Using the attenuation of the borehole radial oscillations to estimate the formation permeability in the presence of mudcake

Sinev A.V.¹, Dorovsky V.N. ¹, Romensky E.I. ^1,2

¹Baker Hughes Incorporated, Novosibirsk, Russia; ²Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

[e-mail]

Application of the acoustic borehole method for measuring the permeability of the porous formation using the Stoneley waves becomes problematic in the presence of mudcake on the borehole surface. This is associated with the strong dependence of attenuation length of Stoneley wave on the rheological properties of the mudcake (Fig. 1)

Direct measurement of the rheological characteristics of the mudcake in a well is an additional difficulty.

It is proposed to use attenuation in time of borehole liquid radial waves to estimate the permeability of porous formation in the presence of mudcake. The main advantages of radial waves are their low sensitivity to the rheological properties of the mudcake and strong dependence of the radial oscillations decrement (time when the magnitude of radial wave is reduced by e times) on the formation permeability.

The calculation model, which is used for investigation of borehole radial oscillations properties, based on the equations of continuum theory of unsteady filtration in saturated porous medium. Properties of mudcake are described by the equations of Maxwell’s viscoelastic model. Waves in the borehole liquid are described by the acoustic equations. All these equations are solved numerically using finite-difference WENO/Runge-Kutta method fifth-order accuracy in space and fourth-order accuracy in time

The computation of radial waves is performed with the use of 1D-model of the borehole in which the computational region is bounded by PML. The long cylindrical source, located at the axis of the borehole, excites the acoustic radial waves in the borehole liquid. A hydrophone, located near the borehole surface in front of the source, registers damped oscillations of the borehole liquid in time. Using the dependence of the pressure oscillation on time, radial waves decrement is calculated (Fig. 2)

The dependencies of decrement on formation permeability with different mudcake rheological properties and mudcake thickness are investigated. The conclusions are:

· decrement decreases with permeability increasing and weakly depends on rheological properties of mudcake (Fig. 3);

· the sensitivity of the de

crement to the mudcake thickness decreases with permeability increasing (Fig. 4).

Fig. 1. The dependence of Stoneley wave attenuation length on inversed relaxation time of shear stresses (χ₀) with different formation permeability, small (0.04 m) borehole radius and high (50 kHz) frequency of source signal

Fig. 2. Changing of pressure in time (mudcake thickness is 1 mm, porous medium permeability is 1 mD) and approximation of the values of extrema by exponential function (decrement is equal 2.5·10^-4 s).

Fig. 3. The depende

nce of decrement on permeability with different inversed relaxation time of shear stresses χ_0.

Fig. 4 The dependence of decrement on inversed relaxation time of shear stresses χ₀ with different values of permeability.

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

[e-mail]

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.

One-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.

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