Low Wetting Phase Saturations Research Articles

Exponential Capillary Pressure Functions in Sedimentary Rocks

The Brooks-Corey power-law capillary pressure model is commonly imposed on core analysis data without verifying the validity of its underlying assumptions. The Brooks-Corey model, originally developed to model the pressure head during the drainage of soil, is only valid at low wetting phase saturations. However, such models are often applied in petroleum production simulations and may lead to erroneous recovery factors when the saturation range of interest is far from the end points. We demonstrate that exponential models work much better for capillary pressure compared to the Brooks-Corey model over a wide saturation range. Mercury injection porosimetry, petrographic image analysis, and magnetic resonance studies suggest that the pore and throat size distribution in many rocks are log-normally distributed. This fact was previously employed to calculate the capillary pressure function as a function of saturation for pore size distributions described by atruncated log-normal distribution. Employing a Taylor series expansion, we simplify the random fractal capillary pressure model of Hunt to Pc = exp(a − bS), where S is the wetting phase saturation, and a and b characteristic of the porous medium. An extensive dataset of seventeen centrifuge capillary pressure measurements were used in this research to demonstrate the merit of the new method. For both sandstones and carbonates, the logarithm of capillary pressure showed a linear relationship with saturation as observed by magnetic resonance imaging centrifuge capillary pressure measurements over a wide saturation range. This work demonstrates that: (a) in semi-log plots of capillary pressure as a function of saturation, capillary pressurewill vary linearly over a wide saturation range, (b) such a plot as described in (a) will show the uni-or bimodal pore size distribution of the rock, (c) the exponential capillary pressure function simplifies analytical modelsthat use the capillary pressure function, for example oil recovery models for fractured reservoirs.

A Pseudo‐Vertical Equilibrium Model for Slow Gravity Drainage Dynamics

AbstractVertical equilibrium (VE) models are computationally efficient and have been widely used for modeling fluid migration in the subsurface. However, they rely on the assumption of instant gravity segregation of the two fluid phases which may not be valid especially for systems that have very slow drainage at low wetting phase saturations. In these cases, the time scale for the wetting phase to reach vertical equilibrium can be several orders of magnitude larger than the time scale of interest, rendering conventional VE models unsuitable. Here we present a pseudo‐VE model that relaxes the assumption of instant segregation of the two fluid phases by applying a pseudo‐residual saturation inside the plume of the injected fluid that declines over time due to slow vertical drainage. This pseudo‐VE model is cast in a multiscale framework for vertically integrated models with the vertical drainage solved as a fine‐scale problem. Two types of fine‐scale models are developed for the vertical drainage, which lead to two pseudo‐VE models. Comparisons with a conventional VE model and a full multidimensional model show that the pseudo‐VE models have much wider applicability than the conventional VE model while maintaining the computational benefit of the conventional VE model.

Image-based relative permeability upscaling from the pore scale

High resolution images acquired from X-ray μ-CT are able to map the internal structure of porous media on which multiphase flow properties can be computed. While the resolution of a few micrometers may be sufficient for capturing the pore space of many sandstones, most carbonates exhibit a large amount of microporosity; pores which are below the image resolution and are not resolved at specific resolution. Neglecting the effect of micropores on fluid flow and transport properties of these rocks can cause erroneous results in particular at partial saturations. Current image-based pore scale models typically only consider macropores for simulating fluid flow. In this paper, we quantify the effect of microporosity on the effective permeability of the wetting phase for heterogeneous model structures with varying amount of micro-to-macro porosity. A multi-scale numerical approach is proposed to couple an average effect of micropores with an explicit representation of macropores. The Brinkman equation is solved using a lattice Boltzmann formulation to facilitate the coupling of Darcy and Stokes equations in micropores and macropores, respectively. The results show good agreement between the fine scale solution and the results of the upscaled models in which microporous regions are homogenised. The paper analyses in particular the choice of the momentum sink parameter at low wetting phase saturations. It is shown that this parameter can be found using either a flux-based calculation of permeability of microporous regions or chosen purely on the basis of the effective permeability of these regions.

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.

Capillary Pressure, Water Relative Permeability, Electrical Conductivity and Capillary Dispersion Coefficient of Fractal Porous Media at Low Wetting Phase Saturations

SUMMARY Transport properties are critical for many reservoir engineering calculations. This work describes recent progress in modeling transport properties of natural porous media at low saturations of a wetting phase, i.e. when total wetting phase saturation Sw is the sum of thin-films and pendular structures inventories. Capillary pressure Pc, wetting phase relative permeability krw, electrical conductivity σw, and capillary dispersion coefficient Dc have been observed to obey power laws in the wetting phase saturation. We relate power-law behavior at low wetting phase saturations, i.e. at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of natural porous media. If wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase we deduce the power laws X=SwbX, with X = Pc, krw, σw and Dc, where for capillary pressure bPc=−1/3−D, for wetting phase relative permeability bkrw=3/m3−D, for electrical conductivity bσw=1/m3−D, and for capillary dispersion coefficient bDc=3−m4−D/m3−D, where m is the exponent in the relation of disjoining pressure and film thickness and D is the fractal dimension of the surface between the pore space and grains or matrix. Recent experimental work lends support to these scaling laws in the cases of natural sandstones and clayey soils. Recent displacement experiments show anomalously rapid spreading of wetting liquid during imbibition into a prewet porous medium. We explain this phenomenon, called hyperdispersion, as viscous flow along fractal pore walls in thin films of thickness h governed by disjoining forces and capillarity.

Scaling of Transport Properties of Reservoir Material at Low Saturations of a Wetting Phase

AbstractTransport properties of natural porous media have been observed to obey scaling laws in the wetting phase saturation. Previous work relates power-law behavior at low wetting phase saturations, i.e., at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of porous media. Here, we present recent combined porousplate capillary pressure and electrical conductivity data of Berea sandstone at low saturations that lend support to the scaling laws. Power law is interpreted in terms of the exponent m in the relation of surface forces and film thickness and the fractal dimension D of the interface between pore space and solid matrix. Simple determination of D from capillary pressure and m from electrical conductivity data can be used to rapidly determine wetting phase relative permeability and capillary dispersion coefficient at low wetting phase saturations.

Evaluation of the High-Speed Centrifuge Technique for Determining Capillary Pressure at Low Wetting-Phase Saturations

ABSTRACTRecent experimental studies of the high-speed centrifuge technique have indicated that the method, if properly used, yields results which are in accordance with other methods. These studies have also shown that the concept of an irreducible wetting phase saturation is not valid. In the present paper work is reported in which these previously presented results are extended to both higher and lower capillary pressures. Air/liquid data have been obtained with n-decane as the wetting phase and are compared with new data (as well as with the previously reported data) for the air/brine system. The study involved 242 days of centrifugation and utilized 10 different Berea plug samples and 5 different high permeability plug samples taken from a producing reservoir.The linear relationship between log Pc and log <Sw> (or log Sw, as observed in previous work) was confirmed for Berea samples over the average saturation range from about 30 percent down to 10 percent. For lower average saturations, the saturation data are not sufficiently precise either to (1) demonstrate conclusively the persistence of this relationship, or (2) prove the breakdown of the Hassler boundary condition. For three of the five producing reservoir samples, it was found that two different linear segments characterized the log Pc versus log <Sw> relationship, with a rather sharp transition occurring in the 30 to 40 percent average saturation range.

Fluids in fractal porous media: scaling of transport properties

Abstract This work describes recent progress in modeling transport properties of natural porous media at low saturations of a wetting phase, i.e. when total wetting phase saturation Sw is the sum of thin-films and pendular structures inventories. Capillary pressure Pc, hydraulic conductivity Kw, electrical conductivity σw, and the capillary dispersion coefficient Dc have been observed to obey power laws in the wetting phase saturation. We relate power-law behavior at low wetting phase saturations, i.e. at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of natural porous media. If wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase we deduce the power laws X = SbXw, with X = Pc, Kw, σw and Dc, where for capillary pressure bPc = -1/(3 − D), for hydraulic conductivity bKw = 3/m(3 − D), for electrical conductivity bσw = 1/m(3 − D), and for capillary dispersion coefficient bDc = [3 − m(4 − D)]/m(3 − D), where m is the exponent in the relation of disjoining pressure and film thickness and D is the fractal dimension of the surface between the pore space and solid matrix. Recent experimental work lends support to these scaling laws in the cases of natural sandstones and clayey soils. Recent displacement experiments show anomalously rapid spreading of wetting liquid during imbibition into a prewet porous medium. We explain this phenomenon, called hyperdispersion, as viscous flow along fractal pore walls in thin films of thickness h governed by disjoining forces and capillarity. Asymptotic analysis of the “capillary diffusion” equation indicates hyperdispersive behavior for -2

Scaling Procedures for Capillary Pressure Data at Low Wetting-Phase Saturations

Summary New capillary pressure data, applicable to the saturation range below 5%, are reported. The method used to obtain these data involved the determination of low-temperature nitrogen adsorption/desorption isotherms. Three types of samples were studied: Berea sandstone, a producing-reservoir sandstone, and microporous chert extracted from the producing-reservoir sandstone. The data for Berea sandstone, when scaled according to the usual Leverett J-function procedure, did not agree with previously reported data for the air/brine system. Because saturation resulting from wetting films is not expected to scale according to the J-function procedure, one cause of the disagreement could be a significant contribution of wetting films to the total saturation in the low-saturation region. Other contributing causes appear to be a 20% difference in surface area between the two sample sets used in the scaling test and a difference in the clay mineral fabric (pore structure) established under two different test conditions.

Fluid distribution and transport in porous media at low wetting phase saturations

Capillary pressure, hydraulic conductivity and the capillary dispersion coefficient have been observed to obey power laws in the wetting phase saturation. The authors relate power-law behaviour at low wetting phase saturations, i.e. at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of natural porous media.

Capillary dispersion in porous media at low wetting phase saturations

Spreading of wetting liquid over a surface by disjoining pressure gradient driven film flow and by capillary pressure gradient driven channel flow is well known. Bacri ( J. Phys. Lett. ( Paris) 46, L467–L473, 1985) reported “anomalously” rapid spreading of wetting liquid during imbibition into a prewet porous medium. We predict quantitatively this phenomenon, called “hyperdispersion,” from viscous flow along pore walls in thin films of thickness h governed by disjoining force and capillarity. Pore radius distribution, pore network topology, and disjoining pressure function Π( h) all determine the magnitude of capillary dispersion. At high capillary pressures, we find that capillary pressure P c , wetting phase relative permeability k rw , and capillary dispersion coefficient D c can obey power laws in saturation S, which is the sum of the thin-film and pendular-structure inventories: S = S film + S ps . If Π ∝ h − m so that S film ∝ P −1/ m c , if S ps ∝ P − b c , and if thin films control flow, two sets of power law behavior exist. In the case 1/ m < b, P c ∝ S − m , k rw ∝ S 3, and D c ∝ S 2− m . In the case 1/ m > b, P c ∝ S −1/ b , k rw ∝ S 3/ mb, and D c ∝ S(3− m− mb)/ mb. The exponents m and b dictate the behavior of D c as the saturation of the wetting phase approaches zero. More complex function Π( h) can lead to nonmonotonic D c ( S). Bacri measured D c values two or three orders of magnitude higher than we predict, implying a distribution of wetting liquid different from any we consider.