Water Saturation Range Research Articles

Influence of wettability on phase connectivity and electrical resistivity

Experimental results have shown that resistivity index can deviate from Archie's law at low conductive phase saturation. Previous works have claimed that wettability and flow history are the two main factors causing this phenomenon. Herein, we investigate how the underlying fluid morphology influences electrical resistivity. We start from digital synchrotron x-ray microcomputed tomography images at different conductive phase saturations. We then simulate two-phase flow at different Capillary numbers and wettabilities to investigate deviations in resistivity index. We discover that other than water saturation the connectivity of water quantified by Euler characteristic is an important parameter in determining electrical resistivity for intermediate to purely oil-wet conditions. Deviations in electrical resistivity are found to start at low Capillary number ($\mathrm{Ca}\ensuremath{\sim}{10}^{\ensuremath{-}5}$) for intermediate and oil-wet conditions for the full range of water saturations. We study correlations between resistivity index, saturation, and Euler characteristic by using the Pearson product-moment correlation and a linear regression model. We find a strong correlation between water saturation and resistivity index for the water-wet case while for the intermediate and oil-wet cases a strong correlation between Euler characteristic and resistivity index was observed. The results are explained in terms of percolation theory and a general relationship for resistivity index is proposed for intermediate-wet to oil-wet systems whereby the percolation parameter is normalized Euler characteristic. The findings explain previously observed deviations in resistivity index measurements and allow for a means to predict Euler characteristic from laboratory core-scale experiments using the proposed percolation model.

NMR Measurements of Tortuosity in Partially Saturated Porous Media

The tortuosity (τ), defined in the present context as the ratio of the free diffusion coefficient to the restricted diffusion coefficient of a contained fluid, is an important but difficult to measure characteristic of a porous medium, particularly when it is partially saturated with water. We develop and apply methodology, based on nuclear magnetic resonance (NMR) pulsed field gradient techniques, to measure τ for various sandstone rock cores as a function of residual water fraction. The NMR methodology requires the use of bipolar pulsed field gradient stimulated echo pulse sequences to avoid systematic errors due to magnetic susceptibility differences and D2O as a stationary immiscible water phase; this was selected as it provides no 1H NMR signal. Tortuosity of the free pore space was successfully measured using liquid ethane as a probe fluid for three different sandstones over the full accessible range of residual water saturation. Generally, the tortuosity was observed to increase with residual water (D2O) content; however, significant variations were observed between the different sandstones.

Modeling water imbibition into coated and uncoated papers

Modeling morphological and hydraulic properties of thin porous media, such as filter layers and papers is highly relevant to various industries. In our previous studies, the X-ray tomography and FIB-SEM methods were applied to capture micro- and nano-scale pores in uncoated paper and coated layer, respectively. Here, the reconstructed pore structures were used to investigate two-phase water imbibition in these porous media. The obtained pore size distributions showed a log-normal probability density function. Such a distribution, together with concepts from critical path analysis and percolation theory, was applied to calculate relative permeability over a wide range of water saturations. Comparison with pore-scale numerical simulations showed the capability of this method to estimate water relative permeability for coated and uncoated papers.

Determination of Hydrogen–Water Relative Permeability and Capillary Pressure in Sandstone: Application to Underground Hydrogen Injection in Sedimentary Formations

To provide quantitative data for the development of underground hydrogen storage in porous sedimentary rocks, capillary pressures and relative permeabilities have been measured for the hydrogen–water system. The tests have been performed on a Triassic sandstone. Two potential underground hydrogen storage conditions (“shallower”: 55 bar, 20 $$^{\circ }\hbox {C}$$ and “deeper”: 100 bar, 45 $$^{\circ }\hbox {C}$$ ) have been investigated. Capillary pressure curves have been measured following a modified semi-dynamic technique. The data have been combined with mercury injection capillary pressure measurements to derive a model for capillary pressure valid over almost the entire water saturation range. Interfacial tensions and contact angles for the hydrogen–water system have been also derived. Relative permeability curves measured with the steady-state technique yield low values for minimum water saturations of $$\sim $$ 40%. When combined with the capillary pressure data, the relative permeability of hydrogen in sandstone can be evaluated for almost the total range of water saturation. Capillary numbers calculated for our relative permeability experiments indicate a capillary-limited flow regime for the hydrogen–water system. Despite the two differing sets of conditions investigated and this flow regime, the relative permeability curves stay very close from each other, an effect attributed to the almost constant viscosity of hydrogen under our pressure and temperature conditions. This is in contrast with other fluid pairs (e.g., $$\hbox {CO}_{2}$$ –water system) where capillary numbers can strongly vary with pressure and temperature. Similarly, capillary pressure data vary little between the experimental conditions. The interpretation of the results would suggest that the relative permeability and capillary pressure results from this study are applicable to a wide range of pressure and temperature conditions.

Estimation of Foam–Flow Parameters for Local Equilibrium Methods by Use of Steady-State Flow Experiments and Optimization Algorithms

Summary Foam has been successfully used in the oil industry for conformance and mobility control in gas-injection processes. The efficiency of a foam-injection project must be assessed by means of numerical models. Although there are several foam-flow models in the literature, the prediction of foam behavior is an important issue that needs further investigation. In this paper, we estimate foam parameters and investigate foam behavior for a given range of water saturation by use of two local equilibrium foam models: the population balance assuming local equilibrium (LE) model and the University of Texas (UT) model. Our method uses an optimization algorithm to estimate foam-model parameters by matching the measured pressure gradient from steady-state foam-coreflood experiments. We calculate the effective foam viscosity and the water fractional flow by use of experimental data, and we then compare laboratory data against results obtained with the matched foam models to verify the foam parameters. Other variables, such as the foam texture and foam relative permeability, are used to further investigate the behavior of the foam during each experiment. We propose an improvement to the UT model that provides a better match in the high-quality regime by assuming resistance factor and critical water saturation as a linear function of the pressure gradient. Results show that the parameter-estimation method coupled with an optimization algorithm successfully matches the experimental data by use of both foam models. In the LE model, we observe different values of the foam effective viscosity for each pressure gradient caused by variations of foam texture and the shear-thinning viscosity effect. The UT model presents a constant effective viscosity for each pressure gradient; we propose the use of resistance factor and critical water saturation as a linear function of the pressure gradient to improve the match in the high-quality regime, when applicable.

Improving unsaturated hydraulic conductivity estimation in soils via percolation theory

Accurate estimation of unsaturated hydraulic conductivity K(Sw) in soils has been of great interest to soil physicists and hydrologists in the past several decades. Although various methods such as a “bundle of capillary tubes” conceptual approach were applied in the literature to theoretically model hydraulic conductivity in term of water saturation, in this study we invoke percolation theory, which quantifies the effect of the interconnectivity of pores on the macroscopic fluid flow. We incorporate the pore-solid interface roughness effect in the hydraulic conductance-pore radius (g-r) relationship, evaluate our K(Sw) model using 104 soil samples from the UNSODA database as well as another 20 soil samples from the Rijtema database, and compare it to the Ghanbarian-Alavijeh and Hunt (2012) model. Generally speaking, we experimentally demonstrate that K(Sw) estimations were improved over the entire range of water saturation when the surface roughness effect was incorporated. However, our model still underestimates the unsaturated hydraulic conductivity at low water saturations (corresponding to K(Sw)<10−4cm/day). We show that after eliminating the effect of non-equilibrium conditions in the measurements K(Sw) estimations were improved substantially. Other plausible sources for K(Sw) underestimation are also discussed.

Cross-formational flow of water into coalbed methane reservoirs: controls on relative permeability curve shape and production profile.

Coalbed methane (CBM) wells tend to produce large volumes of water, especially when there is hydraulic connectivity between coalbed and nearby formations. Cross-formational flow between producing coal and adjacent formations can have significant production and environmental implications, affecting economic viability of production from these shallow reservoirs. Such flows can also affect how much gas can be removed from a coalbed prior to mining and thus can have implications for methane control in mining as well. The aim of this paper is to investigate the impact of water flow from an external source into coalbed on production performance and also on reservoir variables including cleat porosity and relative permeability curves derived from production data analysis. A reservoir model is constructed to investigate the production performance of a CBM well when cross-formational flow is present between the coalbed and the overlying formation. Results show that cleat porosity calculated by analysis of production data can be more than one order of magnitude higher than actual cleat porosity. Due to hydraulic connectivity, water saturation within coalbed does not considerably change for a period of time, and hence, the peak of gas production is delayed. Upon depletion of the overlying formation, water saturation in coalbed quickly decreases. Rapid decline of water saturation in the coalbed corresponds to a sharp increase in gas production. As an important consequence, when cross-flow is present, gas and water relative permeability curves, derived from simulated production data, have distinctive features compared to the initial relative permeability curves. In the case of cross-flow, signatures of relative permeability curves are concave downward and low gas permeability for a range of water saturation, followed by rapid increase afterward for water and gas, respectively. The results and analyses presented in this work can help to assess the impact of cross-formational flow on reservoir variables derived from production data analysis and can also contribute to identifying hydraulic connectivity between coalbed and adjacent formations.

Rock physics modelling in reservoirs within the context of time lapse seismic using well log data

Rock physics provides a link between seismic and reservoir properties. It helps to understand the effects of fluid substitution and reservoir parameters on seismic signatures. Rock physics models are now an integral part of feasibility study of time lapse (4D) seismic surveys and their interpretation. There exist different approaches for the construction of rock physics models within the context of 4D seismic study. The objective of this study is to investigate the predictions of existing rock physics models for time lapse seismic studies using real well data. The pore-filled fluid properties used represent the in situ conditions, while the effective elastic moduli and bulk densities are calculated based on theoretical models. Finally the reflection and amplitude predictions from each model are compared over a range of water saturation. Our results suggest that only Krief’ s model is able to discriminate between porous and non-porous zones effectively. Furthermore, all of the investigated models show increase in velocity with replacement of oil with heavier fluid i.e., water except Wyllie’s model. There is a significant change in seismic amplitude when compared with in situ conditions for this particular lithology.

Gas recovery from depressurized methane hydrate deposits with different water saturations

Natural gas hydrates (NGHs) are new and clean energy resources with significant potential. Many studies have investigated NGHs in an attempt to recover natural gas from NGHs deposits. Additional investigations are still needed to clarify the dissociation characteristics of NGHs to develop safe and efficient recovery methods. In this study, two types of NGH deposits were simulated by forming methane hydrates (MHs) in porous media: the first type was formed with excess gas, and the other type was formed with excess water. The formed MHs were dissociated by depressurization methods. Magnetic resonance imaging (MRI) was used to monitor the liquid water distribution and quantify the MH amounts during formation and dissociation. The results showed that a larger depressurization range enhanced the average rate of MH dissociation and gas production for excess gas conditions. For excess water conditions, the mobility of liquid water was dominant during MH dissociation and hindered methane gas output. Furthermore, a larger depressurization range accelerated MH dissociation. When MH dissociations were compared for various gas-water saturated porous media, liquid water saturation and depressurization range were identified as two key factors affecting MH dissociation.

Simulation-based Determination of Relative Permeability in Laminated Rocks

Reservoir simulation using the extended Darcy's law approach requires relative permeability curves derived either via analytic saturation functions (Corey models etc.) or from special core analysis (SCAL). Since such experimental exploration of the space of influential parameters (pore geometry and wettability) is costly and time consuming, establishing ways to extract ensemble relative permeability from numerical simulation, kri, over the entire range of water saturation is highly desirable. In this work, a Steady State Saturation Variation (SSSV) technique is proposed. It computes ensemble kri(sw) for layered rocks when both capillary and viscous forces are strong.

Saturation effects on the joint elastic–dielectric properties of carbonates

We used a common microstructural model to investigate the cross-property relations between elastic wave velocities and dielectric permittivity in carbonate rocks. A unified model based on validated self-consistent effective medium theory was used to quantify the effects of porosity and water saturation on both elastic properties (compressional and shear wave velocities) and electromagnetic properties (dielectric permittivity). The results of the forward models are presented as a series of cross-plots covering a wide range of porosities and water saturations and for microstructures that correspond to different predominant aspect ratios. It was found that dielectric permittivity correlated approximately linearly with elastic wave velocity at each saturation stage, with slopes varying gradually from positive at low saturation conditions to negative at higher saturations. The differing sensitivities of the elastic and dielectric rock properties to changes in porosity, pore morphology and water saturation can be used to reduce uncertainty in subsurface fluid saturation estimation when co-located sonic and dielectric surveys are available. The joint approach is useful for cross-validation of rock physics models for analysing pore structure and saturation effects on elastic and dielectric responses.

Critical Role of the Immobile Zone in Non-Fickian Two-Phase Transport: A New Paradigm.

Using a visualization setup, we characterized the solute transport in a micromodel filled with two fluid phases using direct, real-time imaging. By processing the time series of images of solute transport (dispersion) in a two fluid-phase filled micromodel, we directly delineated the change of transport hydrodynamics as a result of fluid-phase occupancy. We found that, in the water saturation range of 0.6-0.8, the macroscopic dispersion coefficient reaches its maximum value and the coefficient was 1 order of magnitude larger than that in single fluid-phase flow in the same micromodel. The experimental results indicate that this non-monotonic, non-Fickian transport is saturation- and flow-rate-dependent. Using real-time visualization of the resident concentration (averaged concentration over a representative elementary volume of the pore network), we directly estimated the hydrodynamically stagnant (immobile) zones and the mass transfer between mobile and immobile zones. We identified (a) the nonlinear contribution of the immobile zones to the non-Fickian transport under transient transport conditions and (b) the non-monotonic fate of immobile zones with respect to saturation under single and two fluid-phase conditions in a micromodel. These two findings highlight the serious flaws in the assumptions of the conventional mobile-immobile model (MIM), which is commonly used to characterize the transport under two fluid-phase conditions.

A tensorial description of stresses in triphasic granular materials with interfaces

The description of stress transmission in an unsaturated granular material in the low water saturation range (pendular regime) is studied within the micromechanics of a three-phase medium. Considering an REV (Representative Element Volume) comprised of solid grains and isolated inviscid water menisci whose statistical distributions are known, micro- and macro-relationships can be derived using a volume-averaging of stress for each one of the phases in a manner analogous to the derivation of Love–Weber equation defining stress in a dry granular medium. The main difference with respect to previous works in the literature lies in the homogenization technique whereby singular surfaces such as an air–water interface exhibiting surface tension are treated as an additional phase for which a so-called membrane stress is defined. Well-known contractile skin effects and the anisotropy of capillary stresses in unsaturated soils can be formally identified in the proposed tensorial expression that encompasses the statistics of not only grain contact normals, but also that of menisci spatial orientations and their surfaces, including water saturation. Solid grains are considered strictly incompressible with water being also an incompressible and inviscid liquid. An effective stress tensor that controls the strength of unsaturated granular media is hence proposed and verified based on discrete element modelling (DEM) numerical simulations of triaxial compression and simple shear tests on pendular-state granular soils at different confining pressures and matric suctions. The non-sphericity of the so-called capillary stress is also numerically demonstrated.

Evaluating fractures in rocks from geothermal reservoirs using resistivity at different frequencies

One of the key issues to a successful EGS (Enhanced or engineered Geothermal System) is the creation of a great density of fractures. The detection and characterization of the created fractures is crucial in evaluating the geothermal energy resources in such EGS projects as well as in reservoirs for CO2 sequestration and storage. Methods to evaluate the fractures after stimulations are few, and limited in application. To this end, an approach to detecting and evaluating the fractures using resistivity data measured at different frequencies was developed in this study. The effects of fractures on resistivity measurements at different frequencies have been investigated as a function of water saturation in rocks with different porosity, permeability and lithology. Different rocks (Berea sandstone, and greywacke from The Geysers geothermal reservoir) were used in this study. The permeability of the samples ranged from 0.5 to over 1000 md for the matrix. The frequency ranged from 100 to 100,000 Hz. It was found that the effect of frequency on resistivity is different in rocks with and without fractures, especially in the range of low water saturation. The validity of the Archie equation depends on the existence of fractures, the frequency, and the range of water saturation. The relationship between resistivity and water saturation did not follow the Archie equation at low water saturation in some rocks with fractures. Models for characterizing different types of rocks with specific fracture patterns have been established using the resistivity data measured at different frequencies and different water saturations.

Imbibition of hydraulic fracturing fluids into partially saturated shale

AbstractRecent studies suggest that imbibition of hydraulic fracturing fluids into partially saturated shale is an important mechanism that restricts their migration, thus reducing the risk of groundwater contamination. We present computations of imbibition based on an exact semianalytical solution for spontaneous imbibition. These computations lead to quantitative estimates of an imbibition rate parameter (A) with units of for shale, which is related to porous medium and fluid properties, and the initial water saturation. Our calculations suggest that significant fractions of injected fluid volumes (15–95%) can be imbibed in shale gas systems, whereas imbibition volumes in shale oil systems is much lower (3–27%). We present a nondimensionalization of A, which provides insights into the critical factors controlling imbibition, and facilitates the estimation of A based on readily measured porous medium and fluid properties. For a given set of medium and fluid properties, A varies by less than factors of ∼1.8 (gas nonwetting phase) and ∼3.4 (oil nonwetting phase) over the range of initial water saturations reported for the Marcellus shale (0.05–0.6). However, for higher initial water saturations, A decreases significantly. The intrinsic permeability of the shale and the viscosity of the fluids are the most important properties controlling the imbibition rate.

Effective parameterizations of three nonwetting phase relative permeability models

AbstractDescribing convective nonwetting phase flow in unsaturated porous media requires knowledge of the nonwetting phase relative permeability. This study was conducted to formulate and derive a generalized expression for the nonwetting phase relative permeability via combining with the Kosugi water retention function. This generalized formulation is then used to flexibly investigate the Burdine, Mualem, and Alexander and Skaggs models' prediction accuracy for relative nonwetting phase permeability. The model and data comparison results show that these three permeability models, if used in their original form, but applied to the nonwetting phase, could not predict the experimental data well. The optimum pore tortuosity and connectivity value is thus obtained for the improved prediction of relative nonwetting phase permeability. As a result, the effective parameterization of ( ) parameters in the modified Burdine, modified Mualem, and modified Alexander and Skaggs permeability models were found to be (2.5, 2, 1), (2, 1, 2), and (2.5, 1, 1), respectively. These three suggested models display the highest accuracy among the nine relative permeability models investigated in this study. However, the corresponding discontinuous nonwetting phase and the liquid film flow should be accounted for in future for the improved prediction of nonwetting phase relative permeability at very high and very low water saturation range, respectively.

Experimental research of gas shale electrical properties by NMR and the combination of imbibition and drainage

Gas shale has shown considerable force in gas production worldwide, but little attention has been paid to its electrical properties, which are essential for reservoir evaluation and differentiating absorbed gas and free gas. In this study, experiments are designed to research water saturation establishment methods and electrical properties of gas shale. Nuclear magnetic resonance (NMR) with short echo space (TE) is used to identify water saturation and distribution of saturated pores which contribute to the conductivity. The experimental results indicate that NMR with shorter TE can estimate porosity and fluid distribution better than NMR with longer TE. A full range of water saturation is established by the combination of new-type spontaneous imbibition and semi-permeable plate drainage techniques. Spontaneous imbibition gains water saturation from 0% to near irreducible water saturation, and, semi-permeable plate drainage desaturates from 100% to irreducible water saturation. The RI-Sw curve shows a nonlinear relationship, and can be divided into three parts with different behaviors. The comparative analysis of transverse relaxation time (T2) distribution and RI-Sw curves, indicates that free water, and water trapped by capillarity in the non-clay matrix, differ in terms of electrical conductivity from water absorbed in clay. The new experiments prove the applicability of imbibition, drainage and NMR in investigating electrical properties of gas shale and differentiating fluid distribution which makes contribution to conductivity.

Measuring air–water interfacial area for soils using the mass balance surfactant-tracer method

There are several methods for conducting interfacial partitioning tracer tests to measure air–water interfacial area in porous media. One such approach is the mass balance surfactant tracer method. An advantage of the mass-balance method compared to other tracer-based methods is that a single test can produce multiple interfacial area measurements over a wide range of water saturations. The mass-balance method has been used to date only for glass beads or treated quartz sand. The purpose of this research is to investigate the effectiveness and implementability of the mass-balance method for application to more complex porous media. The results indicate that interfacial areas measured with the mass-balance method are consistent with values obtained with the miscible-displacement method. This includes results for a soil, for which solid-phase adsorption was a significant component of total tracer retention.

Effect of Permeability on Implicit-Texture Foam Model Parameters and the Limiting Capillary Pressure

Accurate modeling of foam rheology on the field scale requires detailed understanding of the correlation between the fundamental properties of foam and the scalable parameters of the porous medium. It has been experimentally observed that foam experiences an abrupt coalescence when the capillary pressure in the porous medium approaches a certain value referred to as the “limiting capillary pressure”, Pc*. Current foam models that treat foam texture implicitly mimic this fundamental behavior with a so-called dry-out function, which contains adjustable parameters like fmdry and epdry (in the STARS foam simulator). Parameter fmdry (called Sw* in other models) represents the water saturation corresponding to the limiting capillary pressure, Pc*, and epdry determines the abruptness of foam coalescence as a function of water saturation. In this paper, using experimental data, we examine the permeability dependence of these parameters. We find that the value of fmdry decreases with increasing permeability. We also find that, for the data examined in this paper, the transition from the high-quality regime to low-quality regime is more abrupt in lower-permeability rocks. This implies that in high-permeability rocks foam might not collapse abruptly at a single water saturation; instead, there is a range of water saturation over which foam weakens. In addition, we address the question of whether Pc* is dependent on formation permeability. We estimate Pc* from data for foam mobility versus foam quality and find, as did Khatib et al. (SPE Reservoir Eng., 1988, 3 (3), 919–926), who introduced the limiting capillary pressure concept, that Pc* can vary with permeability. It increases as permeability decreases, but not enough to reverse the trend of increasing foam apparent viscosity as permeability increases.

A physically based surface resistance model for evaporation from bare soils

AbstractThe resistance to vapor transfer across the soil‐air interface, termed surface resistance, plays an important role in determining the evaporation rate from unsaturated bare soils. A physically based analytical model is developed to describe the surface resistance under varying liquid water saturation. When the vaporization plane remains in the topmost soil layer (TSL), the model considers the vapor transport through the external diffusive layer (EDL), and the hydraulic connection between the capillary water in the TSL and underneath water source for evaporation. When the vaporization plane develops below the TSL, the model predicts the surface resistance by taking into account the development of the dry soil layer, the major barrier for vapor transport at the soil‐drying stage. With the consideration of the soil pore size distribution, the model is applicable to different soil types. The model was validated against six sets of laboratory experiments on the drying process of initially water‐saturated soil columns under nonisothermal conditions. These experiments were conducted using different soil types and/or heat intensities above the soil surface. The model was found to perform well over intermediate and low liquid water saturation ranges while underestimating the surface resistance for the high liquid water saturation range. The results suggest that the model overall represents reasonably well the processes underlying the vapor transfer across the soil‐air interface. Future model improvement may be gained by considering the hydraulic connection between the capillary water and film water in the TSL.