scholarly journals On the Maxwell-Stefan Approach to Multicomponent Diffusion

2011 ◽  
pp. 81-93 ◽  
Author(s):  
Dieter Bothe
Keyword(s):  
Multicomponent Diffusion

Multicomponent Diffusion Revisited: Pair-Mobilities and Consistent Definition of Diffusion Coefficients

2020 ◽  
Author(s):  
Ingo Steinbach ◽  
Julia Kundin ◽  
Katrin Abrahams ◽  
Sergiy V. Divinski
Keyword(s):  
Diffusion Coefficients ◽  
Multicomponent Diffusion ◽  
Definition Of

An Analysis of Coupled Multicomponent Diffusion in Interstitial Tissue

1994 ◽  
Vol 116 (2) ◽  
pp. 164-171 ◽  
Author(s):  
P. D. Schreuders ◽  
K. R. Diller ◽  
J. J. Beaman ◽  
H. M. Paynter
Keyword(s):  
Multicomponent Diffusion ◽  
Frequency Parameter ◽  
Interstitial Tissue ◽  
Specific System ◽  
Species Concentration ◽  
One Dimensional ◽  
Jump Distance ◽  
Local Species ◽  
The Individual ◽  
Graph Form

A one-dimensional multicomponent kinetic model was developed to simulate the interstitial diffusion of macromolecules in a three component system, consisting of water, the macromolecule and the interstitial matrix. Movement of the individual components was modeled as occurring in finite jumps between discrete low energy wells along paths defined in terms of species occupation. The flow rate was expressed as a function of the local species concentration, the jump distance, and a kinetic frequency parameter. The model, implemented in pseudo-bond graph form, was examined by fitting it to data obtained for the transport of fluorescein tagged dextran to determine the kinetic constants for that specific system.

Peculiar Reference Frame in Multicomponent Diffusion

1968 ◽  
Vol 7 (2) ◽  
pp. 319-321 ◽  
Author(s):  
C. M. Yon ◽  
H. L. Toor
Keyword(s):  
Reference Frame ◽  
Multicomponent Diffusion

Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization

2006 ◽  
Vol 9 (05) ◽  
pp. 530-542 ◽  
Author(s):  
Hadi Nasrabadi ◽  
Kassem Ghorayeb ◽  
Abbas Firoozabadi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Thermal Diffusion ◽  
Multicomponent Diffusion ◽  
Compositional Variation ◽  
Horizontal Temperature Gradient ◽  
Two Phase ◽  
Thermogravitational Column

Summary We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes. The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneous and layered media without and with anisotropy in our calculations. Numerical examples for a binary mixture of C1/C3 and a multicomponent reservoir fluid are presented. Results show a strong effect of natural convection in species distribution. Results also show that there are at least two main rotating cells at steady state: one in the gas cap, and one in the oil column. Introduction Proper initialization is an important aspect of reliable reservoir simulations. The use of the Gibbs segregation condition generally cannot provide reliable initialization in hydrocarbon reservoirs. This is caused, in part, by the effect of thermal diffusion (caused by the geothermal temperature gradient), which cannot be neglected in some cases; thermal diffusion might be the main phenomenon affecting compositional variation in hydrocarbon reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et al. 2003). Generally, temperature increases with increasing burial depth because heat flows from the Earth's interior toward the surface. The temperature profile, or geothermal gradient, is related to the thermal conductivity of a body of rock and the heat flux. Thermal conductivity is not necessarily uniform because it depends on the mineralogical composition of the rock, the porosity, and the presence of water or gas. Therefore, differences in thermal conductivity between adjacent lithologies can result in a horizontal temperature gradient. Horizontal temperature gradients in some offshore fields can be observed because of a constant water temperature (approximately 4°C) in different depths in the seabed floor. The horizontal temperature gradient causes natural convection that might have a significant effect on species distribution (Firoozabadi 1999). The combined effects of diffusion (pressure, thermal, and molecular) and natural convection on compositional variation in multicomponent mixtures in porous media have been investigated for single-phase systems (Riley and Firoozabadi 1998; Ghorayeb and Firoozabadi 2000a).The results from these references show the importance of natural convection, which, in some cases, overrides diffusion and results in a uniform composition. Natural convection also can result in increased horizontal compositional variation, an effect similar to that in a thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al. 2006). The combined effect of convection and diffusion on species separation has been the subject of many experimental studies. Separation in a thermogravitational column with both effects has been measured widely (Schott 1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column consists of two isothermal vertical plates with different temperatures separated by a narrow space. The space can be either without a porous medium or filled with a porous medium. The thermal diffusion, in a binary mixture, causes one component to segregate to the hot plate and the other to the cold plate. Because of the density gradient caused by temperature and concentration gradients, convection flow occurs and creates a concentration difference between the top and bottom of the column. Analytical and numerical models have been presented to analyze the experimental results (Lorenz and Emery 1959; Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical studies show that the composition difference between the top and bottom of the column increases with permeability until an optimum permeability is reached. Then, the composition difference declines as permeability increases. The process in a thermogravitational column shows the significance of the convection from a horizontal temperature gradient.

An Improved Multicomponent Diffusion Model for Compositional Simulation of Fractured Unconventional Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Ye Tian ◽  
Chi Zhang ◽  
Zhengdong Lei ◽  
Xiaolong Yin ◽  
Hossein Kazemi ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Fractured Reservoirs ◽  
Multicomponent Diffusion ◽  
Unconventional Reservoirs ◽  
Fickian Diffusion ◽  
Minor Effect ◽  
Matrix Interface ◽  
Fine Grid ◽  
Soaking Time ◽  
Fluid Saturation

Summary Most simulators currently use the advection/diffusion model (ADM), where the total flux comprises Darcian advection and Fickian diffusion. However, significant errors can arise, especially for modeling diffusion processes in fractured unconventional reservoirs, if diffusion is modeled by the conventional Fick’s law using molar concentration. Hence, we propose an improved multicomponent diffusion model for fractured reservoirs to better quantify the multiphase multicomponent transport across the fracture/matrix interface. We first give a modified formulation of the Maxwell-Stefan (MS) equation to model the multicomponent diffusion driven by the chemical potential gradients. A physics-based modification is proposed for the ADM in fractured reservoirs, where fracture, matrix, and their interface are represented by three different yet interconnected flow domains to honor the flux continuity at the fracture/matrix interface. The added interface using a more representative fluid saturation and composition of the interface can hence better capture the transient mass fluxes between fracture and matrix. The proposed approach is also implemented in an in-house compositional simulator. The multicomponent diffusion model is validated with both intraphase and interphase diffusion experiments. Then, the improved model for fracture/matrix interaction is compared with a fine-grid model. The proposed multiple interacting continua (MINC) model with three continua (MINC3) can better match the fine-grid model’s result than the double-porosity (DP) model, which only obtains a fair match at an early time. Then, we simulate a gas huff ‘n’ puff (HnP) well in the Permian Basin to investigate the effect of diffusion within the fractured tight oil reservoir. The simulation reveals that diffusion has a minor effect on the performance of depletion when oil is the dominant phase. For gas HnP, the simulation neglecting diffusion will underestimate the oil recovery factor (RF) but overestimate the gas rate. The DP approach tends to overestimate the RF of heavy components but leads to a similar cumulative oil RF compared with MINC3. With the diffusion included in the simulation, gas HnP performance becomes more sensitive to the soaking time than the model without diffusion. Although increasing the soaking time will lead to a higher RF after considering diffusion, the incremental oil is not sufficiently large to justify a prolonged soaking time.

Reply to comments by Yao on “Multicomponent diffusion”

1967 ◽  
Vol 15 (2) ◽  
pp. 423-424
Author(s):  
T.O. Ziebold ◽  
A.R. Cooper
Keyword(s):  
Multicomponent Diffusion

Multicomponent Diffusion

2020 ◽  
pp. 31-38
Author(s):  
John Newman ◽  
Vincent Battaglia
Keyword(s):  
Multicomponent Diffusion
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