Models reservoir transfers

Models with transfer between mantle reservoirs... 

The simplest box model consists of one reservoir that is fed by a constant flux (Fg) (Figure 8.2). The flux out of a reservoir is the product of the mass of the substance (A/) in the reservoir and a mass transfer constant (k). Box model reservoirs are simply gigantic ideal mixed flow reactors (see Chapter 4) where there is no net generation or consumption of the substance. Over geologic time spans these reactors tend to attain a steady state so that the flux into a reservoir is matched by the flux out, which means that the rate of accumulation in the reservoir is zero and M is constant (M j). The flux out of the reservoir equals a mass transfer constant (k, yr ) times the mass of the substance in the reservoir. 

The inadequacy of the two-box model of the ocean led to the box-diffusion model (Oeschger et al, 1975). Instead of simulating the role of the deep sea with a well-mixed reservoir in exchange with the surface layer by first-order exchange processes, the transfer into the deep sea is maintained by vertical eddy diffusion. In... 

A global representation of the P cycle, by necessity, will be general. It will combine a wide variety of P-containing components into relatively few reservoirs and will parameterize intricate processes and feedback mechanisms into simple first-order transfers. To appreciate the rationale behind the construction of such a model and to understand its limitations, the transfers of P within a hypothetical terrestrial ecosystem and in a generalized ocean system will be discussed first. 

In the catenary model of Fig. 39.14a we have a reservoir, absorption and plasma compartments and an elimination pool. The time-dependent contents in these compartments are labelled X, X, and X, respectively. Such a model can be transformed in the 5-domain in the form of a diagram in which each node represents a compartment, and where each connecting block contains the transfer function of the passage from one node to another. As shown in Fig. 39.14b, the... 

Fig. 39.14. (a) Catenary compartmental model representing a reservoir (r), absorption (a) and plasma (p) compartments and the elimination (e) pool. The contents X, Xa, Xp and X,. are functions of time t. (b) The same catenary model is represented in the form of a flow diagram using the Laplace transforms Xr, Xa and Xp in the j-domain. The nodes of the flow diagram represent the compartments, the boxes contain the transfer functions between compartments [1 ]. (c) Flow diagram of the lumped system consisting of the reservoir (r), and the absorption (a) and plasma (p) compartments. The lumped transfer function is the product of all the transfer functions in the individual links. 

Ionisation processes in IMS occur in the gas phase through chemical reactions between sample molecules and a reservoir of reactive ions, i.e. the reactant ions. Formation of product ions in IMS bears resemblance to the chemistry in both APCI-MS and ECD technologies. Much yet needs to be learned about the kinetics of proton transfers and the structures of protonated gas-phase ions. Parallels have been drawn between IMS and CI-MS [277]. However, there are essential differences in ion identities between IMS, APCI-MS and CI-MS (see ref. [278]). The limited availability of IMS-MS (or IMMS) instruments during the last 35 years has impeded development of a comprehensive model for APCI. At the present time, the underlying basis of APCI and other ion-molecule events that occur in IMS remains vague. Rival techniques are MS and GC-MS. There are vast differences in the principles of ion separation in MS versus IMS. 

Azin R., JafariS.M., et al. Measurement and modeling of C02 diffusion coefficient in saline aquifer at reservoir conditions. 2013 Heat Mass Transfer 49 1603-1612. 

Fig. 2.1. Schematic diagram of a reaction model. The heart of the model is the equilibrium system, which contains an aqueous fluid and, optionally, one or more minerals. The system s constituents remain in chemical equilibrium throughout the calculation. Transfer of mass into or out of the system and variation in temperature drive the system to a series of new equilibria over the course of the reaction path. The system s composition may be buffered by equilibrium with an external gas reservoir, such as the atmosphere.

A unified gas hydrate kinetic model (developed at ARC) coupled with a thermal reservoir simulator (CMG STARS) was applied to simulate the dynamics of CH4 production and C02 sequestration processes in the Mallik geological zones. The kinetic model contains two mass transfer equations one equation transfers gas and water into hydrate, and a decomposition equation transfers hydrate into gas and water (Uddin etal. 2008a). 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

Otherwise, the mixture is called a nonazeotrope. A nonazeotropic mixture has a temperature distribution parallel to that of the thermal reservoir. Note that one of the requirements for the nonazeotropic mixture energy conversion improvement is to have a nonconstant temperature heat source and heat sink. The proper choice of best combination of the nonazeotropic mixture is still not entirely understood. Uncertainties in modeling the thermodynamic and heat-transfer aspects of the nonazeotropic mixture refrigeration cycle are such that the probability of realizing significant net benefits in actual application is also not fully known. 

The power versus efficiency characteristics of the endoreversible Carnot heat engine is a parabolic curve. The endoreversible heat engine is a simple model, which considers the external heat-transfer irreversibility between the heat engine and its surrounding heat reservoirs only. 

They used a Varian Model 5500 liquid chromatograph with three reservoir capability for on-line enrichment methods one reservoir can be used to quantitatively transfer large sample volumes into the column and a binary gradient can then be introduced from the remaining reservoirs. 

Figure 10.31. Schematic diagram of a three-box (reservoir) model of a closed-system geochemical cycle of a substance (e.g., carbon). The reservoir masses are designated Mi, M2, and M3, and the rates of transfer (fluxes) of a substance between boxes are shown as Fy, where i and j = 1,2,3, but i j. The mass balances for the three reservoirs are given by the three differential equations, kjj are first-order rate constants (units of 1/T) and T is time.

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