J-Function - the application of......

**Aries** · 05-08-2011, 05:19 PM

Hi Vinomarky,

Appreciate for your in-depth explanation. I am going over it right now. There are few points that I need some clarifications:

1) I have both mercury and air-brine test. Can I mix the two test? Is the formula for J the same for air-brine?

2) Mercury test goes up on a very high pressure which is not of course does not exist in the reservoir. How can I determine my Swir? In other words how would you determine at which Pc above which you consider water as being connate.

Wealth of knowledge from you. Thanks for your post.

Regards,

Aries

**vinomarky** · 05-09-2011, 02:29 AM

1) I have both mercury and air-brine test. Can I mix the two test? Is the formula for J the same for air-brine?

Yes and no.... In theory yes, the information above should already be sufficient - hint: brine is treated same as water. Often though you will find that your Hg cap pressure and air-brine cap pressure curves differ significantly even when corrected to reservoir Pc. This is most evident when using porous plate capillary tests, but even with air-brine centrifuge there are often significant differences. You'll have to use some judgement as to which is more representative over your zone of interest

2) Mercury test goes up on a very high pressure which is not of course does not exist in the reservoir. How can I determine my Swir? In other words how would you determine at which Pc above which you consider water as being connate.

Ahh - an oft asked question... Classical Res Eng ala most undergrad University would have you believe that there is one Swir value, that cap pressure will tell you what this is and rel perm to water is at zero at this saturation..... Reality is (as usual) somewhat different

EVERY core I have seen has been taken to equivalent reservoir capillary pressures higher than observed in the reservoir, and the water saturation is usually still reducing. By classic theory this should mean I have mobile water from production start... the only problem is that usually we don't. In fact, while the use of cap pressure curves may yield a better view of the initial hydrocarbons in place, the vast majority of your virgin reservoirs will be producing water free at initial conditions - the way around this is to initialize the simulator using J-Function, then take the initial saturation array and re-export as SWL (connate water) - then you honor both the initial hydrocarbon volumes as well as the no initial water. If you do have a case of initial mobile water (I've had less than I can count on one hand) then you need to think about it carefully. It can be done, but I'm not about to spend the time required to elaborate on this workflow here.

So, what is going on then? The following is my opinion - so take it with a grain of salt - but it makes sense to me. If you think of what is happening, you have an initially water saturated rock matrix, consisting of a range of pore throat sizes. As you bubble oil (or gas) into it, the buoyancy forces displace water down from the top, building up differential pressure as it goes. This differential pressure displaces more and more hydrocarbons into increasingly small pore throats. At some point the trap is filled - this will be your initialization point. At this point, if you were able to increase the pressures even further, yet more oil would be squeezed into yet smaller pore throats - so the rock is capable of having its Sw further reduced, just not at these pressures. The oil that IS present though resides in the larger pore throats, and hence will preferentially flow out.

Now, you drill a well and start producing - even though the rock still has some Sw that could be displaced given higher differential pressures, does this necessarily mean that water is now going to be displaced under a modest delta P? The answer in most cases is no. Generally, the oil in the larger pore throats will move first - in short, the critical saturations depend upon the history of the saturation charge (ie where you were on the Pc curve to start with)

How to determine what saturation this is? Well, I'd suggest that using the minimum Sw in the rel perm test would be a good start - this will be dependent upon what fluid velocity was put through the core, but it would be a good starting place. I often simply use the initialized saturations as the critical saturations - which is a bit of a simplification, but yields cases which both honour the OIIP as well as observed water free production

Sometimes you have a blip of water production at the beginning of a wells life - this could be consistent with an initial near-wellbore flowing pressure gradient being able to move some of that remaining mobile water, but as the pressure gradient flattens radially AND the remaining pore throats with water in them become even smaller this peters out... then again, it could also simply be completion fluid coming back :-)

Food for thought.

**Aries** · 05-09-2011, 07:45 PM

Hi vinomarky,

Thanks for taking the time to reply to this thread. Your explanation is superb!!!

For my connate water, I decided to put a cut-off on the pore throat size. Any values less than this, I will assume that water in these pores are connate. Does this sound reasonable?

I've used the procedures you laid out. Have four rock types (electrofacies) as was given by our geophysist. Grouped my Pc's accordingly. Derived the J function and sat vs height also. My knowledge in Petrel is minimal, so that I asked a colleague in the office to load the relationships in Petrel so that I can QC my data.

While this is going on, next step is generating my rel perms tables for Eclipse using SCAL data. Would you mind if you can put a procedure in another topic or thread on how to do it? I know you have some postings with regards to this but I got so confuse.

Nice to have a guy like you in this forum.

Cheers,

Merlon

**vinomarky** · 05-10-2011, 01:46 AM

For my connate water, I decided to put a cut-off on the pore throat size. Any values less than this, I will assume that water in these pores are connate. Does this sound reasonable?

While you can actually estimate pore throat size from Pc data, I don't believe that this is what you are doing. Unless you believe that you are going to have wells producing initial mobile water, I'd assume that all the saturations are connate... you can define one generic rel perm curve for each rock type then use the initialized saturations as the connate values (SWL) and using ENDSCALE Eclipse will scale each of the rel perm tables - have a read about endpoint scaling and saturation functions in the Eclipse technical manual

If you want to specify a cuttoff, below which fluids will move with initial production, then you may be better off by specifying a minimum J value - above which saturations initialized are considered connate and below which (for example) the saturation corresponding to your cutoff J value is considered connate.

I've used the procedures you laid out. Have four rock types (electrofacies) as was given by our geophysicist. Grouped my Pc's accordingly. Derived the J function and sat vs height also.

Sounds fine as long as these electrofacies mean something to the geologist, and that they can in turn populate them through the model sensibly - otherwise you may have great correlation at the wellbores but the other 99.99999% of the reservoir will bear little resemblance to what you are trying to represent.

While this is going on, next step is generating my rel perms tables for Eclipse using SCAL data. Would you mind if you can put a procedure in another topic or thread on how to do it? I know you have some postings with regards to this but I got so confuse.

This is a whole area of discussion, and not one I'm about to outline right now. As a starting point, please consider that your SCAL tests are done on very small core plugs, and that any two of those core plugs - even if close together in the well - will normally give quite different results.... what do you think would be the aggregated characteristic of 1m of core plugs? An interesting exercise is to plot by hand or Excel the rate through three slabs with IDENTICAL rel perm curves, but significantly different permeabilities - sum the output rates and average the saturations at each point in time to calculate an equivalent rel perm curve for the three - it will be surprisingly different from the input curves. In short the rel perm curves you use in your model are not only a function of the rock, but a function of the scale of your vertical layers and heterogeneity that exists within those layers. You only have to take a look at probe permeametry data to understand how much variability actually exists within what looks from logs like a homogeneous piece of rock - this is even before we start addressing the thorny issue of core handling/cleaning/restoration and how that adversely affects test results.

What I normally do (and I'm sure many will disagree) is simply use the endpoints and a representative Corey exponent for the sorts of wettability we'd expect and in effect throw away the tested curve shape behaviour. Use Swir from cap pressure, Komax, Kwmax and Scr/Sor from rel perm tests, and values of nw/no for Corey shape definitions - then history match by varying any/all of the above depending on where the greatest uncertainty lies. Note: If you have imbibition cap pressure curves starting from a drainage charge pressure approximately in the reservoir region, you might want to consider the saturation point where it cross the Pc=0 line to be a reasonable first approximation of Swcr.