Kenneth Stuart Sorbie

Theoretical study of the O(1D) + H2(1Σ g +) reactive quenching process

Classical trajectory calculations have been made for the system O(1 D) + H 2(1Σ g +) →OH(2Π) + H(2 S) using an analytical singlet ground state surface for H 2O. A rate constant of 1·73 × 10-10 cm3 molecule-1s-1 at 300 K has been obtained. The distribution of energy in the products is approximately 30 per cent in translation, 45 per cent in vibration and 25 per cent in rotation. Because of the preponderance of vibrationally long-lived trajectories, statistical theories gave a good interpretation of the gross features of the reaction.

Permeability tensors for sedimentary structures

Accurate modeling of fluid flow through sedimentary units is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. Most sedimentary rocks display structure from the mm or cm scale upwards. Flow simulation should therefore begin with grid blocks of this size in order to calculate effective permeabilities for larger structures. In this paper, we investigate several flow models for sandstones, and examine their impact on the calculation of effective permeability for single phase flow. Crossflow arises in some structures, in which case it may be necessary to use a tensor representation of the effective permeability. We establish conditions under which tensors are required, e.g., in crossbedded structures with a high bedding angle, high permeability contrast, and laminae of comparable thickness. Cases where the off-diagonal terms can be neglected, such as in symmetrical systems, are also illustrated. We indicate how the method of calculating tensor permeabilities may be extended to model multiphase flow in sedimentary structures.

Immiscible flow behaviour in laminated and cross-bedded sandstones

Abstract In this paper, we describe models of water/oil displacement in typical, geologically-structured media. We focus specifically on laminated and cross-bedded structures, since these are almost ubiquitous in clastic sedimentary reservoirs. The importance, for field-scale models, of properly representing the interaction of viscous, capillary and gravitational forces with small-scale heterogeneity is clearly demonstrated. Because the length-scale, δχ, of sedimentary lamination is of order 10−3 to 10−2 m, capillary forces, which are inversely proportional to δχ, may play a very significant role in determining the effective flow behaviour at larger scales. We show that there are important differences in oil recovery between cross-layer flow and along-layer flow. Differences of up to a factor of two in ultimate recovery may be produced by different representations of realistic clastic sedimentary structure (such as parallel lamination, cross-lamination and small-scale faulting). The significance of these findings is in determining the correct scale-up procedure for the multiphase effective flow parameters. We use the term geopseudo to describe correctly-scaled, multi-phase, pseudofunctions which capture the effects of small-scale sedimentary structure. Field-scale reservoir models must take account of these small-scale effects in order to lay claim to reasonable accuracy in production forecasts.

Mixing of injected, connate and aquifer brines in waterflooding and its relevance to oilfield scaling

Abstract Waterflooding is one of the most common methods of oil recovery although it does lead to certain production problems after water breakthrough, e.g. corrosion, scaling, etc. The issue of concern in this paper is mineral scale formation by brine mixing as occurs in barium sulphate (barite, BaSO 4 ) scaling. Barite formation in the production well and tubulars occurs in many oilfields when sulphate-rich injection water (IW) (often seawater (SW)) mixes with barium-rich formation water (FW) close to or in the wellbore. However, when a brine is injected into the reservoir, it may mix to some extent with the formation (or connate) brine deep within the system. Such in situ mixing of barium-rich and sulphate-rich brines would certainly result in barite deposition deep within the reservoir due to the low solubility and rapid kinetics of this precipitation process. Conversely, in order to estimate how much of this type of in situ precipitation might occur in reservoirs, we must be able to model the appropriate displacement processes incorporating the correct level of dispersive brine mixing in the reservoir formation. In this paper, all of the principal mechanisms of brine mixing in waterflood displacements are considered and modelled. Mixing between the IW, the oil leg connate water (CW) and the aquifer water (AQW) is analysed starting from a one-dimensional (1D) frontal displacement, extended Buckley–Leverett (BL) analysis. This particular mechanism occurs in all other types of displacement and reservoir mixing process including those in both heterogeneous layered systems and in areal flooding situations. Of vital importance to brine mixing is the level of reservoir sandbody dispersivity, and field values of this quantity are estimated. Results from the numerical modelling of oil displacement and IW/FW mixing are presented to illustrate various points which arise in the discussion. These calculations show that quite complex patterns of mixing of connate, aquifer and injection brines can occur in relatively simple two-dimensional (2D) systems. The significance of in situ brine mixing to barite scaling is discussed in some detail.

The rheology of pseudoplastic fluids in porous media using network modeling

Abstract This paper considers the rheology of pseudoplastic (shear thinning) fluids in porous media. The central problem studied is the relationship between the viscometric behavior of the polymer solution and its observed behavior in the porous matrix. In the past, a number of macroscopic approaches have been applied, usually based on capillary bundle models of the porous medium. These simplified models have been used along with constitutive equations describing the fluid behavior (usually of power law type) to establish semiempirical macroscopic equations describing the flow of non-Newtonian fluids in porous media. This procedure has been reasonably successful in correlating experimental results on the flow of polymer solutions through both consolidated and unconsolidated porous materials. However, it does not allow an interpretation of polymer flow in porous media in terms of the flows on a microscopic scale; nor does it allow us to predict changes in macroscopic behavior resulting from variations at a microscopic level in the characteristics of the porous medium such as pore size distribution. In this work, we use a network approach to the modeling of non-Newtonian rheology, in order to understand some of the more detailed features of polymjer flow in porous media. This approach provides a mathematical bridge between the behavior of the non-Newtonian fluid in a single capillary and the macroscopic behavior as deduced from the pressure drop-flow rate relation across the whole network model. It demonstrates the importance of flow redistribution within the elements of the capillary network as the overall pressure gradient varies. As an example of a pseudoplastic fluid in a porous medium, we consider the flow of xanthan biopolymer. This polymer is important as a displacing fluid viscosifier in enhanced oil recovery applications and, for that reason, a considerable amount of experimental data has been published on the flow of xanthan solutions in various porous media.

Semiclassical eigenvalues for non-separable bound systems from classical trajectories: The degenerate case

Semiclassical quantum conditions for arbitrary non-separable systems are derived. These lead to energy eigenvalues in good agreement with quantum results for both degenerate and non-degenerate two-dimensional (2D) systems. The applicability of these quantization rules is related to the structure of the caustics of the motion.

Analytical potentials for triatomic molecules from spectroscopic data: II. Application to ozone

A method already described to construct analytical potentials for triatomic molecules from spectroscopic data has been modified to cover several minima on the potential surface. A potential function for O3 has been obtained which satisfies the permutation symmetry of the molecule. It reproduces the harmonic force constants, equilibrium bond lengths and dissociation energy of the molecule and satisfies the criterion that there is no significant barrier to dissociation. The potential gives an optimum D3h configuration 2·76 eV above the true minimum (R = 1·28 A) and there is a transition state for internal isomerization in C2ν configurations which is 0·30 eV below the dissociation limit.

The impact of wettability on waterflooding: Pore-scale simulation

This paper describes the development and implementation of a pore-scale simulator into which pore-wettability effects have been incorporated. Relative permeability and capillary pressure curves from this steady-state model have been analyzed to allow better interpretation of experimental observations from a microscopic standpoint. The simulated capillary pressure data demonstrate that some standard wettability tests (such as Amott-Harvey and free imbibition) may give misleading results when the sample is fractionally wet in nature. Waterflood displacement efficiencies for a range of wettability conditions have been calculated, and recovery is shown to be maximum when the oil-wet pore fraction approaches 0.5. Furthermore, a novel experimental test is proposed that can be used to distinguish between fractionally wet and mixed-wet porous media. To date, no such satisfactory test exists.

Semiclassical eigenvalues for non-separable bound systems from classical trajectories: the higher energy levels

Previously proposed quantum conditions are used to calculate the higher eigenvalues of a simple two-dimensional (2D) potential from classical trajectories. A new modification to our earlier work is introduced to deal with problems arising from the complicated behaviour of the caustics in certain cases. Results are in excellent agreement with quantum-mechanical calculations. Our methods are shown to be competitive with quantum calculations in their ease of application for these upper levels. However, it is not possible to calculate certain semiclassical eigenvalues near the escape energy because corresponding trajectories are ergodic.

New analytic form for the potential energy curves of stable diatomic states

An analytic potential for stable states of diatomic molecules is proposed V=–De(1 +a1r+a2r2+a3r3)e–a1r. The constants a1, a2 and a3 are obtained from the harmonic, cubic and quartic force constants. The potential is shown to be superior to the Hulburt–Hirschfelder potential when tested on a least-squares basis against the spectroscopic RKR potential.