how to change relative permeability curve to match production ratios?

[reservoir_engineer]

dear all,
i am working on simulation study in history match phase.
i perform scal analysis (RP normalization, pc, j-func,...) and i entered one RP and PC curve to my model.
as we all know RP is from small plug used to describe huge reservoir so it is one of most uncertain parameters.
i want to edit this curve to tray to match WC,
what i am asking about is there any most common method used to change RP curve?
i am asking about when i have one averaged curve how i can change it ?
is changes made to Krw or Kro or both(relative permeability ratio)?

best regards,

[vinomarky]

Generally you change your corey exponents as a first approach. Leave your endpoints where SCAL says they were and change corey exponents (changing the curvature of the curves) while staying in the exponent range appropriate for your wettability regime - suggestions below

Water Wet
Low High
No 2 3
Nw 3 6

Oil Wet
Low High
No 3 6
Nw 2 3

Intermediate Wettability
Low High
No 3 5
Nw 3 5

If you need to stray significantly outside of these suggested bounds, then it is a flag that you should possibly consider re-examining your geological model

[reservoir_engineer]

many thanks Vinomarky, it looks good idea.
but i when you have actual scal data, how you do this?

best regards,

[vinomarky]

Simply curve fit to your data the corey equation - essentially calculate normalized water saturations (ie at Swir, Swn = 0 and at Sorw, Swn = 1), and then at any value of Swn, given corey exponents no and nw, Krw = Krwmax * (Swn^nw) and Kro = Kromax * ((1-Swn)^no)

This will give you the best fit corey exponents to represent your measured data - you can then make changes as you see fit to the exponents or indeed even endpoints if warranted. I posted a spreadsheet on another thread about rel perm (search my recent threads - sometime in the last month or so) that you should be able to use to quickly create a family of curves

[reservoir_engineer]

thanks Vinomarky, i already downloaded it.
it is very helpful and many thanks for your help.

[itag]

Doing an intitial sensitivity study by varying Corey exponents allows a structured approach to history matching - however there are other approaches that work backwards from observed differences from model vs actual. Good to consider both approaches.

For example often the krw endpoint value at Sw=1-Sorw need upwards adjustment. The 'evidence' here would be that any pressures at water injectors ( if present) are too high - or if simulated pressure drops are too high. The justification is that lab data often supresses this endpoint becasue of 'the capillary end effect'. BTW - when doing a HM it is usual to operate under voidage control (or total liquids) - not just Oil rate control. To get a pressure match (first) -you want the wells to remove historical voidage - and then focus on wcut ( ie Pmatch followed by S match - maybe with iteration)

Often it is helpful to know the (vertical) scale of your simulation model. If your simulation grid captures salient coarsening upwards/downwards features -> then rock relperm curves have a better chance of working ( and vice versa). What I'm hinting at here - is that sometimes - if your simulation grid is very coarse - you might want to look at various pseudo function approaches - to guide you in how your HM relperm changes should proceed. ( The value of pseudos IMHO is that it should guide changes - rahter than expect pseudo's to work 1st time) For example coarsening down features that allow water to channel/underrun oil often result in Nw ( Corey water exponents) < 1 ( which looks extreme when compared to rock curves). This result is produed by Stiles and Hearn type pseudos . One clue here would be evidence of early water breakthru / coarsen down geometries / reasonable kv/ viscous oil.

It is helpful to also know how the producing fractional flow vs cum oil looks - often you can 'tune' 1D displacement rel-perm curves to provide similar features ( in essence this is almost fitting the JBN unsteady state method- used to estimate lab kr's to field data ....) This fractional flow approach can work OK for strong waterfloods and aquifers where voidage balance applies ( classic Buckley Leverett) ( and is discussed by Dake in his last book).

Perhaps you could tell us about some general features of your observed HM vs actual performance. Is your P match OK ? Do you observe a long fw vs Np tail ? etc

itag

[reservoir_engineer]

thanks Itag,
what i did, is
1-initialization match, by matching the RFT and water saturation for the first drilled well, to be sure that my contacts depths, PC curves , fluids densities and pressure at datum initially are correct.
2-i run the model under total fluid control mode, and i matched the pressure by some sensitivities in aquifer, transmissibilities and mainly in pore volume till i get acceptable RFT match for rest of wells.
3-i am working on Wcut match, previously i was changing the RP data manually, as i always has set of curves for each SATNUM region and i averag them to get one curve, i move this average up or down to match water production but from now i will do this by varying the corey exponent as vinomarky said it looks more scientific. and also changing the KRW endpoint is good idea also.

you mean grain size coarsening? coarsening upward or downward identified by many methods, simplest one by plotting gamma ray and its mirror image in opposite scale directions, if we have cone shape so there is coarsening towards the cone base, am i right?
dear Itag, i don't understand the part related to Pseudo functions and fractional flow match?
could you please give more explanations and upload some documentations related to these items?
thanks,

[vinomarky]

Using Corey exponents & endpoints is not necessarily more 'scientific' but it does make it easier to be more methodical

Itag is talking about understanding how the geology affects your fractional water flow. Lets say you have 5ft vertcial grid block sizes, and while you have correctly represented the average kh of the block, due to the geology they have higher perm at the bottom than the top. If you have active water support/water injection etc, then using lab derived corey curves will probably yield optimistic water breakthrough (ie delayed) response - what will happen in actuality is that water will preferentially flood the bottom of that block as it is (1) at the bottom and (2) more permeable, meaning by the time water reaches the other side of the block you may only have swept 20% of the hydrocarbon volume.

You can use 'pseudo' rel perm curves to take this into account - and it was done quite a bit in days gone past - where you'd take a 1D slab of representative cells, flood it with water and back-construct appropriate rel perm curves to replicate the fractional flow behaviour, and then use these curves instead of lab derived ones. The problem is that they are HIGHLY dependant upon geometry and local geology.

These days (with more compute power) if you come to a situation where you feel you need to develop pseudo type curves then it is a flag that you probably need to revisit your geological model to properly incorporate and represent those heterogeneities so that you don't need to use such discontinuous (ie non smooth behaviour) rock curves

[reservoir_engineer]

thanks vinomarky and Itag,
i get your points,
many thanks.