by Charlie van der Geest, Letícia Bizarre, Aline Melchuna, Ivanei F. Pinheiro and Vanessa C. B. Guersoni, published at Fuel, April 2022, Vol. 313.
Over the past five decades, wax deposition has been widely considered a mass transfer-controlled phenomenon. Despite the highly inaccurate predictions, engineers cannot accurately predict the final thickness of the deposit, the hypothesis that wax deposition is a mass transfer phenomenon was not commonly questioned, but this has recently changed. This paper shows evidence that wax deposition is limited by phase transition (heat transfer), by analyzing a vast experimental matrix previously presented in the literature and clearly showing that the thickness decreases as the Reynolds number increases, which cannot be explained by molecular diffusion alone, also by showing that the Reynolds number does not influence the ratio between the deposit’s thermal resistance and the total thermal resistance (dimensionless temperature) for all cold flow experiments, which is further evidence of phase transition. When comparing the limits of the molecular diffusion approach with the experimental data, without any fitting parameter, one observes that not only the experimental data cannot be predicted, but the trend is also incorrect. When using the phase transition model (heat transfer), the accuracy in the thickness prediction is high, which is evidence that what limits the wax deposition is the phase transition. This shows that heat transfer equations can accurately predict wax deposition thickness. Since all wax deposition simulators have the heat transfer calculations, to improve their predictions, one must only implement a single boundary condition.
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by Charlie van der Geest, Aline Melchuna, Letícia Bizarre, Antonio C. Bannwart and Vanessa C. B. Guersoni, published at Fuel, June 21, Vol. 293.
Wax deposition is a costly problem for the O&G industry, especially for pipelines in cold environments. For at least three decades, the scientific community has overwhelmingly agreed that molecular diffusion is the main mechanism for wax deposition. There are, however, severe problems with models based on molecular diffusion. They rely on untested hypotheses and several empirical correlations; hence, they can hardly predict the experimental data from laboratory. For real fields, the prediction is no better than an educated guess – heuristic solutions. Several research areas in wax deposition need to be better understood, and these are discussed in detail here, with a highlight to the most important concern: the controlling mechanism. Is wax deposition indeed a mass transfer controlled phenomenon? What is the evidence supporting this “general knowledge”? Is it possible that, for some conditions, mass transfer is dominant, and for others, the phase transition mechanism is dominant? Apart from this, we also discuss other issues: the accuracy of empirical correlations for diffusivity, the behavior of crystals in the deposit and how that influences the general deposit behavior, non-Newtonian influence on heat transfer and mass transfer, among others. Wax deposition is a complex topic that has been reviewed over and over. In this review, however, we focus on both presenting what has been discussed in the literature and make a critical analysis. The goal is to increase the general knowledge by highlighting a number of gaps and challenges related to this complex and financially exorbitant issue.
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by Seyed Kourosh Mahjour, Antonio Alberto Souza Santos, Susana Margarida da Graça Santos, Denis José Schiozer, published at Society of Petroleum Engineers, September 2021, SPE-206300-MS.
In greenfield projects, robust well placement optimization under different scenarios of uncertainty technically requires hundreds to thousands of evaluations to be processed by a flow simulator. However, the simulation process for so many evaluations can be computationally expensive. Hence, simulation runs are generally applied over a small subset of scenarios called representative scenarios (RS) approximately showing the statistical features of the full ensemble. In this work, we evaluated two workflows for robust well placement optimization using the selection of (1) representative geostatistical realizations (RGR) under geological uncertainties (Workflow A), and (2) representative (simulation) models (RM) under the combination of geological and reservoir (dynamic) uncertainties (Workflow B). In both workflows, an existing RS selection technique was used by measuring the mismatches between the cumulative distribution
of multiple simulation outputs from the subset and the full ensemble. We applied the Iterative Discretized Latin Hypercube (IDLHC) to optimize the well placements using the RS sets selected from each workflow and maximizing the expected monetary value (EMV) as the objective function. We evaluated the workflows in terms of (1) representativeness of the RS in different production strategies, (2) quality of the defined robust strategies, and (3) computational costs. To obtain and validate the results, we employed the synthetic UNISIM-II-D-BO benchmark case with uncertain variables and the reference fine- grid model, UNISIM-II-R, which works as a real case. This work investigated the overall impacts of the robust well placement optimization workflows considering uncertain scenarios and application on the reference model. Additionally, we highlighted and evaluated the importance of geological and dynamic uncertainties in the RS selection for efficient robust well placement optimization.
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by Salabarría, J.B.V., Lima, P., Devloo, P.R.B., Triana, O.D., presented at XLII Ibero-Latin-American Congress on Computational Methods in Engineering (CILAMCE-2021) | 3rd Pan American Congress on Computational Mechanics, Novermber 2021.
In this research, the mathematical model represents a two-phase flow in a fractured porous reservoir media, where the Darcy law represents the flow in both fractures and matrix. The flux/pressure of the fluid flow is approximated using a hybridized mixed formulation coupling the fluid in the volume with the fluid flow through th fractures. The spatial dimension of the rock matrix is three and and is coupled with two-dimensional discrete frac- tures. The transport equation is approximated using a lower order finite volume system solved through an upwind scheme. The C++ computational implementation is made using the NeoPZ framework, an object oriented finite element library. The generation of the geometric meshes is done with the software Gmsh. Numerical simulations in 3D are presented demonstrating the advantages of the adopted numerical scheme and these approximations are compared with results of other methods.
by Victor B. Oliari, Paulo Rafael Bosing, Denise de Siqueira, Philippe R.B. Devloo, presented at XLII Ibero-Latin-American Congress on Computational Methods in Engineering (CILAMCE-2021) | 3rd Pan American Congress on Computational Mechanics, Novermber 2021.
We present new fully computable a posteriori error estimates for the primal hybrid finite element methods based on equilibrated flux and potential reconstructions. The reconstructed potential is obtained from a local L2 orthogonal projection of the gradient of the numerical solution, with a boundary continuous restriction that comes from a smoothing process applied to the trace of the numerical solution over the mesh skeleton. The equilibrated flux is the solution of a local mixed form problem with a Neumann boundary condition given by the Lagrange multiplier of the hybrid finite element method solution. To establish the a posteriori estimates we divide the error into conforming and non-conforming parts. For the former one, a slight modification of the a posteriori error estimate proposed by Vohral ́ık  is applied, whilst the latter is bounded by the difference of the gradient of the numerical solution and the reconstructed potential. Numerical results performed in the environment PZ Devloo , show the efficiency of this strategy when it is applied for some test model problems.