Bulk foam
Figure 1 shows the foam texture analysis at different concentration of surfactant solutions and at the different elapsed times after they were generated in the static foam analyzer. Moving from left to right for each surfactant concentration in Fig. 1, foam bubbles collapse with elapsed time due to Ostwald ripening or bubble coalescence. This results in larger bubble sizes and smaller bubble density (numbers) as the foam ages and its height decreases. However, an increase in surfactant concentration (moving from top to bottom in Fig. 1) at each elapsed time, results in a better foam texture. The effect of surfactant concentration appears to be optimum at a concentration of 2.5 wt%. Hence, there was no substantial improvement in foam texture beyond this concentration.
The texture of bulk foam at different time steps after bulk foam was generated (0–3600 s). The texture is shown for different surfactant concentrations ranging from 0.02 to 10 wt%.
In terms of the foam stability, as shown in Fig. 2, foam half-life increases with an increase in surfactant concentrations. However, at concentration above 2.5 wt%, the increase of the half-life is not so significant. Similarly, in Fig. 3, the measurement of the surface tension was very steep up to 2.5–5 wt%, after which the reduction was founds to be gradual. It is clear from Figs. 2 and 3 that an asymptote has not been reached, which indicates that slight changes in foam properties occur as surfactant concentration is increased. Nonetheless, an optimum surfactant concentration value is required, which is the concentration beyond which the properties of the foam do not change significantly to justify the associated cost of increasing the concentration. From the analysis of the bulk foam in this study, 2.5 wt% appears to be the optimum concentration. The findings from the investigation of optimum surfactant concentration for foam performance in porous media are presented in the next section.
Foam half-life versus surfactant concentrations.
Surface tension of surfactant solution at various concentrations.
Foam in rock samples
First, the pore characteristics of the rock samples are presented in terms of their capillary pressure curves (Fig. 4) and NMR T2 relaxation distribution (Fig. 5). Table 2 also summarizes other data on pore structure based on micro-CT image-based pore network models and XRD analysis. It is obvious from these figures that the three rock samples are significantly distinct from one another in terms of porosity, permeability, capillary pressures, and pore size distribution. This paves the way for a more holistic study of the impact of a wide range of rock pore structures on foam properties. Sample IDG has a low capillary pressure regime because of the large pore sizes (as illustrated by the long T2 relaxation in Fig. 5), while sample AC has the highest capillary pressure because it has the lowest pore size (short T2 relaxation). Sample B lies between the two extremes in all definitions of pore characters as shown in Table 3.
Capillary pressure curves.
NMR T2 relaxation curves.
Trapped and mobile foam saturation of the rock samples were estimated from measured resistivity values by using Archie’s equation (Eq. 1).
$$ S_{w} = \left( {\frac{{R_{0} }}{{R_{t} }}} \right)^{1/n} $$
(1)
where \({S}_{w}\) is the in-situ water saturation in the rock sample (in fraction), \({R}_{0}\) (ohm-m) is the electrical resistivity of the rock when it is 100% saturated with brine (with dissolved surfactant), \({R}_{t}\) (ohm-m) is the resistivity of the rock at partial water saturation, and ‘n’ is the saturation exponent, a parameter derived during a porous plate resistivity index experiment. Since only two phases were flowing through the porous medium, i.e., liquid and gas, gas, or foamed gas saturation (\({S}_{g}\)) at any instance is estimated with Eq. (2).
$${S}_{g}=1- {S}_{w}$$
(2)
Figures 6, 7, 8, 9, 10 and 11 show different foam properties (trapped foam, apparent viscosity, limiting capillary pressure, mobile-to-trapped foam ratio) versus surfactant concentration in all three rock samples. These foam properties changed as surfactant concentration increased to different degrees.
Effect of surfactant concentration on (A) trapped foam (B) Apparent viscosity of foam, for different permeability.
Effect of surfactant concentration on (A) limiting capillary pressure of foam (B) mobile-to-trapped foam ratio, for different permeability.
Effect of surfactant concentration on (A) trapped foam (B) mobile-to-trapped foam ratio for different pore sizes.
Effect of surfactant concentration on (A) limiting capillary pressure of foam (B) mobile-to-trapped foam ratio, for different pore sizes.
Effect of surfactant concentration on (A) trapped foam (B) apparent viscosity, for different T2LM.
Effect of surfactant concentration on (A) limiting capillary pressure of foam (B) mobile-to-trapped foam ratio, for different T2LM.
In terms of the effect of surfactant concentration on given foam properties, a good agreement was observed among all measured bulk foam properties and foam properties in the rock samples. All static and dynamic foam properties were improved with an increase in surfactant concentration (foam strength). However, disparity occurs when the effect of pore properties was considered in the comparison, which suggests that the comparison of foam properties in different rocks must be done cautiously.
Figures 6, 7, 8, 9, 10 and 11 show how surfactant concentration affects trapped foam, apparent viscosity, and limiting capillary pressure in a variety of rocks with a wide range of pore character: permeability range of 26–5000 mD; average pore size of 4–9 µm; average throat size of 2.7–6 µm. The saturation of trapped foam and consequently the apparent viscosity of foam increase for every increase in surfactant concentration (by extension for every increase in foam strength) and with each rock pore character, represented by a data point in the figures. However, the character of the pores above a threshold value has a reverse effect on the foam properties as seen in Fig. 6. Based on these figures, it appears that an optimum permeability value exists somewhere between 278 and 5000 mD at which foam properties reverse its trend from the initial trend. Interestingly, the reversal (or drop in) trapped foam saturation and apparent viscosity only occur when the surfactant concentration is higher than 0.025 wt%. As the surfactant concentration increases, the severity of the reversal increases (i.e., the curve becomes more concave). The exact reason for this requires a more comprehensive study. There is almost a complete overlap between surfactant concentration of 2.5 wt and 5 wt%, for foam trapping (Fig. 6) and limiting capillary pressure (Fig. 7).
The similarity between the behavior of foam trapping and the apparent viscosity of foam shows that trapped foam saturation is mainly governed by the apparent viscosity of foam.
The limiting capillary pressures of foam also increase when surfactant concentration increases (Fig. 7A). However, with respect to changes in permeability, the limiting capillary pressure of foam differs from other foam properties (i.e. trapped foam saturation and its apparent viscosity). The limiting capillary pressure decreases as permeability increases. This is expected because the capillary pressure regimes in high-permeability rocks are not as high as in lower-permeability rocks. Hence, since foam limiting capillary pressure is the most direct measure of foam strength12, foam is stronger in low-permeability rock than in high-permeability rock, and with an increase in surfactant concentration, it further increases the strength of generated foam (Fig. 7A). There is also no reversal in the limiting capillary pressure trend as was observed in the case of trapped foam saturation and apparent viscosity in Fig. 6.
Since increasing surfactant concentration increased trapped foam saturation (Fig. 6A), it is then expected that mobile foam saturation decreases as surfactant concentration increases as shown in Fig. 7B. Similarly, for the same reason, the mobile-to-trapped foam decreases with an increase in permeability, with a similar reversal at the same threshold permeability value in Fig. 6A.
Based on the results in Figs. 6 and 7, it can be suggested that trapped foam saturation directly affects apparent viscosity and mobile-to-trapped foam ratio. Hence, trapped foam saturation or any of its dependent variables can be used to compare foam performance in rocks of the same pore character. However, it cannot be said that foam strength increases with increased trapping when comparing two different rock pore geometry since trapping and limiting capillary pressure have a different correlation with the change in pore geometry.
It was earlier shown that foam with large bubbles corresponds to weak foam based on bulk foam analysis in Fig. 1. Also, rocks with large pores, large throats, and high permeability enhance the formation of large bubbles (large foam texture) since foam assumes the structure of the pores where they are generated. The tendency of weak (coarse) foam to flow is also lower because of low differential pressure and low flow velocity across high permeability rock19,21,22. Hence, they remain trapped due to insufficient pressure drop present in high permeability rocks. As a result, trapped foam saturation is expected to rise with increased permeability and vice versa. The limiting capillary pressure of foam also decreases with an increase in permeability (Fig. 7), a confirmation that high permeability rocks generate weaker foam than lower permeability rocks. It therefore becomes difficult to judge if higher trapped foam saturation in one rock sample relative to another is an indication of stronger foam or weaker foam.
The aforementioned foam properties were plotted with other rock pore characters (average pore size, average throat size, and the log mean of T2 relaxation). These foam properties have similar responses to the variation in these pore characters as shown in Fig. 8 (Trapped foam and apparent viscosity versus pore size); Fig. 9 (limiting capillary pressure and mobile-to-trapped foam ratio versus pore size); Fig. 10 (trapped foam and apparent viscosity versus NMR T2); and Fig. 11 (limiting capillary pressure and mobile-to-trapped foam ratio versus NMR T2). Average pore size can also be represented in terms of the logarithmic mean of NMR T2 relaxation since T2 relaxation has a one-to-one relationship with pore size. The larger the pore size, the longer the T2 relaxation time.
To determine the optimum surfactant concentration for foam in porous media, each of the foam properties was plotted against surfactant concentration for the three rock samples tested (Figs. 12, 13, 14 and 15). From the results, it can be concluded that the optimum surfactant concentration for foam trapping, apparent viscosity, mobile-to-trapped foam ratio, and limiting capillary pressure appears to be 1 wt%, in sample B and IDG, while that for sample AC appears to be 2.5 wt%. This optimum value is similar for bulk foam, which is 2.5 wt%.
Trapped foam saturation versus surfactant concentration for three samples.
Apparent viscosity of foam versus surfactant concentration for three rock samples.
Average mobile-to-trapped foam ratio versus surfactant concentration in three rock samples.
Limiting capillary pressure of foam versus surfactant concentration in three rock samples.
Comparison between bulk foam and foam in porous media
The findings above have a significant implication when comparing foam properties measured by a different group of researchers or measured using different experimental procedures. Static foam analyzers have a porous disk at their base with varying permeability or pore size distributions. For example, the pore size distribution of the porous disk in the static foam analyzer used in this study is 40–100 µm. If another group of researchers working elsewhere with a foam analyzer (with an average pore size of say 4 µm) conduct a similar experiment with the same surfactant type and concentration, they may not be able to replicate the results. This is because both research groups use static foam analyzers with different base porous disks, whose individual pore sizes fall on two different extremes of the threshold pore size/permeability values reported in Figs. 8 and 10. There is a variety of specifications of static foam analyzers available, with the pore sizes of the base porous disk (filter) ranging from 0.5 to 100 µm11,12,16,23, which makes the experimental conditions differ, especially the capillary pressure. Some other foam analyzers do not use a porous disk to generate foam, but by mere mixing gas and surfactant solution at defined speeds like in a blender9,24. Since the foam texture or bubble size is dependent on the pore size of the porous discs25 or the mixing speed, the rate of foam decay, half-life, and other foam properties can defer among the foam analyzers for the same foam formulation. It is therefore a good practice for researchers to report more information about the static foam analyzer used in the reported tests such as the average pore size of base porous disk, the procedure for generating foam in the foam column (gas sparging or blender method), gas bubbling rate through the disk (for gas sparging foam analyzer), the stirring rate (for a blender type of foam analyzer). There is also a concern about whether static foam tests measure foam stability only or whether it gives an indication of foam strength26. Hence, for a fair comparison between static foam and dynamic foam, the porous disk or filter in the static foam analyzer must have a similar pore geometry as the rock samples used in core flooding experiments.
