1D Simulations for Microbial Enhanced Oil Recovery with Metabolite Partitioning

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its ”disappearance,” so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil–water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with.     

The Semi-Arc Automorphism Group of a Graph with Application to Map Enumeration

A map is a connected topological graph cellularly embedded in a surface. For a given graph Γ, its genus distribution of rooted maps and embeddings on orientable and non-orientable surfaces are separately investigated by many researchers. By introducing the concept of a semi-arc automorphism group of a graph and classifying all its embeddings under the action of its semi-arc automorphism group, we find the relations between its genus distribution of rooted maps and genus distribution of embeddings on orientable and non-orientable surfaces, and give some new formulas for the number of rooted maps on a given orientable surface with underlying graph a bouquet of cycles B_n, a closed-end ladder L_n or a Ringel ladder R_n. A general scheme for enumerating unrooted maps on surfaces(orientable or non-orientable) with a given underlying graph is established. Using this scheme, we obtained the closed formulas for the numbers of non-isomorphic maps on orientable or non-orientable surfaces with an underlying bouquet B_n in this paper.     

Propylene polymerizations with a binary metallocene system—Chain shuttling caused by trimethylaluminium between active catalyst centers

Propylene was polymerized at varying trimethylaluminium (TMA) concentration with a homogeneous binary metallocene catalyst system activated by methylaluminoxane (MAO) in an attempt to better understand interactions between active catalyst sites and to clarify the role of the TMA as a chain shuttling agent. TMA‐free polymerization conditions were obtained by chemical treatment of MAO solution with 2,6‐di‐tert‐butyl‐4‐methylphenol (BHT). A binary catalyst system consisting of catalyst precursors diphenylmethyl(cyclopentadienyl)(9‐fluorenyl)zirconium dichloride ( 1 ) producing high M_w syndiotactic polypropylene and rac‐dimethylsilylbis(4‐tert‐butyl‐2‐methyl‐cyclopentadienyl)zirconium dichloride ( 2 ) producing low M_w isotactic polypropylene was investigated. At the studied polymerization conditions, chain shuttling between the active catalysts caused by TMA was confirmed. The chain shuttling reactions caused changes in catalyst activity, molecular weights, melting behavior, and polymer microstructure. We propose that TMA is capable to transfer a growing polymer chain from catalyst 2 to catalyst 1 , and a stereoblock copolymer is formed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1364–1376, 2007     

Structure–property transition‐state model for the copolymerization of ethene and 1‐hexene with experimental and theoretical applications to novel disilylene‐bridged zirconocenes

Ethene homopolymerization and copolymerization with 1‐hexene were performed with three new tetramethyldisilylene‐bridged zirconocene catalysts with 2‐indenyl ligand ( A ), 2‐tetrahydroindenyl ligand ( B ), and tetramethyl‐cyclopentadienyl ligand ( C ) and with methylaluminoxane as a cocatalyst. Catalysts A and B showed substantial comonomer incorporation, resulting in a copolymer melting temperature more than 20° lower than that of the corresponding homopolymer. In contrast, catalyst C produced a copolymer with a low 1‐hexene content and a high melting temperature. The reduction in the molecular weight with 1‐hexene addition also correlated well with the comonomer incorporation. For all three catalysts, the homopolymer and copolymer unsaturations indicated frequent chain termination after 1‐hexene insertion and a high degree of chain‐end isomerization during the homopolymerization of ethene. The chain transfer to Al in the cocatalyst also appeared to be important. The comonomer response could be correlated with the structural properties of the catalyst, as derived from quantum chemical calculations. A linear model, calibrated against recent experiments with unbridged (Me_nC₅H_5?n)₂ZrCl₂ catalysts, suggested that the low comonomer incorporation obtained with catalyst C was caused partly by a narrow opening angle between the aromatic ligands and partly by steric hindrance in the transition state of comonomer insertion. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1622–1631, 2003     

Certificates of Primal or Dual Infeasibility in Linear Programming

In general if a linear program has an optimal solution, then a primal and dual optimal solution is a certificate of the solvable status. Furthermore, it is well known that in the solvable case, then the linear program always has an optimal basic solution. Similarly, when a linear program is primal or dual infeasible then by Farkas's Lemma a certificate of the infeasible status exists. However, in the primal or dual infeasible case then there is not an uniform definition of what a suitable basis certificate of the infeasible status is.In this work we present a definition of a basis certificate and develop a strongly polynomial algorithm which given a Farkas type certificate of infeasibility computes a basis certificate of infeasibility. This result is relevant for the recently developed interior-point methods because they do not compute a basis certificate of infeasibility in general. However, our result demonstrates that a basis certificate can be obtained at a moderate computational cost.     

Regular abelian Banach algebras of linear maps of operator algebras

With H a complex Hilbert space we study regular abelian Banach subalgebras of the Banach algebra of bounded linear maps of B(H) into itself. If a ? b denotes the map x → axb, a, b, x ? B(H), it is shown that normalized positive maps in algebras of the form A ? A with A an abelian C¹-algebra, can be described by a generalized Bochner theorem.     

Factorization of Transport Coefficients in Macroporous Media

We prove the fundamental theorem about factorization of the phenomenological coefficients for transport in macroporous media. By factorization we mean the representation of the transport coefficients as products of geometric parameters of the porous medium and the parameters characteristic of the multicomponent fluid saturating the porous space. The two permeabilities of the porous medium, the convective and the diffusional ones, are separated. A similarity between the diffusional permeability and the porosity–tortuosity factor of the Kozeny–Carman theory is demonstrated. We do not make any specific assumption about stochastic or deterministic structure of the porous medium. The fluxes in fluid on the pore level are described by general relations of the non-equilibrium thermodynamics.     

Optical analysis of the light emission from porous silicon: a hybrid polyatom surface-coupled fluorophor

The most extensive data set yet generated correlating photoluminescence excitation (PLE) and photoluminescence (PL) spectra is presented for aged (equilibrated) porous silicon (PS) samples. The observed features, which are temperature independent over the range 10-300 K, show a detailed correlation with the results of photoacoustic spectroscopy (PAS) and with molecular electronic structure calculations. The observed energy level patterns are reproduced in the photoabsorption (PA) of PS films released after the etching of a silicon wafer. It is concluded that the energy level pattern found for the photoluminescing surface of PS results from a structure which is neither uniquely molecule- or bulk-like but represents a hybrid form for which the density of states associated with a polyatomic vibrationally excited surface-bound fluorophor dominates the nature of the observed features which are not those of a semiconductor. These fluorophor features are broadened and shifted to lower excitation energy as a result of the intimate presence of the silicon surface to which the fluorophor is bound. The dominance of the surface-bound fluorophor accounts for the temperature-independent PLE and PL features. The observed spectral features are thus suggested to be the result of a strong synergistic interaction in which the silicon surface influences the location of surface-bound fluorophor excited states whereas the nature of the vibrationally excited surface-bound fluorophor coupling to the silicon surface provides the mechanism for an enhanced vibronic structure dominated interaction and energy transfer. The observed PLE, PL, PAS, and PA measurements are found to be consistent with previous photovoltaic and photoconductivity measurements, correlating well with a surface-bound oxyhydride-like emitter. This study suggests the important role that the overtone structure of a molecule bound to a surface can play as one forms a hybrid system.