Theoretical comparison of two setups for capillary pressure measurement by centrifuge

Abbasi, Jassem; Andersen, Pål Østebø

doi:10.1016/j.heliyon.2022.e10656

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…9 The COUCSI problem can be solved numerically with finite difference (FD) approaches using, e.g., reservoir simulators. 10,11 Analytical solutions can be derived for very specific saturation functions or piston-like displacement. 12−14 Semianalytical solutions were derived by McWhorter & Sunada 15 that hold for any input parameters and saturation functions, except being limited to ET.…”

Section: Introductionmentioning

confidence: 99%

“…The COUCSI problem can be solved numerically with finite difference (FD) approaches using, e.g., reservoir simulators. , Analytical solutions can be derived for very specific saturation functions or piston-like displacement. − Semi-analytical solutions were derived by McWhorter & Sunada that hold for any input parameters and saturation functions, except being limited to ET. Bjørnarå and Mathias noted numerical challenges in evaluating their solution and proposed more stable s. Numerical approaches are usually required for more complex problems involving more general geometries or changing boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Abbasi,

Andersen

2023

Energy Fuels

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The application of physics-informed neural networks (PINNs) is investigated for the first time in solving the onedimensional countercurrent spontaneous imbibition (COUCSI) problem at both early and late time (i.e., before and after the imbibition front meets the no-flow boundary). We introduce the utilization of Change-of-Variables as a technique for improving the performance of PINNs. We formulated the COUCSI problem in three equivalent forms by changing the independent variables. The first describes saturation as a function of normalized position X and time T; the second as a function of X and Y = T 0.5 ; and the third as a sole function of Z = X/T 0.5 (valid only at early time). The PINN model was generated using a feed-forward neural network and trained based on minimizing a weighted loss function, including the physics-informed loss term and terms corresponding to the initial and boundary conditions. All three formulations could closely approximate the correct solutions, with water saturation mean absolute errors around 0.019 and 0.009 for XT and XY formulations and 0.012 for the Z formulation at early time. The Z formulation perfectly captured the self-similarity of the system at early time. This was less captured by XT and XY formulations. The total variation of saturation was preserved in the Z formulation, and it was better preserved with XY-than XT formulation. Redefining the problem based on the physics-inspired variables reduced the nonlinearity of the problem and allowed higher solution accuracies, a higher degree of loss-landscape convexity, a lower number of required collocation points, smaller network sizes, and more computationally efficient solutions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Abbasi,

Andersen

2023

Energy Fuels

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Study on the permeability and capillary pressure of spiral woven mesh for flat-plate heat pipes

Tan,

Pang,

et al. 2024

Applied Thermal Engineering

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Intercept Method for Accurately Estimating Critical Fluid Saturation and Approximate Transient Solutions with Production Time Scales in Centrifuge Core Plug Experiments

Andersen

2023

SPE EuropEC - Europe Energy Conference Featured at the 84th EAGE Annual Conference &Amp; Exhibition

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The centrifuge experiment is used to measure capillary pressure in core plugs by forced displacement (imbibition or drainage): strong gravitational forces (imposed by rotation) displace fluid held in place by capillary forces. This setup is also used to measure and establish critical saturation, the saturation where a fluid loses connectivity and can no longer flow. Obtaining this saturation is challenging as the capillary end effect causing outlet fluid accumulation theoretically only vanishes at infinite rotation speed. Practical speed limitations include maintaining core integrity and avoiding unrepresentative capillary desaturation. In tight or strongly wetted media the capillary forces are strong and more challenging to overcome. Firstly, we demonstrate an ‘intercept method’ to estimate critical saturation. It states that average saturation is proportional to inverse squared rotation speed (at high speeds) allowing to determine critical saturation by linear extrapolation of a few measurements to the intercept where inverse squared speed is zero. The linear trend is valid once the core saturation profile contains the critical saturation. The result follows as the saturation profile near the outlet is invariant and only compressed while the other saturations equal the critical saturation. Although it was assumed the gravitational acceleration is uniform (reasonable for short cores and long centrifuge arm), the result was highly accurate even for extremely non-uniform gravity along the core: the data are linear and the correct critical saturation value is estimated. This was justified by that the end effect profile is uniformly compressed even under those conditions since most of it is located in a narrow part of the core. Secondly, an analytical solution is derived for transient production after the rotation speed is increased starting from an arbitrary initial state towards equilibrium. For this result we assume the outlet profile compresses also during the transient stage. The two regions have fixed mobilities, while the regions occupy different lengths with time. Time as function of production has a linear term and logarithmic term (dominating late time behavior). An analytical time scale is derived which scales all production curves to end (99.5 % production) at same scaled time. We validate the intercept method for high rotation speed data with synthetical and experimental data. For the synthetical data, the input critical saturation is reproduced both for uniform and highly non-uniform gravity along the core. Given the same input as a reservoir simulator, including saturation functions, the analytical transient solution is able to predict similar time scales and trends in time scale (with e.g. rotation speed and viscosity) as numerical simulations. The numerical simulations however indicate that the saturations travel with highly different speeds rather than as a uniformly compressed profile. Especially saturations near the critical saturation are very slow and caused production to span 5 log units of time (the analytical solution predicted 2-3) when the critical saturation was in the core. The correlation better matched low speed data where the critical saturation had not entered the core.

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Theoretical comparison of two setups for capillary pressure measurement by centrifuge

Cited by 5 publications

References 31 publications

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Time Using Physics-Informed Neural Networks

Study on the permeability and capillary pressure of spiral woven mesh for flat-plate heat pipes

Intercept Method for Accurately Estimating Critical Fluid Saturation and Approximate Transient Solutions with Production Time Scales in Centrifuge Core Plug Experiments

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