In recent years, research activity on the recovery technique known as low salinity waterflooding has sharply increased. The main motivation for field application of low salinity waterflooding is the ...improvement of oil recovery by acceleration of production (‘oil faster’) compared to conventional high salinity brine injection. Up to now, most research has focused on the core scale by conducting coreflooding and spontaneous imbibition experiments. These tests serve as the main proof that low salinity waterflooding can lead to additional oil recovery. Usually, it is argued that if the flooding experiments show a positive shift in relative permeability curves, field application is justified provided the economic considerations are also favorable. In addition, together with field pilots, these tests resulted in several suggested trends and underlying mechanisms related to low salinity water injections that potentially explain the additional recovery.
While for field application one can rely on the core scale laboratory tests which can provide the brine composition dependent saturation functions such as relative permeability, they are costly, time consuming and challenging. It is desirable to develop predictive capability such that new candidates can be screened effectively or prioritized. This has not been yet achieved and would require under-pinning the underlying mechanism(s) of the low salinity response.
Recently, research has intensified on smaller length scales i.e. the sub-pore scale. This coincides with a shift in thinking. In field and core scale tests the main goal was to correlate bulk properties of rock and fluids to the amount of oil recovered. Yet in the tests on the sub-pore scale the focus is on ruling out irrelevant mechanisms and understanding the physics of the processes leading to a response to low salinity water. Ultimately this should lead to predictive capability that allows to pre-select potential field candidates based on easily obtained properties, without the need of running time and cost intensive tests.
However, low salinity waterflooding is a cooperative process in which multiple mechanisms acting on different length and time scales aid the detachment, coalescence, transport, banking, and eventual recovery of oil. This means investigating only one particular length scale is insufficient. If the physics behind individual mechanisms and their interplay does not transmit through the length scales, or does not explain the observed fast and slow phenomena, no additional oil may be recovered at core or field scale.
Therefore, the mechanisms are not discussed in detail in this review, but placed in a framework on a higher level of abstraction which is ‘consistency across the scales’. In doing so, the likelihood and contribution of an individual mechanism to the additional recovery of oil can be assessed. This framework shows that the main uncertainty lies in how results from sub-pore scale experiments connect to core scale results, which happens on the length scale in between: the pore-network scale.
On the pore-network scale two different types low salinity responses can be found: responses of the liquid-liquid or the solid-liquid interfaces. The categorization is supported by the time scale differences of the (optimal) response between liquid-liquid and solid-liquid interfaces. Differences in time scale are also observed between flow regimes in water-wet and mixed-wet systems. These findings point to the direction of what physics should be carried from sub-pore to core scale, which may aid in gaining predictive capability and screening tool development. Alternatively, a more holistic approach of the problems in low salinity waterflooding is suggested.
In this literature survey, different aspects of dynamics of two-phase flow in porous media are discussed. This review is based on the results of developed dynamic pore-network models and their ...applications. Thus, those concepts of dynamics of two-phase systems are addressed that have been already discussed in previous studies. Since it is not always possible to study different aspects of laboratory experiments, dynamic pore-network models were developed to gain new insights into the process. This characteristic is the major advantage of pore-network models, which give a better understanding of the physics of a process at pore scale as well as at the scale of representative elementary volume. Dynamic pore-network models are reviewed under different classifications; structure, computational algorithm, and local rules and applications.
Key Points
Solute dispersion is a function of soil saturation
The relation between solute dispersivity and saturation is non‐monotonic.
Solute dispersivity is maximum at intermediate saturations.
It ...is known that in variably saturated porous media, dispersion coefficient depends on Darcy velocity and water saturation. In one‐dimensional flow, it is commonly assumed that the dispersion coefficient is a linear function of velocity. The coefficient of proportionality, called the dispersivity, is considered to depend on saturation. However, there is not much known about its dependence on saturation. In this study, we investigate, using a pore network model, how the longitudinal dispersivity varies nonlinearly with saturation. We schematize the porous medium as a network of pore bodies and pore throats with finite volumes. The pore space is modeled using the multidirectional pore‐network concept, which allows for a distribution of pore coordination numbers. This topological property together with the distribution of pore sizes are used to mimic the microstructure of real porous media. The dispersivity is calculated by solving the mass balance equations for solute concentration in all network elements and averaging the concentrations over a large number of pores. We have introduced a new formulation of solute transport within pore space, where we account for different compartments of residual water within drained pores. This formulation makes it possible to capture the effect of limited mixing due to partial filling of the pores under variably saturated conditions. We found that dispersivity increases with the decrease in saturation, it reaches a maximum value, and then decreases with further decrease in saturation. To show the capability of our formulation to properly capture the effect of saturation on solute dispersion, we applied it to model the results of a reported experimental study.
This study introduces PoreFlow, a pore-network modeling tool capable of simulating fluid flow and multi-component reactive and adsorptive transport under saturated and variably saturated conditions. ...PoreFlow includes a variety of modules, such as: pore network generator, drainage simulator, calculation of pressure and velocity distributions, and modeling of reactive solute transport accounting for advection and diffusion. The pore space is represented using a multi-directional pore-network capable of capturing the random structure of a given porous media with user-defined directional connectivities for anisotropic pore structures. The chemical reactions can occur within the liquid phase, as well as between the liquid and solid phases which may result in an evolution of porosity and permeability. Under variably saturated conditions the area of interfaces changes with degree of the fluid saturation.
PoreFlow uses complex formulations for more accurate modeling of transport problems in presence of the nonwetting phase. This is done by refining the discretization within drained pores. An implicit numerical scheme is used to solve the governing equations, and an efficient substitution method is applied to considerably minimize computational times. Several examples are provided, under saturated and variably saturated conditions, to demonstrate the model applicability in hydrogeology problems and petroleum fields. We show that PoreFlow is a powerful tool for upscaling of flow and transport in porous media, utilizing different pore scale information such as various interfaces, phase distributions and local fluxes and concentrations to determine macro scale properties such as average saturation, relative permeability, solute dispersivity, adsorption coefficients, effective diffusion and tortuosity. Such information can be used as constitutive relations within continuum scale governing equations to model physical and chemical processes more accurately at the larger scales.
•Developing a pore network model to quantify fluid flow and transport processes.•PoreFlow simulates variably saturated flow and multi-component reactive transport.•A simulator for equilibrium or kinetic reactions is coupled to the model.•PoreFlow is a powerful tool for upscaling of flow and transport in porous media.•PoreFlow results in constitutive relations to be used in continuum scale models.
Pore network models of two‐phase flow in porous media are widely used to investigate constitutive relationships between saturation and relative permeability as well as capillary pressure. However, ...results of many studies show a discrepancy between calculated relative permeability and corresponding measured values. Often, calculated values overestimate the measured values. An important feature of almost all pore network models is that the resistance to flow is assumed to come from pore throats only; i.e., the resistance of pore bodies to the flow is considered to be negligible compare to the resistance of pore throats. We contend that this simplification may considerably affect the results for relative permeability curves. In this study, we present a new formulation for pore network modeling of two‐phase flow, which allows for the calculation of wetting phase fluxes in the edges of (partially) drained pores. In a quantitative investigation, we have shown the significance of this effect. The pore space is represented by cubic pore bodies and parallelepiped pore throats in a Multi‐Directional Pore Network model. This model allows for a distribution of coordination numbers ranging between 1 and 26. This topological property, together with geometrical distributions of pore sizes, is used to mimic the microstructure of real porous media. In the presence of the nonwetting phase, the wetting fluid is considered to fill only spaces along edges of cubic pore bodies. We show that the resistance to the flow of the wetting phase within these filaments of fluids are comparable to the resistance to the wetting phase flow within pore throats. Resulting saturation‐relative permeability relationships show very good agreement with measured curves. Explicit representation of wetting phase filaments and calculation of different fluxes within pore bodies may also lead to improved predictions of transport properties such as dispersivities and mass transfer coefficients.
Key Points
We present a new formulation for pore‐network modeling of two‐phase flow
The resistance of pore bodies to the flow is taken into account
Resulting saturation‐relative permeability relationships are shown and discussed
To gain insight in relationships among capillary pressure, interfacial area, saturation, and relative permeability in two-phase flow in porous media, we have developed two types of pore-network ...models. The first one, called tube model, has only one element type, namely pore throats. The second one is a sphere-and-tube model with both pore bodies and pore throats. We have shown that the two models produce distinctly different curves for capillary pressure and relative permeability. In particular, we find that the tube model cannot reproduce hysteresis. We have investigated some basic issues such as effect of network size, network dimension, and different trapping assumptions in the two networks. We have also obtained curves of fluid–fluid interfacial area versus saturation. We show that the trend of relationship between interfacial area and saturation is largely influenced by trapping assumptions. Through simulating primary and scanning drainage and imbibition cycles, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (
P
c
–
S
w
–
a
nw
) points as well as to relative permeability, saturation, and interfacial area (
k
r
–
S
w
–
a
nw
) points. The two fitted three-dimensional surfaces show very good correlation with the data points. We have fitted two different surfaces to
P
c
–
S
w
–
a
nw
points for drainage and imbibition separately. The two surfaces do not completely coincide. But, their mean absolute difference decreases with increasing overlap in the statistical distributions of pore bodies and pore throats. We have shown that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure–saturation (
P
c
–
S
w
) and the relative permeability–saturation (
k
r
–
S
w
) curves.
Understanding the mobilisation of trapped globules of non-wetting phase during two-phase flow has been the aim of numerous studies. However, the driving forces for the mobilisation of the trapped ...phases are still not well understood. Also, there is little information about what happens within a globule before, at the onset and during mobilization. In this work, we used micro-particle tracking velocimetry in a micro-fluidic model in order to visualise the velocity distributions inside the trapped phase globules prior and during mobilisation. Therefore, time-averaged and instantaneous velocity vectors have been determined using fluorescent microscopy. As a porous medium, we used a polydimethylsiloxane (PDMS) micro-model with a well-defined pore structure, where drainage and imbibition experiments were conducted. Three different geometries of trapped non-wetting globules, namely droplets, blobs and ganglia were investigated. We observed internal circulations inside the trapped phase globules, leading to the formation of vortices. The direction of circulating flow within a globule is dictated by the drag force exerted on it by the flowing wetting phase. This is illustrated by calculating and analyzing the drag force (per unit area) along fluid-fluid interfaces. In the case of droplets and blobs, only one vortex is formed. The flow field within a ganglion is much more complex and more vortices can be formed. The circulation velocities are largest at the fluid-fluid interfaces, along which the wetting phase flows and decreases towards the middle of the globule. The circulation velocities increased proportionally with the increase of wetting phase average velocity (or capillary number). The vortices remain stable as long as the globules are trapped, start to change at the onset of mobilization and disappear during the movement of globules. They reappear when the globules get stranded. Droplets are less prone to mobilization; blobs get mobilised in whole; while ganglia may get ruptured and get mobilised only partially.
In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution
(
0.9
μ
m
)
. ...Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of
400
×
400
×
150
μ
m
3
and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure–saturation
imbibition curves for various domain sizes. We studied the directional dependence of
curves by simulating water penetration into the layer from various directions. We did not find any significant difference between
curves in different directions. We studied the effect of compression of paper on
curves. We found that up to 30% compression of the paper layer had very small effect on the
curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them.
Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore‐scale parameters on nanoparticle ...deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore‐scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection‐diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first‐order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle‐collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore‐scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1‐D concentration field. The latter is fitted to the 1‐D advection‐dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore‐scale simulations are performed for three values of Péclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Péclet numbers (Pe = 0.05) and by a kinetic model at high Péclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1‐D concentration field. Correlation equations for the pore‐averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple‐linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore‐scale parameters. The correlation equations, which follow a power law relation with nine pore‐scale parameters, are found to be consistent with the column‐scale and pore‐scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore‐scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.
Key Points:
Expressions for mass transfer rate coefficients between bulk and wall regions
Deposition rate coefficients follow a power law relation with pore‐scale parameters
Correlation equations qualitatively agree with colloid filtration theory
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