A New Design of Steady-State Type Experiments for Simultaneous Estimation of Two-Phase Flow Functions

Urkedal, H.; Ebeltoft, Einar; Nordtvedt, Jan-Erik; Watson, A. T.

doi:10.2118/64532-pa

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…For steady-state flow, saturations do not change over time. The overwhelming majority of experimental studies including numerical simulations (Lake 1989;Tiab and Donaldson 2004;Langaas et al 1996;Chen and Wood 2001;Cable et al 2000;Urkedal et al 2000) show that in steady-state experiments, apart from sample heterogeneity and end-effects (Huang and Honarpour 1996), the saturation gradients are small, i.e., ∇ S w ≈ 0. Under such conditions, the ∂ H α /∂ S α ∇ S α terms vanish.…”

Section: Casementioning

confidence: 99%

Comparison of Two-Phase Darcy’s Law with a Thermodynamically Consistent Approach

2011

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The extended Darcy's law is a commonly used equation for the description of immiscible two-phase flow in porous media. It dates back to the 1940s and is essentially an empirical relationship. According to the extended Darcy's law, pressure gradient and gravity are the only driving forces for the flow of each fluid. Within the last two decades, more advanced and physically based descriptions for multiphase flow in porous media have been developed. In this work, the extended Darcy's law is compared to a thermodynamically consistent approach which explicitly takes the important role of phase interfaces into account, both as entities and as parameters. In this theoretically derived approach, forces related to capillarity and interfaces appear as driving/resisting forces, in addition to the traditional terms. It turns out that the extended Darcy's law and the thermodynamically based approach are compatible if either (i) relative permeabilities are a function of saturation only, but capillary pressure is a function of saturation and specific interfacial area or (ii) relative permeabilities are a function of saturation and saturation gradients. Theoretical considerations suggest that the former alternative is only valid in case of reversible displacement while in the general case (irreversible displacement), the latter alternative is relevant. Keywords

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Section: Casementioning

confidence: 99%

Comparison of Two-Phase Darcy’s Law with a Thermodynamically Consistent Approach

2011

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“…Reliable interpretation of relative permeabilities requires well designed experiments for accurate determination of both oil and water (or gas) relative permeability, and for retaining the accuracy in the entire saturation range. Steady-state flow experiments fulfil both of these requirements (Urkedal et al 2000).…”

Section: Interpretation Of Scal Experimentsmentioning

confidence: 88%

A Versatile Representation of Upscaled Relative Permeability for Field Applications

Lomeland

Hasanov

Ebeltoft

et al. 2012

SPE Europec/Eage Annual Conference

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A suitable approach to achieve a fit-for-purpose model for field application is upscaling of reservoir properties. However, upscaling of saturation functions like relative permeability is still a source of debate and is frequently omitted due to its inconvenient complexity. Upscaling of these functions, whether by steady-state methods or other techniques, typically generates a complex myriad of relative permeability curves that is challenging to handle pragmatically. This study investigates whether a threeparameter correlation of relative permeability is able to represent the saturation function for fine grid simulation models with the most common heterogeneities, coarse grid simulation models with upscaled properties in addition to verify two-phase core-flow experiments.Implementation of the proposed three-parameter correlations of the relative permeability in the algorithm of full field simulators will overcome the representation challenges of present published upscaling methods.Upscaling of each coarse grid block individually can then be handled pragmatically, and hence provide fit-forpurpose models for field application. Statoil is acknowledged for giving permission to publish the experimental results. Vilgeir Dalen is acknowledged for valuable contributions and advices during the work of this paper. Egil Boye Petersen Jr. and Eimund Gilje are acknowledged for valuable discussions. Weatherford Petroleum Consultancy, Norway is acknowledged for including the new correlation in the core flow simulator Sendra.

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“…The sensitivity matrix necessary for LCA was calculated for the true parameters using a semi-analytical algorithm (see, e.g., [13,14]) incorporated in the coreflood simulator. Thus, calculation of sensitivity coefficients for all parameters and data points required only one run of the simulator.…”

Section: Description Of Numerical Experimentsmentioning

confidence: 99%

“…The values of these functions are of higher interest than the values of the parameters. Thus, rather than looking at confidence intervals for individual parameters, the uncertainty in the estimates is more conveniently given as pointwise confidence intervals for the flow functions, as defined by equation (14). Figure 3 shows the estimated flow functions from the MCA in case A all, together with 95% pointwise confidence intervals.…”

Section: Use Of Lcamentioning

confidence: 99%

Assessing the validity of a linearized accuracy measure for a nonlinear parameter estimation problem

et al. 2001

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We consider accuracy assessment for the inverse problem of recovery of unknown coefficient functions in differential equations from data containing random errors. The set of PDEs constituting the current forward model describes a special case of two-phase porous-media flow. We are concerned mainly with two issues. (1) When is it valid to calculate parameter accuracies for the current nonlinear estimation problem by a linearized method, linearized covariance analysis (LCA)? (2) Can the validity of LCA be assessed without performing an accurate, but computationally very expensive, Monte Carlo analysis (MCA)? For both issues, special emphasis is put on parameter subsets for which LCA predicts high accuracy. The curvature measures of nonlinearity (CMNs) are a potential alternative to MCA. CMNs are approximate, but considerably less expensive to compute. In this paper, we apply LCA, CMNs and MCA to several instances of the current model. We address issue 1 by comparing LCA and MCA results, and issue 2 by including also CMN results in the analysis. It is found that CMN and MCA results lead to identical and negative conclusions concerning the validity of LCA. However, if the real concern is parameter subsets where LCA predicts high accuracy, these conclusions, based on calculations involving all of the parameters, were often misleading. Use of specially designed subset CMNs is essential to avoid this. A potential explanation, which may have implications also for other parameter estimation problems, is presented.

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A New Design of Steady-State Type Experiments for Simultaneous Estimation of Two-Phase Flow Functions

Cited by 8 publications

References 15 publications

Comparison of Two-Phase Darcy’s Law with a Thermodynamically Consistent Approach

Comparison of Two-Phase Darcy’s Law with a Thermodynamically Consistent Approach

A Versatile Representation of Upscaled Relative Permeability for Field Applications

Assessing the validity of a linearized accuracy measure for a nonlinear parameter estimation problem

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