Polynomial chaos expansions are frequently used by engineers and modellers for uncertainty and sensitivity analyses of computer models. They allow representing the input/output relations of computer models. Usually only a few terms are really relevant in such a representation. It is a challenge to infer the best sparse polynomial chaos expansion of a given model input/output data set. In the present article, sparse polynomial chaos expansions are investigated for global sensitivity analysis of computer model responses. A new Bayesian approach is proposed to perform this task, based on the Kashyap information criterion for model selection. The efficiency of the proposed algorithm is assessed on several benchmarks before applying the algorithm to identify the most relevant inputs of a double-diffusive convection model.

A new semianalytical solution is developed for the velocity‐dependent dispersion Henry problem using the Fourier‐Galerkin method (FG). The integral arising from the velocity‐dependent dispersion term is evaluated numerically using an accurate technique based on an adaptive scheme. Numerical integration and nonlinear dependence of the dispersion on the velocity render the semianalytical solution impractical. To alleviate this issue and to obtain the solution at affordable computational cost, a robust implementation for solving the nonlinear system arising from the FG method is developed. It allows for reducing the number of attempts of the iterative procedure and the computational cost by iteration. The accuracy of the semianalytical solution is assessed in terms of the truncation orders of the Fourier series. An appropriate algorithm based on the sensitivity of the solution to the number of Fourier modes is used to obtain the required truncation levels. The resulting Fourier series are used to analytically evaluate the position of the principal isochlors and metrics characterizing the saltwater wedge. They are also used to calculate longitudinal and transverse dispersive fluxes and to provide physical insight into the dispersion mechanisms within the mixing zone. The developed semianalytical solutions are compared against numerical solutions obtained using an in house code based on variant techniques for both space and time discretization. The comparison provides better confidence on the accuracy of both numerical and semianalytical results. It shows that the new solutions are highly sensitive to the approximation techniques used in the numerical code which highlights their benefits for code benchmarking.

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Existing analytical and semianalytical solutions for density-driven flow (DDF) in porous media are limited to 2-D domains. In this work, we develop a semianalytical solution using the Fourier Galerkin method to describe DDF induced by salinity gradients in a 3-D porous enclosure. The solution is constructed by deriving the vector potential form of the governing equations and changing variables to obtain periodic boundary conditions. Solving the 3-D spectral system of equations can be computationally challenging. To alleviate computations, we develop an efficient approach, based on reducing the number of primary unknowns and simplifying the nonlinear terms, which allows us to simplify and solve the problem using only salt concentration as primary unknown. Test cases dealing with different Rayleigh numbers are solved to analyze the solution and gain physical insight into 3-D DDF processes. In fact, the solution displays a 3-D convective cell (actually a vortex) that resembles the quarter of a torus, which would not be possible in 2-D. Results also show that 3-D effects become more important at high Rayleigh number. We compare the semianalytical solution to research (Transport of RadioACtive Elements in Subsurface) and industrial (COMSOL Multiphysics®) codes. We show cases (high Raleigh number) where the numerical solution suffers from numerical artifacts, which highlight the worthiness of our semianalytical solution for code verification and benchmarking. In this context, we propose quantitative indicators based on several metrics characterizing the fluid flow and mass transfer processes and we provide open access to the source code of the semianalytical solution and to the corresponding numerical models. SHAO ET AL.10,094

Depleted gas reservoirs are appealing targets for carbon dioxide (CO 2 ) sequestration because of their storage capacity, proven seal, reservoir characterization knowledge, existing infrastructure, and potential for enhanced gas recovery. Low abandonment pressure in the reservoir provides additional voidage-replacement potential for CO 2 and allows for a low surface pump pressure during the early period of injection. However, the injection process poses several challenges. This work aims to raise awareness of key operational challenges related to CO 2 injection in low-pressure reservoirs and to provide a new approach to assessing the phase behavior of CO 2 within the wellbore. When the reservoir pressure is below the CO 2 bubble-point pressure, and CO 2 is injected in its liquid or supercritical state, CO 2 will vaporize and expand within the well-tubing or in the near-wellbore region of the reservoir. This phenomenon is associated with several flow assurance problems. For instance, when CO 2 transitions from the dense-state to the gas-state, CO 2 density drops sharply, affecting the wellhead pressure control and the pressure response at the well bottom-hole. As CO 2 expands with a lower phase viscosity, the flow velocity increases abruptly, possibly causing erosion and cavitation in the flowlines. Furthermore, CO 2 expansion is associated with the Joule–Thomson (IJ) effect, which may result in dry ice or hydrate formation and therefore may reduce CO 2 injectivity. Understanding the transient multiphase phase flow behavior of CO 2 within the wellbore is crucial for appropriate well design and operational risk assessment. The commonly used approach analyzes the flow in the wellbore without taking into consideration the transient pressure response of the reservoir, which predicts an unrealistic pressure gap at the wellhead. This pressure gap is related to the phase transition of CO 2 from its dense state to the gas state. In this work, a new coupled approach is introduced to address the phase behavior of CO 2 within the wellbore under different operational conditions. The proposed approach integrates the flow within both the wellbore and the reservoir at the transient state and therefore resolves the pressure gap issue. Finally, the energy costs associated with a mitigation process that involves CO 2 heating at the wellhead are assessed.

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