Svein M. Skjaeveland

Two-phase pressure test analysis

A theoretical basis is given for well test analysis of solution-gas and gas-condensate reservoirs in the infinite-acting period. The study is limited to radial flow with a fully penetrating well in the center of the drainage area. Porosity and absolute permeability are constants and gravitational and capillary effects are neglected. The tests are conducted at constant surface rate. An analytical expression for the pressure - saturation relationship is derived from the time-dependent gas- and oil-flow equations. This relationship can be used at the wellbore to generate pseudopressure functions for drawdown and buildup that allow test interpretation using the liquid analogy. Theoretical developments are examplified by simulated drawdown and buildup tests in a solution-gas drive reservoir. 7 refs.

Water-Oil Capillary Pressure and Wettability Measurements Using Micropore Membrane Technique

This paper describes a new technique to simultaneously measure the capillary pressure curves and wettability indices for an oil - brine - rock system. By improving the porous plate method, the full cycle of four capillary pressure curves, i.e. spontaneous and forced drainage and imbibition, is measured in days instead of months. This is achieved by the use of thin oil- and water-wet micropore membranes and short samples with large diameter. Measurements have been done on sandstone and carbonate cores with wettabilities ranging from strongly water-wet to oil-wet. A reduction in experimental time by a factor of 10 or more is gained by the new method for a full cycle of the four capillary pressure curves. In addition, a new measure of wettability is suggested as an improvement of the USBM test, incorporating all four areas between the capillary pressure curves and the saturation axis. The new wettability index may be conceived as an extension of the Amott test, with the four saturation intervals weighted by the corresponding areas under the capillary pressure curve and may better discriminate between mixed-wet and spotted-wet samples.

Physically Based Capillary Pressure Correlation for Mixed-Wet Reservoirs From a Bundle-of-Tubes Model

It is shown that the main characteristics of mixed-wet capillary pressure curves with hysteretic scanning loops can be reproduced by a bundle-of-triangular-tubes model. Accurate expressions for the entry pressures are employed, truly accounting for the mixed wettability and the diverse fluid configurations that arise from contact-angle hysteresis and pore shape. The simulated curves are compared with published correlations that have been suggested by inspection of laboratory data from core plug experiments.

Capillary Pressure Correlation for Mixed-Wet Reservoirs

Summary For water-wet reservoirs, several expressions may be used to correlate capillary pressure, or height above the free water level, with the water saturation. These correlations all feature a vertical asymptote at the residual water saturation where the capillary pressure goes to plus infinity. We have developed a general capillary pressure correlation that covers primary drainage, imbibition, secondary drainage, and hysteresis scanning loops. The graph exhibits an asymptote at the residual saturation of water and of oil where the capillary pressure goes to plus and minus infinity, respectively. The shape of the correlation is simple yet flexible as a sum of two terms, each with two adjustable parameters and is verified by laboratory experiments and well-log data. An associated hysteresis scheme is also verified by experimental data. The correlation can be used to make representative capillary pressure curves for numerical simulation of reservoirs with varying wettability and to model and interpret flooding processes.

Capillary pressure scanning curves by the micropore membrane technique

Experimental procedures have been developed for capillary pressure hysteresis measurements. Capillary drainage and imbibition bounding curves (complete bounding cycle) and a number of scanning curves have been measured for a water-wet Berea core and an oil-wet reservoir core by the micropore membrane technique. The curves are measured both with stepwise and continuous change of the differential pressure. A continuous and slow change of capillary pressure gives considerable savings in experimental time. Reversibility of scanning curves is observed for the Berea core when the range of saturation reversal is less than 5% and may be explained by a pinning effect. The oil-wet reservoir core, however, exhibits a hysteresis loop even for this small saturation range. For saturation reversals in excess of 5%, the scanning curves for both samples form closed loops that are similar in shape to the bounding loop, i.e., for each sample, all hysteresis loops have the same shape but different sizes. This fact may be used to improve the algorithm for hysteresis modelling.

Steady-State Relative Permeability Measurements Corrected for Capillary Effects

A new method is presented which enables to interpret steadystate flow experiments eliminating errors caused by the capillary end-effect. This is achieved by retaining the capillary term in the equations that are used to inteqxet the flow data. The standard experimental procedure has to be extended to include variations in both total flowrate and the ratio of phase flowrates. Consistent values of saturation and relative permeability of each phase are then calculated at the inlet end. Necessary modifications in laboratory procedures and influence of hysteresis are discussed and the theoretical Ao.ralfimmamt ~~ u“ . U.”p. .“s.. o.ommlifiid h.r nanmmrir-1 cim~llntinri nf vA-~..y.m.lvu u, ..-.1”1 .“LU .7U,lu.a. s”,, “, coreflood experiments. Introduction During a steady-state procedure-for measurement of relative permeability curves, the total flowrate of oil and water is usually kept constant while their ratio is changed at the inlet end of the core. After a change, it is necessary to wait until equilibrium in the core is re-established, i.e., when both the pressure drop and the effluent flowrate ratio do not change with time. The individual flowrates and the pressure drop is then used to calculate the individual phase relative permeability values by Darcy’s law, relating them to the average saturation in the core, determined by material balance. The main inaccuracies of this method stem from the basic assumption that the capillary pressure can be neglected** ’13. disrnbu~ion along the core ;S non-uniform, and the pressure dmn is ~ff~~~n[ in IXKh nhme. The caDillarv effects are —.= -. =..—. . -—r...-—, difficult to avoid even if the total flowrate is high and for some rocks high flowrate cannot be reached for reasons like limited equipment capacity or stress that may cause rock damage. In this paper a new steady-state technique is described that includes capillary effects. The proposed experimental setup is not very much different from that of the conventional steady-state method. For a fixed fractional flow at the inlet, a number of steadystate experiments is required with varying total flowrate to include the capillary effect in the analysis of the data. The capillary pressure curve has to be measured separately. Theofy The following standard equations describe one-dimensional, two-phase flow of immiscible, incompressible fluids in a porous medium7, ~~i aPi Ui=– — ax’ i = 1,2 ap ut=– kkt@–k?@ Uh UA PC(S) =P2–P,. (1) From Eqs. (1) it follows that the expression for the velocity of the f~st phase is

Modelling of wettability alteration processes in carbonate oil reservoirs

Previous studies have shown that seawater may alter the wettability in the direction of more water-wet conditions in carbonate reservoirs. The reason for this is that ions from the salt (sulphat, magnesium, calsium, etc) can create a wettability alteration toward more water-wet conditions as salt is absorbed on the rock. In order to initiate a more systematic study of this phenomenon a 1-D mathematical model relevant for spontaneous imbibition is formulated. The model represents a core plug on laboratory scale where a general wettability alteration (WA) agent is included. Relative permeability and capillary pressure curves are obtained via interpolation between two sets of curves corresponding to oil-wet and water-wet conditions. This interpolation depends on the adsorption isotherm in such a way that when no adsorption of the WA agent has taken place, oil-wet conditions prevail. However, as the adsorption of this agent takes place, gradually there is a shift towards more water-wet conditions. Hence, the basic mechanism that adsorption of the WA agent is responsible for the wettability alteration, is naturally captured by the model. Conservation of mass of oil, water, and the WA agent, combined with Darcys law, yield a 2x2 system of coupled parabolic convection-diffusion equations, one equation for the water phase and another for the concentration of the WA agent. The model describes the interactions between gravity and capillarity when initial oil-wet core experiences a wettability alteration towards more water-wet conditions due to the spreading of the WA agent by molecular diffusion. Basic properties of the model are studied by considering a discrete version. Numerical computations are performed to explore the role of molecular diffusion of the WA agent into the core plug, the balance between gravity and capillary forces, and dynamic wettability alteration versus permanent wetting states. In particular, a new and characteristic oil-bank is observed. This is due to incorporation of dynamic wettability alteration and cannot be seen for case with permanent wetting characteristics. More precisely, the phenomenon is caused by a cross-diffusion term appearing in capillary diffusion term.

Relative permeability hysteresis in micellar flooding

Abstract This paper presents two-phase relative permeability curves for drainage and imbibition measured by the displacement method for (1) excess water-microemulsion, and (2) excess oil-microemulsion. The results show that the relative permeability curves are process dependent, even at the low interfacial tension of 0.1 mN/m for microemulsion-water, and 0.005 mN/m for microemulsion-oil. Three-phase displacement experiments are interpreted by Virnovskiis theory, which is an extension of the two-phase JBN-method. The measured three-phase relative permeability curves are compared with those from Stones method I. A new hysteresis scheme is implemented in a chemical simulator and allows for saturation reversal at any point, with different curvatures for drainage and imbibition. The validity of Virnovskiis theory is demonstrated, also when the relative permeabilities exhibit hysteresis.

Three-Phase Capillary Pressure Correlation For Mixed-Wet Reservoirs

We present new three-phase capillary pressure correlations that could be employed to model the dynamics of three-phase transition zones in mixed-wet reservoirs. The capillary pressures are expressed as a sum of two terms. One term is a function of a decreasing saturation and the other term a function of an increasing saturation. Thus the correlations depend on the type of displacement process, i.e., the direction of saturation change. The two-saturation dependency, together with the inclusion of adjustable parameters, ensures that the correlations account for different wettability conditions, saturation histories, and different relationships between the three capillary pressures. The correlations are compatible with a smooth transition between twoand three-phase flow if one of the phases appears or disappears. In particular, if the gas saturation becomes zero, it is shown that the correlations are reduced to a previously published two-phase correlation validated for oil/water systems in mixed-wet rock. Capillary pressure curves for various conditions, computed using a previously developed bundle-of-triangular-tubes model, are compared with the correlations, and the match is excellent in all cases. Finally, the correlations are validated experimentally by centrifuge measurements performed on water-wet cores.

Relative Permeability From Capillary Pressure

A new theory is reviewed for single-component, two-phase flow in porous media. It includes wettability and capillary pressure as integral parts of the thermodynamic description and does not make use of the relative permeability concept. However, by providing a capillary pressure correlation, we are able to extract relative permeabilities and to show good consistency between rock property correlations.