Pore-Scale Modeling of Waterflooding in Mixed-Wet-Rock Images: Effects of Initial Saturation and Wettability

SPE Journal ◽  
2013 ◽  
Vol 19 (01) ◽  
pp. 88-100 ◽  
Author(s):  
Y.. Zhou ◽  
J.O.. O. Helland ◽  
D.G.. G. Hatzignatiou
Keyword(s):  
Contact Angle ◽  
Capillary Pressure ◽  
Water Saturation ◽  
Solid Surfaces ◽  
Initial Water ◽  
Cross Sectional ◽  
Flow Rates ◽  
The Cross ◽  
Capillary Pressures ◽  
Saturation Profiles

Summary We simulate transient behavior of viscous- and capillary-dominated water invasion at mixed-wet conditions directly in scanning-electron-microscope (SEM) images of Bentheim sandstone by treating the pore spaces as cross sections of straight tubes. Initial conditions are established by drainage and wettability alteration. Constant rate or differential pressure is imposed along the tube bundle. The phase pressures vary with positions along the tube length but remain unique in each cross section, consistent with 1D core-scale models. This leads to a nonlinear system of equations that are solved for the interface positions as a function of time. The cross-sectional fluid configurations are computed accurately at any capillary pressure and wetting condition by a semianalytical model that is based on free-energy minimization. The fluid conductances are estimated by newly derived explicit expressions that are shown to be in agreement with numerical computations performed directly on the cross-sectional fluid configurations. An SEM image of Bentheim sandstone is taken as input to the developed model for simulating the evolution of saturation profiles during waterfloods for different flow rates and several mixed-wet conditions, which are established with various initial water saturations and contact angles. It is demonstrated that the simulated saturation profiles depend strongly on initial water saturation at mixed-wet conditions. The saturation profiles exhibit increasingly gradual behavior in time as the contact angle, defined on the oil-wet solid surfaces, increases or the initial water saturation decreases. Front menisci associated with positive capillary pressures promote oil displacement by water, whereas for large and negative capillary pressures at small flow rates, oil displaces water because the associated front menisci retract. This results in the development of pronounced gradual saturation fronts at mixed-wet conditions. The waterfloods simulated at conditions established with a large initial water saturation and small contact angle on the oil-wet solid surfaces exhibit sharp Buckley-Leverett saturation profiles for high flow rates because the capillary pressure is small and less important. The shape of the saturation profiles is interpreted on the basis of the simulated capillary pressure curves and the corresponding fluid configurations occurring in the rock image.

scholarly journals Effects of Foam Microbubbles on Electrical Resistivity and Capillary Pressure of Partially Saturated Porous Media

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3385 ◽  
Author(s):  
Abdulrauf R. Adebayo ◽  
Abubakar Isah ◽  
Mohamed Mahmoud ◽  
Dhafer Al-Shehri
Keyword(s):  
Porous Media ◽  
Electrical Resistivity ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Water Saturation ◽  
Porous Plate ◽  
Fluid Distribution ◽  
Cross Sectional ◽  
Injection Process ◽  
Saturation Exponent

Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas–water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.

Formation Damage Issues Impacting the Productivity of Low Permeability, Low Initial Water Saturation Gas Producing Formations

2005 ◽  
Vol 127 (3) ◽  
pp. 240-247 ◽  
Author(s):  
D. Brant Bennion ◽  
F. Brent Thomas
Keyword(s):  
Capillary Pressure ◽  
Water Saturation ◽  
The United States ◽  
Gas Production ◽  
Pressure Effects ◽  
Formation Damage ◽  
Low Permeability ◽  
Gas Reservoirs ◽  
Initial Water ◽  
The Impact

Very low in situ permeability gas reservoirs (Kgas<0.1mD) are very common and represent a major portion of the current exploitation market for unconventional gas production. Many of these reservoirs exist regionally in Canada and the United States and also on a worldwide basis. A considerable fraction of these formations appear to exist in a state of noncapillary equilibrium (abnormally low initial water saturation given the pore geometry and capillary pressure characteristics of the rock). These reservoirs have many unique challenges associated with the drilling and completion practices required in order to obtain economic production rates. Formation damage mechanisms affecting these very low permeability gas reservoirs, with a particular emphasis on relative permeability and capillary pressure effects (phase trapping) will be discussed in this article. Examples of reservoirs prone to these types of problems will be reviewed, and techniques which can be used to minimize the impact of formation damage on the productivity of tight gas reservoirs of this type will be presented.

A Dimensionless Capillary Pressure Function for Imbibition Derived From Pore-Scale Modeling in Mixed-Wet-Rock Images

SPE Journal ◽  
2012 ◽  
Vol 18 (02) ◽  
pp. 296-308 ◽  
Author(s):  
Y.. Zhou ◽  
J.O.. O. Helland ◽  
D.G.. G. Hatzignatiou
Keyword(s):  
Capillary Pressure ◽  
Water Saturation ◽  
Wettability Alteration ◽  
Scale Model ◽  
Pore Scale ◽  
Pressure Function ◽  
Initial Water ◽  
Scale Modeling ◽  
Pore Scale Modeling ◽  
Capillary Pressure Curves

Summary It has been demonstrated experimentally that Leverett's J-function yields almost unique dimensionless drainage capillary pressure curves in relatively homogeneous rocks at strongly water-wet conditions, whereas for imbibition at mixed-wet conditions, it does not work satisfactorily because the permeability dependency on capillary pressure has been reported to be weak. The purpose of this study is to formulate a new dimensionless capillary pressure function for mixed-wet conditions on the basis of pore-scale modeling, which could overcome these restrictions. We simulate drainage, wettability alteration, and imbibition in 2D rock images by use of a semianalytical pore-scale model that represents the identified pore spaces as cross sections of straight capillary tubes. The fluid configurations occurring during drainage and imbibition in the highly irregular pore spaces are modeled at any capillary pressure and wetting condition by combining the free-energy minimization with an arc meniscus (AM)-determining procedure that identifies the intersections of two circles moving in opposite directions along the pore boundary. Circle rotation at pinned contact lines accounts for mixed-wet conditions. Capillary pressure curves for imbibition are simulated for different mixed-wet conditions in Bentheim sandstone samples, and the results are scaled by a newly proposed improved J-function that accounts for differences in formation wettability induced by different initial water saturations after primary drainage. At the end of primary drainage, oil-wet-pore wall segments are connected by many water-wet corners and constrictions that remain occupied by water. The novel dimensionless capillary pressure expression accounts for these conditions by introducing an effective contact angle that depends on the initial water saturation and is related to the wetting property measured at the core scale by means of a wettability index. The accuracy of the proposed J-function is tested on 36 imbibition capillary pressure curves for different mixed-wet conditions that are simulated with the semianalytical model in scanning-electron-microscope (SEM) images of Bentheim sandstone. The simulated imbibition capillary pressure curves and the reproduced curves, based on the proposed J-function, are in good agreement for the mixed-wet conditions considered in this study. The detailed behavior is explained by analyzing the fluid displacements occurring in the pore spaces. It is demonstrated that the proposed J-function could be applied to mixed-wet conditions to generate a family of curves describing different wetting states induced by assigning different wetting properties on the solid surfaces or by varying the initial water saturation after primary drainage. The variability of formation wettability and permeability could be described more accurately in reservoir-simulation models by means of the proposed J-function, and hence the opportunity arises for improved evaluation of core-sample laboratory experiments and reservoir performance.

A Study of Gravity Counterflow Segregation

1962 ◽  
Vol 2 (02) ◽  
pp. 185-193 ◽  
Author(s):  
E.E. Templeton ◽  
R.F. Nielsen ◽  
C.D. Stahl
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Capillary Pressure ◽  
Closed System ◽  
Fractional Flow ◽  
Flow Rates ◽  
Flow Equations ◽  
Actual Flow ◽  
Capillary Pressures ◽  
Darcy Equations

Abstract It has been customary, in predicting saturation changes, to use the Leverett "fractional flow formula", obtained by eliminating the unknown pressure gradient from the generalized Darcy equations for the separate phases. The formula presents difficulties in the case of counterflow, since the "fractional" flow may be negative, greater than unity, or, in the case of a closed system, infinite. Recently, it has been shown by several authors that the corresponding equations (with capillary pressure and gravity terms) for actual flow of the phase may be used just as well. These equations are in agreement with Pirson's statement that, if the two mobilities differ considerably from each other in a closed system, the flow is largely governed by the lower value. The present study was undertaken because of an apparent lack of experimental data on gravity counterflow with which to test the theory. A 4-ft sandpacked tube in a vertical position was employed. Electrodes for determining saturations by resistivity were spaced along the tube, one phase being always an aqueous salt solution. Air, heptane, naphtha, or Bradford crude oil was used for the other phase. A reasonably uniform initial saturation was set up by pumping the phases through the system, after which the tube was shut in and saturation profiles obtained at definite intervals. Cumulative flows over certain horizontal levels were obtained by integration of the distributions; hence, differentiation of the cumulative flows with respect to time gave instantaneous flow rates. To compare experimental and theoretical flow values, capillary pressures were assumed given by the final saturation-distribution curve. The upper part corresponds to the "drainage" region and the lower part to the "imbibition" region, where trapping of the nonwetting phase occurred. While calculations indicated that the capillary pressure saturation function and, probably, the relative permeability saturation functions changed during the segregation, the relation of the measured rates to saturation distributions are in general accord with the frontal-advance equation. It appears that the Darcy equations, as modified for the separate phases, are generally valid for counterflow due to density differences. The usual method of predicting saturation changes, which involves a continuity equation and the elimination of the unknown pressure gradient from the flow equations, should therefore be applicable. However, the need for advance knowledge of drainage and imbibition "capillary pressures" and relative permeabilities during various stages presents difficulties. Introduction The present study was undertaken because of a seeming lack of experimental data relating to vertical counterflow of fluids of different densities in porous media. In particular, it was desired to determine whether data obtained from these laboratory tests were in accordance with certain mathematical treatments of counterflow which have been proposed. The gravity "correction" has been incorporated into the flow equations (and, hence, into displacement theory) nearly as long as both have been used. Field and laboratory data have generally borne out the validity of the theory as applied, for instance, to downward displacement by gas, with all fluids moving downward. However, the modifications for counterflow have only recently been pointed out. It has been customary to use fractional flow rates instead of actual flow rates in displacement calculations. In the case of counterflow, this results in negative values, values greater than unity and, when rates are equal and opposite, in infinite values. As pointed out by Sheldon, et al, and by Fayers and Sheldon, actual flow rates may be used just as well. The fact that these may be of opposite signs for the two fluids does not present any difficulty. SPEJ P. 185^

scholarly journals Integrated rock typing and pore facies analyses in a heterogeneous carbonate for saturation height modelling, a case study from Fahliyan Formation, the Persian Gulf

2021 ◽  
Vol 11 (4) ◽  
pp. 1577-1595
Author(s):  
Rasoul Ranjbar-Karami ◽  
Parisa Tavoosi Iraj ◽  
Hamzeh Mehrabi
Keyword(s):  
Capillary Pressure ◽  
Water Saturation ◽  
High Energy ◽  
Carbonate Reservoir ◽  
Reservoir Rock ◽  
Initial Water ◽  
Rock Types ◽  
Rock Typing ◽  
Pore Types ◽  
Fitting Parameters

AbstractKnowledge of initial fluids saturation has great importance in hydrocarbon reservoir analysis and modelling. Distribution of initial water saturation (Swi) in 3D models dictates the original oil in place (STOIIP), which consequently influences reserve estimation and dynamic modelling. Calculation of initial water saturation in heterogeneous carbonate reservoirs always is a challenging task, because these reservoirs have complex depositional and diagenetic history with a complex pore network. This paper aims to model the initial water saturation in a pore facies framework, in a heterogeneous carbonate reservoir. Petrographic studies were accomplished to define depositional facies, diagenetic features and pore types. Accordingly, isolated pores are dominant in the upper parts, while the lower intervals contain more interconnected interparticle pore types. Generally, in the upper and middle parts of the reservoir, diagenetic alterations such as cementation and compaction decreased the primary reservoir potential. However, in the lower interval, which mainly includes high-energy shoal facies, high reservoir quality was formed by primary interparticle pores and secondary dissolution moulds and vugs. Using huge number of primary drainage mercury injection capillary pressure tests, we evaluate the ability of FZI, r35Winland, r35Pittman, FZI* and Lucia’s petrophysical classes in definition of rock types. Results show that recently introduced rock typing method is an efficient way to classify samples into petrophysical rock types with same pore characteristics. Moreover, as in this study MICP data were available from every one meter of reservoir interval, results show that using FZI* method much more representative sample can be selected for SCAL laboratory tests, in case of limitation in number of SCAL tests samples. Integration of petrographic analyses with routine (RCAL) and special (SCAL) core data resulted in recognition of four pore facies in the studied reservoir. Finally, in order to model initial water saturation, capillary pressure data were averaged in each pore facies which was defined by FZI* method and using a nonlinear curve fitting approach, fitting parameters (M and C) were extracted. Finally, relationship between fitting parameters and porosity in core samples was used to model initial water saturation in wells and between wells. As permeability prediction and reservoir rock typing are challenging tasks, findings of this study help to model initial water saturation using log-derived porosity.

Measurement of Equivalent Pore Radius and Contact Angle Within Porous Media

2015 ◽  
Author(s):  
Saitej Ravi ◽  
David Horner ◽  
Saeed Moghaddam
Keyword(s):  
Contact Angle ◽  
Capillary Pressure ◽  
Pore Radius ◽  
Working Fluid ◽  
Test Liquid ◽  
Capillary Radius ◽  
First Order ◽  
Wick Structure ◽  
Capillary Pressures ◽  
Two Parameters

The equivalent pore radius (i.e. capillary radius) and contact angle determine the capillary pressure generated in a porous medium. The most common method to determine these two parameters is through measurement of the capillary pressure generated by a test liquid and a reference liquid (i.e. a liquid with near-zero contact angle). The rate of rise technique commonly used to determine the capillary pressure results in significant uncertainties. In this study, we utilize our recently developed technique for independent measurement of the capillary pressure and permeability to determine the equivalent capillary radii and contact angle of water within micropillar wick structures. In this method, the experimentally measured dryout threshold of a wick structure at different wicking lengths is fit to Darcy’s law to extract the capillary pressure generated by the test liquid. The equivalent capillary radii of different wick geometries are determined by measuring the capillary pressures generated using n-hexane as the working fluid. It is found that the equivalent capillary radius is dependent on the diameter of pillars as well as the spacing between pillars. The equivalent capillary radii of micropillar wicks determined using the new method are found to be up to 7 times greater than the current geometry-based first order estimates. The contact angle subtended by water at the walls of the micropillars was determined by measuring the capillary pressure generated by water within the arrays and the measured capillary radii for the different geometries. This contact angle was determined to be 52.7°.

New Pseudo Functions To Control Numerical Dispersion

1975 ◽  
Vol 15 (04) ◽  
pp. 269-276 ◽  
Author(s):  
J.R. Kyte ◽  
D.W. Berry
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Three Dimensional ◽  
Vertical Cross Section ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Cross Sectional ◽  
One Dimensional ◽  
Sectional Model ◽  
The Cross

Abstract This paper presents an improved procedure for calculating dynamic pseudo junctions that may be used in two-dimensional, areal reservoir simulations to approximate three-dimensional reservoir behavior. Comparison of one-dimensional areal and two-dimensional vertical cross-sectional results for two example problems shows that the new pseudos accurately transfer problems shows that the new pseudos accurately transfer the effects of vertical variations in reservoir properties, fluid pressures, and saturations from the properties, fluid pressures, and saturations from the cross-sectional model to the areal model. The procedure for calculating dynamic pseudo-relative permeability accounts for differences in computing block lengths between the areal and cross-sectional models. Dynamic pseudo-capillary pressure transfers the effects of pseudo-capillary pressure transfers the effects of different pressure gradients in different layers of the cross-sectional model to the areal model. Introduction Jacks et al. have published procedures for calculating dynamic pseudo-relative permeabilities fro m vertical cross-section model runs. Their procedures for calculating pseudo functions are procedures for calculating pseudo functions are more widely applicable than other published approaches. They demonstrated that, in some cases, the derived pseudo functions could be used to simulate three-dimensional reservoir behavior using two-dimensional areal simulators. For our purposes, an areal simulator is characterized by purposes, an areal simulator is characterized by having only one computing block in the vertical dimension. The objectives of this paper are to present an improved procedure for calculating dynamic pseudo functions, including a dynamic pseudo-capillary pressure, and to demonstrate that the new procedure pressure, and to demonstrate that the new procedure generally is more applicable than any of the previously published approaches. The new pseudos previously published approaches. The new pseudos are similar to those derived by jacks et al. in that they are calculated from two-dimensional, vertical cross-section runs. They differ because (1) they account for differences in computing block lengths between the cross-sectional and areal models, and (2) they transfer the effects of different flow potentials in different layers of the cross-sectional potentials in different layers of the cross-sectional model to the areal model. Differences between cross-sectional and areal model block lengths are sometimes desirable to reduce data handling and computing costs for two-dimensional, areal model runs. For very large reservoirs, even when vertical calculations are eliminated by using pseudo functions, as many as 50,000 computing blocks might be required in the two-dimensional areal model to minimize important errors caused by numerical dispersion. The new pseudos, of course, cannot control numerical pseudos, of course, cannot control numerical dispersion in the cross-sectional runs. This is done by using a sufficiently large number of computing blocks along die length of the cross-section. The new pseudos then insure that no additional dispersion will occur in the areal model, regardless of the areal computing block lengths. Using this approach, the number of computing blocks in the two-dimensional areal model is reduced by a factor equal to the square of the ratio of the block lengths for the cross-sectional and areal models. The new pseudos do not prevent some loss in areal flow-pattern definition when the number of computing blocks in the two-dimensional areal model is reduced. A study of this problem and associated errors is beyond the scope of this paper. Our experience suggests that, for very large reservoirs with flank water injection, 1,000 or 2,000 blocks provide satisfactory definition. Many more blocks provide satisfactory definition. Many more blocks might be required for large reservoirs with much more intricate areal flow patterns. The next section presents comparative results for cross-sectional and one-dimensional areal models. These results demonstrate the reliability of the new pseudo functions and illustrate their advantages pseudo functions and illustrate their advantages over previously derived pseudos for certain situations. The relationship between two-dimensional, vertical cross-sectional and one-dimensional areal reservoir simulators has been published previously and will not be repeated here in any detail. Ideally, the pseudo functions should reproduce two-dimensional, vertical cross-sectional results when they are used in the corresponding one-dimensional areal model. SPEJ P. 269

Pore-Scale Modeling of Wettability Effects and Their Influence on Oil Recovery

1999 ◽  
Vol 2 (01) ◽  
pp. 25-36 ◽  
Author(s):  
A.B. Dixit ◽  
S.R. McDougall ◽  
K.S. Sorbie ◽  
J.S. Buckley
Keyword(s):  
Crude Oil ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Aging Process ◽  
Water Saturation ◽  
Contact Angles ◽  
Initial Water ◽  
Water Imbibition ◽  
Pore Level ◽  
Capillary Pressure Curves

Summary The wettability of a crude oil/brine/rock system influences both the form of petrophysical parameters (e.g., Pc and krw/kro) and the structure and distribution of remaining oil after secondary recovery. This latter issue is of central importance for improved oil recovery since it represents the "target" oil for any IOR process. In the present study, we have developed a three-dimensional network model to derive capillary pressure curves from nonuniformly wetted (mixed and fractionally wet) systems. The model initially considers primary drainage and the aging process leading to wettability alterations. This is then followed by simulations of spontaneous water imbibition, forced water drive, spontaneous oil imbibition and forced oil drive—i.e., we consider a complete flooding sequence characteristic of wettability experiments. The model takes into account many pore level flow phenomena such as film flow along wetting phase clusters, trapping of wetting and nonwetting phases by snapoff and bypassing. We also consider realistic variations in advancing and receding contact angles. There is a discussion of the effects of additional parameters such as the fraction of oil-wet pores, mean coordination number and pore size distribution upon fractionally and mixed wet capillary pressure curves. Moreover, we calculate Amott oil and water indices using the simulated curves. Results indicate that oil recovery via water imbibition in weakly water-wet cores can often exceed that obtained from strongly water-wet samples. Such an effect has been observed experimentally in the past. The basic physics governing this enhancement in spontaneous water imbibition can be explained using the concept of a capillarity surface. Based on these theoretical calculations, we propose a general "regime based" theory of wettability classification and analysis. We classify a range of experimentally observed and apparently inconsistent waterflood recovery trends into various regimes, depending upon the structure of the underlying oil- and water-wet pore clusters and the distribution of contact angles. Using this approach, numerous published experimental Amott indices and waterflood data from a variety of core/crude oil/brine systems are analyzed. Introduction In crude oil/brine/rock (COBR) systems, pore level displacements of oil and brine and hence the corresponding petrophysical flow parameters (e.g., Pc and krw/kro) describing these displacements are governed by the pore geometry, topology and wettability of the system. A number of excellent review papers are available that describe experimental investigations of the effect of wettability on capillary pressure and oil-water relative permeability curves.1–5 In COBR systems, wettability alterations depend upon the mineralogical composition of the rock, pH and/or composition of the brine, crude oil composition, initial water saturation, reservoir temperature, etc.6–12 Therefore, in recent years, interest in restoring the wettability of reservoir core using crude oil and formation brine has greatly increased.3,4,13,14 In this approach, cleaned reservoir core is first saturated with brine and then oil flooded to initial water saturation using crude oil. The core containing crude oil and brine is then aged to alter its wettability state. Wettability measurements, such as Amott and USBM tests, and waterflood experiments are then typically conducted on the aged core. This entire process broadly mimics the actual flow sequences in the reservoir; consequently, the wettability alterations are more realistic than those achieved using chemical treatment methods. During the aging process, wettability may be altered to vastly different degrees depending upon many factors, including those mentioned above. In addition, aging time, thickness of existing water films and wetting film disjoining pressure isotherms also play important roles. Hence, the final wettability state of a re-conditioned core will generally be case specific.

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