TY - CONF
AB - Phenomenological equations for the poroelastic behavior of a double porosity medium have been formulated and the coefficients in these linear equations identified. The generalization from a single porosity model increases the number of independent coefficients from three to six for an isotropic applied stress. In a quasistatic analysis, the physical interpretations are based upon considerations of extremes in both spatial and temporal scales. The limit of very short times is the one most relevant for wave propagation, and in this case both matrix porosity and fractures are expected to behave in an undrained fashion, although our analysis makes no assumptions in this regard. For the very long times more relevant for reservoir drawdown, the double porosity medium behaves as an equivalent single porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At the mesoscopic scale pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. We show explicitly how to generalize the quasistatic results to incorporate wave propagation effects and how effects that are usually attributed to squirt flow under partially saturated conditions can be explained alternatively in terms of the double-porosity model. The result is therefore a theory that generalizes, but is completely consistent with, Biot's theory of poroelasticity and is valid for analysis of elastic wave data from highly fractured reservoirs.
AU - Berryman, J. G.
AU - Wang, H. F.
T2 - Mathematical Methods in Geophysical Imaging V
ED - Hassanzadeh, Siamak
KW - double porosity
SP - 58
EP - -69
T1 - Double-porosity modeling in elastic wave propagation for reservoir characterization
UR - http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=958382
VL - 3453
PY - 1998
ER -
TY - JOUR
AB - We determine finite-frequency kernels for wave propagation in porous media based upon adjoint methods. These sensitivity kernels may be obtained based upon two numerical simulations for each source: one calculation for the current model and a second, `adjoint', calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. The adjoint equations for a porous medium are identical to the usual Biot equations, with the exception of the adjoint source term, which involves time-reversed measurements of the differences between simulations and data. Isotropic poroelastic wave propagation is governed by eight primary model parameters which appear in the original Biot equations. These parameters include four moduli: the shear modulus of the frame plus three bulk moduli. We consider two alternative parameterizations: one involving density-normalized moduli corresponding to squared wave speeds, and a second involving the poroelastic shear and compressional wave speeds. The alternative parameterizations lead to density-sensitivity kernels that are small, reflecting the fact that the traveltime of a poroelastic wave is governed by wave speed, not density. We systematically investigate and illustrate the sensitivity of the fast and slow compressional waves and the shear wave to the poroelastic model parameters using a 2-D spectral-element method. The poroelastic sensitivity kernels presented herein form the basis of tomographic imaging and inversion in porous media.
AU - Morency, C.
AU - Luo, Y.
AU - Tromp, J.
JO - Geophys. J. Int.
KW - poroelasticity
KW - adjoint
SP - 1148
EP - -1168
T1 - Finite-frequency kernels for wave propagation in porous media based upon adjoint methods
UR - http://gji.oxfordjournals.org/content/179/2/1148.short
VL - 179
PY - 2009
ER -
TY - JOUR
AB - We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as `type II' or `Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach.We perform various benchmarks involving poroelastic wave propagation and acoustic--poroelastic and poroelastic--poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance.
AU - Morency, C.
AU - Tromp, J.
JO - Geophys. J. Int.
KW - spectral-element
KW - poroelasticity
KW - Computational seismology
KW - Theoretical seismology
KW - Wave propagation
SP - 301
EP - -345
T1 - Spectral-element simulations of wave propagation in porous media
UR - http://gji.oxfordjournals.org/content/175/1/301.short
VL - 175
PY - 2008
ER -
TY - JOUR
AB - The equations governing the linear acoustics of composites with two isotropic porous constituents are derived from first principles using volume-averaging arguments. The theory is designed for modeling acoustic propagation through heterogeneous porous structures. The only restriction placed on the geometry of the two porous phases is that the overall composite remains isotropic. The theory determines the macroscopic fluid response in each porous phase in addition to the combined bulk response of the grains and fluid in the composite. The complex frequency-dependent macroscopic compressibility laws that are obtained allow for fluid transfer between the porous constituents. Such mesoscopic fluid transport between constituents within each averaging volume provides a distinct attenuation mechanism from the losses associated with the net Darcy flux within individual constituents as is quantified in the examples.
AU - Pride, S. R.
AU - Berryman, J. G.
JO - Physical Review
KW - double porosity
SP - 036603
T1 - Linear dynamics of double-porosity dual-permeability materials. I. Governing equations and acoustic attenuation
UR - http://journals.aps.org/pre/abstract/10.1103/PhysRevE.68.036603
VL - 68
PY - 2003
ER -
TY - JOUR
AB - A theory of wave propagation in fractured porous media is presented based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. In microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. The macroscopic constitutive relations of elastic porous media saturated by one or two fluids and saturated fractured porous media can be obtained from the constitutive relations developed in the paper. In the simplest case, the final set of governing equations reduce to Biot's equations containing the same parameters as of Biot and Willis.
AU - Tuncay, K.
AU - Corapcioglu, Y.
JO - Transport in Porous Media
KW - double porosity
SP - 237
EP - -258
T1 - Wave propagation in fractured porous media
UR - http://link.springer.com/article/10.1007%2FBF00167098
VL - 23
PY - 1996
ER -