Comparison of Water Content‐Pressure Head Data Obtained by Equilibrium, Steady‐State, and Unsteady‐State Methods

Topp, G. C.; Klute, A.; Peters, D. B.

doi:10.2136/sssaj1967.03615995003100030009x

Cited by 153 publications

(128 citation statements)

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“…8 that the dynamic capillary pressure curves are always above the steady state capillary pressure curve. This is consistent with experimental observations of Topp et al (1967), who compared the correlation between capillary force and water saturation during steady and unsteady flows, observed that during unsteady state, the dynamic capillary pressure is significantly higher than that performed under equilibrium or steady state. Topp et al (1967) Fig.…”

Section: Unsteady State Capillary Pressure Curvesupporting

confidence: 92%

“…Hence, the capillary pressure-saturation relationship curves obtained under equilibrium conditions cannot adequately describe the relationship between capillary force and saturation within hours. In fact, Topp et al (1967), Davidson et al (1966), Smiles et al (1971), and Vachaud et al (1972) showed that both the retention characteristic and the hydraulic conductivity characteristic are different under the static equilibrium/steady state and unsteady state cases, and they depend on both the history and the change in rate of saturation. Hence, if dynamic non-equilibrium occurs between the water content and the water potential during transient water flow, the water retention characteristic measured in the laboratory under equilibrium cannot be reliably applied to that under transient flow.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of Dynamic Two-Phase Flow During Multistep Air Sparging

Gao

Meegoda

2012

Transp Porous Med

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Air sparging is an in situ soil/groundwater remediation technology, which involves the injection of pressurized air through air sparging well below the zone of contamination. To investigate the rate-dependent flow properties during multistep air sparging, a rule-based dynamic two-phase flow model was developed and applied to a 3D pore network which is employed to characterize the void structure of porous media. The simulated dynamic two-phase flow at the pore scale or microscale was translated into functional relationships at the continuum-scale of capillary pressure-saturation (P c -S) and relative permeabilitysaturation (K r -S) relationships. A significant contribution from the air injection pressure step and duration time of each air injection pressure on both of the above relationships was observed during the multistep air sparging tests. It is observed from the simulation that at a given matric potential, larger amount of water is retained during transient flow than that during steady flow. Shorter the duration of each air injection pressure step, there is higher fraction of retained water. The relative air/water permeability values are also greatly affected by the pressure step. With large air injection pressure step, the air/water relative permeability is much higher than that with a smaller air injection pressure step at the same water saturation level. However, the impact of pressure step on relative permeability is not consistent for flows with different capillary numbers (N ca ). When compared with relative air permeability, relative water permeability has a higher scatter. It was further observed that the dynamic effects on the relative permeability curve are more apparent for networks with larger pore sizes than that with smaller pore sizes. In addition, the effect of pore size on relative water permeability is higher than that on relative air permeability.

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Section: Unsteady State Capillary Pressure Curvesupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Simulation of Dynamic Two-Phase Flow During Multistep Air Sparging

Gao

Meegoda

2012

Transp Porous Med

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“…However, these studies address drainage and imbibition behavior on a laboratory scale, which describe only one facet of multiphase flow in fractured reservoirs. Experimental evidence [14,34,35,51,52,54,56,58,59,63] supports a more general description of capillary pressure and relative permeability functions, which includes a nonequilibrium effect. Reservoir interpretation that does not recognize the potential for reduced recovery because of non-equilibrium effects may lead to an overestimation of the recovery.…”

Section: Introductionmentioning

confidence: 61%

“…For water-wet media with a finite contact angle, it is possible that the delay time is a few months. This effect is observed in many spontaneous imbibition experiments [14,34,35,51,52,54,56,58,59,63]. During the transition, the wetting-fluid relative permeability is higher than in steady-state conditions.…”

Section: Non-equilibrium Effectsmentioning

confidence: 75%

Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

Salimi

Bruining

2011

Comput Geosci

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Recovery from incompletely water-wet fractured reservoirs can be extremely low. A reason for the low recovery is related to wetting issues, whereas the reason for slow recovery can be the non-equilibrium behavior of capillary pressure. One of the non-equilibrium theories is developed by Barenblatt et al. and it modifies both capillary pressure and relative permeabilities. The other theory is developed by Hassanizadeh et al. and it only deals with non-equilibrium effects for capillary pressure. To incorporate non-equilibrium in larger-scale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the nonequilibrium effects are included. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use simulations to determine the range of delay times and capillary-damping coefficients for which discernable effects occur in terms of oil recovery. It is shown that at low Peclet numbers, i.e., when the residence time of the fluids in the fracture is long with respect to the imbibition time, incorporation of delay times of the order of few months have no significant effect on the oil recovery. However, when the Peclet number is large, the delay times reduce the rate of oil recovery. We discuss for which values of the delay time (Barenblatt) and capillary-damping coefficient (Hassanizadeh), significant delays in oil production occur.

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“…Accordingly, the capillary pressure data obtained in an experiment may not be correct unless the P c -S w relationships account for their dependence on the rate of change of fluid saturation (dS w /dt). A number of experiments have shown that the P c -S w curves at equilibrium and dynamic conditions are different (Topp et al 1967;Smiles et al 1971;Vachaud et al 1972;Mirzaei 2012, 2013;Mirzaei and Das 2013). The dependence of the capillary pressure curves on dS w /dt is known as the dynamic effect in capillary pressure relationship Mirzaei and Das 2007;Das et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Artificial Neural Network to Determine Dynamic Effect in Capillary Pressure Relationship for Two-Phase Flow in Porous Media with Micro-Heterogeneities

et al. 2014

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An artificial neural network (ANN) is presented for computing a parameter of dynamic two-phase flow in porous media with water as wetting phase, namely, dynamic coefficient (τ), by considering micro-heterogeneity in porous media as a key parameter. τ quantifies the dependence of time derivative of water saturation on the capillary pressures and indicates the rates at which a two-phase flow system may reach flow equilibrium. Therefore, τ is of importance in the study of dynamic two-phase flow in porous media. An attempt has been made in this work to reduce computational and experimental effort by developing and applying an ANN which can predict the dynamic coefficient through the "learning" from available data. The data employed for testing and training the ANN have been obtained from computational flow physics-based studies. Six input parameters have been used for the training, performance testing and validation of the ANN which include water saturation, intensity of heterogeneity, average permeability depending on this intensity, fluid density ratio, fluid viscosity ratio and temperature. It is found that a 15 neuron, single hidden layer ANN can characterize the relationship between media heterogeneity and dynamic coefficient and it ensures a reliable prediction of the dynamic coefficient as a function of water saturation.

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Comparison of Water Content‐Pressure Head Data Obtained by Equilibrium, Steady‐State, and Unsteady‐State Methods

Cited by 153 publications

References 0 publications

Simulation of Dynamic Two-Phase Flow During Multistep Air Sparging

Simulation of Dynamic Two-Phase Flow During Multistep Air Sparging

Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

Artificial Neural Network to Determine Dynamic Effect in Capillary Pressure Relationship for Two-Phase Flow in Porous Media with Micro-Heterogeneities

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