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  3. Example Arguing to Provide the Right Data

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- [Stein] So, the next is to present an example where this presented workflow are used to arguing to provide the right data. So, what we see here is three tracks with curves. In the first track, we see the porosity calculated by applying the density log. The scale is zero to .5. And here, we can see that the porosity's quite low, close to five porosity units, telling us that this is a marginal field. The middle track illustrate the resistivity responses at logarithmic scale, from two to 200 ohmmeter. And we have two curves. The red curve is the response from the laterolog, and the black curve is the response from the induction log, telling us that the different principle of measurement respond some different to the rock. And the last track is the water saturation calculated by applying Archie's equation, scale zero to one. And the red curve is the water saturation calculated by applying the laterolog. And the black curve is the water saturation calculated by applying the induction log. And here, we clearly see that the water saturation and then also the hydrocarbon pore fraction will depend on our choice of resistivity curve. And that is also the main issue at this field. This is a large field with many wells, and the different well are acquired with different principle of measurement. And addition to that, it is also acquired by different method, and all showing some spread in the resistivity responses. So, the big question here is how to provide the right data to increase the confidence in the water saturation calculation. If you look at this curve responses here, we clearly see that if we can increase the confidence in the resistivity, we will increase the confidence in the water saturation calculation. But is the resistivity log the right data to focus on? As mentioned in the presentation, error and error propagation should be evaluated from the very beginning in the petrophysical So, if we don't know which of the curve, laterolog or induction log, or which one though, that leading the resistivity closest to the true value, or we can't explain this difference, this spread in responses is part of the error in our water saturation calculations. One very simple approach to this issue is to apply the mean value of the different responses, illustrated by this light blue color, and the final error on that mean value, defined by the spread in the different responses. Here, .3 multiplied by the mean value, illustrated by this dotted blue color, seems to pick up the spread in these two curves. So, done by applying this mean resistivity with the uncertainty into Archie's equation, we get these results. The light blue color illustrate the water saturation calculated by Archie and the mean value from the different log response. And the aqua band, illustrated by this dotted line, is given by the uncertainty in the resistivity, defined by the spread in the resistivity curve. And here, we see it is a significant uncertainty in the water saturation calculation, given by the uncertainty in the resistivity responses. But what about the contribution from the uncertainty in the porosity, contribution from uncertainty in the cementation factor, saturation exponent, and also from the uncertainty in the water resistivity? We should always evaluate and include all the uncertainty in all calculation because the value of spending money and resources to reduce the uncertainty in the resistivity is very restricted if its impact on the third is small while the real uncertainty are in the first. Therefore, to provide the right data, you should always do the petrophysics in a proper way that include the following four point from the beginning in the petrophysical Always start as use the best-suited model. In this case, density porosity and Archie's water saturation is fine. Then, define the input to these values, but with the errors. And here, I will not comment the value in the errors in this, to these parameters. Third, the error is the resistivity is already discussed. That is defined by the spread in the different response test, equal .3 multiplied by the mean value. But we should also mark the uncertainty in the cementation factor, which is .3, and the uncertainty in the Rhomatrix, which is .04, which is not that large. Then, we should also define the distribution on the interpolated tables and the correlation between the variables. In this case, to simplify, we assume symmetrical distribution plus/minus the same value on all input and no correlation between the variables. So then, by giving this information into the computer and pushing the calculate button, we get the results like this. What we see here, these two track illustrate the porosity calculations, and these two track illustrate the water saturation calculations. And what we see here is that the uncertainty in the water saturation is quite large. We can also mark that the contribution from the relatively large uncertainty in the resistivity log, which is illustrated by this light color here, the contribution from this has a minor impact compared with the contribution from the cementation factor, the red color, and the contribution from the porosity calculation, the yellow color. So, if you really want to reduce the uncertainty in the water saturation calculation, the data, to provide the right data to reduce that, is to provide the right data to increase the confidence in the cementation factor and the porosity calculations. So, the cementation factor, it can be difficult to reduce the uncertainty. But in that case, we can evaluate to acquire more core data or maybe learning direct measurement that have a potential to give information about the cementation factor can be evaluated. For the porosity, we can, of course, evaluate to learn an independent calculation for porosity, for instance, including NMR too, sonic too, or maybe more core data. Or if we want to continue with the density porosity, we clearly see here that if we should reduce the uncertainty in the porosity, the key to success are to reduce the uncertainty in the Rhomatrix, the yellow color here. And in that case, we can evaluate to learn element to get the curve of the Rhomatrix. So, this example illustrate that if we should provide the right data to increase the confidence in the water saturation and hydrocarbon pore fraction, I will spend my money on increase the confidence in Rhomatrix and in the cementation factor. To illustrate the large impact the Rhomatrix had on the hydrocarbon pore fraction, I will show some statistics. Here, we see the statistics for the porosity calculation. This is the statistics for the water saturation calculation. And this is for the hydrocarbon pore fraction. These statistics is calculated with the Rhomatrix 2.72 gram per cc, which is the field value. So, if you look at the same statistics, but in this case, we apply Rhomatrix 2.68, which are within the expected uncertainty in Rhomatrix, we obtain these results. Here, we see by changing the Rhomatrix from 2.72 to 2.68, we reduce the porosity from .06 to .03, and we increase the water saturation from .3 to .5, and the hydrocarbon pore fraction is reduced from .04 to .017. The volume is more than, reduced by more than the half, only by changing the Rhomatrix from 2.72 to 2.68. And to say, do the same sensitivity for the cementation factor, we have the results like this. Here, we see the statistics with the field value on the cementation factor 1.7. And if we increase this cementation factor to 2.0, which also are within the expected uncertainty, we see that we increase the water saturation from .3 to .5 and decrease the hydrocarbon pore fraction a lot. So, the message, main message with this, this example is to illustrate that to provide the right data, all the parameters with error and error propagation should be evaluated from the very beginning. And the presented example illustrate that the key parameter to increase the confidence in the density porosity and the water saturation was, in this case, the Rhomatrix and the cementation factor. And the resistivity, which was the starting issue, has a minor impact. And if we think about these results, that make also sense, this is a marginal field, low porosity, and the main content the logarithm are the matrix. So, small variation and small uncertainty in parameters that is related to matrix will have a big impact on all results. So, that was the presentation. And as a final comment to this presentation, I will say that, in this presentation may be, and I like to say hopefully is a matter of course, but the goal with this presentation are to try to increase to see an increased use of algo as a integral part of petrophysical deliveries.