Geomodel Upscaling

How much is there and how will it flow?

Beneath your feet lies a reservoir. There are two essential things we need to know about that thing.

How much HC is there.

How easily will it flow.

The petrophysical metrics which inform us of how much HC is there is Equivalent HC Column, feet or metres, and how easily it will come out is Flow Capacity, mdft or mdm. Note that these are both accumulated values, not averages.

The petrophysicist’s task is to measure these two essential as accurately and as finely as possible with the means at his/her disposal.  The petrophysicist is better equipped to do so than any other team member.  Having done this the petrophysical EHC and kh must become the absolute reference for these fundamental characteristics.  The first requirement of any model, at whatever scale, which purports to describe the resource, must be to equal to the petrophysical EHC and petrophysical kh at the well tracks.  Permeability averaging is the servant of this requirement, not the master. Whatever means has been adopted to ‘average’ permeability must honour the petrophysical reference at the well track. If it does not the model is wrong, period.

Naturally, if the geomodeler believes that the petrophysical EHC or kh is wrong then the petrophysicist must diligently address that concern using valid well test kh values in the petrophysical evaluation (see IPRC, IPCFR). However, this has nothing whatever to do with the geomodel’s averaging method.  Once the petrophysical kh is as fully evaluated as possible, the geomodel averaging method – whatever that may be – must be re-engineered to equal the petrophysical kh.

The simplest way to address this common problem is for the team to stop thinking k_average and start thinking k flow capacity !

Upscaling Geomodels – Permeability Averaging vs Permeability Sum

Imagine your reservoir as a road cutting.  It contains a certain amount of hydrocarbons (EHC, m) and has a certain Flow Capacity (kh, mDm) regardless of what scale we choose to describe it at: 15cm (logs), 1m (static geo-model) or 5m (reservoir simulation geo-model).  All models must honor these facts.  If they do not they are wrong.  These facts should not be glossed over as “an upscaling problem”, a dismissive attitude commonly expressed in meetings.  The permeability averaging method is not a fact about the reservoir. It’s flow capacity is.  The averaging method must equal our best estimate of kh and is simply that mathematical device which achieves the petrophysical value for kh in the upscaled cell. If the petrophysicist is competent the best estimate of kh will be the petrophysical well test calibrated, effective kh. This is the reference.

Can one Geo-cell k value serve two separate functions, SwHt & kh?

The “averaged” permeability’s impact on the geo-cell Saturation-height calculation must be treated subsequently to honor the petrophysical EHC, but this subsequent use of averaged k must not be allowed cause k to deviate from the cell’s factual petrophysical kh value.  The double use of the geo-cell’s k value carries the potential to cause problems.  A single value of k may not be able to yield the correct answers of petrophysical EHC and petrophysical kh, rather these reference values must be honored by whatever mathematical device is necessary to enable k to calculate its derivatives correctly.  A heterogeneity variance k factor, from the petrophysicist for each geo-cell interval in the log data, may be inserted into the geo-cell saturation height and/or kh formula to achieve equality in EHC and kh across all scales of reservoir description. The k variance factor is a tuning parameter, a mathematical device which achieves the objective (as with m and n in Archie’s equation..). The final result must be the petrophysical EHC and kh at all scales.

Geomodel Checksums. The geo-modeller should export the geo-model’s grid upscaled, summed EHC and kh down each well track back into petrophysical software.  The total EHC and Flow Capacity (kh) of the rock must be equal at all scales.  Common symptoms of problems are fudged Relative perms, kver/khor, or HCIIP to match history.  

Summary. The geo modeller’s objective is to match petrophysical EHC and kh.  A single k value may not meet that requirement. Two k values may be required, one for saturation height and EHC (k_ehc) and one for kh (k_kh).  A k variance factor per geo-cell in the Swht and/or kh equations may allow one k value to serve these two functions.