Xudong Jing

Predicting the permeability of sandstone from image analysis of pore structure

A model is developed that allows accurate prediction of the permeability of a core sample of sedimentary rock, based on two-dimensional image analysis of its pore structure. The pore structure is idealized as consisting of a cubic network of pore tubes, with the tubes having an arbitrary distribution of cross-sectional areas and shapes. The areas and perimeters of the individual pores are estimated from image analysis of scanning electron micrographs of thin sections, with appropriate stereological corrections introduced to account for the angle between axis of the pore tube and plane of the thin section. The individual conductances of each tube are estimated from the measured areas and perimeters, using the hydraulic radius approximation. Variations in the pore diameter along the length of the tube are accounted for with a “constriction factor” whose derivation is based on laminar flow through an irregular tube. Effective-medium theory is used to find the effective single-tube conductance, based on the m...

An investigation of the effect of wettability on NMR characteristics of sandstone rock and fluid systems

Abstract Predicting reservoir wettability and its effect on fluid distribution and hydrocarbon recovery remains one of the major challenges in reservoir evaluation and engineering. Current laboratory based techniques require the use of rock–fluid systems that are representative of in situ reservoir wettability and preferably under reservoir conditions of pressure and temperature. However, the estimation of reservoir wettability is difficult to obtain from most laboratory experiments. In theory, it should be possible to determine the wettability of reservoir rock–fluid systems by nuclear magnetic resonance (NMR) due to the surface-sensitive nature of NMR relaxation measurements. Thus, NMR logs should in principle be able to give an indication of reservoir wettability, however, as yet there is no proven model to relate reservoir wettability to NMR measurements. Laboratory NMR measurements in representative and well-characterised rock–fluid systems are crucial to interpret NMR log data. A series of systematic laboratory experiments were designed using a range of sandstone core plugs with the aim of investigating the feasibility of using NMR measurements as a means to determine wettability. NMR T 2 spectrum measurements were performed in reservoir core plugs at different saturations and wettability states. The samples were first cleaned by hot solvent extraction, then saturated with brine and a drainage/imbibition cycle performed. At the lowest brine saturation the same samples were aged in crude oil and a further drainage/imbibition cycle performed. NMR transverse relaxation time, T 2 , was measured on fully saturated samples, at residual saturations and some intermediate saturation values. The wettability of the samples is evaluated using the Archies saturation exponent and by Amott-Harvey wettability index. The wettability of the cores studied ranged from mixed-wet to oil-wet. The NMR T 2 results for cleaned and aged reservoir core plugs, containing oil and water, show that fluid distribution and wettability can be deduced from such measurements. The results on aged core plugs suggest that the oil occupies a wide range of pore sizes and is in contact with the pore walls. The results presented in the paper suggest that NMR T 2 relaxation has the potential to be an alternative technique to evaluate rock wettability in the laboratory and in the reservoir.

Laminar flow through irregularly-shaped pores in sedimentary rocks

Steady-state, laminar flow of an incompressible fluid through prismatic tubes of irregular but constant cross-section is investigated. Several approximations for the hydraulic conductance (Saint-Venant, Aissen, hydraulic radius), some of which were originally proposed for the mathematically analogous problem of torsion of a prismatic elastic bar, are examined and tested for regular geometric shapes for which analytical solutions exist. For such shapes, the Saint-Venant and Aissen approximations are typically within 15% of the exact conductance, whereas the hydraulic radius approximation may be in error by as much as 50%. Conformal mapping and the boundary element method are then used to study the hydraulic conductance of sandstone pores from SEM images of Berea and Massilon sandstone. For these irregular shapes, the hydraulic radius approximation is much more accurate than either the Saint-Venant or Aissen approximation. Moreover, the errors in the hydraulic radius approximation may be of either sign, and thereby partially cancel out when large numbers of pores are considered, whereas the other two methods tend always to overestimate the hydraulic conductance of rock pores.

Dimensionless groups for three-phase gravity drainage flow in porous media

Abstract The downward displacement of oil by gas (either through gas cap expansion or by gas injection) at the crest of the reservoir is an attractive method of oil recovery. The drainage of oil under gravity forces is a potentially efficient method as it can reduce the remaining oil saturation to below that obtained after waterflooding. This paper describes a series of experiments of gas invasion under gravity-dominated conditions with special attention to the effects of wettability and water saturation on three-phase flow. The experiments were performed in bead-pack models by spontaneous gas invasion at both low and high water saturations with a spreading oil. Different oil recovery rates were observed depending on the wettability of the beads and initial water saturation. At irreducible water saturation, the process appeared to be less efficient for the oil-wet conditions, while similar oil recoveries are observed for both oil-wet and water-wet media at residual oil saturation. Different recovery rates occur with different fluid morphology, which depend on the matrix wettability and the balance between gravity, viscous and capillary forces. The results have been analysed using dimensionless groups. The Bond ( N B ) and capillary numbers ( N C ) were modified to include the 3-phase effects of gas, oil and water. However, for these cases the Bond and capillary numbers alone were insufficient to fully describe the dynamics of oil recovery by gravity drainage. Therefore, a new dimensionless group combining the effects of gravity and viscous forces to capillary forces was defined as: N = N B + A ( μ d / μ g ) N C , where A is a scaling factor (in all our experiments A =−17225) and ( μ d / μ g ) is the viscosity ratio between the displaced and displacing phase. A linear relationship was found between this new group and the total recovery for all the scenarios tested. The slope was approximately 40 for three cases, i.e., water-wet case at irreducible water saturation, and water-wet and oil-wet cases at residual oil saturation. The oil-wet case at irreducible water saturation has a larger slope, probably due to the blocking effect of water. These experimental results may be used as a benchmark to test theoretical models of three-phase flow under gravity dominated conditions. The new dimensionless group should improve the understanding of the pore scale mechanisms so that these processes can be included in the development of network models and in the processes of upscaling laboratory results.

Creeping flow through a pipe of varying radius

Creeping flow of a Newtonian fluid through tubes of varying radius is studied. Using an asymptotic series solution for low Reynolds number flow, velocity profiles and streamlines are obtained for constricted tubes, for various values of constriction wavelength and amplitude. A closed-form expression is derived to estimate the pressure drop through this type of tube. The results obtained with this new expression are compared to data from previous experimental and numerical studies for sinusoidally constricted tubes. Good agreement is found in the creeping flow regime for the pressure drop versus flow rate relationship. Our method offers an improvement over the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation), which does not account for the wavelength of the constrictions.

Laboratory investigation of wettability and hysteresis effects on resistivity index and capillary pressure characteristics

Abstract This paper focuses on the experimental aspects of resistivity index and water/oil capillary pressure measurements. A novel experimental procedure using water-wet and oil-wet membranes has been developed. Six potential electrodes and two current electrodes are used to provide resistivity readings across the sample and for seven adjacent intervals along the length of the core plug. The resistivity profile along the core length enables assessment of saturation distribution and end effects. The desaturation tests mimic different displacement processes that could occur during the history of the reservoir, for example, the displacement of water by oil during the initial hydrocarbon migration; the displacement of oil by mud filtrate around the wellbore during drilling and the displacement processes during the formation of transition zones under gravity/capillary forces and during waterflooding. Results from our studies indicate that both the phase-dependent and cycle-dependent hysteresis should be taken into consideration for resistivity index and capillary pressure measurements. The hysteresis effects also depend on the wettability of the rock samples.

Creeping Flow Through an Axisymmetric Sudden Contraction or Expansion

Creeping flow through a sudden contraction/expansion in an axisymmetric pipe is studied. Sampsons solution for flow through a circular orifice in an infinite wall is used to derive an approximation for the excess pressure drop due to a sudden contraction/ expansion in a pipe with a finite expansion ratio. The accuracy of this approximation obtained is verified by comparing its results to finite-element simulations and other previous numerical studies. The result can also be extended to a thin annular obstacle in a circular pipe

Effect of stress on the hydraulic conductivity of rock pores

Abstract We have made a detailed study of the effect of cross-sectional shape on the hydraulic conductance of rock pores. We consider laminar flow through a single tube with an irregular cross-section; constriction effects, and interconnectedness of pores, will be studied in a future work. We employ three approximate methods: the hydraulic radius approximation, which attempts to correlate the conductivity with the perimeter/area ratio, the Aissen approximation, which utilises a mean value of the conductance of the largest (smallest) circles that can be inscribed (circumscribed) inside (outside) the pore, and the Saint-Venant approximation, which is based on the polar moment of inertia of the shape. The Boundary Element Method is used to provide nominally “exact” estimates of the conductivity, but at the expense of large amounts of computational time. All four methods have been tested on pore shapes from SEM (Scanning Electron Microscope) images of thin-sections of Berea and Massilon sandstone. Surprisingly, the hydraulic radius approximation is the most accurate of the three approximate methods, giving, on average, less than 1% error. Finally, we combine these methods with previous results on the effect of stress on pore deformation, to study the stress-dependence of pore conductivity.

Network modelling of mixed-wettability on electrical resistivity, capillary pressure and wettability indices

Abstract This paper presents a network model that examines the effects of a physical development of pore-scale wettability on various petrophysical characteristics (in particular, electrical resistivity and capillary pressure) for a full-flooding cycle. The model incorporates pore-scale displacement mechanisms that are physically based. Models with different wettability type (correlated and uncorrelated to pore size), various fractions of mixed-wet pores and water advancing contact angles have been investigated. In each case, Amott–Harvey and USBM wettability indices have also been calculated and compared. A detailed description of wettability at the pore-scale was simulated to allow both water- and oil-wet regions existing within a single pore. Crevices of the pore space play a crucial role in simulating observed experimental electrical resistivity trends. This is because water in the crevices maintains continuity through the tube and conducts electrically. Our results suggest resistivity curves for non-uniform wettability samples show hysteresis and trends similar to experimental observations. Different wettability types can give a variety of electrical resistivity behaviour. This has important implications in determining the water saturation, from electric logs, of hydrocarbon reservoirs.

Comparison of methods for upscaling permeability from the pore scale to the core scale

Several methods are compared for estimating the core-scale permeability of a rock whose pore space is idealized as consisting of a cubic network of pore tubes having a distribution of pore-scale hy ...