Development of algorithms and software for the quantitative interpretation of electrical logging archival data

Vologdin f.V., Nikitenko m.N.

A.A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, Russia

drgvalior@gmail.com

Geological and geophysical data are recorded at all stages of the exploration of oil and gas reserves. Generalization of these data is related with interpretation and reinterpretation of the long-term exploration data. Clarification of the oil and gas reserves parameters is based on the use of the well log archival data.

At present, the archives contain a significant amount of old electrical logging data. These data are presented by diagrams of lateral well logging and induction well logging. Quantitative interpretation of this archive data will help us in exploration of oil and gas reserves. That’s why we need to improve the interpretation quality of the old archival data with using modern principles of quantitative interpretation.

The main goal is to create algorithms and software for the quantitative interpretation of electrical logging archival data. The basic idea is a complex inversion of lateral well logging and induction well logging. As a result of this inversion we`ll obtain common geoelectrical model. The inversion is based on a detailed analysis of quasi solutions of the one-dimensional inverse problem. This method involves exhaustive search of geoelectric parameters (formation resistivity, invaded zone radius and resistivity).

The range of searched geoelectric parameters is large enough. So searches of the exact solution consist of several stages. On the first step we use coarse grid to find quasi solutions. On the second step we analyze the quasi solution set. If this set is within the error range then we have the exact solution. Else we use fine grid to find exact solution within the quasi solution set.

There is a large dispersion of invaded zone parameters within the wide quasi solution set. In such cases we replace invaded zone radius and invaded zone resistivity by the general parameter with using statistical data. So we need to search two parameters (general parameter and formation resistivity) instead of three (formation resistivity, invaded zone radius and resistivity). After finding general parameter and formation resistivity we can give the formation resistivity as an exact solution. Also we can find invaded zone parameters with using exhaustive search of general parameters on a fine grid. The most accurately determined geoelectric parameter of all is formation resistivity, which is determined mainly by the focused low-frequency induction tool.

O ne-dimensional numerical simulation in the layered-homogeneous geoelectric environment was used in solving of the direct problem. With the help of numerical simulation programs look-up tables for three parameters (invaded zone resistivity, invaded zone radius and formation resistivity) were calculated. As the result of these calculations we obtained theoretical apparent resistivity for full range of model parameters. Theoretical apparent resistivity was compared with experimental apparent resistivity using the residual function , where N – number of signals, - experimental apparent resistivity, - theoretical apparent resistivity. To increase the performance of the numerical

Fig. Initial model and interpretation results of synthetic data.

- initial model

- interpretation results

inversion software B-spline interpolation was used. The resulting gain in speed allows for a quantitative interpretation not only in formation mode, but in dotted mode.

Software was tested on synthetic data. We have chosen two types of models: one-dimensional cylindrical layered models and two-dimensional models. Interpretation results of one-dimensional cylindrical layered models were accurate for a high amount of benchmarks. Interpretation results of two-dimensional models were accurate in formation mode, but during the interpretation in dotted mode, there are uncertainties of geoelectric parameters near the boundaries of formations.

In the result of the quantitative interpretation we obtain the true geoelectric model parameters. Fig. shows the initial models and interpretation results of synthetic data in formation mode. Examples show the high accuracy of the formation resistivity calculation.

References:

1. Kaufman A.A., 1965. “Theory of induction logging”, Siberian Dept. of Nauka Press, Novosibirsk.

2. Dachnov V.N., 1985. “Geophysical methods of collectors’ properties definition of oil-gas saturated rocks”. Moscow: Nedra, 310 p.

3. Antonov Y.N., Privorotsky B.I., 1975. “Induction well logging”, Siberian Dept. of Nauka Press, Novosibirsk.