A Theory for Relative Permeability of Unconventional Rocks With Dual-Wettability Pore Network

Summary Recent studies show that the pore network of unconventional rocks, such as gas shales, generally consists of inorganic and organic parts. The organic part is strongly oil-wet and preferentially imbibes the oleic phase. In contrast, the inorganic part is usually hydrophilic and preferentially imbibes the aqueous phase. Conventional theories of relative permeability, which are based on uniform wettability, cannot be applied to determine phase permeability in unconventional rocks with dual-wettability behavior. The objective of this paper is to extend the previous theories to model relative permeability of dual-wettability systems in which oleic and aqueous phases can both act as wetting phases in hydrophobic and hydrophilic pore networks, respectively. In the first part of the paper, we review and discuss the results of scanning electron microscopy (SEM), organic petrography, mercury injection capillary pressure (MICP), and comparative water/oil imbibition experiments conducted on several samples from the Triassic Montney tight gas siltstone play of the Western Canadian Sedimentary Basin. We also discuss various crossplots to understand the reasons behind the observed dual-wettability behavior, and to investigate the spatial distribution and morphology of hydrophilic and hydrophobic pores. In the second part, Purcell's model (Purcell 1949) is extended to develop a conceptual model for relative permeability of gas and water in a dual-wettability system such as the Montney tight gas formation. Finally, the proposed model is compared with measured relative permeability data. The results suggest that the submicron pores within solid bitumen/pyrobitumen are strongly water-repellant; therefore, they prefer gas over water under different saturation conditions. This part of the pore network is usually represented by a long tail at the lower end of the pore-throat-size distribution determined from MICP. The proposed relative permeability model describes single-phase flow of gas through the tail part, and two-phase flow of gas and water through the remaining bell-shaped part of the pore-throat-size distribution, which dominantly represents inorganic micropores. On the basis of our model, by increasing the fraction of water-repellant submicron pores, gas relative permeability decreases for a fixed water saturation. This decrease is ascribed to the reduction of the average size of flow conduits for the gas phase.

Download Full-text

Towards Relative Permeability Measurements in Tight Gas Formations

E3S Web of Conferences ◽

10.1051/e3sconf/202014605001 ◽

2020 ◽

Vol 146 ◽

pp. 05001

Author(s):

Denis Dzhafarov ◽

Benjamin Nicot

Keyword(s):

Steady State ◽

Relative Permeability ◽

Water Saturation ◽

Gas Permeability ◽

Tight Gas ◽

Two Phase ◽

Pressure Step ◽

Injection Ratio ◽

Insight Into ◽

Good Agreement

Relative permeability is a concept used to convey the reduction in flow capability due to the presence of multiple fluids. Relative permeability governs the multiphase flow, therefore it has a significant importance in understanding the reservoir behavior. These parameters are routinely measured on conventional rocks, however their measurement becomes quite challenging for low permeability rocks such as tight gas formations. This study demonstrates a methodology for relative permeability measurements on tight gas samples. The gas permeability has been measured by the Step Decay method and two different techniques have been used to vary the saturations: steady state flooding and vapor desorption. Series of steady-state gas/water simultaneous injection have been performed on a tight gas sample. After stabilization at each injection ratio, NMR T2, NMR Saturation profile and low pressure Step Decay gas permeability have been measured. In parallel, progressive desaturation by vapor desorption technique has been performed on twin plugs. After stabilization at each relative humidity level the NMR T2 and Step Decay gas permeability have been measured in order to compare and validate the two approaches. The techniques were used to gain insight into the tight gas two phase relative permeability of extremely low petrophysical properties (K<100 nD, phi < 5 pu) of tight gas samples of Pyrophyllite outcrop. The two methods show quite good agreement. Both methods demonstrate significant permeability degradation at water saturation higher than irreducible. NMR T2 measurements for both methods indicates bimodal T2-distributions, and desaturation first occurs on low T2 signal (small pores). Comparison of humidity drying and steady-state desaturation technique has shown a 12-18 su difference between critical water saturation (Swc) measured in gas/water steady-state injection and irreducible saturation (Swirr) measured by vapor desorption.

Download Full-text

Promediando curvas de permeabilidad relativa en yacimientos de metano en mantos de carbón con flujo bifásico en Queensland, Australia.

Revista Científica y Tecnológica UPSE ◽

10.26423/rctu.v4i1.250 ◽

2017 ◽

Vol 4 (1) ◽

pp. 129-140

Author(s):

Jorge Ordóñez ◽

José Villegas ◽

Alamir Alvarez

Keyword(s):

Relative Permeability ◽

Water Saturation ◽

Single Layer ◽

Absolute Permeability ◽

Phase Flow ◽

Two Phase ◽

Desorption Process ◽

Gas Desorption ◽

Relative Permeability Curves ◽

Single Set

En el presente trabajo se propone el uso de un único set de curvas de permeabilidad a ser empleado en los estudios de simulación y caracterización de yacimientos de gas en mantos de carbón (CBM), en vez del uso común de un set de curvas para cada estrato individual. Para comprobar la aplicabilidad de este procedimiento, se simula un yacimiento usando ambos métodos: el resultado de producción debe ser similar en ambas simulacionesEl modelo para promediar la permeabilidad absoluta en un flujo monofásico, fue usado para el caso de predecir un promedio de permeabilidad relativa para un yacimiento con flujo bifásico. Luego de correr varios casos y corroborar que la ecuación propuesta no cumplía las expectativas, el enfoque del trabajo fue explicar el por qué del no funcionamiento de la ecuación propuesta. Una posible explicación fue la no consideración de la gravedad, que acorde a varias simulaciones presentadas, es un parámetro principal en las curvas de producción. La saturación de agua tampoco puede excluirse de la ecuación que prediga este promedio. Por tanto si se quiere presentar una ecuación para el cálculo de promedio de permeabilidades relativas, es fundamental que tanto la gravedad como la saturación de agua estén incluidas en esta ecuación.Abstract This paper tries to average relative permeability in a way that instead of using different sets of relative permeability curves to different layers, one single set could be used in one single layer, and to get similar production results as if different layers and different relative permeability were used instead. The model to average absolute permeability in a single-phase flow system was used to predict two-phase flow average relative permeability. After running different cases and corroborating that the equation proposed did not match the expectations. The focus of this work was changed in order to explain why the equation was not working. A possible explanation of why the equation is not accurate could be that the equation is not considering the influence of gravity. Gravity plays a very important role in reservoirs. After gas desorption process occurs, free gas migrates to top layers and water migrates to bottom layers. Water saturation could not be excluded from the equation that averages relative permeability curves. The effects of gravity should be considered too, if you want to get an equation to predict production behaviour by using one average equation in a single layer.

Download Full-text

Pore-Scale Perspective of Gas/Water Two-Phase Flow in Shale

SPE Journal ◽

10.2118/205019-pa ◽

2021 ◽

pp. 1-19

Author(s):

Tao Zhang ◽

Farzam Javadpour ◽

Jing Li ◽

Yulong Zhao ◽

Liehui Zhang ◽

...

Keyword(s):

Relative Permeability ◽

Single Phase ◽

Two Phase Flow ◽

Water Saturation ◽

Water Film ◽

Phase Flow ◽

Pore Scale ◽

Two Phase ◽

Relative Permeability Curve ◽

Nanoporous Media

Summary The transport behaviors of both single-phase gas and single-phase water at nanoscale deviate from the predictions of continuum flow theory. The deviation is greater and more complex when both gas and liquid flow simultaneously in a pore or network of pores. We developed a pseudopotential-based lattice Boltzmann (LB) method (LBM) to simulate gas/water two-phase flow at pore scale. A key element of this LBM is the incorporation of fluid/fluid and fluid/solid interactions that successfully capture the microscopic interactions among phases. To calibrate the model, we simulated a series of simple and static nanoscale two-phase systems, including phase separation, a Laplace bubble, contact angle, and a static nanoconfined bubble. In this work, we demonstrate the use of our proposed LBM to model gas/water two-phase flow in systems like a single nanopore, two parallel nanopores, and nanoporous media. Our LBM simulations of static water-film and gas-film scenarios in nanopores agree well with the theory of disjoining pressure and serve as critical steps toward validating this approach. This work highlights the importance of interfacial forces in determining static and dynamic fluid behaviors at the nanoscale. In the Applications section, we determine the water-film thickness and disjoining pressure in a hydrophilic nanopore under the drainage process. Next, we model water imbibition into gas-filled parallel nanopores with different wettability, and simulate gas/water two-phase flow in dual-wettability nanoporous media. The results showed that isolated patches of organic matters (OMs) impede water flow, and the water relative permeability curve cuts off at water saturation [= 1–volumetric total organic carbon (TOC)]. The residual gas saturation is also controlled by the volumetric TOC, ascribed to the isolation of organic patches by the saturating water; therefore, the gas relative permeability curve cuts off at water saturation (= 1–volumetric TOC).

Download Full-text

Calculation Model of Relative Permeability in Tight Sandstone Gas Reservoir with Stress Sensitivity

Geofluids ◽

10.1155/2021/6260663 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Jin Yan ◽

Rongchen Zheng ◽

Peng Chen ◽

Shuping Wang ◽

Yunqing Shi

Keyword(s):

Relative Permeability ◽

Pore Radius ◽

Water Saturation ◽

Stress Sensitivity ◽

Tight Sandstone ◽

Gas Reservoir ◽

Two Phase ◽

Permeability Model ◽

Irreducible Water Saturation ◽

Tight Gas Reservoir

During the development of tight gas reservoir, the irreducible water saturation, rock permeability, and relative permeability change with formation pressure, which has a significant impact on well production. Based on capillary bundle model and fractal theory, the irreducible water saturation model, permeability model, and relative permeability model are constructed considering the influence of water film and stress sensitivity at the same time. The accuracy of this model is verified by results of nuclear magnetic experiment and comparison with previous models. The effects of some factors on irreducible water saturation, permeability, and relative permeability curves are discussed. The results show that the stress sensitivity will obviously reduce the formation permeability and increase the irreducible water saturation, and the existence of water film will reduce the permeability of gas phase. The increase of elastic modulus weakens the stress sensitivity of reservoir. The irreducible water saturation increases, and the relative permeability curve changes little with the increase of effective stress. When the minimum pore radius is constant, the ratio of maximum pore radius to minimum pore radius increases, the permeability increases, the irreducible water saturation decreases obviously, and the two-phase flow interval of relative permeability curve increases. When the displacement pressure increases, the irreducible water saturation decreases, and the interval of two-phase flow increases. These models can calculate the irreducible water saturation, permeability and relative permeability curves under any pressure in the development of tight gas reservoir. The findings of this study can help for better understanding of the productivity evaluation and performance prediction of tight sandstone gas reservoirs.

Download Full-text

Effect of Temperature on Oil/Water Relative Permeabilities of Unconsolidated and Consolidated Sands

Society of Petroleum Engineers Journal ◽

10.2118/12116-pa ◽

1985 ◽

Vol 25 (06) ◽

pp. 945-953 ◽

Cited By ~ 28

Author(s):

Mark A. Miller ◽

H.J. Ramey

Keyword(s):

Relative Permeability ◽

Room Temperature ◽

Water Saturation ◽

High Water ◽

Distilled Water ◽

Relative Permeabilities ◽

Two Phase ◽

Dynamic Displacement ◽

Irreducible Water Saturation ◽

Increasing Temperature

Abstract Over the past 20 years, a number of studies have reported temperature effects on two-phase relative permeabilities in porous media. Some of the reported results, however, have been contradictory. Also, observed effects have not been explained in terms of fundamental properties known to govern two-phase flow. The purpose of this study was to attempt to isolate the fundamental properties affecting two-phase relative permeabilities at elevated temperatures. Laboratory dynamic-displacement relative permeability measurements were made on unconsolidated and consolidated sand cores with water and a refined white mineral oil. Experiments were run on 2-in. [5.1-cm] -diameter, 20-in. [52.-cm] -long cores from room temperature to 300F [149C]. Unlike previous researchers, we observed essentially no changes with temperature in either residual saturations or relative permeability relationships. We concluded that previous results may have been affected by viscous previous results may have been affected by viscous instabilities, capillary end effects, and/or difficulties in maintaining material balances. Introduction Interest in measuring relative permeabilities at elevated temperatures began in the 1960's with petroleum industry interest in thermal oil recovery. Early thermal oil recovery field operations (well heaters, steam injection, in-situ combustion) indicated oil flow rate increases far in excess of what was predicted by viscosity reductions resulting from heating. This suggested that temperature affects relative permeabilities. One of the early studies of temperature effects on relative permeabilities was presented by Edmondson, who performed dynamic displacement measurements with crude performed dynamic displacement measurements with crude and white oils and distilled water in Berea sandstone cores. Edmondson reported that residual oil saturations (ROS's) (at the end of 10 PV's of water injected) decreased with increasing temperature. Relative permeability ratios decreased with temperature at high water saturations but increased with temperature at low water saturations. A series of elevated-temperature, dynamic-displacement relative permeability measurements on clean quartz and "natural" unconsolidated sands were reported by Poston et al. Like Edmondson, Poston et al. reported a decrease in the "practical" ROS (at less than 1 % oil cut) as temperature increased. Poston et al. also reported an increase in irreducible water saturation. Although irreducible water saturations decreased with decreasing temperature, they did not revert to the original room temperature values. It was assumed that the cores became increasingly water-wet with an increase in both temperature and time; measured changes of the IFT and the contact angle with temperature increase, however, were not sufficient to explain observed effects. Davidson measured dynamic-displacement relative permeability ratios on a coarse sand and gravel core with permeability ratios on a coarse sand and gravel core with white oil displaced by distilled water, nitrogen, and superheated steam at temperatures up to 540F [282C]. Starting from irreducible water saturation, relative permeability ratio curves were similar to Edmondson's. permeability ratio curves were similar to Edmondson's. Starting from 100% oil saturation, however, the curves changed significantly only at low water saturations. A troublesome aspect of Davidson's work was that he used a hydrocarbon solvent to clean the core between experiments. No mention was made of any consideration of wettability changes, which could explain large increases in irreducible water saturations observed in some runs. Sinnokrot et al. followed Poston et al.'s suggestion of increasing water-wetness and performed water/oil capillary pressure measurements on consolidated sandstone and limestone cores from room temperature up to 325F [163C]. Sinnokrot et al confirmed that, for sandstones, irreducible water saturation appeared to increase with temperature. Capillary pressures increased with temperature, and the hysteresis between drainage and imbibition curves reduced to essentially zero at 300F [149C]. With limestone cores, however, irreducible water saturations remained constant with increase in temperature, as did capillary pressure curves. Weinbrandt et al. performed dynamic displacement experiments on small (0.24 to 0.49 cu in. [4 to 8 cm3] PV) consolidated Boise sandstone cores to 175F [75C] PV) consolidated Boise sandstone cores to 175F [75C] with distilled water and white oil. Oil relative permeabilities shifted toward high water saturations with permeabilities shifted toward high water saturations with increasing temperature, while water relative permeabilities exhibited little change. Weinbrandt et al. confirmed the findings of previous studies that irreducible water saturation increases and ROS decreases with increasing temperature. SPEJ P. 945

Download Full-text

Imaging and Resistivity Studies of Saturation Gradients in Two-Phase Flow in 3-D Porous Media

MRS Proceedings ◽

10.1557/proc-464-371 ◽

1996 ◽

Vol 464 ◽

Cited By ~ 1

Author(s):

E. H. Kawamoto ◽

Po-Zen Wong

Keyword(s):

Computed Tomography ◽

Porous Media ◽

Two Phase Flow ◽

Water Saturation ◽

Glass Beads ◽

Water Phase ◽

Phase Flow ◽

Two Phase ◽

Vertical Column ◽

X Ray

ABSTRACTWe have carried out x-ray radiography and computed tomography (CT) to study two-phase flow in 3-D porous media. Air-brine displacement was imaged for drainage and imbibition experiments in a vertical column of glass beads. By correlating water saturation Sw with resistance R, we find that there is a threshold saturation S* ≈ 0.2, above which R(SW) ∼ Sw−2, in agreement with the empirical Archie relation. This holds true for both drainage and imbibition with littlehysteresis, provided that Sw remains above S*. Should Sw drop below S* during drainage, R(Sw) rises above the Archie prediction, exhibiting strong hysteresis upon reimbibition. This behavior suggests a transition in the connectivity of the water phase near S*, possibly due to percolation effects.

Download Full-text

Distribution of the Oil Phase Obtained Upon Imbibition of Water

Society of Petroleum Engineers Journal ◽

10.2118/570-pa ◽

1964 ◽

Vol 4 (01) ◽

pp. 49-55 ◽

Cited By ~ 28

Author(s):

Pietro Raimondi ◽

Michael A. Torcaso

Keyword(s):

Primary Production ◽

Relative Permeability ◽

Water Saturation ◽

Initial Conditions ◽

Flow Behavior ◽

Phase System ◽

Residual Oil ◽

Two Phase ◽

Connate Water ◽

Phase Water

Abstract The distribution of the oil phase in Berea sandstone resulting from increasing and decreasing the water saturation by imbibition was investigated Three types of distribution were recognized: trapped, normal and lagging. The amount of oil in each of these distributions was determined as a function of saturation by carrying out a miscible displacement in the oil phase under steady-state conditions of saturation. These conditions were maintained by flowing water and oil simultaneously in given ratios and by using a displacing solvent having essentially the same density and viscosity as the oil.A correlation shows the amount of trapped oil at any saturation to be directly proportional to the conventional residual oil saturation Sir The factor of proportionality is related to the fractional permeability to the water phase. Part of the oil which was not trapped was displaced in a piston- like manner (normal part) and part was eluted gradually (lagging part). The observed phenomena are more than of mere academic importance. Oil which is trapped may well provide the fuel essential for forward combustion and thus be beneficial. On the contrary, in tertiary recovery operations, it is this trapped oil which seems to make current techniques uneconomic. Introduction A typical oilfield may initially contain connate water and oil. After a period of primary production water often enters the field either from surrounding aquifers or from surface injection. During primary production evolution and establishment of a free gas saturation usually occurs. The effect and importance of this third phase is fully recognized. However, this investigation is limited to a two- phase system, one wetting phase (water) and one non-wetting phase (oil). The increase in water content of a water-wet system is termed imbibition. In a relative permeability-saturation diagram such as the one shown in Fig. 1, the initial conditions of the field would he represented by a point below a water saturation of about 35 per cent, i.e., where the imbibition and the drainage curves to the non-wetting phase nearly coincide. When water enters the field the relative permeability to oil decreases along the imbibition curve. At watered-out conditions the relative permeability to the oil becomes zero. At this point a considerable amount of oil, called residual oil, (about 35 per cent in Fig. 1) remains unrecovered. Any attempt to produce this oil will require that its saturation be increased. In Fig. 1 this would mean retracing the imbibition curve upwards. In addition, processes like alcohol and fire flooding, which can be employed at any stage of production, involve the complete displacement of connate water and an increase, or imbibition, of water saturation ahead of the displacing front. Thus, in several types of oil production it is the imbibition-relative permeability curve which rules the flow behavior. For this reason a knowledge of the distribution of the non-wetting phase, as obtained through imbibition, whether "coming down" or "going up" on the imbibition curve, is important. SPEJ P. 49^

Download Full-text