Initial saturation

[dipak_m]

Dear friends,
How I determine the initila saturation of the model (petrel model) from capillary pressure (Pc) -height function

Thanks

[barbod]

Mr. Dipak

There are some ways of saturation distribution in static models using Pc functions. The only thing that you should consider is the Pc function within the transition zone. You may distribute the critical water saturation using the bivariate relationship between the effective porosity and saturation outside the transition zone, then propagate the critical water saturation all over the reservoir and then incorporate the Pc function in transition zone. You have different ways of implementing that. I just guide you through the simplest ways you can do it. One way is to use it(Pc) in trend tab in your petrophysical modeling process. The other is to use it as a secondary variable in co-located SGS. keep in mind that the results are different because of the way in which the saturation is modeled.

[vinomarky]

If you have a continuous function fit for capillary pressure vs saturation then you simply;
(1) Convert to height above free water level (FWL) vs Sw with appropriate sigma Cos Theta ratios and relative water/hydrocarbon densities
(2) Use petrel property calculator to create Sw property as function of height above FWL (-FWL - Cell Depth) as well as any of the poro/perm you have fitted to - note Petrel uses increasing depth as increasingly negative. The Cell depth is an inbuilt property - I think it is simply Depth()
(3) QC - to ensure Sw is always greater than Swir and less than 1.0

Done

[dipak_m]

Dear vinomarky

Please elaborate to understand properly.

[vinomarky]

Assuming you have a function of lab measured capillary pressure as a function of water saturation and permeability Pc = Fn(Sw, K)

Depending on how you measured the capillary pressure, you first need to convert to equivalent reservoir conditions -> Pc(Res) = Pc(lab) X SigmaCos(Theta)Res/SigmaCos(Theta)Lab

Lab Conditions Interfacial tension x Cos(Contact Angle) aka Sigma Cos(Theta)
Air-Water 72
Oil-Water 42
Air-Mercury 367
Air-Oil 24

Reservoir Conditions
Water-Oil 26
Water-Gas 50

So, if your capillary pressure function is lab measured Air-Mercury test, and you have a Water oil reservoir system, the first conversion is;

Pc(Res) = Pc(lab) X 26 / 367

Then, to convert this reservoir pressure to a hydrocarbon column height you do the following;
h (ft) = Pc(res)/((Rho Water - Rho Hydrocarbon) x 0.433) Rho is in SG

You now have transformed your lab capillary pressure function into a saturation height function;
h = fn(Sw, K)

Rearrange to get Sw = fn(h, K) (Where h = height above free water level)

You then simply use the Petrel property calculator and plug in your equation to calculate for each cell the Sw

[dipak_m]

Dear vinomarky

Thank you very much for your quick and valubale reply. Now it is very clear to me. Please five me the exact formula of Sw=fn(h,k).

[vinomarky]

There is no 'exact formula'. The formula is the transformation of whatever capillary pressure function you have fitted to your data

There are many different curve fit functions in use - each just as valid as the other - differentiated only by how well they mimic your lab data. If you don't have a capillary pressure function fit to lab data already, then you can't even start this process. Depending upon (a) whether or not capillary pressure effects are important in your case and (b) the degree of accuracy required/uncertainty encountered, you may instead elect to ignore capillary pressure and initialize with Rel perm endpoints

Using capillary pressure is normally most important when you have a significant proportion of your structure in the transition zone (low relief and/or low perm structures).

[dipak_m]

Dear Vinomarky,
I will be thankful if you give me some literature to derived trasformation to get initial saturation.
Thanks

[vinomarky]

Ok - I'm not sure if we are understanding one another here

Just to be clear - we are not deriving anything

We are curve fitting a function (and there is no one magical function to use) to measured data

Please confirm that you have measure data

If you have measured data, then there are many many different possible functions to use (indeed, make up your own if you like - as long as it fits), some of the more common are;
J-Function, modified J-function, Leverett, Lambda, and Thomeer

A simple function to use (already transformed to be Sw = Fn(Height) ) that is quite well behaved is the following;

Swi = (1-SWIR)*(Alpha+HAFWL)/(Alpha+(Beta*HAFWL))+SWIR

Where Alpha & Beta are fit parameters, HAFWL = Height above free water level and Swir is known (and/or fitted) from tests

[dipak_m]

Dear Vinomarky,
I have centrifuge capillary pressure data. I try to establish a equation with J-function.
Thanks