Efficiency of diffusion controlled miscible displacement in fractured porous media

Experiments were performed to study the diffusion process between matrix and fracture while there is flow in fracture. 2-inch diameter and 6-inch length Berea sandstone and Indiana limestone samples were cut cylindrically. An artificial fracture spanning between injection and production ends was created and the sample was coated with heat-shrinkable teflon tube. A miscible solvent (heptane) was injected from one end of the core saturated with oil at a constant rate. The effects of (a) oil type (mineral oil and kerosene), (b) injection rates, (c) orientation of the core, (d) matrix wettability, (e) core type (a sandstone and a limestone), and (f) amount of water in matrix on the oil recovery performance were examined. The process efficiency in terms of the time required for the recovery as well as the amount of solvent injected was also investigated. It is expected that the experimental results will be useful in deriving the matrix–fracture transfer function by diffusion that is controlled by the flow rate, matrix and fluid properties.     

A higher-order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions

We propose a hybrid numerical scheme to discretize a class of singularly perturbed parabolic reaction–diffusion problems with robin-boundary conditions on an equidistributed grid. The hybrid difference scheme is developed by using a modified backward difference scheme in time, a combination of the cubic spline and exponential spline difference scheme in space. The proposed scheme uses a cubic spline difference scheme for the discretization of robin-boundary conditions. For the time discretization of the problem, we use the standard uniform mesh while a layer adapted equidistributed grid is generated for the spatial discretization. By equidistributing a curvature-based monitor function, the spatial adaptive grid is able to capture the presence of parabolic boundary layers without using any prior information about the solution. Parameter uniform error estimates are derived to illustrate an optimal convergence of first-order in time and second-order in space for the proposed discretization. The accuracy of the proposed scheme is confirmed by the numerical experiments that underpin the theoretical analysis.     

Asymmetric synthesis of α-amino acids by reduction of N-tert-butanesulfinyl ketimine esters

A highly regio- and diastereoselective reduction of various N-tert-butanesulfinyl ketimine esters with L-Selectride resulting in the formation of α-amino acids is reported. This method is quite general and also practical for the preparation of both enantiomers of aryl or aliphatic α-amino acids in high yields.     

Theoretical Development of a Novel Equation for Dynamic Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

In oil recovery from fractured reservoirs, dynamic spontaneous imbibition (DSI) plays an important role. Conventional equations used for characterizing dynamic spontaneous imbibition neglect the effects of the driving forces acting across the wetting and non-wetting phases which are flowing in opposite directions. Such effects, defined as interfacial coupling effects (ICE), are known to cause a decrease in the calculated flow rate in drainage processes. Moreover, none of the numerical models have considered a variable inlet saturation (S*) for DSI. A new theoretical model has been developed using generalized transport equations to describe dynamic spontaneous imbibition for immiscible two-phase flow processes. The inclusion of interfacial coupling effects provides a more accurate way to describe dynamic spontaneous imbibition. Furthermore, the addition of variable inlet saturation allows one to establish whether the inlet-face saturation (S*) increases from the initial saturation to 1−Sro, or whether it can remain constant and equal to one minus the residual saturation to the non-wetting phase (1−Sro).     

Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

Journal of Optimization Theory and Applications - There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an...     

Synthesis of ultra‐low‐molecular‐weight polyethylene wax using a bulky Ti(IV) aryloxide–alkyl aluminum catalytic system

Complexes of titanium(IV) with bulky phenolic ligands such as 2‐tert‐butyl‐4 methylphenol, 2, 4‐di‐tert‐butyl phenol and 3,5‐di‐tert‐butyl phenol were prepared and characterized. These catalyst precursors, formulated as [Ti(OPh*)_n(OPrⁱ)_4?n] (OPh* = substituted phenol), were found to be active in polymerization of ethylene at higher temperatures in combination with ethylaluminum sesquichloride (Et₃Al₂Cl₃) as co‐catalyst. It was observed that the reaction temperature and ethylene pressure had a pronounced effect on polymerization and the molecular weight of polyethylene obtained. In addition, this catalytic system predominantly produced linear, crystalline ultra‐low‐molecular‐weight polyethylenes narrow dispersities. The polyethylene waxes obtained with this catalytic system exhibit unique properties that have potential applications in surface coating and adhesive formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

Spanning trees with many leaves in cubic graphs

For a connected graph G let L(G) denote the maximum number of leaves in any spanning tree of G. We give a simple construction and a complete proof of a result of Storer that if G is a connected cubic graph on n vertices, then L(G) ? [(n/4) + 2], and this is best possible for all (even) n. The main idea is to count the number of “dead leaves” as the tree is being constructed. This method of amortized analysis is used to prove the new result that if G is also 3-connected, then L(G) ? [(n/3) + (4/3)], which is best possible for many n. This bound holds more generally for any connected cubic graph that contains no subgraph K₄ - e. The proof is rather elaborate since several reducible configurations need to be eliminated before proceeding with the many tricky cases in the construction.     

The height of ideals and regular sequences

Summary We prove that given a Noetherian ringR and a finitely generatedR-inoduleM, there exists a finite set of prime idealsΛ inR such that the depth of an arbitrary idealI onM is determined by the height ofI modulo each of the primes inΛ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring. This article was processed by the author using the Springer-Verlag T_EX P Jourlg macro package 1991.     

Recent advances in modeling response-time distributions in real-time systems

Real-time systems are an important class of process control systems that need to respond to events under time constraints, or deadlines. Such systems may also be required to deliver service in spite of hardware or software faults in their components. This fault-tolerant characteristic is especially critical in systems whose failure can cause economic disaster and/or loss of lives. This paper reports recent research in the area of analytical modeling of the three major characteristics of real-time systems: timeliness, dependability, and external environmental dependencies. The paper starts with a brief introduction to analytical modeling frameworks such as Markov models and stochastic petri nets. This is followed by an examination of advances in modeling response-time distributions, reliability, distributed messaging services, and software fault-tolerance in real-time systems.     

An Approach for Microprobe Measurement and Modeling for Millimeter-Wave Application

This paper describes a simple method to check the performance of microprobe. The two-port S-parameters of the microprobe are determined by one-port S-parameters measurement using HP 8510XF Network Analyzer. Based on the measurement, an equivalent circuit model for the microprobe is presented and good agreement between the measurement results and modeling results is obtained.