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

ansi_87@ngs.ru

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.