Experimental measurement of dynamic effect in capillary pressure relationship for two‐phase flow in weakly layered porous media

Well‐defined laboratory experiments have been conducted to determine the significance of dynamic effect in capillary pressure relationships for two‐phase flow in weakly heterogeneous (layered) porous media. The heterogeneous layers are composed of a fine sand layer sandwiched between two coarse sand layers. Dynamic and quasi‐static capillary pressure–saturation (P^c–S) and ?S/?t–t relationships are determined, which are then used to determine the dynamic effect, indicated by a dynamic coefficient (τ). As well known, τ establishes the speed at which flow equilibrium (?S/?t = 0) is reached. In consistent with previous studies, τ is found to be a nonlinear function of saturation that depends on the medium permeability and the intensity of heterogeneity. τ values increase in the regions of less permeability (fine sand) in the domain. However, the τ–S functional dependence follows similar trends at different locations within the domain including regions of different permeability. We argue that saturation weighted average of local τ–S curves can be used as an effective τ–S curve for the whole domain which, when done, follows an exponential trend too. The effective τ–S curves suggest that the effective τ values for the porous layers lie between the τ values of coarse and fine sands at the same water saturation, and it is dominated by the τ values of coarse sand as it occupied the maximum volume of the domain. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 59: 1723–1734, 2013     

Dynamic effects in capillary pressure relationships for two‐phase flow in porous media: Experiments and numerical analyses

Well defined experiments and numerical analyses are conducted to determine the importance of dynamic effect in capillary pressure relationships for two‐phase flow in porous media. Dynamic and quasi‐static capillary pressure‐saturation (P^c‐S_w) and, ?S_w/?t‐t curves are determined. These are then used to determine the dynamic effects, indicated by a dynamic coefficient (τ) in the porous domains which establishes the speed at which flow equilibrium (?S_w/?t = 0) is reached. τ is found to be a nonlinear function of saturation which also depends on the medium permeability. Locally determined τ seems to increase as the distance of the measurement point from the fluid inlet into the domain increases. However, the functional dependence τ‐S_w follows similar trends at different locations within the domain. We argue that saturation weighted average of local τ‐S_w curves can be defined as an effective τ‐S_w curve for the whole domain which follows an exponential trend too. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 58: 3891–3903, 2012     

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

Numerical simulations for core‐scale capillary pressure (P^c)‐saturation (S) relationships have been conducted for a supercritical carbon dioxide‐water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO₂. As the P^c‐S relationships depend on both S and time derivative of saturation ( ) yielding what is known as the “dynamic capillary pressure effect” or simply “dynamic effect,” this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide‐water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO₂ (scCO₂)‐water flow is reached. The simulations in this work involved the solution of the extended version of Darcy's law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried out for three‐dimensional cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best‐fit straight line plotted between (1) the differences in dynamic and equilibrium capillary pressures against (2) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO₂‐water system increases as the saturation decreases. From a practical point of view, it implies that the time to reach capillary equilibrium during geological sequestration of CO₂ is an important factor and should be accounted for while simulating the flow processes, for example, to determine the CO₂ storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for scCO₂‐water flow as well as τ values. These issues are addressed in this article. © 2014 American Institute of Chemical Engineers AIChE J 60: 4266–4278, 2014     

Dynamic effects on capillary pressure–Saturation relationships for two‐phase porous flow: Implications of temperature

Work carried out in the last decade or so suggests that the simulators for multiphase flow in porous media should include an additional term, namely a dynamic coefficient, as a measure of the dynamic effect associated with capillary pressure. In this work, we examine the dependence of the dynamic coefficient on temperature by carrying out quasi‐static and dynamic flow simulations for an immiscible perchloroethylene–water system. Simulations have been carried out using a two‐phase porous media flow simulator for a range of temperatures between 20 and 80^°C. Simulation domains represent 3‐D cylindrical setups used by the authors for laboratory‐scale investigations of dynamic effects in two‐phase flow. Results are presented for two different porous domains, namely the coarse and fine sands, which are then interpreted by examining the correlations between dynamic coefficient(s) and temperature, time period(s) required for attaining irreducible water saturation, and the dynamic aqueous/nonaqueous phase saturation and capillary pressure plots. The simulations presented here maintain continuity from our previous work and address the uncertainties associated with the dependency of dynamic coefficient(s) on temperature, thereby complementing the existing database for the characterization of dynamic coefficients and subsequently enabling the users to carry out computationally economical and reliable modeling studies. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 58: 1951–1965, 2012     

Characteristics of air–water two‐phase flow in a 3‐mm smooth tube

Two‐phase flow pattern and friction characteristics for an air–water system in a 3.17 mm smooth tube are reported in this study. The range of mass flux is between 50 and 700 kg/m²s. The experimental data show that the two‐phase friction multipliers are strongly related to the flow pattern. For a stratified‐wavy flow pattern, a mass‐flux dependence of the two‐phase multipliers is seen. For a non‐stratified flow pattern, the two‐phase frictional multipliers are comparatively independent of mass flux. Correlations of the frictional multipliers are developed for stratified and non‐stratified flow. To use the appropriate correlation in different regime, a simple criterion is proposed.     

Oil–water two‐phase flow in microchannels: Flow patterns and pressure drop measurements

This paper investigates oil–water two‐phase flows in microchannels of 793 and 667 µm hydraulic diameters made of quartz and glass, respectively. By injecting one fluid at a constant flow rate and the second at variable flow rate, different flow patterns were identified and mapped and the corresponding two‐phase pressure drops were measured. Measurements of the pressure drops were interpreted using the homogeneous and Lockhart–Martinelli models developed for two‐phase flows in pipes. The results show similarity to both liquid–liquid flow in pipes and to gas–liquid flow in microchannels. We find a strong dependence of pressure drop on flow rates, microchannel material, and the first fluid injected into the microchannel.     

Shear dispersion in combined pressure‐driven and electro‐osmotic flows in a capillary tube with a porous wall

An analytical expression is derived for the shear dispersion during transport of a neutral nonreacting solute within a coupled system comprised of a capillary tube and a porous medium under the combined effects of pressure‐driven and electro‐osmotic flows. We use the Reynolds decomposition technique to obtain a dispersion coefficient by considering a sufficiently low wall or zeta potential that accounts for the combined flows. The coupled dispersion coefficient depends on the Debye–Hückel parameter, Poiseuille contribution fraction, and Péclet number. The developed model also provides a shear dispersion coefficient for an impervious capillary tube (noncoupled system). The ratio of the coupled (porous wall) and noncoupled (impervious) dispersion coefficients reveals that it is essential to include the transport of chemical species from the tube to the porous medium in several important physical situations. These findings have implications for design of chemical species transport in porous microfluidic networks and separation of emulsions in microchannel‐membrane systems. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3981–3995, 2015     

Analysis of roll wave characteristics under low liquid loading two‐phase flow conditions

An experimental study is conducted using a 0.152‐m ID facility to investigate the wave characteristics of two‐phase stratified wavy flow in horizontal pipelines. The experiments are conducted under low liquid loading condition, which is very commonly observed in wet gas pipelines. The experiments are conducted with water as the liquid phase, and repeated with 51 wt % of monoethylene glycol (MEG) in the aqueous phase to analyze the effects of MEG presence on wave characteristics. The experimental range of this study covers superficial gas velocity, v_Sg, values of 9–23 m/s and superficial liquid velocity, v_SL, values of 0.01–0.02 m/s. Similar test matrices are completed for the cases with and without MEG in the aqueous phase. A conductivity probe system is used to measure the wave characteristics at the liquid–gas interface. These characteristics include the wave celerity, frequency, amplitude, length, and liquid film thickness. The experimental oil–air wave characteristics data of Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) is also used for comparison purposes. The trends in the resulting wave characteristics with respect to input parameters are investigated, for oil, water, or MEG–water mixture as the liquid phase. Common predictive methods for interfacial wave celerity, including shallow water theory, Watson (Proceedings of the 4th International Conference in Multi‐Phase Flows, Nice, France. 1989:495–512), Paras et al. (Int J Multiphase Flow. 1994;20(5):939–956), Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029), and Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) are evaluated in comparison with the experimental data. The results of the wave frequency correlation of Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029) are also compared with the experimental wave frequency data. Lastly, a correlation is developed to predict the relative wave amplitude, as a function of superficial gas Weber number and liquid velocity number. Most of the commonly used two‐phase stratified flow models are developed with the assumption of steady‐state conditions, and neglect the transient wave effects. This study provides valuable experimental results on wave characteristics of stratified wavy flow for different types of liquid phase. Moreover, a comprehensive analysis of the parameters affecting the wave characteristics of stratified wavy flow is presented. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3177–3186, 2017     

Medium composition effects on solute partitioning in solid–liquid two‐phase bioreactors

Biphasic systems such as two‐phase partitioning bioreactors (TPPBs) have been used to alleviate biological inhibition by sequestering inhibitory compounds within an immiscible phase. The use of solid polymer beads as this auxiliary phase provides a fully biocompatible alternative to potentially toxic organic solvents. While guidelines exist for the rational selection of the polymer phase, the effect of the aqueous phase composition on molecular sequestration has not been explored in the literature. This work aims to identify aspects of medium composition that influence the partitioning of target molecules into the sequestering phase. Using benzaldehyde as the target molecule and Hytrel G3548L (DuPont) as the polymer phase, pH, temperature, salt and glucose concentrations, as well as ethanol concentrations, were examined for their effects on the partition coefficient. pH and temperature were observed to have no significant effect on benzaldehyde partitioning. Salt and glucose additions increased the partition coefficient by 173% and 30%, respectively, compared with pure reverse osmosis (RO) water, while increasing ethanol concentration was found to decrease the partition coefficient from 44 ( ± 1.6) to 1 ( ± 0.3). Strategic changes to the aqueous phase can be made to improve affinity of the sequestering phase for target molecules. This provides a simple and cost‐effective method to potentially improve TPPB system performance. Copyright © 2010 Society of Chemical Industry     

Influence of horizontal return bend on the two‐phase flow pattern in a 6.9 mm diameter tube

The two‐phase flow pattern for air‐water mixtures inside a 6.9 mm U‐tube is reported to have curvature ratios of 3?7.1. At a lower total mass flux of 50 kg/m²·s and a quality of 0.1, or at a larger curvature ratio of 7.1, no influence on the flow patterns is seen. However, if the curvature ratio is reduced to 3, the flow pattern in the recovery region just after the return bend is temporally turned from stratified flow into annular flow. For a quality larger than 0.4, the annular flow pattern prevails in the entire tube. For G = 400 kg/m²·s and x < 0.01, the size of the plug in the downstream is usually larger than that in the upstream due to the coalesce in the return bend. This coalescence phenomenon continues to further increase the total mass flux at the lower quality region. For a total mass flux above 500 kg/m²·s, the bubbly flow pattern in the upstream region may become intermittent.     

CFD analysis of two‐phase turbulent flow in internal airlift reactors

The hydrodynamic performance of three internal airlift reactor configurations was studied by the Eulerian–Eulerian k–ε model for a two‐phase turbulent flow. Comparative evaluation of different drag and lift force coefficient models in terms of liquid velocity in the riser and downcomer and gas holdup in the riser was highlighted. Drag correlations as a function of Eötvös number performed better results in comparison to the drag expressions related to Reynolds number. However, the drag correlation as a function of both Reynolds and Eötvös numbers fitted well with experimental results for the riser gas holdup and downcomer liquid velocity in configurations I and II. Positive lift coefficients increase the liquid velocity and decrease the riser gas holdup, while opposite results were obtained for negative values. By studying the effects of bubble size and their shape, the smaller bubbles provide a lower liquid velocity and a gas holdup. The effects of bubble‐induced turbulence and other non‐drag closure models such as turbulent dispersion and added mass forces were analysed. The gas velocity and gas holdup distributions, liquid velocity in the riser and downcomer, vectors of velocity magnitude and streamlines for liquid phase, the dynamics of gas holdup distribution and turbulent viscosity at different superficial gas velocities for different reactor configurations were computed. The effects of various geometrical parameters such as the draft tube clearance and the ratio of the riser to the downcomer cross‐sectional area on liquid velocities in the riser and the downcomer, the gas velocity and the gas holdup were explored. © 2011 Canadian Society for Chemical Engineering     

Effect of tube diameter on two‐phase flow patterns in mini tubes

The effect of tube diameter on two‐phase flow patterns was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6, and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01–50 and 0.01–3 m/s, respectively. The gas and liquid flow rates were measured and the two‐phase flow pattern images were recorded using high‐speed CMOS camera. The flow patterns observed were dispersed bubbly, bubbly, slug, slug‐annular, wavy‐annular, stratified, and annular flows. These flow patterns were not observed in all the test diameters, but were found to be unique to particular tube diameters, confirming the effect of tube diameter on the flow pattern. The data obtained were compared to existing experimental data and flow regime transition maps which show generally reasonable overall agreement at the larger diameters, but significant differences were observed with the smaller diameter tubes.     

Pressure drop for single and two‐phase flow of non‐newtonian liquids in helical coils

New experimental results on pressure loss for the single and two‐phase gas‐liquid flow with non‐Newtonian liquids in helical coils are reported. For a constant value of the curvature ratio, the value of the helix angle of the coils is varied from 2.56° to 9.37°. For single phase flow, the effect of helix angle on pressure loss is found to be negligible in laminar flow regime but pressure loss increases with the increasing value of helix angle in turbulent flow conditions. On the other hand, for the two‐phase flow, the well‐known Lockhart‐Martinelli method correlates the present results for all values of helix angle (2.56‐9.37°) satisfactorily under turbulent/laminar and turbulent/turbulent conditions over the following ranges of variables as: 0.57 ≤ n′ ≤ 1; Re′ < 4000; Re_l < 4000; Re_g < 8000; 8 ≤ x ≤ 1000 and 0.2 ≤ De′ ≤ 1000.     

Prediction of two‐phase pressure drop and liquid holdup in co‐current gas–liquid downflow of air–Newtonian systems through packed beds

The dependency of pressure drop and liquid holdup on phase velocities, geometry of the column and packing materials as well as on the physical properties have been analyzed. Our experimental data (825 data points obtained using four liquid systems and three different particles) along with those of the available literature (776 data point from five different sources) were used for the analysis. The applicability and the limitations of the literature correlations were evaluated using the available data. Based on the analysis, new correlations for the estimation of pressure drop and liquid holdup, valid for low and high interaction regimes have been developed using the available data, with a wide range of variables. Copyright © 2005 Society of Chemical Industry