Date of publication: May 4^{th} 2018, by Matt Bowyer

Modelling water saturation can be a complex task and I often find myself thinking that even in a "simple environment", generating the necessary logs, saturation height functions and applying those functions to a reservoir model is a pretty daunting task.

Generally speaking, over the past 6-7 years the job of saturation modelling has fallen on my shoulders, a geologist! Why, I hear you ask? Well, because I didn't have an in house petrophysicist to ask and I was responsible for all aspects of the static model. Am I unique in this respect?

Most of the time I suspect generating saturation height functions is the petrophysicists responsibility. They have the experience and know how. In companies with an in house petrophysicist, do they have enough time to do all of the necessary analysis for the assets they're responsible for? Or do they calculate the required logs and leave calculating the saturation height functions to geologists or engineers because they don't have enough time? It seems to me that petrophysicists are required in all companies, but at the moment I think are in preciously short supply.

So, getting back to modelling water saturation … to give an example, my workflow would probably look something like this:

Start in Petrel (other software packages are available … I have also done this workflow in Jewel Suite!); use a calculator statement to calculate a porosity log for each of my wells, usually using density and sonic … write a long IF statement here, incorporating the zone and facies logs, to specify changes in fluid or matrix densities / transit times. If I have core, import the data and use that to QC my log derived porosity.

Then use the same methodology, Petrel calculator, to calculate an Archie water saturation log for each well. If a core analysis report is available, get a m n from there, a fluid sample would help out with Rw, or, if not, build a Pickett Plot (!) to get m and Rw.

Before I talk about deriving a height function, I am going to take the liberty of assuming we have plotted up our pressure data, whacked a couple of appropriate gradients through the points and worked out our FWL … we can then input this into the fluid contacts in Petrel, and generate a height above contact property / log which we'll use for generating a height function.

I now have 2 options to create a saturation height function (I'm dealing with log data … for now …) … I can use the function window in Petrel to plot Sw or BVW against height above contact and use the regression … I'm not overly keen on the Petrel regression and 'rawcrossplots' that are generated. It's a bit cumbersome and the audit trail isn't always clear.

My second option is to export the appropriate logs to Excel, and use a specific method, for example, the Cuddy FOIL function or Skelt-Harrison formula. So for the former plot BVW against height on log axes and a power law regression gives us the "a" and "b" constants. For the latter plot Sw against Height and use an exponential regression to get the constants. Problems with using Excel … it takes a while to export, manipulate / crop etc. the data and paste into Excel. It takes even longer and a few more rows / columns if I'm dealing with multiple wells. If a typo has crept in somewhere, I have a headache. But I can lay it all out in such a fashion that it's easy to see what I have done.

I generally find myself using Excel for the derivation of the saturation height functions for the ease of being able to use Cuddy or Skelt-Harrison, especially now that I have a spreadsheet setup where all I need to do is import the logs. If I'm using a single well, I'll skip the Petrel step, and use another (yes, another - but this one's bigger) spreadsheet which calculates porosity and Archie Sw, and then calculates saturation height functions.

I have now created a saturation height function!

Skipping over the step of log data QC and getting the correct, for example, resistivity log, what safeguards or "top tips" would you suggest to help the geologist when they are tasked with building a saturation height function? Is there anything that terrifies you about me performing petrophysical analysis such as this?

Geologists, how do you go about saturation modelling? Is your workflow similar to myself, or something a little different?

And engineers … please do say how good and bad saturation models affect your lives … Also I'm keen to know how you go about it … do you use log based approaches, cap curves only, or a combination of the two?

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