Wednesday, November 15, 2017

Modeling Versus Inversion

The distinction between modeling -frequently "forward modeling" - and inversion is sometimes muddied. The latter typically attempts to "back out" true resistivity, Rt, directly from the log with a minimum of assumptions. The best known example of this approach is vertical deconvolution through the use of inverse filters. In its purest form , this method requires only that the vertical response function (VRF) of the tool be known acuretely. In practice, VRFs are usually formation dependent, so approximations must be used.



Neverthelss, deconvolution has been employed successfully, running in real time on logging unit computers. Artifacts may appear, however, if inverse filter overeach in trying to achieve fine vertical resolution or if the 2D assumptions implicit in the filter are violated. 

In modeling, on the other hand, the analyst suggest an environmental model. This trial model includes a description of the borehole and formation geometry and "parameter values" - number assigned to variables such as borehole diamter and bedding dip, thickness and resistivity. Then, the tool of physics - a model in its own right- is used to compute an expected log, which is compared with the field log. If the match is not good enough, the inital trial model is altered and the calculation repeated. This proccess is iterated until the two logs match satisfactorily. Several criteria for the quality of match are used, from simple eyeballing to the more sophisticated least-squares and maximum entropy methods. The model's geometry or parameter changes are executed interactively, using the analyst's intuition and experience, or automatically, if computers and programs of sufficient power are available. 



Modeling intrinsically yields consistency with the field log, even though the solution is not unique. This nonuniqueness is seldom a serious problem, however, because the range of possible formation models can be severely constrained by local knowledge from cores and logs. An extreme example of this condition shows two grossly different models that predict the same deep induction log. But in practice, almost any additional log with vertical resolution of about 1 foot (30cm) or less (gamma ray, EPT Electromagnetic Propagation Tool, dipmeter, or photoelectric factor, PE) would resolve this ambiguity.






 The economic importance of modeling is illustrated by a North Sea reserves calculation based on induction log interpretation carried out with a Schlumberger program called Induction Sonde in Multilayered Media (ISMLM). This is a 1D induction modeling code for layered media that neglects borehole and invasion effects. It handles up to 150 parallel dipping layers. Invasion was considered negligible because the well was drilled with oil-base mud.

  The measured deep induction log, inital trial formation model and computed log are shown in the first model. High resolution details of the trial model were provided by an EPT log. The effects of the first model revision are based on the analyst's experience. The analyst changes the thicknesses of conductive beds, add layers to the sands, and improves the depth match between the induction and EPT curves. Since visible discrepancies between the field log and the modeled log remained, further model revisions were needed to achieve the final results. The final model reduced the well's estimated average water saturation from 9.7% to 7.2 %. Because the hole is deviated 56 degree, the log mesured depth (MD) are greater than the true vertical depths (TVD), and bed thicknesses are similiary magnified. 


Forward modeling is serving needs other than conventional log interpretation, such as guidng the bit while drilling deviated or horizontal wells and evaluating the influence of adjacent beds on horizontal well logs.


 





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