Study of an aqueous foam flow in horizontal pipes.

NÓLIDES GUZMÁN, PH.D.^*, OVADIA SHOHAM, PH.D.^**, RAM MOHAN, PH.D.^***

^*Escuela de Ingeniería Química, Facultad de Ingeniería, Universidad Central de Venezuela. Venezuela.

^**Petroleum Engineering Department, The University of Tulsa, U.S.A.

^***Mechanical Engineering Department, The University of Tulsa, U.S.A.

Several sets of experimental data were acquired for an aqueous two-phase foam flow in horizontal pipes, including flow pattern maps and rheological flow behavior. The data were acquired in two pipe diameters under various inlet flow conditions, utilizing a commercial surfactant, F-450, at two concentrations. The experimental results were plotted on a Taitel and Dukler (1976) flow pattern map predicted for the experimental flow conditions. As this model does not predict accurately the transition boundaries for foam flow, modifications of the original model were carried out for matching the experimental data. Different rheological models were tested for characterizing the behavior of the studied aqueous foam. The results obtained show that this foam flow behaves as non-Newtonian flow, following the Power Law model. It was also observed that foam rheology is flow pattern dependent. Comparison between the developed models and the acquired experimental data shows a good agreement.

Keywords: foam, foam rheology, aqueous foam, two-phase foam flow, foam flow patterns.

Varios grupos de datos experimentales fueron obtenidos para el flujo bifásico de espuma en tuberías horizontales; estos incluyen: mapas de patrones de flujo y comportamiento reológico del flujo. Los datos fueron obtenidos para dos diámetros de tubería a varias condiciones de flujo de entrada, utilizando el surfactante comercial F-450 a dos concentraciones. Los resultados experimentales fueron representados en el mapa de patrones de flujo de Taitel y Dukler (1976) predicho a las condiciones experimentales de flujo. Como este modelo no predice apropiadamente los límites de transición para flujo de espuma, se requirieron modificaciones del modelo original para ajustarlo a los datos experimentales. Se probaron diferentes modelos reológicos para caracterizar el comportamiento de la espuma acuosa estudiada. Los resultados muestran que este flujo de espuma se comporta como no Newtoniano, siguiendo el modelo de la Ley de Potencia. También se observó que la reología de la espuma depende del patrón de flujo. Las comparaciones entre los modelos desarrollados y los datos experimentales muestran buen ajuste.

Recibido: noviembre de 2006 Recibido en forma final revisado: abril de 2007

Foams are useful in many industrial applications, such as in paper processing, fire-fighting, and enhanced oil recovery (EOR). However, in other processes the production of foam is often an unwanted consequence. A proper design of a foam flow system requires an understanding of the physical phenomena involved. The nature of the foam, i.e., its structure, foamability, stability, and its overall rheological properties can determine both  the economical and technical successes of an industrial process.

Several models have been developed for foam characterization to relate the different effects observed on foams. Scientists who have studied foamy fluids rheology have used different models for foam characterization. Utilizing the model that better represents the foam flow behavior enables more accurate prediction of the pressure drop. This requires that all the characteristic parameters of the foam are known.

Rheology can be evaluated using different equipments. Among the most commonly used are: Couette rheometer, circulating pipe rheometer and single-pass pipe rheometer. In the present study, a single-pass pipe rheometer was used for foam characterization due to its simple design and suitability for the flow conditions that were covered in this research.

This study was carried out at the Tulsa University Separation Technology Projects (TUSTP). The rheology section, installed in a two-phase flow facility, consisted of 56 ft long 1 in. and 2 in.-diameter horizontal pipes (Figure 1). Two absolute pressure transducers are placed one at each end of the rheology section, for measurement of the pressure at the inlet and at the outlet of the pipes, enabling determination of the foam flow pressure drop. Also, a visualization window is installed in each pipe for flow pattern observations.

Water and surfactant are mixed in a tee to form the surfactant solution. This solution and compressed air are combined in a mixing-tee to promote foam formation. The generated foam flows through a static mixer to ensure homogeneity of the flow. The foam then flows through the rheology section where all measurements are acquired. Downstream, the flow enters into a separation tank where the air is vented into the atmosphere and the surfactant solution is drained.

Data were acquired for various inlet flow conditions: superficial gas velocity between 20 and 70 ft/s and superficial liquid velocity between 0.25 and 0.85 ft/s, using commercial surfactant (F-450) at two concentrations of 0.02 and 0.04% vol./vol..

As can be seen, the results for the two surfactant concentrations are similar. Also, the Taitel and Dukler (1976) model (represented by the solid lines) does not predict accurately the stratified to non-stratified and the slug to annular transition boundaries for foam flow. Modifications of the original model are required for matching the experimental data.

Note that flow patterns were also observed in the 1 in.-diameter rheology pipe section. For this case, only annular flow was observed for all flow conditions.

The experimental data are plotted in figure 6 in the form of natural log of wall shear stress vs. natural log of shear rate. The figure demonstrates that there are two different regions; one corresponding to stratified flow conditions while the other is for non-stratified (slug and annular) flow conditions. Within each region, the flow behaves according to the Power Law model, as the data exhibit straight lines, with different slopes for the stratified and the non-stratified cases.

Various rheological models were tested against the experimental data of foam flow acquired in this study. The best correlation with the data was obtained with the Power Law Model, as shown in figure 6.

For the Power Law Model, the shear stress vs. shear rate is given by:

The following equations were obtained by correlating the experimental data, using the form of the Law of the Wall. The consistency index for the stratified flow regime is given by:

Kf_s = a_s In(Re_M) + b_s,  (3)

which is valid for the range:

4x10³ < Re_SL < 2x10⁴ and 10³ < Re_M < 10⁶

Similarly, for non-stratified flow:

valid for the range 8x10³ < Re_SL < 3X10⁴ and 10³ < Re_M < 10⁷.

a_i = A_i . In(Re_SL) + A₂,  (5)

b_i = B_i . In(Re_SL) + B₂, = (6)

The superficial liquid Reynolds number and the mixture Reynolds number are defined, respectively, by

The definition of the mixture Reynolds number is similar to the one presented by Briceño and Joseph (2003) for selflubrication transport of aqueous foams.

Stratified to non-Stratified Transition

Figures 2 and 3 show that Taitel and Dukler (1976) model underpredicts this transition boundary, namely, the predicted transition occurs at lower superficial velocities, as compared with the experimental data.

Slug to Annular Transition

Figure 8 presents a comparison between the predictions of the original Taitel and Dukler (1976) model, the modified model based on Eqs. 9 and 10, and the experimental data. As can be observed, the predictions of the modified model agree closely with the experimental data.

The power law model was modified for aqueous foam flow.

Comparison between the developed correlation and model modifications with the acquired experimental data shows good agreement.

The authors acknowledge the financial support of Universidad Central de Venezuela and Tulsa University Separation Technology Projects (TUSTP).

Re = Reynolds number

EXP = experimental

M = mixture

NS = non-stratified

S = stratified

SG = superficial gas

SL = superficial liquid

A = annular flow

mod = model

dat = experimental data

SF = stratified flow

SL = slug flow