Reduced order models for describing dispersion and reaction in monoliths

Ratnakar, Ram R.; Bhattacharya, Madhuchhanda; Balakotaiah, Vemuri

doi:10.1016/j.ces.2011.09.056

Cited by 27 publications

(25 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the study by series expansion and through illustration in Chatwin (1970), the longitudinal normality of the mean concentration has been well established at a time scale of 1.0R 2 /D, as verified by other studies (Houseworth 1984;Stokes & Barton 1990;Phillips & Kaye 1996). A generalized dispersion model was presented in Gill (1967), Gill & Sankaras (1970), Gill & Sankarasubramanian (1971), and strides towards a certain exact averaging model were made recently by applying the Lyapunov-Schmidt technique of bifurcation theory (Ratnakar & Balakotaiah 2011;Ratnakar, Bhattacharya & Balakotaiah 2012). Asymptotic analyses for the dispersion (Phillips & Kaye 1996, 1997 and numerical simulations of the transport process (Houseworth 1984;Stokes & Barton 1990;Shankar & Lenhoff 1991) have also been carried out.…”

mentioning

confidence: 92%

Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

Chen

2014

J. Fluid Mech.

125

View full text Add to dashboard Cite

Associated with Taylor's classical analysis of scalar solute dispersion in the laminar flow of a solvent in a straight pipe, this work explores the approach towards transverse uniformity of concentration distribution. Mei's homogenization technique is extended to find solutions for the concentration transport. Chatwin's result for the approach to longitudinal normality is recovered in terms of the mean concentration over the cross-section. The asymmetrical structure of the concentration cloud and the transverse variation of the concentration distribution are concretely illustrated for the initial stage. The rate of approach to uniformity is shown to be much slower than that to normality. When the longitudinal normality of mean concentration is well established, the maximum transverse concentration difference remains near one-half of the centroid concentration of the cloud. A time scale up to 10R 2 /D (R is the radius of the pipe and D is the molecular diffusivity) is suggested to characterize the transition to transverse uniformity, in contrast to the time scale of 0.1R 2 /D estimated by Taylor for the initial stage of dispersion, and that of 1.0R 2 /D by Chatwin for longitudinal normality.

show abstract

mentioning

confidence: 92%

Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

Chen

2014

J. Fluid Mech.

125

View full text Add to dashboard Cite

show abstract

“…Regarding the accuracy (and validity) of the present model with respect to simpler or more complex models, the following comments (which are substantiated in references [22][23][24][25][26][27][28][29][30][31][32]) are appropriate: (i) The simplest of the models, namely the one dimensional pseudo-homogeneous plug flow model is structurally unstable and does not show ignition/extinction but only parametric sensitivity (ii) The pseudo-homogeneous model with no axial gradients (which is included as a special case of our model when interphase gradients are negligible) is robust but is good only for very small axial length scales and hydraulic diameters (micro-channels) [Remark: Structural stability or robustness here implies that the bifurcation and/or qualitative features do not change when the model is perturbed by including spatial gradients or other phenomena as long as the perturbations are small, see [30]] (iii) The 2-D boundary layer models (of parabolic type) that ignore axial diffusion (conduction) are structurally unstable, index infinity differential-algebraic system (and are not initial value problems). Further, as explained in the literature articles [23,26], most computational codes do not consider the Gibbs' phenomenon (which does not disappear even for arbitrarily small mesh size and leads to incorrect fluxes and temperature overshoot at the point of ignition) and compute only a single solution.…”

Section: Model Developmentmentioning

confidence: 98%

“…However, when the velocity profile is fully developed before entering the reactive section (e.g. fully developed laminar flow in a channel where a part of the fore section is not coated or reactive), three modes (simple spatial average, where homogeneous rate is evaluated, mixing-cup average, which is the experimentally measured value and the value at the wall, where the catalytic rate is evaluated) are necessary to describe the local (transverse) gradients [25,29]. We do not consider this more general three-mode lumped model in this work.…”

Section: Model Developmentmentioning

confidence: 99%

Bifurcation analysis of thermally coupled homogeneous–heterogeneous combustion

Alam

West

Balakotaiah

2015

Chemical Engineering Journal

Self Cite

View full text Add to dashboard Cite

“…(6) as follows: (10) Note that the ratio of volumes of oil-phase to gas-cap (␣) is already known. The Henry's constant can also be measured independently by other methods.…”

Section: Estimation Of Henry's Constantmentioning

confidence: 99%

“…Molecular diffusion is one of the core transport phenomenon in various disciplines of science and engineering, including chemical engineering [1][2][3][4] , polymer science [5] , Biology [6][7] , combustion technology [8] , automobile industries [9][10][11] , petroleum engineering (tertiary recovery in CO2 flooding [12][13][14][15][16] ; Vapex [17][18] ; solution gas drive process [19] ; drilling fluid [20] ; acid fracturing [21][22] ) and many more. In Petroleum engineering applications, the molecular diffusion plays a very important role in various reservoir processes; especially in the oil recovery processes where convective forces are not dominant or when direct frontal contact and mixing is not possible.…”

Section: Introductionmentioning

confidence: 99%

Measurement of Gas Diffusivity in Heavy Oils/Bitumens using Pressure-Decay Test

Ratnakar

Dindoruk

2014

SPE Annual Technical Conference and Exhibition

Self Cite

View full text Add to dashboard Cite

Molecular diffusion plays a very important role in various reservoir processes; especially in the oil recovery processes where convective forces are not dominant or when direct frontal contact and mixing is not possible. For example, in heavy oil and bitumen recovery, injected light hydrocarbons can diffuse into the oil beyond the potential fronts and/or convective zones and promote the effectiveness of the displacement process, and therefore, reduce in-situ viscosities which in turn enhance the oil recovery.Similarly, diffusive mixing can also be a dominant mechanism in the gas re-dissolution process even in lighter hydrocarbon systems. For example, it controls how much gas will be dissolved in oil and how long it will take to dissolve, in the absence of mechanical/convective mixing, as in the case of reservoir re-pressurization. The extent of dissolution of a gas into oil is governed by its solubility but the rate is controlled by molecular diffusivity and solubility, both. Thus accurate determination of these parameters is essential to design and understand displacement processes.Despite the significance of diffusion in various aspects of oil recovery, there are very few experimental studies available in the literature addressing the diffusion of gas in heavy oils. Experimental work is most commonly based on the Pressure-decay concept. However, the parameter inversion in these tests relies on an error function solution that neglects the transient processes at the gas-oil interface and assumes constant saturation concentration. This assumption is not appropriate because pressure in the gas cap changes continuously as gas is dissolved in the oil and hence the gas solubility varies with time. One of the major issues related to this experimental process is that it takes a long time (order of several days to few months) to achieve steady state (converged) solution to determine diffusivity.In this work, we have 1. Experimentally investigated the diffusion of methane in heavy oils as well as light oils using pressure-decay test; 2. Captured the transient effect at the gas-oil interface transient properly by expressing gas solubility in terms of Henry's constant in the model (1-dimensional diffusion equation coupled with pressure decline due to gas dissolution); 3. Developed the exact solution of the model and shown that after long time, pressure decays exponentially in time with an exponent that depends on diffusivity as well as solubility;4. Presented the inversion technique, determined the diffusivity and other parameters from late transient pressure data, and showed the convergence in their estimates; and, 5. Most importantly, we have developed a cut off criterion permitting us to stop the experiments while still being able to extract the converged diffusivity values (this is important in situations when the experiment is stopped prematurely for technical or other reasons).

show abstract

Reduced order models for describing dispersion and reaction in monoliths

Cited by 27 publications

References 18 publications

Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

Bifurcation analysis of thermally coupled homogeneous–heterogeneous combustion

Measurement of Gas Diffusivity in Heavy Oils/Bitumens using Pressure-Decay Test

Contact Info

Product

Resources

About