Relative reactivity enhancement of (Me5Cp)2ZrCl2 in mixture with (1,2,4-Me3Cp)2ZrCl2 during ethene/1-hexene copolymerization

Dual-site ethene/1-hexene copolymerizations with MAO-activated (1,2,4-Me₃Cp)₂ZrCl₂ and (Me₅Cp)₂ZrCl₂ catalysts were performed. Copolymers with narrow molecular weight distributions and bimodal short chain branching distributions could be produced. The combined catalyst system demonstrates a number of discrepancies from an expected average behavior of the individual sites. Dual-site (1,2,4-Me₃Cp)₂ZrCl₂/(Me₅Cp)₂ZrCl₂ systems produce copolymers with lower incorporation than expected. Clear evidences for relative activity enhancement of the (Me₅Cp)₂ZrCl₂ catalyst in the mixture were observed in melting endotherms and Crystaf profiles. Molecular weights obtained by the mixture were higher than for any of the individual catalysts. A similar effect is observed for a dual-site system of the (1,2,4-Me₃Cp)₂ZrCl₂ catalyst together with the Me₄Si₂(Me₄Cp)₂ZrCl₂ catalyst as an alternative to (Me₅Cp)₂ZrCl₂.     

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.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

The converse of the four vertex theorem

We establish the converse to the four vertex theorem without the positivity condition.

     

Pressure and trimethylaluminum effects on ethene/1‐hexene copolymerization with methylaluminoxane‐activated (1,2,4‐Me3Cp)2ZrCl2: Trimethylaluminum suppression of standard termination reactions after 1‐hexene insertion

Ethene homopolymerizations and copolymerizations with 1‐hexene were catalyzed by methylaluminoxane‐activated (1,2,4‐Me₃Cp)₂ZrCl₂. Investigations of the effects of various pressures on the homopolymerizations and copolymerizations and of the effects of different concentrations of trimethylaluminum (TMA) on the copolymerizations were performed. The characteristics of the ethene/1‐hexene copolymers agreed with expectations for changes in the ethene concentration: the incorporation of 1‐hexene decreased, whereas the melting point and crystallinity increased, with increasing pressure. The main termination mechanism of the homopolymerizations was β‐hydrogen transfer to the monomer. Termination mechanisms resulting in vinylidene unsaturations dominated in the copolymerizations. Standard termination mechanisms producing vinyl and trans‐vinylene unsaturations occurred in parallel and were not influenced by the ethene or TMA concentration. In addition, some chain transfer to TMA, producing saturated end groups after hydrolysis, occurred. Copolymerizations with different additions of TMA, with the other polymerization conditions kept constant, showed that the catalytic productivity [tons of polyethylene/(mol of Zr h)], the 1‐hexene incorporation, and the molecular weight (from gel permeation chromatography) were independent of the TMA concentration. Surprisingly, the vinylidene content decreased almost linearly with increasing TMA concentration. TMA might have coordinated to the catalytic site after 1‐hexene insertion and rotation to the β‐agostic state and, therefore, suppressed the standard termination reactions after 1‐hexene insertion. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2584–2597, 2005     

On the nonequilibrium segregation state of a two-phase mixture in a porous column

The problem of segregation of a two-phase multicomponent mixture under the action of thermal gradient, gravity and capillary forces is studied with respect to component distribution in a thick oil-gas-condensate reservoir. Governing equations are derived on the basis of nonequilibrium thermodynamics. A steady state of the two-phase mixture with nonzero diffusion fluxes and exchange between phases is described. In the case of binary mixtures analytical formulae for saturation, component distribution and flow in the two-phase zone are obtained.     

Displacement of trapped oil from water-wet reservoir rock

Displacement of oil trapped in water-wet reservoirs was analyzed using percolation theory. The critical capillary number of the CDC (Capillary Desaturation Curve) was be predicted based on the pore structure of the medium. The mobilization and stability theories proposed by Stegemeier were used to correlate oil cluster length to the capillary number needed to mobilize the trapped oil. Under the assumption that all pore chambers have the same size, a procedure was developed using the drainage capillary pressure curve and effective accessibility function to predict the CDC curve for a given medium. The prediction of critical capillary numbers was compared with the experimental data from 32 sandstone samples by Chatzis and Morrow. Also, the CDC curve of one sandstone sample was calculated using the procedure developed in this work and compared with the measured data. Very good agreements were obtained.Nomenclature a average radius of a liquid filament [m] - c constant - D pore throat diameter [m] - D _a advancing diameter of an oil cluster [m] - D _af average flowing diameter of the medium [m] - D _da controlling diameter of the medium [m] - D _r receding diameter of an oil cluster [m] - D _X difficulty index - f ratio of length to average radius of an oil cluster - F _i interfacial forces [N] - F _p force from pressure gradient [N] - g wettability function - k absolute permeability [m²] - l length of an oil cluster [m] - l _m mobile oil cluster length [m] - l _s stable oil cluster length [m] - l _w wavelength [m] - n* relative length of an oil cluster - N _c 1 capillary number defined by Equation (1) - N _c 2 capillary number defined by Equation (2) - P _b probability of oil filling a pore - P _c percolation threshold value - p _c capillary pressure [N/m²] - r radius of a pore [m] - r _e average pore radius [m] - S _n the nonwetting phase saturation - S _or residual oil saturation - S _orn normalized oil saturation - v Darcy flow rate [m/s] - X _t total fraction of pores - X _t ^a accessibility - X _e ^a effective accessibility - (D) pore throat size distribution function - _a advancing contact angle - _r receding contact angle - porosity - density of the liquid [kg/m³] - constant in Equation (4) - dynamic length of an oil cluster [m] - interfacial tension [N/m] - viscosity [N/(m s)] - p pressure gradient [N/m³]