Pore-by-Pore Modelling,Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data

We predict waterflood displacement on a pore-by-pore basis using pore network modelling. The pore structure is captured by a high-resolution image. We then use an energy balance applied to images of the displacement to assign an average contact angle, and then modify the local pore-scale contact angles in the model about this mean to match the observed displacement sequence. Two waterflooding experiments on oil-wet rocks are analysed where the displacement sequence was imaged using time-resolved synchrotron imaging. In both cases the capillary pressure in the model matches the experimentally obtained values derived from the measured interfacial curvature. We then predict relative permeability for the full saturation range. Using the optimised contact angles distributed randomly in space has little effect on the predicted capillary pressures and relative permeabilities, indicating that spatial correlation in wettability is not significant in these oil-wet samples. The calibrated model can be used to predict properties outside the range of conditions considered in the experiment.

     

Synthesis and structure of novel (S)-1,6-dialkylpiperazine-2,5-diones and (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones

Eleven (S)-1,6-dialkylpiperazine-2,5-diones and five (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones were prepared in three steps from the corresponding (S)-α-amino acid esters comprising of reductive N-alkylation, N-acylation and cyclisation. The synthesis of (S)-1,6-dialkylpiperazine-2,5-diones has a broad scope allowing preparation of diketopiperazines with primary and secondary alkyl groups at N(1), while the synthesis of (3S,6S)-1,3,6-trialkylpiperazine-2,5-diones is limited to compounds with primary alkyl groups at N(1). Reductive alkylation of amino acid ester hydrochlorides by catalytic hydrogenation in the presence of a carbonyl compound proved to be a simple, efficient and general method for the preparation of stable (storable) α-alkylamino acid ester hydrochlorides. The structures of the novel compounds were determined by NMR and X-ray diffraction.     

Transformations of enaminones. A simple one-pot synthesis of imidazolone derivatives

Ethyl (5-benzoyl-2-oxo-3-substituted-2,3-dihydro-1H-imidazol-1-yl)carbamates 7 were prepared by the Michael addition of diethyl azodicarboxylate (3) to (E)-3-(dimethylamino)-1-phenylprop-2-en-1-one (2) followed by substitution of the dimethylamino group with primary amines 5a–n to afford a mixture of (E) and (Z) diethyl 1-(1-(substituted)amino)-3-oxo-3-phenylprop-1-en-2-yl)hydrazine-1,2-dicarboxylates (6a–n), followed by cyclization to give final products 7a–n. The intermediate 6i was isolated and characterized and transformed into 7i. All imidazolones 7a–n were synthesized in one pot reaction sequences with individual reactions being very clean.     

The Riesz Basis Property of an Indefinite Sturm–Liouville Problem with Non-Separated Boundary Conditions

We consider a regular indefinite Sturm–Liouville eigenvalue problem ?f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in a neighborhood of the turning points. We identify a class of non-separated boundary conditions for which, in addition to the local behavior of r in a neighborhood of the turning points, local conditions on r near the boundary are needed for the Riesz basis property. As an application, it is shown that the Riesz basis property for the periodic boundary conditions is closely related to a regular HELP-type inequality without boundary conditions.     

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions. II

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be selected to form a Riesz basis of a corresponding weighted Hilbert space.      

On the location of critical points of polynomials

Given a polynomial of degree and with at least two distinct roots let . For a fixed root we define the quantities and . We also define and to be the corresponding minima of and as runs over . Our main results show that the ratios and are bounded above and below by constants that only depend on the degree of . In particular, we prove that , for any polynomial of degree .

     

1,3-dipolar cycloaddition of diazomethane to azolopyridazines. The synthesis of isomeric 7-methyl-7h- and 8-methyl-8h-pyrazolo[4,3-d]azolopyridazmes

1,3-Dipolar cycloaddition of diazomethane to 6-chloro substituted azolopyridazines 1-4 produces isomeric pairs of 7-methyl-7H- 9-12 and 8-methyl-8H-pyrazolo[4,3-d]azolopyridazines 13-16 . The nucleophilic substitution of chlorine at position 6 affords the corresponding 6-amino 17, 20, 23, 26, 29,32,35 and 38 , 6-methoxy 18, 21, 24, 27, 30,33, 36 , and 39 and 6-hydrazino derivatives 19, 22, 25, 28, 31, 34, 37 , and 40 of these tricyclic systems.