On the relative importance of global and squirt flow in cracked porous media

A unified theory of global and squirt flow in cracked porous media was developed several years ago on the basis of a combination of the dynamic T-matrix approach to rock physics. The theory has been successfully used to model ultrasonic velocity and attenuation anisotropy measurements in real rocks under pressure. At the same time, it was recently pointed out that this theory, which contain an established theory of interconnected cracks as a special case contains an error related to fluid mass conservation. The error was recently corrected, and this paper represents an attempt to perform a systematic study of the implications of unified theory for the relative importance of global and squirt flow in cracked porous media characterized by different microstructures and fluid mobilities. Our numerical results suggest that squirt flow dominates over global flow and global flow appears to be more important at higher frequencies for more realistic models of microstructure. The attenuation peak of squirt flow move towards lower frequencies with the increasing fluid viscosity i.e. changing saturating fluid from water to oil, while the global flow attenuation peak move towards higher frequencies with increasing fluid viscosity. A previous observation of negative velocity dispersion in unified theory still remain, even if we use the correct effective wave number, when dealing with the phenomenon of wave-induced fluid flow in models of cracked porous media where global flow effects dominates. The attenuation peak of the global flow obtained using the correct wave number is always shifted to the left as compared to the approximate solution. At seismic frequencies global flow effects are not so important and needs very high permeability and low viscosity to have an effect.submittedVersionPreprin

Editorial: Journal of Pragmatic Constructivism creates understanding about functioning practices

This editorial introduces the journal and the content of the issu

Homotopy analysis of the Lippmann-Schwinger equation for seismic wavefield modeling in strongly scattering media

We present an application of the homotopy analysis method for solving the integral equations of the Lippmann-Schwinger type, which occurs frequently in acoustic and seismic scattering theory. In this method, a series solution is created which is guaranteed to converge independent of the scattering potential. This series solution differs from the conventional Born series because it contains two auxiliary parameters ε and h and an operator H that can be selected freely in order to control the convergence properties of the scattering series. The ε-parameter which controls the degree of dissipation in the reference medium (that makes the wavefield updates localized in space) is known from the so-called convergent Born series theory; but its use in conjunction with the homotopy analysis method represents a novel feature of this work. By using H = I (where I is the identity operator) and varying the convergence control parameters h and ε, we obtain a family of scattering series which reduces to the conventional Born series when h = −1 and ε = 0. By using H = γ where γ is a particular preconditioner and varying the convergence control parameters h and ε, we obtain another family of scattering series which reduces to the so-called convergent Born series when h = −1 and ε ≥ εc where εc is a critical dissipation parameter depending on the largest value of the scattering potential. This means that we have developed a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. By performing a series of 12 numerical experiments with a strongly scattering medium, we illustrate the effects of varying the (ε, h, H)-parameters on the convergence properties of the new homotopy scattering series. By using (ε, h, H) = (0.5, −0.8, I) we obtain a new scattering series that converges significantly faster than the convergent Born series. The use of a non-zero dissipation parameter ε seems to improve on the convergence properties of any scattering series, but one can now relax on the requirement ε ≥ εc from the convergent Born series theory, provided that a suitable value of the convergence control parameter h and operator H is used.publishedVersio