6 million

But this approach, like the class example above grates on our sense of the geology.

Now, let’s look at the two prospects as separate ones. The probability of finding up-dip reserves at location 2 might be 20%.  The mean of the sub-salt reserves is probably something like 17BCF.

The economic value of the up-dip reserves would be $1 X 17BCF X 20% = $3.4 million.  The mean reserves in the amplitude are 10 BCF with a Pg of 80%.  The economic value of the amplitude-supported reserves would be:

$1 X 10BCF X 80% = $8 million.

The two combined yield a total value of only $11.4 million compared to the previous $21.6 million.

This valuing process sits much better on our conscience.  We clearly have two prospects here.  This is best illustrated by the realization that the up-dip location is much more risky than the down-dip amplitude location.  It leads to the two prospect – two Pg model.  It is clear here that the 80% probability at location 1 is tied with the amplitude supported reserve case.  Were the first well to work, then drilling up-dip to reserves is usually a good thing, but here it cannot be assumed that it guarantees having sand up-dip. An 80% assumption for the up-dip reserves is not justified even with success down-dip.


One should be careful of “a prospect within a prospect” duality, where a low risk - low reserve prospect is coupled with high reserve prospect.  It is very tempting to use the low risk Pg for all of the reserves.  Doing so only overstates the value and reserves, setting us up for big disappointments down the road after the first, low-risk well is drilled.
How do we recognize these?  If the geologic model used to explain P90 reserve size is different than geologic model needed to explain the P10 reserves, one should expect prospect duality is present.  Another way to recognize these is to consider different locations for the initial test within the area used for the reserve distribution.  When the probabilities suddenly jump for locations that lie roughly near one another, then one should suspect two models are being used.

For example, if a location is proposed inside a bright spot while the area up-dip of the bright spot is necessary for the P10 case reserves, then try a thought experiment starting at the first well consider tests farther and farther up-dip.  If the probabilities of finding pay at two nearby locations dramatically differ, then two models are present.

Characterizing a prospect with one Pg and one reserves curve is appropriate when there is one geologic model.  If we consider a four-way structure, then for any proposed location inside the closure, the trapping model is always the same.  The only consideration is how much it fills up.  The probability of logging pay at any given location as we move down structure decreases uniformly.  We assume a log normal distribution for the fill up, and estimate a Pg for being on that curve.  Similarly, when we consider a bright-spot’s edges, there may be some difficulty in pinning down the actual extent, but we consider it decreasingly likely that it continues, the farther we try to extend it. So, the lognormal reserves distribution and one Pg can describe this.

Believing in a high likelihood of finding a small amount of pay somewhere in a proposed well is not the same as believing it’s an economic venture.  As for mixing the prospects by using one Pg, it shouldn’t happen.  We will end up with inflated reserves that we must pay for later in the game.  Focus on the geology, be fair, and above all, stress accuracy.

The flip side of this is that we need to accept accurate portrayal of the geology even if it means high Pg’s.  We need to guard against the pressure to obviate geology that comes in the form of suppressing the P99 reserve size.  Pg’s should reflect the geology- as should the reserve curves we use.  In the case of a DHI amplitude, we might expect the P90 and P10 areas should be adjusted until the mean and mode are not far from the best guess case of the amplitude size.  The Pg should be allowed to range fairly high in such a case, provided the calculated Pc can be justified by industry experience.

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