Modeling Variable Density Flow and Solute Transport in Porous Medium: 2. Re‐Evaluation of the Salt Dome Flow Problem

Case 5, Level 1 of the international HYDROCOIN groundwater flow modeling project is an example of idealized flow over a salt dome. The groundwater flow is strongly coupled to solute transport since density variations in this example are large (20%).Several independent teams simulated this problem using different models. Results obtained by different codes can be contradictory. We develop a new numerical model based on the mixed hybrid finite elements approximation for flow, which provides a good approximation of the velocity, and the discontinuous finite elements approximation to solve the advection equation, which gives a good approximation of concentration even when the dispersion tensor is very small. We use the new numerical model to simulate the salt dome flow problem.In this paper we study the effect of molecular diffusion and we compare linear and nonlinear dispersion equations. We show the importance of the discretization of the boundary condition on the extent of recirculation and the final salt distribution. We study also the salt dome flow problem with a more realistic dispersion (very small dispersion tensor). Our results are different to prior works with regard to the magnitude of recirculation and the final concentration distribution. In all cases, we obtain recirculation in the lower part of the domain, even for only dispersive fluxes at the boundary. When the dispersion tensor becomes very small, the magnitude of recirculation is small. Swept forward displacement could be reproduced by using finite difference method to compute the dispersive fluxes instead of mixed hybrid finite elements.     

Modeling Variable Density Flow and Solute Transport in Porous Medium: 1. Numerical Model and Verification

A new numerical model for the resolution of density coupled flow and transport in porous media is presented. The model is based on the mixed hybrid finite elements (MHFE) and discontinuous finite elements (DFE) methods. MHFE is used to solve the flow equation and the dispersive part of the transport equation. This method is more accurate in the calculation of velocities and ensures continuity of fluxes from one element to the adjacent one. DFE is used to solve the convective part of the transport equation. Combined with a slope limiting procedure, it avoids numerical instabilities and creates a very limited numerical dispersion, even for high grid Peclet number.Flow and transport equations are coupled by a standard iterative scheme. Residual based criterion is used to stop the iterations. Simulations of an unstable equilibrium show the effects of the criteria used to stop the iterations and the stopping criterion in the solver. The effects are more important for finer grids than for coarser grids.The numerical model is verified by the simulation of standard benchmarks: the Henry and the Elder test cases. A good agreement is found between the revised semianalytical Henry solution and the numerical solution. The Elder test case was also studied. The simulations were similar to those presented in previous works but with significantly less unknowns (i.e. coarser grids). These results show the efficiency of the used numerical schemes.     

Overtone spectra and anharmonic resonances in haloacetylenes

In this work preliminary results are reported on an extensive vibrational analysis of the molecules HCCX and DCCX with X = F and Cl, in which a number of anharmonic resonances are analysed. The importance of quartic anharmonic resonances in these molecular types is reported involving the effective constants K₁₂₄₄ and K₁₂₅₅, and these are related to the corresponding resonances in acetylene and its isotopomers. The correct analysis of Fermi resonances and quartic anharmonic resonances is important not only in reproducing the high overtone energy levels, but also in fitting the observed rotational constants, and in determining the _r constants and hence the equilibrium rotational constants. In this paper we revise our recent analysis of the equilibrium structure of HCCF in the light of these effects.     

Stereoselective Retentive Domino Transmetalations of Secondary Alkyllithium Compounds to Functionalized Secondary Alkylcopper Reagents

Functionalized secondary alkyllithium reagents obtained by I/Li exchange from the corresponding secondary alkyl iodides undergo two successive transmetalations with Me₃SiCH₂ZnBr?LiBr and CuBr?2 LiCl?Me₂S to provide functionalized secondary alkylcopper compounds with high retention of configuration. These alkylcopper derivatives react further with electrophiles such as alkynyl esters, acid chlorides, allylic chlorides, ketals, ethylene oxide, and 3‐iodocyclopentanone with high retention of configuration. A related sequence of transmetalations with MeMgI and LaCl₃?2 LiCl allows a retentive addition of secondary alkyllithium reagents to acetone. The influence of the solvent on the configurational stability of secondary alkylzinc reagents is described.     

Organocatalytic Cascade Reactions: Towards the Diversification of Hydroisochromenes and Chromenes through Two Different Activation Modes

The organocatalytic enantioselective syntheses of functionalized hydroisochromenes and chromenes by trienamine‐mediated [4+2]‐cycloaddition/nucleophilic ring‐closing and iminium‐ion/aminal‐mediated oxa‐Michael/Michael/nucleophilic ring‐closing with 2‐nitroallylic alcohols are presented. The corresponding cycloadducts, with up to five stereocenters, are formed in good yield and excellent enantioselectivities. The synthetic applications of the obtained products have been demonstrated.     

Reductive lithiation of methyl substituted diarylmethylsilanes: application to silanediol peptide precursors

Reductive lithiation of methyl-substituted diarylmethylsilanes using lithium naphthalenide represents a practical method for the preparation of the corresponding silyl lithium reagents. Their addition to chiral sulfinimines affords versatile precursors to silanols and silanediols. The replacement of the currently used diphenylsilane motif by a more labile diarylsilane moiety allows the selective hydrolysis of one or two aryl groups by treatment with TFA.     

Diastereoselective Synthesis of Open‐Chain Secondary Alkyllithium Compounds and Trapping Reactions with Electrophiles

A practical stereoselective iodide–lithium exchange was used in the first general preparation of functionalized stereodefined acyclic secondary nonstabilized lithium reagents from the corresponding secondary alkyl iodides. These lithium reagents react with various electrophiles including carbon electrophiles with high retention of configuration. Kinetic data on the configurational stability of these acyclic alkyllithium reagents are given. This methodology offers a new entry to chiral synthons for the stereoselective synthesis of open‐chain molecules.     

Direct Access to Multifunctionalized Norcamphor Scaffolds by Asymmetric Organocatalytic Diels–Alder Reactions

A general organocatalytic cross‐dienamine activation strategy to produce chiral multifunctionalized norcamphor compounds having a large diversity in substitution pattern is presented. The strategy is based on a Diels–Alder reaction of an amino‐activated cyclopentenone reacting with most common classes of electron‐deficient olefins, such as nitro‐, ester‐, amide‐, and cyano‐substituted olefins, chalcones, conjugated malononitriles, CF₃‐substituted enones, and fumarates. The corresponding norcamphor derivatives are formed in good yield, excellent enantioselectivities, and with complete diastereoselectivity. Furthermore, it is demonstrated that quaternary stereocenters and spiro norcamphor compounds can be formed with high stereoselectivity. The present development provides a simple, direct, and efficient approach for the preparation of important norcamphor scaffolds.