Saturation height function

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
- Only curve fits to a single curve - need to fit successive cap pressure curves and then trend the Lambda parameters in order to create a function that fits a continuum of properties

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