SEISMIC-DERIVED ROCK TRUE RESISTIVITY (Rt ) REVISITED. PART II: REFORMULATION USING WYLLIE’S TIME-AVERAGE MODEL

Abstract

This paper is the second of a three-part presentation. As highlighted in the previous paper (Part I, Widarsono & Mendrofa, 2006), the main objective of the study is to re-evaluate the potential of acoustic impedance as a source of resistivity data. This essentially came from the very idea of extracting information of resistivity (Rt ), data that plays a very important role in the determination of water saturation in reservoir, from seismic-derived acoustic impedance (AI).

As observed in the past view years, there have been a lot of efforts devoted to the extraction of water saturation information from seismic. However, as Widarsono & Mendrofa (2006) put it, most of the efforts were mainly based on pattern recognition activities with little attention was given to the theoretical aspects of relationships between seismic signals and water saturation. The work reported in this threepart presentation is concentrated more as re-establishing (a reformulation of works reported in Widarsono & Saptono, 2003; 2004) the theoretical relationship between resistivity and acoustic impedance.

In the Part I (Widarsono & Mendrofa, 2006), a reformulation between the classical Gassmann acoustic velocity model and shally sand models of Modified Simandoux and Hossin is presented. In the reformulation, a new resistivity function of acoustic impedance has been established. In principle, whenever acoustic impedance data from seismic has been made available resistivity data for the determination of fluid saturation can be estimated.

Despite the theoretical correctness of the resistivity function presented in the Part I, practicallity is not the function’s best aspect. In other words, the resistivity function is not an easy one to be used practically. Various parameters (e.g. matrix moduli) have to be assumed, since the data cannot easily measured even in the laboratory. This is indeed the main reason why gassmann model, and others such as Biot, has not been used much in day-to-day practices such as log interpretation for porosity determination.

Being aware of such difficulties, in 1954 M.R.J. Wyllie et al proposed their “time average” model (named after its proportional averaging of pore fluid, rock matrix, and shale transit time values to represent transit time of a fluid-filled porous medium) for any practical uses related to P-wave velocity in porous media. Due to its simplicity, the model, as well as its subsequent modifications, has been used extensively since then in some areas especially in log analysis for porosity determination. Considering this simplicity aspect, this three-part study also adopted Wyllie “time average” model into its reformulation works. This Part II paper presents the formulation using Wyllie and the two shally sand models following the same manner that was adopted and presented in the Part I paper.

Summarily, the objectives of the works presented in this paper are:

- To establish a model/method to obtain formation rock true resistivity (Rt ) from seismic-derived acoustic impedance (AI),

- To provide correction/modification onto previous works reported in Widarsono & Saptono (2003, 2004), and

- To provide a simpler alternative to the resistivity function yielded from the reformulation works presented in Part I paper (Widarsono & Mendrofa, 2006)