Comparative assessment of three‐phase oil relative permeability models

Ranaee, Ehsan; Riva, Mònica; Porta, Giovanni; Guadagnini, Alberto

doi:10.1002/2016wr018872

Cited by 17 publications

(9 citation statements)

References 56 publications

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“…These results suggest the following: (a) E ( Y | Y * ) and

E (()|, Y, {boldY}^{*}) \pm \sqrt{V (()|, Y, {boldY}^{*})}

are respectively very close to

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

and

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k}) \pm \sqrt{V (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})}

when

P (()|, {\overset{M}{true}}_{k}, {boldY}^{*}) \geq 90 %

(see Figure ); (b) E ( Y | Y * ) can provide better estimates than

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

when the individual models of the set considered yield very different results (see Figure ); and (c) the KIC‐based

Var (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

is always smaller than its counterparts based on the other IC considered for a given experiment (see Figures and ). These results are consistent with observations by Ranaee, Riva, Porta, and Guadagnini (), who noted that model‐averaged estimates were virtually coinciding with those associated with the most skilful model in their study when the latter was characterized by

P (()|, {\overset{M}{true}}_{k}, {boldY}^{*}) \geq 95 %

. They are also consistent with the results of Winter and Nychka (), who note that a model average can only be more skilful than the model identified as best solely when the individual models in the collection produce very different forecasts.…”

Section: Resultsmentioning

confidence: 99%

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

Xia

Tong

et al. 2018

Hydrological Processes

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We investigate our ability to assess transfer of hexavalent chromium, Cr(VI), from the soil to surface runoff by considering the effect of coupling diverse adsorption models with a two-layer solute transfer model. Our analyses are grounded on a set of two experiments associated with soils characterized by diverse particle size distributions.Our study is motivated by the observation that Cr(VI) is receiving much attention for the assessment of environmental risks due to its high solubility, mobility, and toxicological significance. Adsorption of Cr(VI) is considered to be at equilibrium in the mixing layer under our experimental conditions. Four adsorption models, that is, the Langmuir, Freundlich, Temkin, and linear models, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes are associated with the highest release of Cr(VI) to runoff. We compare the relative abilities of the four models to interpret experimental results through maximum likelihood model calibration and four model identification criteria (i.e., the Akaike information criteria [AIC and AIC C ] and the Bayesian and Kashyap information criteria). Our study results enable us to rank the tested models on the basis of a set of posterior weights assigned to each of them.A classical variance-based global sensitivity analysis is then performed to assess the relative importance of the uncertain parameters associated with each of the models considered, within subregions of the parameter space. In this context, the modelling strategy resulting from coupling the Langmuir isotherm with a two-layer solute transfer model is then evaluated as the most skilful for the overall interpretation of both sets of experiments. Our results document that (a) the depth of the mixing layer is the most influential factor for all models tested, with the exception of the Freundlich isotherm, and (b) the total sensitivity of the adsorption parameters varies in time, with a trend to increase as time progresses for all of the models. These results suggest that adsorption has a significant effect on the uncertainty associated with the release of Cr(VI) from the soil to the surface runoff component.

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“…These results suggest the following: (a) E ( Y | Y * ) and

E (()|, Y, {boldY}^{*}) \pm \sqrt{V (()|, Y, {boldY}^{*})}

are respectively very close to

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

and

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k}) \pm \sqrt{V (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})}

when

P (()|, {\overset{M}{true}}_{k}, {boldY}^{*}) \geq 90 %

(see Figure ); (b) E ( Y | Y * ) can provide better estimates than

E (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

when the individual models of the set considered yield very different results (see Figure ); and (c) the KIC‐based

Var (()|,, Y, {boldY}^{*}, {\overset{M}{true}}_{k})

P (()|, {\overset{M}{true}}_{k}, {boldY}^{*}) \geq 95 %

Section: Resultsmentioning

confidence: 99%

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

Xia

Tong

et al. 2018

Hydrological Processes

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“…Caudle et al (1951) were among the first to highlight the impact of hysteresis effects (hereinafter denoted as HEs) on the values of relative permeability of a non-wetting phase. Occurrence of such effects for the non-wetting and the intermediate wetting phases have been documented by a set of experimental (e.g., Oak, 1990;Alizadeh and Piri, 2014a;Moghadasi et al, 2016) and theoretical (e.g., Killough, 1976;Carlson, 1981;Larsen and Skauge, 1998;Blunt, 2000;Shahverdi and Sohrabi, 2013;Kianinejad et al, 2015;Ranaee et al, 2017Ranaee et al, , 2016 studies. The main reasons underpinning the lack of reversibility of the saturation paths observed under three-phase conditions are (i) trapping of the nonwetting phase during imbibition, (ii) remobilization of the intermediate phase through a layer drainage displacement mechanism, and (iii) wettability alteration (change) during drainage and imbibition (Piri and Blunt, 2005;Van Dijke et al, 2006;Suicmez et al, 2007;Sohrabi et al, 2008).…”

Section: Introductionmentioning

confidence: 96%

“…Ranaee et al (2015) develop a sigmoid-based model for the evaluation of HEs on three-phase oil relative permeability. Ranaee et al (2016Ranaee et al ( , 2017 assessed the applicability of such a formulation in comparision with a set of widely used (non-hysteretic) as well as recently developed (hysteretic) models in reproducing oil relative permeability data collected under coreflooding laboratory experiments.…”

Section: Introductionmentioning

confidence: 99%

Numerical Assessment Of Water Alternating Gas Practices In The Presence Of Hysteresis Effects On Relative Permeability

Ranaee¹,

Inzoli²,

Riva³

et al. 2018

Proceedings

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Water Alternating Gas (WAG) injection is one of the most successful enhanced oil recovery approaches. Properly accounting for the hysteretic effects of relative permeabilities is a critical issue encountered in numerical simulations of WAG at the mesoscale. Ranaee et al. (2015) proposed a sigmoid-based model for three-phase oil relative permeability, incorporating key physical effects taking place at the pore scale. The model can then be jointly used with the Larsen and Skauge (1998) model, accounting for gas relative permeability hysteresis, to develop a formulation for three-phase relative permeability suitable for reservoir simulation. In this study we illustrate the impact of this joint formulation on a field scale setting through a suite of numerical simulations of WAG injection targeting a reservoir model inspired to real life cases. The analysis is performed by embedding the illustrated relative permeability models in the black oil model implemented in the Matlab Reservoir Simulation Toolbox (Lie et al., 2011). We assume non-hysteretic behavior for water relative permeability under water-wet conditions and characterize it upon relying on corresponding laboratory-scale data. As a baseline, the results are compared against a scenario in the absence of three-phase relative permeability hysteresis. The computational domain is heterogeneous, the spatial distributions of porosity and absolute permeability varying across the ranges of [0.02 -0.3] and [0.1 -2600 mD], respectively. The model is set at equilibrium conditions, production being driven by three peripheral injectors and five up-dip producers. A given flow rate is assigned to each injector and a target value of liquid production rate is imposed at the producing wells. The numerically evaluated production rates constitute our target state variables. The schedule of the injectors is set to achieve a preliminary waterflooding phase followed by a WAG injection scheme. The latter is implemented by periodically switching the injected phase between water and gas for two injectors, the third injector continuously injecting water. The numerical simulations are performed through a fully implicit discretization of the equations governing the system dynamics. To minimize computational costs, we employ an algebraic multi-grid method and resort to a multi-processor high performance clustered computer system. Our results suggest that hysteretic effects are important across significant portions of the studied reservoir system. Field production responses are associated with a simultaneous increase of ultimate oil recovery and a corresponding decline of the gas-oil ratio when hysteretic effects are included in the simulations.

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“…Commercial black-oil simulators (e.g., Schlumberger Geo-Quest, 2010) typically consider k ro as the result of a saturation-weighted interpolation (Baker, 1988) and/or through the Stone (1970Stone ( , 1973 models. Ranaee et al (2016) show that Stone-type models lead to loss of hyperbolic flow behavior (see also Juanes and Patzek, 2004;and Bianchi Janetti et al, 2015 for detailed analyses on this condition) in some ranges of fluid saturations under three-phase conditions. As such, these models do not capture the detailed physics of the three-phase flow in porous systems for some saturation scenarios.…”

Section: Strategy I (S I )mentioning

confidence: 92%

“…Caudle et al (1951) were among the first to highlight the impact of hysteresis effects (hereinafter denoted as HEs) on the values of relative permeability of a non-wetting phase. Occurrence of such effects for the non-wetting and the intermediate wetting phases have been documented by a set of experimental (e.g., Oak, 1990;Kalaydjian et al, 1997;Suicmez et al, 2007;Alizadeh and Piri, 2014a;Chukwudeme et al, 2014;Moghadasi et al, 2016) and theoretical (e.g., Killough, 1976;Carlson, 1981;Larsen and Skauge, 1998;Blunt, 2000;Shahverdi and Sohrabi, 2013;Kianinejad et al, 2015;Ranaee et al, 2015Ranaee et al, , 2016Khorsandi et al, 2018) studies. A complete characterization of HEs for three-phase flow systems is still challenging due to complex pore-scale mechanisms driving fluid displacement.…”

Section: Introductionmentioning

confidence: 98%

Hysteresis effects of three-phase relative permeabilities on black-oil reservoir simulation under WAG injection protocols

Ranaee

Inzoli

Riva

et al. 2019

Journal of Petroleum Science and Engineering

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We study the impact of explicitly including hysteresis effects (HEs) for relative permeabilities in numerical simulations of enhanced oil recovery approaches grounded on the application of Water Alternate Gas (WAG) injection protocols. Our work explores the significance of hysteresis exhibited by the relative permeability of the non-wetting and/or intermediate wetting phases on the results of reservoir simulations performed within a black-oil modeling approach. We consider four diverse strategies that can be employed to model relative permeabilities of fluid phases under WAG scenarios implemented in a water-wet system following primary waterflooding. The effects of all these modeling strategies are assessed in terms of field oil efficiency (FOE) and gas oil ratio (FGOR) evaluated at the total production lifetime of the reservoir, as compared against a base case where only waterflooding is applied to promote oil recovery. Two of these strategies are implemented and used in typical commercial black-oil reservoir simulators and either neglect hysteresis or consider it only for the gas phase. We then examine a procedure where only hysteresis for relative permeability of the oil phase is considered. Finally, we explicitly consider hysteresis of both non-and intermediate-wetting phases. Our results generally show that including HEs yields an increased FOE and a decreased FGOR. This is consistent with the observation that when injection well controls are set at an optimum value, a non-negligible portion of the domain is associated with saturation paths corresponding to three-phase flow conditions, where saturation history can play a significant role. As compared against a base case where waterflooding is considered as the sole strategy for oil recovery, including hysteresis on three-phase relative permeabilities in the numerical simulations of WAG promotes an increased net present value. We also analyze the impact on reservoir simulation responses of the main WAG injection parameters, i.e., (i) injection rate of gas and water, and duration of (ii) WAG cycles, and (iii) primary waterflooding.

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Comparative assessment of three‐phase oil relative permeability models

Cited by 17 publications

References 56 publications

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

Numerical Assessment Of Water Alternating Gas Practices In The Presence Of Hysteresis Effects On Relative Permeability

Hysteresis effects of three-phase relative permeabilities on black-oil reservoir simulation under WAG injection protocols

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