Kagan Tuncay

Wave propagation in poroelastic media saturated by two fluids

A theory of wave propagation in isotropic poroelastic media saturated by two immiscible Newtonian fluids is presented. 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. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcys law. The coefficients of macroscopic constitutive relations are expressed in terms of measurable quantities in a novel way. The theory demonstrates the existence of three compressional and one rotational wave. The third compressional wave is associated with the pressure difference between the fluid phase and dependent on the slope of the capillary pressure-saturation relation.

Modeling biogeochemical processes in subterranean estuaries : Effect of flow dynamics and redox conditions on submarine groundwater discharge of nutrients

A two-dimensional density-dependent reactive transport model, which couples groundwater flow and biogeochemical reactions, is used to investigate the fate of nutrients (NO3 −, NH4 +, and PO4) in idealized subterranean estuaries representing four end-members of oxic/anoxic aquifer and seawater redox conditions. Results from the simplified model representations show that the prevalent flow characteristics and redox conditions in the freshwater-seawater mixing zone determine the extent of nutrient removal and the input of nitrogen and phosphorus to coastal waters. At low to moderate groundwater velocities, simultaneous nitrification and denitrification can lead to a reversal in the depth of freshwater NO3 − and NH4 +-PO4 plumes, compared to their original positions at the landward source. Model results suggest that autotrophic denitrification pathways with Fe2+ or FeS2 may provide an important, often overlooked link between nitrogen and phosphorus biogeochemistry through the precipitation of iron oxides and subsequent binding of phosphorus. Simulations also highlight that deviations of nutrient data from conservative mixing curves do not necessarily indicate nutrient removal.

Body waves in poroelastic media saturated by two immiscible fluids

A study of body waves in elastic porous media saturated by two immiscible Newtonian fluids is presented. We analytically show the existence of three compressional waves and one rotational wave in an infinite porous medium. The first and second compressional waves are analogous to the fast and slow compressional waves in Biots theory. The third compressional wave is associated with the pressure difference between the fluid phases and dependent on the slope of capillary pressure-saturation relation. Effect of a second fluid phase on the fast and slow waves is numerically investigated for Massillon sandstone saturated by air and water phases. A peak in the attenuation of the first and second compressional waves is observed at high water saturations. Both the first and second compressional waves exhibit a drop in the phase velocity in the presence of air. The results are compared with the experimental data available in the literature. Although the phase velocity of the first compressional and rotational waves are well predicted by the theory, there is a discrepancy between the experimental and theoretical values of attenuation coefficients. The causes of discrepancy are explained based on experimental observations of other researchers.

Solute-specific pore water irrigation: Implications for chemical cycling in early diagenesis

In one-dimensional (1D) early diagenetic models, bioirrigation is typically represented by a nonlocal mass transfer or bioirrigation coefficient, . Usually, all pore water species are assigned the same . Here, we show that this assumption can lead to significant errors in estimates of bioirrigation intensities. Using a simplified early diagenetic reaction network, we compute the 3D concentration fields of major pore water species around a vertical burrow, as well as the solute fluxes across the burrow wall. From these results, corresponding 1D vertical profiles are derived. The profiles show pronounced differences from one solute to another. Dissolved O2 systematically exhibits the highest values, while fast oxygenation kinetics near the burrow wall result in near-zero values for aqueous Fe . For nitrate, use of a species-averaged profile may even lead to an erroneous prediction of the direction of the irrigation flux across the water-sediment interface. The large differences in profiles reflect the variable effects of biogeochemical processes on pore water concentration fields of reactive solutes near the burrow wall. Even for inert solutes, however, determination of can be ambiguous. Transient simulations mimicking the intrusion into the sediment of an inert tracer during an incubation experiment yield apparent mixing intensities that depend on the incubation time.

Effective stress principle for saturated fractured porous media

An effective stress principle for saturated fractured porous media is proposed based on the double-porosity representation. Both the solid grains and the fractured porous medium are assumed to be linearly elastic materials. The derivation employs volume averaging technique to obtain macroscopic scale expressions. Two parameters, the bulk modulus of the fractured medium and bulk modulus of the porous matrix, are introduced in the formulation. The final expression reduces to the one obtained by Biot and Willis [1957], Skempton [1960], Nur and Byeerle [1971], and Verruijt [1984] when the volume fraction of the fractures vanishes, that is, for a nonfractured porous medium.

Wave propagation in fractured porous media

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 Darcys 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 Biots equations containing the same parameters as of Biot and Willis.

Parallel implementation of a velocity-stress staggered-grid finite-difference method for 2-D poroelastic wave propagation ☆

Abstract Numerical simulation of wave propagation in poroelastic media demands significantly more computational capability compared to elastic media simulation. Use of serial codes in a single scientific workstation limits the size of problem. To overcome this difficulty, a parallel velocity-stress staggered-grid finite-difference method is developed for efficient simulation of wave propagation in 2-D poroelastic media. The finite difference formulation of Biots theory has the properties of fourth order accuracy in space and second order accuracy in time. The model is decomposed into small subdomains for each processor. After each processor updates wavefields within its domain, the processors exchange the wavefields via message passing interface (MPI). The parallel implementation reduces the computational time and also allows one to study larger problems. From our numerical experiment, consistent with other 1-D experiments, it is found that the presence of heterogeneity of porous medium can produce significant P-wave attenuation in the seismic frequency range.

Transcriptional regulatory network refinement and quantification through kinetic modeling, gene expression microarray data and information theory.

BackgroundGene expression microarray and other multiplex data hold promise for addressing the challenges of cellular complexity, refined diagnoses and the discovery of well-targeted treatments. A new approach to the construction and quantification of transcriptional regulatory networks (TRNs) is presented that integrates gene expression microarray data and cell modeling through information theory. Given a partial TRN and time series data, a probability density is constructed that is a functional of the time course of transcription factor (TF) thermodynamic activities at the site of gene control, and is a function of mRNA degradation and transcription rate coefficients, and equilibrium constants for TF/gene binding.ResultsOur approach yields more physicochemical information that compliments the results of network structure delineation methods, and thereby can serve as an element of a comprehensive TRN discovery/quantification system. The most probable TF time courses and values of the aforementioned parameters are obtained by maximizing the probability obtained through entropy maximization. Observed time delays between mRNA expression and activity are accounted for implicitly since the time course of the activity of a TF is coupled by probability functional maximization, and is not assumed to be proportional to expression level of the mRNA type that translates into the TF. This allows one to investigate post-translational and TF activation mechanisms of gene regulation. Accuracy and robustness of the method are evaluated. A kinetic formulation is used to facilitate the analysis of phenomena with a strongly dynamical character while a physically-motivated regularization of the TF time course is found to overcome difficulties due to omnipresent noise and data sparsity that plague other methods of gene expression data analysis. An application to Escherichia coli is presented.ConclusionMultiplex time series data can be used for the construction of the network of cellular processes and the calibration of the associated physicochemical parameters. We have demonstrated these concepts in the context of gene regulation understood through the analysis of gene expression microarray time series data. Casting the approach in a probabilistic framework has allowed us to address the uncertainties in gene expression microarray data. Our approach was found to be robust to error in the gene expression microarray data and mistakes in a proposed TRN.

Sedimentary basin deformation: an incremental stress approach

Abstract A key component of sedimentary basin evolution is the spatial distribution and temporal variation of stress and deformation. The many deformation processes (poroelasticity, fracturing, irreversible nonlinear viscosity, and pressure solution) are inextricably bound in a tightly coupled network which, in turn, is coupled to a myriad of basin diagenetic, thermal and hydrologic processes. In the approach presented here, the various deformation processes are integrated through an incremental stress approach. Together with mass, momentum and energy conservation, this approach yields a complete, fully coupled basin model that captures basin and fault phenomena that are beyond the scope of simpler or decoupled models. Many of the most interesting basin phenomena are not only dependent on multiple, coupled processes but also are fundamentally three-dimensional. To address this three-dimensional complexity, we have developed a numerical simulator using a moving, adapting, accreting finite element grid which is allowed to deform and to grow and adapt with the addition of sediment to capture smaller sedimentary features. As a result, our fully coupled, comprehensive model allows one to solve a number of key problems in basin and fault dynamics. These include compaction, fractured reservoir and compartment genesis and dynamics. Examples illustrating these applications are presented for idealized systems and the Piceance Basin (Colorado) and the Permian Basin (West Texas). The incremental stress rheology is found to be a powerful formalism for integrating basin hydrology, diagenesis and mechanics.

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biots theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.