Imbibition Relative Permeability Curves Research Articles

An accelerated process-based method for the accurate computation of relative permeability from direct simulations of two-phase flow on micro-computed tomography images of porous media

Pore-scale forces have significant effects on the macroscopic behavior of multi-phase flow through porous media. We develop a robust and accurate accelerated process-based method for the computation of relative permeability from direct simulations of pore-scale two-phase flow on micro-computed tomography images. In the pressure drop calculation, we take advantage of an existing analysis that establishes a relationship between pore-scale forces and Darcy-scale pressure drops using an energy-conservation approach. We establish a thermodynamically consistent approximation of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each flowing phase for the first time within the context of a free-energy lattice Boltzmann method (LBM). In addition, we propose and test a new computationally efficient partial-mirror periodic boundary condition for a fully coupled visco-capillary pore-scale flow simulator based on a free-energy LBM. The new boundary condition is imposed only in the main flow direction and significantly reduces the computational cost of the process-based relative-permeability computation protocol at a small compromise on accuracy.We first compute primary-drainage and subsequent imbibition relative permeability curves for a reservoir sandstone rock sample. We use this real-reservoir dataset to validate the pressure drop computation method and the partial-mirror periodic boundary condition. We then simulate the entire drainage and imbibition cycle using an extensively studied Berea sandstone dataset. We quantitatively demonstrate that pore-scale direct numerical simulation-based relative permeability curves computed with our novel process-based method agree well with experimental steady-state relative permeability measurements. We also quantitatively demonstrate that the new partial-mirror periodic boundary condition accelerates the relative permeability computations 4 to 13 times.

Improved method for complete gas-brine imbibition relative permeability curves

Standard test methods for measuring imbibition gas-brine relative permeability on reservoir core samples often lead to non-uniform brine saturation. During co-current flow, the brine tends to bank up at the sample inlet and redistributes slowly, even with fractional flow of gas to brine of 400:1 or more. The first reliable Rel Perm point is often only attained after a brine saturation of around Sw=40% is achieved, leaving a data gap between Swirr and this point. The consequent poor definition of the shape of the Rel Perm function can lead to uncertainty in the performance of gas reservoirs undergoing depletion drive with an encroaching aquifer or subjected to a water flood. We have developed new procedures to pre-condition brine saturation outside of the test rig and progress it in small increments to fill in the data gap at low Sw, before continuing with a co-current flood to the gas permeability end-point. The method was applied to series of sandstone samples from gas reservoirs from the NW Shelf of Australia, and a Berea standard. We found that the complete imbibition relative permeability curve is typically ‘S’ shaped or has a rolling over, convex-up shape that is markedly different from the concave-up, Corey Rel Perm curve usually fitted to SCAL test data. This finding may have an economic upside if the reservoir produces gas at a high rate for longer than was originally predicted based on the old Rel Perm curves.

Complete gas-brine imbibition relative permeability curves increase confidence in gas field performance

The standard methods used for measuring gas relative permeability during brine imbibition have been found to be inadequate as the resulting curves are incomplete and may include invalid points. CSI...

A New Methodology to Characterize Wettability Alteration in Network Modeling

abstract In network models, the characterization of wettability for porous media is of great significance. In this article, an index, F, called the wettability alteration index, is defined and applied to evaluate the degree of wettability change after drainage displacement. This new parameter is also analyzed as a function of interfacial tension, size and shape of pores, and capillary pressure. A new method to characterize the wettability of a porous medium after primary drainage is proposed. The imbibition relative permeability curves obtained using the wettability alteration index are compared to those obtained using traditional methods.

Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.

Drainage and imbibition relative permeabilities at near miscible conditions

The changes in gas and oil relative permeabilities as miscibility is approached are of particular importance in multi-contact miscible displacements. These changes are a function of the detailed phase behaviour of the fluids and their physical properties as well as the properties of the porous medium itself. In this work, we investigate the behaviour of two-phase drainage and imbibition relative permeability curves of four, different, equilibrated fluid pairs from a three component, two-phase system (cyclohexene, isopropyl alcohol and water) that exhibits a critical point at ambient conditions. The tie-lines of these fluid pairs are at varying distances from the system's critical point. Equilibrium phase compositions and interfacial tensions (IFT) were determined for each of the four fluid pairs. Dynamic displacements were then performed in a linear two dimensional, bead-pack. Unsteady state, drainage and imbibition relative permeabilities were determined for the various pre-equilibrated mixtures. The experimental results show a clear change in relative permeability as the fluid pairs approach the critical point. As the interfacial tension decreases the non-wetting phase relative permeability increases more rapidly than the wetting phase relative permeability and hysteresis becomes less important. Two correlations [Coats, K.H., 1980. An equation of state compositional model: SPE J, 20 (5): 363-376.; Whitson, C.H., and Fevang, Ø., 1997. Generalized pseudo pressure well treatment in reservoir simulation. In Proc., IBC Conference on Optimization of Gas Condensate Fields.], commonly used to model the changes in relative permeability with interfacial tension, and the development of miscibility, were compared with the experimental data. The Coats correlation, which uses a single adjustable parameter to model the changes in both relative permeabilities and residual oil saturation as a direct function of the IFT, yielded an unacceptable match to the experimentally determined fractional flow. However the Whitson–Fevang correlation, which relates the changes in relative permeability to the capillary number using two adjustable weighting functions, presents a satisfactory match.

A technique for measuring two-phase relative permeability in porous media via X-ray CT measurements

A novel method for computing two-phase relative permeability curves from the results of spontaneous imbibition experiments is presented. Using a specially constructed imbibition cell and an X-ray Computed Tomography (CT) scanner, we obtain accurate measurement of saturation profiles along the length of cores as a function of time. The saturation profile history allows direct computation of the relative permeability for both phases from a single experiment when used in combination with a previously measured capillary pressure curve. Results are unique within experimental error. The proposed procedure works equally well for spontaneous and forced cocurrent imbibition. It was tested thoroughly using synthetic and experimental spontaneous imbibition data, for water–air and water–oil systems. Study showed that the pressure-gradient history can be neglected during calculations of air–water relative permeability; however, pressure-gradient data improves the accuracy of measurement for viscous oil flowing at high water saturation. Test results are described within the paper. Advantages include the incorporation of capillary forces and no requirement for steady-state conditions. This method is useful to measure imbibition relative permeability curves, especially in low permeability rocks at relatively low wetting phase saturations. In such systems, it is laborious to reach multiple steady states and capillary forces are significant so that classical unsteady-state techniques do not apply.

Effect of Brine Salinity and Crude-Oil Properties on Oil Recovery and Residual Saturations

SummaryCentrifuge experiments were conducted on Berea cores to measure the drainage and imbibition relative permeabilities in two-and three-phase systems. Three crude oils, Prudhoe Bay and Shell Mars A-1 and A-20 crude were used in our tests. No effect on oil recovery was obtained in the drainage experiments when the crude oil was displaced by air at connate water. However, in the imbibition experiments the oil recovery increased significantly with the salinity of the connate brine. The salinity of the displacing brine had no significant influence on the oil recovery. The relative permeability curves obtained during drainage were also found to be insensitive to the salinity of the brine. However, the imbibition relative permeability curves show strong salinity dependence. A comparison of the two crude oils and a nonpolar mineral oil indicates that the more water-wetting Mars crude oil shows a higher oil relative permeability at the same bond number compared to the mixed-wetting Prudhoe Bay crude oil. The salinity dependence of the residual saturations and the relative permeabilities clearly indicate that the change in wetting properties of the rocks surfaces from water-wet to mixed-wet during the drainage process is an important factor controlling the imbibition relative permeability curves. This suggests that the performance of waterfloods will be strongly affected by the composition of the crude oil and its ability to wet the rock surfaces, the salinity of the connate brine in the reservoir, and the height above the oil/water contact.

Use of Geology in the Interpretation of Core-Scale Relative Permeability Data

Summary A number of factors, such as wettability, pore-size distribution, and core-scale heterogeneity, are known to affect the measured relative permeability in core plug samples. This paper focuses on the influence of geological structure at the laminaset scale on water-oil imbibition relative permeability curves. The endpoint positions and curve shapes vary as a function of the type of internal heterogeneity, the flow rate, and the assumptions on the pore-scale petrophysics (e.g. wettability). Interaction between the capillary forces and heterogeneity can occur at the cm-dm scale, which results in widely varying two-phase flow behavior for rocks with the same single-phase permeability. The geometry of heterogeneity as expressed in standard geological descriptions (e.g., cross-laminated, ripple-laminated, plane-laminated) can be translated into features of the expected relative permeability behavior for each rock type, thus aiding the interpretation of relative permeability data. We illustrate how our findings can help to interpret sets of relative permeability data from the field, using some examples from the Admire sand, El Dorado Field, Kansas.

Novel Relations for Drainage and Imbibition Relative Permeabilities

Abstract Exponential four- and five-parameter equations are proposed for gas/oil drainage and water/oil imbibition relative permeability curves. These equations match the experimentally determined curves, in particular at and near their initial points and endpoints, better than standard Corey et al.1 and polynomial approximations. Some of these parameters have a physical meaning; the others can be determined by nonlinear regression on the experimental data points, and can be adjusted to represent pseudorelative permeability curves. The proposed equations are particularly suitable to describe gas percolation in numerical model simulation of dissolved-gas-drive reservoirs.

Imbibition Relative Permeability in Unconsolidated Porous Media

Abstract Experimental work is reported which shows that consolidated rocks and unconsolidated porous media exhibit different imbibition flow behavior. At a given saturation the imbibition nonwetting permeabilities for a rock are smaller than the drainage permeabilities. The contrary happens for unconsolidated aggregates - imbibition nonwetting permeabilities are larger than drainage ones. A similar difference is observed for the wetting phase. Imbibition permeabilities are larger than drainage ones for a consolidated rock but smaller than drainage permeabilities for an unconsolidated medium. The results of these differences are examined for two cases.Flooding Efficiency - Craig's scheme for the computation of production history of a five-spot water flood is shown to agree extremely well with experimental results obtained when using a system packed with glass spheres if imbibition relative permeability curves are used.Alcohol-Slug Displacement - Published theory on oil displacement by alcohol slugs bas been questioned despite the apparent agreement between predicted and observed results. The present work suggests that, if imbibition relative permeability curves characteristic of the unconsolidated media used in the early experiments had been available to make the predictions, the inadequacy of the theory would have been immediately evident. The experimental work shows that poorly consolidated formations tend to behave like unconsolidated media. Finally, it is shown that the difference in imbibition behavior is directly related to pore-size distribution and cementation. PART 1 - THE FLOW BEHAVIOR OF UNCONSOLIDATED AGGREGATES Introduction Experiments on scaled models of field reservoirs are useful for studying new displacement processes which are incompletely understood. Even when a mathematical description is possible, the solution might be difficult and complex. An answer obtained from a scaled model is extremely valuable in such cases. A great amount of work, therefore, has been devoted to the derivation of scaling laws. Similarity groups have been defined which assumethat the relative permeability curves of the prototype and the model are the same whether the displacement is an imbibition or a drainage process andthat there is a linear relationship between the capillary pressure of the model and the prototype. For practical reasons (simplicity in the preparation of models, duration of the experiments, etc.), the porous media of laboratory models are usually unconsolidated packs of sand or glass particles. Hence, unless the capillary and flow characteristics of unconsolidated and consolidated systems are identical, the model data are applicable only to unconsolidated formations. The usefulness of scaled-model studies may then be seriously restricted since most oil-bearing sands are consolidated. Perkins and Collins suggested the use of model and prototype curves normalized with respect to both relative permeability and saturation to improve compliance with scaling criteria. Even this technique does not give a satisfactory model-prototype match. This paper reports an observation of two-phase flow in unconsolidated sands which shows that, for most displacements, "scaling" in the strict sense of the word is not even qualitatively feasible with a sand model. It provides, however, a firm foundation for testing a theory by matching it with observed performance of laboratory-size models. EXPERIMENTAL As a part of a basic study of packed aggregates, the relative permeability of glass-spheres and sand-grain packs was measured with capillary control. The fluids were oil and air. SPEJ