The ultimate test for any technique that bears the claim of permeability prediction from well log data, is accurate and verifiable prediction of permeability for wells from which only the well log data is available. So far all the available models and techniques have been tried on data that includes both well logs and the corresponding permeability values. This approach at best is nothing more than linear or nonlinear curve fitting. The objective of this paper is to test the capability of the most promising of these techniques in independent (where corresponding permeability values are not available or have not been used in development of the model) prediction of permeability in a heterogeneous formation.
Since the empirical approaches for permeability prediction are mostly directed toward developing mathematical models from given data in particular formations, it has been shown that they lack the required generalization capability for the purposes of this study. These approaches have concentrated on modeling formation permeability as a function of porosity and irreducible water saturation. These models will be briefly discussed. The main focus of this paper will be on two techniques that show potentials in achieving the goal that was mentioned above. These techniques are Multiple Regression" and "Virtual Measurements using Artificial Neural Networks." For the purposes of this study several wells from a heterogeneous formation in West Virginia were selected. Well log data and corresponding permeability values for these wells were available. In separate tests all data from an entire well were designated and put aside.
The techniques were applied to the remaining data and a permeability model for the field was developed. The model was then applied to the well that was separated from the rest of the data earlier and the results were compared. This approach will test the generalization power of each technique. After all, this is the way that these techniques are used in the real life situations.
The result will show that although Multiple Regression provides acceptable results for wells that were used during model development, (good curve fitting,) it lacks a consistent generalization capability, meaning that it does not perform as well with data it has not been exposed to (the data from well that has been put aside). On the other hand, Virtual Measurement technique provides a steady generalization power. This technique is able to perform the permeability prediction task even for the entire wells with no prior exposure to their permeability profile.
In the first part of this paper, different methodologies that are available for permeability prediction were thoroughly reviewed. These methodologies can be divided into three categories: empirical, statistical, and neural modeling. In empirical modeling, the approach usually can be summarized by measuring porosity and irreducible water saturation of the cores and developing mathematical models relating porosity and irreducible water saturations to permeability. Next step in this approach is to get the best estimate of porosity and irreducible water saturation from logs and then use them to predict permeability. One of the most important contributions that different investigators employing this method have made is the establishment of a relationship between porosity, irreducible water saturation, and permeability. Short comings of this approach can be summarized as follows: to get permeability one needs to know porosity (actually effective porosity, which is the portion of the porosity that is not isolated and is connected to the pore network and is therefore contributing to the flow) and irreducible water saturation. These parameters are most accurately measured in the laboratory using core samples. However, the point is if core samples are available to measure the effective porosity and irreducible water saturation, why not measure permeability instead of predicting it. To overcome this problem, effective porosity and irreducible water saturation is then estimated (calculated) with a certain degree of accuracy from well logs to be used in the empirically developed model. it should be noted that porosity calculated from logs is not necessarily effective porosity and calculating irreducible water saturation from well log responses is not a well-established method.