Saturation height function

[dipak_m]

Dear Memebers,
Is there any software or Excel based programe avaiable to model saturation from the capillary-pressure derived saturationheight function?
Thanks

[vinomarky]

Not sure what you are asking for....

It's simple math to transform capillary pressure plot to a Sw vs height above free water plot - if this is what you want, let me know and it's a easy solution (specify what sort of cap pressure test - fluids & mechanism, as well as what fluids and their densities in your reservoir). There are a number of functions you could then try to use to fit a general equation to this plot - Lambda, J-Func etc....

The harder bit is to take a few cap pressure curves, and decide how to apply them to all the different bits of rock in your model - 99.9999%+ of which do not have exactly the same properties to that which had the cap pressure measurement performed upon - Look to relate your Lambda/J-func etc relationships to your various cap pressure tests through perm, poro, facie or some combination of all the above..... no silver bullet

[Shakespear]

Please look here regarding what vinomarky is referring to

[link Point to another website Only the registered members can access]

[dipak_m]

Dear Vinomarky,
Is it possible to give some examples with calculations for Lamda or J-function where you calculate saturation from cap data?

I am confused the use of SWATINTand SWL in Eclipse. Where and how I use SWATINT or SWL in Eclipse?

Thanks

[vinomarky]

I'll send you some lambda J-func info when I get to the office in the morning

With regs to SWATINIT and SWL - It depends upon whether you think you actually have mobile water at initial saturation. Often - even when not at SWIR - a hydrocarbon column still will not flow any initial water. In these cases I'd just use SWL for simplicity. If, on the other hand, you have initial mobile water low in the column which you need to match then you should use SWATINIT and separately specify SWCR etc..

[dipak_m]

Tahnks Vinomarky.
When I use SWATINIT, is it required to use SWCR separatly with it?

[vinomarky]

Assuming you already have your capillary pressure data transformed into height above FWL vs Sw relationship, then there are a number of paths you can take - I've listed some below along with my thoughts as to their strengths/weaknesses but they are non-exhaustive

Plot up your data, take into account how much knowledge of your reservoir you really have (no point in using an overly complex approach if your data is limited), and choose a method that fits data best, while fitting into your workflow appropriately.

Often, if the transition zone is not a big effect (higher perm, more relief) then the best method is simply characterizing Swir as a function of Perm, and using SWL via OPERATE keyword to initialize saturations along with endpoint scaling. Unless (a) you have enough data to warrant characterizing the transition zone and want to further tighten up the hydrocarbons initially in place or (b) expect that the transition zone with it's higher water saturation will significantly affect production behaviour, then it is quite normal to have so much uncertainty in your other variables that characterizing the transition zone is almost background noise... your time would be better spent understanding the bigger issues first with a simpler model.

The below methods only needed if the transition zone becomes important to characterize.

1. J-Function
Advantages:
- Relatively simple way to initialize your capillary pressure, as it is supported natively in Eclipse.
- Creates a relationship that is easily applied to wide ranges of perm/poro rock
- Can be somewhat tuned through use of exponents other than 0.5 to K and Poro
- Often used when not much cap pressure data is available

Disadvantages:
- Often applied without much testing as to it's applicability
- Tuning is not very flexible - often not the best fit
- Hinges on the relationship between K/PHI, meaning that your static model properties away from well control need to be populated honouring this relationship (ie good facie model and thought going into how their families of perm/poro are co-populated required) in order for it to remain valid

Given model saturation, perm, porosity & height above free water level
J = Pc x Sqrt(K/Phi) / Sigma.Cos(Theta)
Pc = Capillary pressure (psi - Bottom Hole, not lab data)
Sigma.Cos(Theta) = Interfacial tension x Cos(Contact Angle)
= 26 (Water-Oil) or 50 (Water-Gas)

Where
Pc = HAFWL x (Rhow - Rhohc) x 1.2406
HAFWL = Height above FWL (m)
Rhow / Rhohc = Water and Hydrocarbon density (SG)
1.2406 = Conversion (psi/m)

Method:
Calculate J value for each known saturation cell (logs etc)
Plot J vs known Sw (altogether &/or by facie)
If reasonable relationship(s) evident, use J vs Sw as proxy for your Saturation height function

For any unknown saturation block, saturation is calculated as follows;
Calculate J (from K/PHI and HAFWL)
Calculate/Lookup Sw


2. Lambda Function
Advantages:
- Quite flexible, good way to fit data that is difficult to fit with other relationships

Disadvantages:
- Complex
- Not nativley supported in Eclipse - requires either external Sw calculation in Petrel OR (with new ECL 2010 ability to use dummy arrays and perform array multiplication) use of a dummy array of HAFWL property to calculate at run-time

Normally only used to fit against a single parameter (usually K), but could also look at how well it fits against PORO or even SQRT(K/PORO) if you wanted. The Lambda function is just a curve fit method


Fitted Lambda function Sw = [a x (HAFWL^-lambda)] + B
a = a1 x log(perm) + a2
lambda = L1 x log(perm) + L2
B = b1 x log(perm) + b2
where a1, a2, L1, L2, b1, b2 are constants that need to be fit to your data


3. No-name function (don't know what name it has)
Advantages:
- Simple math, easy to fit to a single function, and in turn parameterize those fitted constants to extrapolate for continuum of properties

Disadvantages:
- Not supported nativley in Eclipse - similar comment to the Lambda function
- Predicated on permeability dominating the saturation characteristics (usually ok)

Method:
First, fit a relationship of Swir from your data such as (example);
SWIR=a*LN(PERM) + b (or whatever works best for you)

Second, fit a function of Swi to your curve data as;
SWI=(1-SWIR)*(Alpha+HAFWL)/(Alpha+(Beta*HAFWL))+SWIR

Where a, b, Alpha & Beta are all constants that you need to fit to your data


As far as your question on using SWCR etc, I could answer this and a nunmber of followup questions, but instead I encourage you to read the Eclipse technical manual (By default located C:\ecl\Version#\eclipse\ecl_td\ecl_td.pdf), especially the section on Saturation Table Scaling

[dipak_m]

Thanks Vinomarky.
This will be vey useful materials for me.
Thanks once again

[Shakespear]

Great help "vinomarky" !!!!

I encourage you to read the Eclipse technical manual

This can not be stressed enough. It is the only way to master this stuff.

Capillary pressures and relative perms are frequently a problem for beginners in this area. It might be good to make a separate "knowledge base" sticky thread for these two areas. It could be as simple as cut-and-paste what is already on the threads regarding this. What do you think vinomarky ?

[vinomarky]

Sure - sounds good. I was kinda hoping this would be stickied or similar, as I've seen a few similar questions so decided to spend half an hour and answer a bit more thoroughly than usual - then I'd be able to point to it in future. Creating a knowledge base section, as long as it is maintained by admins to ensure it did not become a digital dustbin sounds like a good idea

[Shakespear]

I am leaving in an hour (gone for 3-5 days), but if someone else does not do it (Main hancho) then when I get back I will do it. Perhaps it will be good to discuss how to present it so it has some structure. I was thinking text along with graphics to make things clear and then a DATA file for go and try it on a Eclipse sample data set. :-)

I am open to other ideas

[dipak_m]

Dear Shakespear & Vinomarky,
I think initialization of a model is very very important part of simulation. Many of us have not clear idea how to initialize the model. Here one has to know the right use of rel perm and cap dat. It will be better to start a thread on intialization with rel perm and cap data. I earlier requeted Temr to introduce a chapter on initialization with Eclipse Step by Step. But he is ver busy person.
Thanks