Geomodel Upscaling

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

How much is there.

How easily will it come out.

The petrophysical metrics which inform us of how much 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, of course 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 is 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 kh!

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 cannot be dismissed as “an upscaling problem”, an attitude commonly expressed in meetings.  The permeability averaging method is not a fact about the reservoir. It’s flow capacity, kh, is.  The averaging method must equal our best estimate of kh and is simply the mathematical device which achieves this value for kh in the upscaled cell. The best estimate of kh is typically the petrophysical well test calibrated, effective kh.  The “averaged” permeability’s impact on the geo-cell Saturation-height calculation must be treated subsequently to honor the petrophysical EHC, but must not be allowed to violate the cell’s factual kh value.  A heterogeneity variance k factor, from the petrophysicist for each geo-cell interval in the log data, may be inserted into the saturation height 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 our objective (as with m and n in Archie’s equation..). The final result must be equal EHC and kh at all scales.

Geomodel Checksums.  Export the geo-model’s grid upscaled, summed EHC and kh back into petrophysical software.  The total EHC and Flow Capacity of the rock must be equal at all scales.  Symptoms of problems are fudged Relative perms, kver/khor, or HCIIP to history match.