Nonlinear Behaviour of Mass Transfer Mechanisms in Solvent Oil Recovery

2017 ◽  
Vol 379 ◽  
pp. 181-188 ◽  
Author(s):  
Shelley Lorimer ◽  
Caine Smithaniuk

Literature has indicated that, experimentally, solvent fronts in hybrid thermal solvent recovery processes progress more rapidly than what can be predicted using current approximations and more rapidly than thermal processes alone [1]. The equations that govern thermal multiphase flow through porous media are extremely complex and it is very difficult to decouple the contribution of the mass transfer mechanisms from the thermal effects. This paper explores the behavior of the mass transfer mechanisms in these processes through an examination of the nonlinear one-dimensional advection diffusion/dispersion (ADD) equation using finite difference methods. Earlier work [2] indicated that the linear ADD equation, using physically estimated parameters for diffusion and dispersion coefficients obtained from the literature, could not account for the solvent front progression rate predicted by Edmunds [3]. The results in this preliminary study indicate that the nonlinear effects are important in predicting the progression of a solvent front using the one dimensional ADD equation. The shapes and rate of propagation of the concentration profiles are influenced by both velocity and diffusion functionality. These results are more consistent with the solvent front propagation rate predicted by Edmunds [3]. These results also suggest that including nonlinear effects in traditional reservoir simulation software may be necessary in the modeling of solvent processes. Further work is needed to explore and understand the influence of the velocity and diffusion functionality necessary to mimic the behaviour observed in thermal solvent recovery processes and to further increase the understanding of their impact on solvent front propagation.

2016 ◽  
Vol 367 ◽  
pp. 77-85 ◽  
Author(s):  
Shelley Lorimer ◽  
Ryan Boehnke ◽  
Brigida Meza

The mechanisms of mass transfer in thermal solvent enhanced oil recovery processes and the influence of grid size in the numerical simulation of these processes is not well understood [1, 2]. The literature has indicated that, experimentally, solvent fronts progress more rapidly that what can be predicted using current approximations [3]. It has also been shown that under certain modelling conditions with coarser grid meshes, the influence of numerical errors can be substantial. The equations that govern thermal/solvent multiphase flow through porous media are extremely complex and it is very difficult to decouple the contribution of the mass transfer mechanisms from the thermal effects. This paper was written to increase the understanding of the mass transfer mechanisms in hybrid thermal solvent recovery processes through sensitivity study using a numerical solution of the linear one dimensional advection diffusion/dispersion (ADD) equation. This equation was modeled using finite difference methods. The effects of grid size were examined to verify the use of this method, and the results were then used to examine the sensitivity of the equation to the parameters that govern the mass transfer mechanisms (advection velocity, diffusion and dispersion coefficients).In particular, a range of values for diffusion and dispersion coefficients were selected for the sensitivity study, and one advection velocity. These values were then used to numerically solve the ADD equation to assess the impact of each mechanism (advection, diffusion and dispersion) and their contribution to the movement of the solvent front. The parameters chosen for this study were based on values obtained from the literature for advection velocity, diffusion and dispersion coefficients consistent with a gravity drainage thermal/solvent oil recovery process. This sensitivity study has indicated that all three mechanisms (advection, diffusion and dispersion) must be included to have the solvent front progress at rates that are consistent with experimental solvent front advance rates published in the literature to date [1]. This result suggests that diffusion alone cannot account for the movement of the solvent front within the ranges of values that have been studied.


2019 ◽  
Vol 390 ◽  
pp. 168-192
Author(s):  
Shelley Lorimer ◽  
Timothy Artymko

Literature has indicated that, experimentally, solvent fronts in hybrid solvent recovery processes progress more rapidly than what can be predicted using current approximations and more rapidly than thermal processes alone. Research using finite differences to model the nonlinear advection, diffusion and dispersion (ADD) equation suggests that nonlinear mass transfer effects are important in predicting the rate of solvent advance. Nonlinearities can be ascribed to both diffusion and flow velocity functionality. Earlier work using linear concentration dependent diffusion and log-linear velocity behaviour confirmed the importance of nonlinear effects when compared to linear theory that uses constant diffusion, dispersion and velocity coefficients. The mathematical nature of the nonlinear ADD equation further suggests that the shape of concentration dependent diffusion and flow velocity will affect the shape of the solvent concentration profiles, and influence the rate of propagation of the solvent front. This research focuses on results obtained using finite differences to explore the effects of various diffusion and velocity functionalities that affect the solvent rate propagation using a nonlinear ADD equation. The results obtained from this analysis indicate that these functionalities determine the shape of the solvent concentration profile. The concentration dependent diffusion and velocity functions were chosen according to recent literature which proposes experimentally obtained functions to more accurately model solvent penetration in the media. Preliminary results from this study suggest that the velocity functionality has more influence on the process at both the lab and field scales for the parameters considered in this study. The shapes of the concentration profiles are affected by both diffusion functionality and velocity functionality.


2021 ◽  
Vol 58 (1) ◽  
pp. 1-21
Author(s):  
Harto Saarinen ◽  
Jukka Lempa

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.


1999 ◽  
Vol 10 (06) ◽  
pp. 1025-1038 ◽  
Author(s):  
A. BENYOUSSEF ◽  
N. BOCCARA ◽  
H. CHAKIB ◽  
H. EZ-ZAHRAOUY

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.


AIChE Journal ◽  
2016 ◽  
Vol 63 (6) ◽  
pp. 2394-2408 ◽  
Author(s):  
Matthieu Roudet ◽  
Anne‐Marie Billet ◽  
Sébastien Cazin ◽  
Frédéric Risso ◽  
Véronique Roig

2012 ◽  
Vol 16 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Wenxi Wang ◽  
Qing He ◽  
Nian Chen ◽  
Mingliang Xie

In the study a simple model of coagulation for nanoparticles is developed to study the effect of diffusion on the particle coagulation in the one-dimensional domain using the Taylor-series expansion method of moments. The distributions of number concentration, mass concentration, and particle average volume induced by coagulation and diffusion are obtained.


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