In order to reduce the operation count in vibration correlation methods, e.g., vibrational configuration interaction (VCI) theory, a tensor decomposition approach has been applied to the analytical representations of multidimensional potential energy surfaces (PESs). It is shown that a decomposition of the coefficients within the individual n-mode coupling terms in a multimode expansion of the PES is feasible and allows for convenient contractions of one-dimensional integrals with these newly determined factor matrices. Deviations in the final VCI frequencies of a set of small molecules were found to be negligible once the rank of the factors matrices is chosen appropriately. Recommendations for meaningful ranks are provided and different algorithms are discussed.

We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, we make use of the Maxwell–Stefan theory in a thermodynamically consistent way. For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.

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We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a di use-interface concept. Precisely, we suggest a compressible Navier-Stokes-Allen-Cahn model following [5]. Basic properties of the model are discussed. To cope with the fluid-wall interaction, we derive thermodynamically consistent boundary conditions that account for dynamic contact angles. We briefly discuss an discontinuous Galerkin scheme which approximates the energy dissipation of the system exactly and illustrate the results with a series of numerical simulations. Currently, these simulations are restricted to static contact angle boundary conditions.

This paper describes special aspects and problems encountered when analysing transient pressure tests in low permeability formations. A constant rate approach has been widely used in oil and gas industry for analysing well tests. However, in low permeability formations special problems arise in applying the constant rate analysis method. First, using the constant rate approach the pretest borehole history must be approximated. As it acts as a long term constant pressure injection or production event while drilling through the test interval it results in the creation of a non-uniform pressure distribution in the vicinity of the borehole. Numerous field examples show that after the packer system is set a distinct pressure build-up or fall-off occurs. The non-uniform pretest pressure distribution cannot be neglected in the analysis of the subsequent test events e.g. DST sequence. Significant errors may occur in estimation of the reservoir parameters, in particular the initial pressure. Second, the use of the constant rate approach in analysing the DST sequence in low permeability formations leads to errors unless the rate sequence, and thus superposition function, is constructed properly. A new method of rate discretisation for the initial discontinuous events (the beginning of the 1st. and 2nd. DST flow period) is presented and the errors resulting from neglecting the true rate sequence are discussed. Field examples present the application of both concepts. The main objective of this paper is to show that by simple measures it is possible to take account of borehole history and apply rate discretisation to improve the accuracy of interpretation when using standard constant rate analysis software. Introduction Most of the standard petroleum interpretation software (Interpret/2, Pansystem, Weltest and others) use a constant rate solution to solve the diffusivity equation for a variety of reservoir models and boundary conditions. New, powerful computers and sophisticated data acquisition allow for exact interpretation of tests with strongly varying rates. Complex rate history does not prevent from using rigourous multirate superposition analysis provided the rate sequence is known. However, when testing low permeability intervals special problems arise since the rates necessary for such analysis are often not available. The first type of the problem occur if test events are preceded by unrecorded flow events in the test interval due to so called "pressure history". Numerous analyses of tests showed that the borehole history characterization was of crucial importance for correct interpretation of the data in low permeability formations. The typical example for such influence is that after the packer system is set and the shut-in valve closed a distinct pressure build-up or fall-off occurs. The non-uniform pretest pressure distribution cannot be neglected in the analysis of the subsequent test events e.g. DST sequence. Significant errors may occur in estimation of the reservoir parameters, in particular the initial pressure. Due to usually extreme small mud losses during drilling it is not possible to rely on the drilling fluid monitoring data to derive the historical rates. Alternative methods are applied to estimate these rates. A good practice for historical rate determination is the direct measurement of fluid level change in the test string prior to the initial pressure recovery phase; this is generally recommended when testing low permeability formations. Deriving the historical rate from the water level measurement gives reliable results, except when major pressure differences occur in the test interval shortly before testing. P. 393^