Upscaling geochemical reaction rates using pore-scale network modeling

Geochemical reaction rate laws are often measured using crushed minerals in well-mixed laboratory systems that are designed to eliminate mass transport limitations. Such rate laws are often used directly in reactive transport models to predict the reaction and transport of chemical species in consolidated porous media found in subsurface environments. Due to the inherent heterogeneities of porous media, such use of lab-measured rate laws may introduce errors, leading to a need to develop methods for upscaling reaction rates. In this work, we present a methodology for using pore-scale network modeling to investigate scaling effects in geochemical reaction rates. The reactive transport processes are simulated at the pore scale, accounting for heterogeneities of both physical and mineral properties. Mass balance principles are then used to calculate reaction rates at the continuum scale. To examine the scaling behavior of reaction kinetics, these continuum-scale rates from the network model are compared to the rates calculated by directly using laboratory-measured reaction rate laws and ignoring pore-scale heterogeneities. In this work, this methodology is demonstrated by upscaling anorthite and kaolinite reaction rates under simulation conditions relevant to geological CO₂ sequestration. Simulation results show that under conditions with CO₂ present at high concentrations, pore-scale concentrations of reactive species and reaction rates vary spatially by orders of magnitude, and the scaling effect is significant. With a much smaller CO₂ concentration, the scaling effect is relatively small. These results indicate that the increased acidity associated with geological sequestration can generate conditions for which proper scaling tools are yet to be developed. This work demonstrates the use of pore-scale network modeling as a valuable research tool for examining upscaling of geochemical kinetics. The pore-scale model allows the effects of pore-scale heterogeneities to be integrated into system behavior at multiple scales, thereby identifying important factors that contribute to the scaling effect.     

Nature and rates of fine-sedimentation on a mid-shelf: “La Grande Vasière” (Bay of Biscay,France)

The study area, “La Grande Vasière” (LGV), stretches out on the French Atlantic continental shelf (at ca. 100 m water depth), along 250 km from the Glénan Islands at the north to the southwest of Rochebonne at the south. Box-cores were sampled in this mid-shelf area during four cruises in June 1995, and in April, June and September 2002. They were investigated using sedimentological approaches (X-radiographs and grain-size analyses) and radionuclide studies (²¹⁰Pb geochronology and excess ²³⁴Th). The main results are: (1) the surficial sediments are generally organized into a decimetre-scale fining up sequence which can be the result of extreme storms; (2) an upper mixing layer of 7–20 cm reflects an important biological benthic activity and/or the impact of fishing (i.e. trawlers); (3) a thin (i.e. a few mm) surficial mud-rich layer is the result of the present-day sedimentation; (4) an apparent annual sedimentation rate of 1–3 mm is recorded in several loci of the study area. Some seasonal variations appear, corresponding to the deposition of fine material from April to September, and to the reworking and the re-suspension during the winter. This fine material is the result of the decantation of estuarine plumes, mainly the Loire and the Vilaine rivers, over the study area. LGV lies (1) under the influence of a winter-to-spring thermo-haline wedge that acts as a filter for the transfer of fine river-borne material to the slope and the open sea, and (2) below water depths where the mean swell action permits sedimentation, mainly in summer.     

Comment on ‘Aspects of 1D seismic modelling using the Goupillaud principle’ by Evert Slob and Anton Ziolkowski1

The paper by Slob and Ziolkowski (1993) is apparently a comment on my paper (Szaraniec 1984) on odd-depth structure. In fact the basic understanding of a seismogram is in question. The fundamental equation for an odd-depth model and its subsequent deconvolution is correct with no additional geological constraints. This is the essence of my reply which is contained in the following points.

• 1 The discussion by Slob and Ziolkowski suffers from incoherence. On page 142 the Goupillaud (1961) paper is quoted: “… we must use a sampling rate at least double that… minimum interval…”. In the following analysis of such a postulated model Slob and Ziolkowski say that “… two constants are used in the model: Δt as sampling rate and 2Δt as two-way traveltime”. By reversing the Goupillaud postulation all the subsequent criticism becomes unreliable for the real Goupillaud postulation as well as the odd-depth model.
• 2 Slob and Ziolkowski take into consideration what they call the total impulse response. This is over and above the demands of the fundamental property of an odd-depth model. Following a similar approach I take truncated data in the form of a source function, S(z), convolved with a synthetic seismogram (earth impulse response), R?(z), the free surface being included. The problem of data modelling is a crucial one and will be discussed in more detail below. By my reasoning, however, the function may be considered as a mathematical construction introduced purely to work out the fundamental property. In this connection there is no question of this construction having a physical meaning. It is implicit that in terms of system theory, K(z) stands for what is known as input impedance.
• 3 Our understandings of data are divergent but Slob and Ziolkowski state erroneously that: “Szaraniec (1984) gives (21) as the total impulse response…”. This point was not made. This inappropriate statement is repeated and echoed throughout the paper making the discussion by Slob and Ziolkowski, as well as the corrections proposed in their Appendix A, ineffective. Thus, my equation (2) is quoted in the form which is in terms of the reflection response G^sc and holds true at least in mathematical terms. No wonder that “this identity is not valid for the total impulse response” (sic), which is denoted as G(z). None the less a substitution of G for G^sc is made in Appendix A, equation (A3). The equation numbers in my paper and in Appendix A are irrelevant, but (A3) is substituted for (32) (both numbers of equations from the authors’ paper). Afterwards, the mathematical incorrectness of the resulting equation is proved (which was already evident) and the final result (A16) is quite obviously different from my equation (2). However, the substitution in question is not my invention.
• 4 With regard to the problem of data modelling, I consider a bi-directional ID seismic source located just below the earth's surface. The downgoing unit impulse response is accompanied by a reflected upgoing unit impulse and the earth response is now doubled. The total impulse response for this model is thus given by where (—r₀) =— 1 stands for the surface reflection coefficient in an upward direction. Thus that is to say, the total response to a unit excitation is identical with the input impedance as it must be in system theory. The one-directional 1D seismic source model is in question. There must be a reaction to every action. When only the downgoing unit impulse of energy is considered, what about the compensation?
• 5 In more realistic modelling, an early part of a total seismogram is unknown (absent) and the seismogram is seen in segments or through the windows. That is why in the usual approach, especially in dynamic deconvolution problems, synthetic data in the presence of the free surface are considered as an equivalent of the global reflection coefficient. It is implicit that model arises from a truncated total seismogram represented as a source function convolved with a truncated global reflection coefficient.

Validation or invalidation of the truncation procedure for a numerically specified model may be attempted in the frame of the odd-depth assumption. My equations (22) and (23) have been designed for investigating the absence or presence of truncated energy. The odd-depth formalism allows the possibility of reconstructing an earlier part of a seismogram (Szaraniec 1984), that is to say, a numerical recovery of unknown moments which are unlikely designed by Slob and Ziolkowski for the data.     

Comments on “Steady- and transient-state inversion in hydrogeology by successive flux estimation” by P. Pasquier and D. Marcotte

Pasquier and Marcotte [Pasquier P, Marcotte D. Steady- and transient-state inversion in hydrogeology by successive flux estimation. Adv Wat Res 2006;29:1934–52] propose some modifications to the Comparison Model Method (CMM), in order to apply it to transient 3D ground water flow data for conductivity identification. We present some remarks on that paper to improve the comprehension of the basic features of the CMM and of the real value of the novelties introduced by Pasquier and Marcotte.     

Basaltic ignimbrite-like rocks on Saikhan Volcano, northeastern Khangai, Mongolia: Mineralogic and geochemical evidence

Rocks having a pseudofluidal ignimbrite texture have been found on Saikhan Volcano in northeastern Khangai, Mongolia. The rocks have a typically nodular banded texture. The fiamme and the bands vary in width between a few millimeters to a few centimeters. These rocks have the same bulk composition as trachybasalts and do not differ from the ordinary trachybasalts found on this volcano in the form of dikes and lavas. The difference consists in the composition of glasses and minerals, as well as in the concentration of CO₂ (which is higher in the ignimbrite-like rocks). The glasses in the ignimbrite-like rocks show a trend from basaltic trachyandesites to tephriphonolites and foidites, thus indicating the liquidus crystallization of clinopyroxene. The glasses in the lavas and dikes have a trachyte composition, indicating a residual origin following the crystallization of olivine and Ti-magnetite. Much of the pyroxenes (∼20%) in the ignimbrite-like rocks show calculated pressures during their generation to have been in the range of 6.5–14 kbars, while all pyroxenes in the ordinary lavas and dikes crystallized at pressures below 0.3 kbars. It thus follows that the magmas that have produced the ignimbrite-like rocks began crystallizing in the subcrustal magma chamber under fluid-saturated conditions, whence they were rapidly transported to the surface.