calculation procedure for exponent of capillary pressure curve from laboratory data

[hojbarnaz]

Dear member

i went through Reservoir Engineer handbook authored by tarek ahmed
where he mentioned the following two analytical equation that generally uses reservoir enginner in simulation for capillary pressure curve generation
for oil-water
Pcwo=(Pc)@Swc * ((1-sw-sor)/(1-Swc-Sor))^np

for gas water
Pcgo=(Pc)@Slc *((Sg-Sgc)/(1-Slc-Sgc))^npg
where
Slc=Swc+Sorg
my question is how this exponent i.e. np and npg are calculated from laboratory data
if some body can explain the detail procedure for calculation to be perform in excel
it will be helpful for us

[Shakespear]

They are related to wettability and would be use as a fitting parameter. So if you have the capillary pressure curve, adjust the parameter until you get a fit between the equation and the actual lab data. Simple

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[hojbarnaz]

They are related to wettability and would be use as a fitting parameter. So if you have the capillary pressure curve, adjust the parameter until you get a fit between the equation and the actual lab data. Simple

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dear shakespear thanks for sharing your idea , i am uploading my laboratory file

[link Point to another website Only the registered members can access] if you can do a favour on it
thanks

[vinomarky]

First step is QC - frankly I don't believe that you have three independent core samples with identical porosity and permeability

Your goal is to characterize capillary pressure in the reservoir. In order to do so, you need to specify the fluids in your lab test (brine / oil?) and the fluids in your reservoir before we can go much further

[hojbarnaz]

sorry there was some mistake during population
i have reloaded the file

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dear vinomarky if you could explain the facts little bit with my data

[hojbarnaz]

sorry there was some mistake during population
i have reloaded the file

[link Point to another website Only the registered members can access]
dear vinomarky if you could explain the facts little bit with my data

air-water meaurment as reported in scal report

[vinomarky]

... and the fluids in your reservoir before we can go much further

OR, you can just read the recent extensive posting on Saturation height functions at ;

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In particular posts 7, 30 and 38

Oh, and I still have problems believing your data - 420mD rock Sw down to 1%??? I don't think so... I even find it hard to believe that you could get 360mD rock down to 3% Sw..... Please check it all properly.... I don't even see saturations that low in multi Darcy rock.....

[hojbarnaz]

Oh, and I still have problems believing your data - 420mD rock Sw down to 1%??? I don't think so... I even find it hard to believe that you could get 360mD rock down to 3% Sw..... Please check it all properly.... I don't even see saturations that low in multi Darcy rock.....[/QUOTE]

DEAR VINOMARKY
I HAVE CHECKED SCAL REPORT THAT WAS DONE IN 1998 AND IT REPORTS LIKE THAT ,
SO IF WE DISCARD THOSE TWO DATA SET , AND TRY ON OTHER WHAT IS YOUR OPINION AND SIGINIFICANCE ON REST DATA SET

[vinomarky]

1. Your J-function values appear strange. Were different fluids used in the cap pressure tests? I get different sets of values, so would recommend going back and recalculating all your J values (depends on what fluids your test was run with and you have in your reservoir). Note: I previously stated that J varied linearly with Pc, this is correct for given perm/poro, but that is obviously incorrect with different samples (different perm/poro)... sorry, getting late here and had a 'brain fart'

2. Once J's are recalculated, and plotted against Sw, there is still quite a lot of scatter - certainly not a single family of saturation behaviour, even if you take out the test going down to 1% Sw.

3. Lumping them altogether and I get a spread of 15% Sw midway up the curve - not really good enough. The first two samples (183211 and 183221) appear to exhibit similar poorer saturation behaviour (more dispersed clays? - different facie?) - I'd probably try to understand why (talk to your geos and petro's) - you may need one set of curves for these types of rocks, and another for the rest. Adopting this approach and you get reasonable J-function behaviour for the two families (still not great but down to ~6% spread mid way up the curve)

Were the 1% Sw and 3% Sw tests done with the same methodology and at same time as other tests? I have removed the 1% test, but really have problems believing 3% even. The problem though is that you don't have much data to go on in the first place - suggest you match incorporating the data, and then without the data and see what the impact is on your model - use as one of your uncertainty parameters

And no, I'm not going to post the spreadsheet - read the posts I suggested above and try to work through it yourself - I'm teaching people how to fish here... :-)... it took me about 15-minutes....

[itag]

Folks
I have an interest in cap pressure data - and had a quick look at the data.
Firstly some of the data is just plain "bad" - particularly the last 2 ( high perm) sets as Sw is lowered. Now the "why"

Centrifuge cap pressure require a model-based interpretation in the lab. The original 'Hasler Bruner' theory used in the early 90's by one well known lab produces quite different results to that based on 'Forbes' particularly when the Pc data doesn't asymptote. (check what method was used for your data). Secondly - if you spin a sample too fast - ie at very high rpm , you exceed recommended Bond # parameters - and literally desaturate the core beyond what is reasonable for the reservoir. In that regard saturation of 1% are entirely possible in the lab ... they area just meaningless for your intended application. My immediate thought would be that this is likley what happened - but without knowing the centrifuge dimensions/conditions this is guesswork. Either way these samples are not meaninful at lower Sw's

Looking at the rest of your data - sample 183281 plots "out of perm order". There may be reasons for this - eg different facies. There is also another reason that I have seen reported in the literature and that is incomplete sample cleaning /preparation prior to testing that has left many small pores non-water wet. See SCA2006-16 for a very convincing discussion of this effect ( and how simple hg cap-pressure measurement can help identify this effect ). SCA are papers presented by the Society of Core Analysts and are freely available on the web.

If we discard this out-of-order sample, this leaves you with 3 possible candidates.

The next analysis needs to define a normalised saturation S*. Your formulaes above need to be adjusted for drainage conditions that start from Sw=1. use S*=(Sw-Swir)/(1-Swir). You may need to iterate a bit on Swir for each data set - but you can use the lowest Sw in most cases. For sample 2 I used 0.28

No simply plots pc vs S* on a log-log plot seeking straight line trends ( for the exponents). We note some curvature at very high Sw - which again we tend to discount if "spin-up" a time offset effects impact experiment. Whats left is surprisingly OK. I get a slope of about -0.8 which implies a Lambda of 1.25 ( which is also reasonable)

I ended up fitting J*ScosT= 9.3*(S*)^-1/1.25 to the valid data. 2 out of 3 match quite well and the third is acceptable.
Sample 183291 plots up OK using Swir of 0.08.

The 3 remaining data sets make reasonable sense ... they have the right ordering of entry pressure effects.

[vinomarky]

Thanks itag - some useful comments, and you've also obviously had quite some experience on the topic.

When the objective is to create a saturation function for use in a simulator (and I need to model the transition zone, otherwise SWL's are good enough) I normally first try a J-function fit in terms of real saturation (often with exponents not equal to 0.5 though) because it is the easiest to then implement inside Eclipse. When you start going to normalized saturations and/or taking into account entry pressure, then you usually find yourself having to model the saturations outside of Eclipse and feeding it as a static array. This approach is ok, but is not as conducive to making quick perm mult changes in the deck when history matching and especially when doing uncertainty runs... If I have to go this route, then quite often other functions (ie Lambda) yield even better matches

If the fit is good enough, then I usually prefer the simpler method :-)

[hojbarnaz]

[QUOTE=itag;126509]Folks
I have an interest in cap pressure data - and had a quick look at the data.
Firstly some of the data is just plain "bad" - particularly the last 2 ( high perm) sets as Sw is lowered. Now the "why"

Centrifuge cap pressure require a model-based interpretation in the lab. The original 'Hasler Bruner' theory used in the early 90's by one well known lab produces quite different results to that based on 'Forbes' particularly when the Pc data doesn't asymptote. (check what method was used for your data). Secondly - if you spin a sample too fast - ie at very high rpm , you exceed recommended Bond # parameters - and literally desaturate the core beyond what is reasonable for the reservoir. In that regard saturation of 1% are entirely possible in the lab ... they area just meaningless for your intended application. My immediate thought would be that this is likley what happened - but without knowing the centrifuge dimensions/conditions this is guesswork. Either way these samples are not meaninful at lower Sw's

Looking at the rest of your data - sample 183281 plots "out of perm order". There may be reasons for this - eg different facies. There is also another reason that I have seen reported in the literature and that is incomplete sample cleaning /preparation prior to testing that has left many small pores non-water wet. See SCA2006-16 for a very convincing discussion of this effect ( and how simple hg cap-pressure measurement can help identify this effect ). SCA are papers presented by the Society of Core Analysts and are freely available on the web.

If we discard this out-of-order sample, this leaves you with 3 possible candidates.

The next analysis needs to define a normalised saturation S*. Your formulaes above need to be adjusted for drainage conditions that start from Sw=1. use S*=(Sw-Swir)/(1-Swir). You may need to iterate a bit on Swir for each data set - but you can use the lowest Sw in most cases. For sample 2 I used 0.28

No simply plots pc vs S* on a log-log plot seeking straight line trends ( for the exponents). We note some curvature at very high Sw - which again we tend to discount if "spin-up" a time offset effects impact experiment. Whats left is surprisingly OK. I get a slope of about -0.8 which implies a Lambda of 1.25 ( which is also reasonable)

I ended up fitting J*ScosT= 9.3*(S*)^-1/1.25 to the valid data. 2 out of 3 match quite well and the third is acceptable.
Sample 183291 plots up OK using Swir of 0.08.

The 3 remaining data sets make reasonable sense ... they have the right ordering of entry pressure effects
dear
itag
if you could provide your analysis file , will be helpful to understand and realize on about the procedure you speak, as i am layman in this subject and learning from experts like you little bit