By Sumon Bhattacharyya

This article was first published on LinkedIn, July 4th, 2016

To follow the tradition, let me begin this article by quoting Ernst Friedrich “Fritz” Schumacher who was an internationally influential economic thinker, statistician and economist in Britain, serving as Chief Economic Advisor to the UK National Coal Board for two decades, who has captured the concept of simplicity in a few brilliant words. Though an “intelligent fool” is bit of an oxymoron but it tells you a lot about human behaviour.

In my previous article I left it to some questions on geological processes and complexities of the geological processes. However, in this section I would try to analyse the concepts we take it for granted in the geological modelling world before I even go and discuss the issues on facies and petrophysical modelling. To start with I would discuss the geological model framework or which modeller fancifully call “geocellular model” or in simple terms “grid”.

We will begin by understanding the reservoir top and geometries to represent the top and also interpretability of these tops (If you are observing I did not mention base and there is a perfectly valid reason for that!!! I will leave it on to you to guess!!). As I had mentioned earlier it is extremely challenging to interpret the tops as it seldom provides you with a consistent surface. To add to the agony of the process, in the model we further coarsen the surface by choosing a much coarser mesh (remember the surfaces are always represented by a mesh whether in 2D or 3D) than the interpretation it self. Does it matter?? Well to answer this question, try changing the cell size from 12.5m (e.g. seismic bin size) to 100 m and observe the difference. There is no way in the world you can fit the geometry of a mesh defined by finer cell to that of a coarser cell size. But why? The reason is actually quite simple, the surface is mathematically represented as a mesh and the mesh includes many polygons (cells). Now each cell (polygon) is of a certain size and has only limited edges. So if you increase the size of the polygon (for that matter even the direction of the grid) from fine to coarse, there is no way you can match all the edges defined by finer size polygons. This essentially implies that in only one case cell size does not matter and you know it !!! Of course, it’s a flat surface which I don’t think any of us have ever encountered. So what is the scale of change (Oops!! Possibly one of the commonest word used .. but can’t help.. bottom line is you know now why the geologists are so hung up about the scale of observation with hammers and coins being used to give an idea on scale) and the implication of it?Interesting question right!! Well when you change scale (from finer to coarser) the surface is no longer exactly at the same depth position as the input and there would be depth variation in the resultant surface. (By the way, this is one of the reasons as to why a simple depth sampling of the seismic data always as a matter of rule get sampled incorrectly into the geological modeling grid (It’s a completely different topic but thought I should let you know…. ). How big the difference is would depend on the characteristic of surface. In any case, you would always hear arguments that the seismic resolution and error related to depth conversion is within the limit of this adjustments so doesn’t matter (or does it??). In fact in my opinion, it does matter when you move things from seismic to the geological model. It does matter when you release well prognosis reports using top surface derived from the geological model or you release a deviated well bore design based on models.. There are several evidences to prove this but this is beyond the scope of this article (If any one of you want more details send me a note).

To the frustration of my geophysicist friends who had spent months interpreting the reservoir top in great details the geological modeller just simply wipes off all the details with a single click. (To give you an idea of how that feeling is – think of the frustration you have when a geological model built over months is changed significantly by reservoir engineer). Of course, you would have arguments to make the grid to be equivalent to seismic resolution (e.g. 12.5m) using stacked sugar cube cells (like what you have in seismic) but whether this actually helps or not is a completely different question.

However, what the above observation tells us is simply no matter what you do, you cannot logically have an exact representation of the subsurface as visualized in seismic (with its own errors) even on a reservoir (container) definition – let alone the geology you are trying to represent within the model. So what does it mean?? It simply means that a geological model is in reality a “cartoon” of the reservoir which is built to address certain issues and provide solutions related to it. The GeoScience world is dominated by several compromises (which has been cleverly named as assumptions) and we have to live with it (either we have no choice or the mathematics is too complicated to quantify). The bottom line for all this is to understand that there is no perfect solution and the design of the model should be related to problem you are trying to address.

Coming back to the second important part of the grid building is of course how you layer the model. This again as everyone would tell you depends on geology of the reservoir. It is indeed true that this is dependent on geology but the important question is what choices you have??? Does parallel to base (following the base of the reservoir), parallel to top (following the top of the reservoir), follow another arbitrary plane and conformal (adjusting between top and base of the reservoir geometrically implying the number of layers are constant between top and bottom of reservoir but the size of the cell is changed vertically to adjust geometrical change) enough? So what does reservoir layering looks like in reality. The answer to this question lies in the simple diagram (figures speaks louder than words) of tidal channel shown below.
After Armas and Sanchez “Hybrid coastal edges in the Neuquén Basin (Allen Formation, Upper Cretaceous, Argentina)

Facies associations: Tidal channel (TC) and intertidal flats (ITF): GtT lithofacies in tidal channel; B. StT lithofacies in tidal channel, show sigmoidal set and mud drape; C. HfT lithofacies with millimeter coal levels. D. Outcrop and lithofacies identified in Tidal channel (TC) and Intertidal flats (ITF).

Now tell me what is the layering scheme that you can recommend to consistently represent the layers you are observing on the figure above (imagine this to be top and bottom of the reservoir zone). Sorry I couldn’t hear you correctly!! Did you just say I don’t know!!! Bravo!! You have said it now.. the first step towards understanding a problem is to realise it and as Shakespeare rightly puts forward in Hamlet (1.5, 167-8) “There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy (Science)”.

Not knowing is not necessarily a bad thing as some wise man has said  “no information is still information”… You are right, we have no idea on how to correctly represent the layering scheme!!! And even if theoretically you can create millimeter layers do you exactly know how the layers behave in three dimension?? The more relevant question is “Does it really matter??” What would you gain if you retain the layering scheme as you observe in the section above.. This question is more relevant than actually preserving the layering you are observing in the section above. What problems you will encounter if the layers in the model cut-across the very depositional framework you are trying to model?? The answer to this question lies in your understanding of the reservoir and flow dynamics of it. Think in the lines of flow – what impairs the flow in this reservoir?? Is it the vertical permeability which is a constraint?? What is the laterally connectivity of the reservoir?? What would prevent or enhance or change the direction of flow within the reservoir?? The answer to these question will tell you whether you are right or wrong!!! If you don’t know the answer – ask your peers from other disciplines (Did I actually tell you that each one of us are Geoscientist no matter what specialisation we have as we are all trying to understand the subsurface)  and you would feel the “nirvana” for sure.. The answer to this question is definitely non trivial.. but there is no harm in trying. And the important part of trying is to put an effort together irrespective of the discipline and science you are representing…

This is where I would like to introduce the term “Conceptual Geological Model”. You have to know what you are expecting before you decide how you create it?? If you don’t know what you are expecting – you can dig yourself a big hole and sink in it… More on it later!!!

As a side note, we all know that geology is dynamic by nature and to simply capture it using static statistical methods is possibly not doing justice to the science of geology. Think of provenance (source of sediments), changes in climate over millions of years and its deposition including subsequent processes related to compaction and diagenesis. It is not an easy thing to capture in entirety. Time is the crucial deciding factor which we have always ignored in the static world. However, if we understand the reason we are creating the geological model we can get what we are looking for!! The important part is to know what you want before getting into the details. FYI, there have been efforts to quantify this in the modelling world but on a very fine scale with not so thick sediment. The problem to quantify this is the requirement to know what has happen year on year while our reservoir were being deposited and needless to say this whole exercise is non-trivial.

I hate to see my blog getting bigger than expected but unfortunately as it is known that the first step towards understanding a complex mathematical equation is to simplify it. It seems that my simplification is taking more words than I thought it would. Keep writing and liking ….

Tell your friends!