## Calibrated appraisal

The calibrated approach to prospect appraisal has been described by Nederlof (1979) and Sluyk & Nederlof (1984) in some detail. As was explained before, the philosophy behind it is that any model of the "petroleum system" is likely to be imperfect. In the practice of appraisal using a model, there are two sources of uncertainty: the uncertainty of the input variables ("input noise") and the uncertainty about the model ("model noise"). Calibration can try to study both problems.

First, input uncertainty can be reduced by a formal use of experience data bases. For instance a porosity estimate is required as an input. We can make a guess, a single number. Then start thinking about how certain we are about that number and, being honest, we "sprinkle" some uncertainty around our single number, in other words, we input a probability distribution.

A calibration of porosity statements would make a more or less formal use of the data available, by selecting the well data that are representative of the undrilled situation, e.g. same formation, facies, depth, etc. Statistical rules will tell what the uncertainty about the mean of those observations is, depending on the number of wells available in the area. A further step may be to take any two-dimensional autocorrelation into account. Porosity maps and kriging would possibly give a reasonable estimate for the undrilled well, if such approach is practical. Note that with kriging both the estimate and it's uncertainty (variance) is estimated. The judgment about input variables can be significantly improved by this baesian approach to estimation and prior distributions of variables.

The process just described can be termed "input calibration". This is obviously what many geologists have been doing over the years with more or less sophistication.

Second, the "model can be calibrated". This involves the realization that Mother Nature cannot always be trusted. In the geological context one might say: "We do not know exactly what Mother Nature has done in the geological past". Our understanding is imperfect. A trivial example may illustrate this: a simple appraisal assumes that the amount of oil to be expected is proportional to the average porosity, apart from other factors, such as size of trap, depth, pressure etc. Now the importance of a difference between 10% and 20% may mean twice as much oil. But it could also be that there was no HC charge ("hcc") and hence for both porosities the result is zero. The effect of porosity as a parameter in the model is not perfect. This painfully obvious example is accompanied by a host of other, far more complex situations where the model may appear perfectly correct and logical, but is still imperfect, such as the famous petroleum system model. Model calibration tries to measure how far the model is from reality.

When using a calibrated appraisal method, both the input noise and the calibration (model) noise are transmitted to the final result: expectation curve.

How would we calibrate a model? The first thing to realize is the multivariate nature of the petroleum process. The second point is the dichotomy between the so-called yes/no questions and the questions about quantities.

The petroleum process (What goes on in the petroleum system) is in the calibrated process broken down into components that involve generation, migration, timing, trapping, retention and recovery. Each of these components is already a multivariate problem. For instance the generation phase involves the SR-type or yield, the richness, the volume of SR and the maturity. One of the reasons why models of the petroleum process are imperfect is that we do not have or can measure the required physical parameters. For instance, If richness of SR is measured by Total Organic Carbon content (TOC) then this itself may not be perfectly related to the yield of the SR. Part of the TOC may be inert. It may be difficult enough to estimate the expected TOC within the drainage area of a prospect, estimating the % of TOC that is inert may be totally impossible or at least highly impractical. TOC is what one would call a "proxy" variable. The real thing we would like to have may be something like "effective TOC", or some parameter derived from S1, S2 and S3 measures of ROCKEVAL. So, TOC is the proxy for effective TOC. And so there are many examples where a compromise is found between what is practical and what would be desired.

A practical prospect appraisal tool must be able to work with imperfect data, such as that which can be gathered from farm-in information in a data room, or what has been published and released by geological surveys. Such a requirement excludes many sophisticated variables from the appraisal model and therefore the proxy variables are the next best solution.

The multivariate analysis of well documented case histories measures the model noise. To do this, sets of data are required about conclusively drilled dry structures and proven accumulations. Also the geological situation around the prospect must be fairly well known.

Several calibrations can be made. Sluyk and Nederlof describe a charge calibration that measures HC charge for a prospect and that shows the relative importance to charge of a number of geological proxy variables. Then also a retention calibration is described where the top-seal capacity to hold HC columns is related to the lithology, depth and thickness of the sealing formation (Nederlof & Mohler, 1981).

GAEA50 uses also the full material balance and a retention calibration, but in a slightly modified modeling. For instance the timing aspect is not calibrated, so that users may use their own models to study the synchronicity of HC charge and growth of trap capacity with the sophisticated software that is now available.

Another difference with the Sluyk & Nederlof publication is that the details of the required regression constants are not available. It is possible, however, to reconstruct an "artificial worldwide calibration" on the basis of what is given in the article, provided fairly large standard deviations for the regression coefficients are assumed. In such a way the GAEA50 calibration serves as a reasonable "a priori" calibration that can be improved upon by any local calibration made by a GAEA50 user. Without such improvements to accuracy with a user-calibration the model noise in GAEA50 is of course rather large but realistic under the circumstances.
The calibration constants in Gaea50 are stored in the my proprietory GaeaCalib database.

In the author's experience, models, kept simple because otherwise they could not serve in the average appraisal situation, are quite noisy! Nevertheless, they have proven over many years of application to be helpful and able to provide a reasonable prospect ranking, that otherwise would have been much less reliable.