productivity index determination

[amahaminer]

Hi all
can we determine productivity index from DST data in its flow periods?
if so,is the value obtained remains constant as long the Pwf(bottom hole flowing pressure) is higher than bubble point press?
knowing that i have applied eqn J=Q/(Ps-Pwf) on DST data, it gave J=5.2
but two months later memory gauges were run in hole to measure (bottom hole flowing pressure)
& i calculated J from its data & it gave a value of J=1.5
i got confused ....why did it change??which is correct??who am i??
AnY IdEas???

[vinomarky]

You are comparing a transient situation (DST) with a steady (or pseudo steady) state situation

Or in other words, in the DST case the effective external reservoir radius (undisturbed pressure) may only be 50m, while at steady state it may be closer to 1000m

The difference of ln(re/rw) (assuming 50m re and 0.1m rw) is 6.2 vs 9.2 - so a 50% reduction of your PI can easily be attributed just to this effect. Add in possibility of fines migration and rel perm changes and they add up. Additionally, you could have seen some reservoir pressure depletion during your production, so if you are still using the Pi (initial reservoir pressure) you will be getting a pessimistic view of the PI (productivity index)

Another possibility is if you have high perm streaks/lenses of small volume but connected to larger low perm reservoir (like a frac), then the high perm streak will give you a transient squirt of rate before it depletes after which the rate would be controlled by the rate at which the low perm reservoir can contribute.

In short - both measurements may be correct.... your job is to understand what has changed

[amahaminer]

Thanks vinomarky for ur answer i really got benfits from it
regarding the effect of re& relative perm i think their effect is clear from eqn:
J=(.007808 Ko h)/(Mo Bo ln⁡(.472 re/rw))
so do u suggest that damage occured to the res.? i believe that as after one year only of prod. the res pres decreased from Pi=6818 to Ps=6350 &water cut increased to 80% then well ceased to flow naturally this may be due to damage,isnot it??
but u didn't answer me about should productivity index be cont above bubble point pres?
about ur words(then the high perm streak will give you a transient squirt of rate before it depletes after which the rate would be controlled by the rate at which the low perm reservoir can contribute) would u advice me to a refernce to read about this subject as iam still beginner and i feel u r proffesional (0.0)
thanks in advance

[vinomarky]

No - I am not suggesting that damage has occurred, I am suggesting that you should investigate whether this is likely

Damage will not cause a reduction in reservoir pressure - Pr reduction is due to withdrawal volumes, size, connectivity & support

Watercut increasing to 80% can be due to any number of issues - proximity to water laterally & vertically, geological heterogeneity, presence of fractures as well as wellbore integrity are just a few issues that can cause this. Going from 0-80% watercut - assuming normally pressured reservoir - will reduce your available drawdown when naturally flowing from (depending on oil gravity) from ~1350psi to ~250 psi - a 5 fold reduction - this could be a big part of your 'problem' straight away if you are not properly taking into account the increasing BHFP's that are occurring. The solutions to this would be water shutoff (if possible - normally difficult) or installation of pump and simply handling the produced water.

Under ideal conditions & steady state assumptions, yes the PI should remain constant above Pb - but you have neither ideal conditions, nor two observations at steady state which to compare

Regarding high perm streaks - think through how two layers of finite extent (one a thin very high perm - say 2,000md x 10cm, the other a thick low perm - say 5mdx10m) will behave - from a productivity and rate of decline decline point of view - now superimpose their behavior in time and you'll see what I mean.

Suggest that you spend less time looking for the 'right answer', and more time trying to understand the problem - the geology, production characteristics etc.... I'm not coming up with the thoughts above because I have a checklist of 'right answers', but because I am thinking through and developing (a number of ) possible implications from the observations you are describing

Good luck

[l1nk3r]

Hi all,
well, i was reading your answer vinomarky, and you are right in some aspects, like geologist characteristics, stratigraphics.. but i was wondering, when you held a DST in the well, you've to open production increasing the chokes, so, this way you can perturb the formation as long as possible. Analysis of some buildup periods allow to determine reservoir limits, making sure that the test reaches a high re. In That way, you can use the flowing bottom hole pressure recorded to determine the PI, after several flowing periods, and it's perfectly a right PI, just with stabilizated rates. Please, correct me if i'm wrong.

best regards.

[vinomarky]

If you have reached a (pseudo) steady state, having reached physical or pressure boundaries during your test, then yes you are right - This rarely occurs in commercial discoveries as the time is simply too long

What you can get from your DST is the formation characteristics, pressure etc, which you can use in conjunction with your understanding of how big the container is to forecast how production will change (usually reduce, neglecting skin effects) over time as a function of withdrawl rate/cum

[vinomarky]

By way of example to illustrate, using Earlougher's analytical transient (approximation) production equation of the form;
q = kh.dP / [162.6 Bo.Visc.{log t + log (k / phi.visc.Ct.Rw^2)-3.23 + 0.87S}] (Since it's purely transient, the external reservoir radius is not present in the equation - it hasn't been 'seen' yet)

Assuming we are testing an oil well, with;
k = 153 mD
h = 30 ft
dP = 500 psi
Bo = 1.1
visc = 0.8 cP
Poro = 0.18
rw = 0.35ft
Ct = 1.06e-5 psi-1
S = 0

The final rate after;
2 hours of test would be = 2,728 bpd (PI = 5.45 bpd/psi)
4 hours of test would be = 2,600 bpd (PI = 5.2 bpd/psi)
12 hours of test would be = 2,415 bpd (PI = 4.8 bpd/psi)
1 week of test would be = 2,065 bpd (PI = 4.15 bpd/psi)

The analogous Darcy (steady state) flowrate would be 2,100 bpd (assuming re = 2,630 ft). The point at which the two plots cross over occurs at ~115 hours of production, meaning you'd have to produce with 500psi drawdown for almost 5 days before reaching something approaching steady state under these conditions, and that the apparent PI (as compared against the final PI after flowing for 4 hours) would have dropped by 20%

This is real 'back of the envelope' stuff here, but it's a nice way to get a feel for what to expect before you go to your well test and simulator software. It also helps you get an idea of the expected orders of magnitude. In your case with a 70% PI reduction, I suspect that while the transient effect plays a part, the biggest issue lies elsewhere - namely pressure depletion (small pool) and/or damage/restrictions.

[l1nk3r]

I think that it must be what we expect in theory, but in practice i'm still thinking that a Very good performance of a DST, with high DP and disturbing completely the formation, within 2 o 3 days of test, you can gathering a lot of information, characteristics, pressures, reaching a pseudo steady state, usefull to determine a very realistic PI. I mean, well test provide answers from the original dynamic response of the reservoir, instead analytic calculations with fisic equations. However, both methods allow you to get an idea of "expected orders of magnitude" of the reservoir's PI.

[vinomarky]

My point is not that a DST (especially an extended one) will not aid in characterising the reservoir well - quite the contrary it is an excellent tool and yields lots of information.

My point is simply by taking the final DST rate, often while some transient effect is still going on as well as possibly different skin - and dividing by the drawdown to get an instantaneous PI is prone to problems when you later want to compare that against the completed well after a couple months of production and expect the same number. If indeed you had done a DST over a number of days, and the skin was similar, then yes you'd normally expect quite similar PI's, but it is rare these days to do multi-day tests

[mid]

Why dont you use PLT with three production rates to determine PI and reservoir pressure out of it