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Analysis Techniques to Measure Accurate Particle Size Distribution
Amit Agrawal, Sr Tech. Professional, Production Enhancement, Jajati Nanda, Sr Technologist, Analytical Services, Halliburton Technology Center (India) - Pune and Sumit Songire, Technologist Production Enhancement, Halliburton Technology Center (India) - Pune Selection of the proper sand size for a gravel pack completion can be one of the most important factors in completing an oil or gas well. The optimum size gravel, when placed around a properly sized screen, helps provide maximum productivity with reduced sand production.

Numerous theories on gravel sizing have been developed over the last 50 to 60 years. Early work by Coberly and Wagner1 suggested that if the gravel stops the largest 10 per cent of the formation sand, these larger grains will, in turn, stop the remaining 90 per cent of the formation sand.
For selecting the slot opening for sand control application, Coberley’s1 work showed that spherical grains form stable bridges on openings larger than the diametre of the formation grain, the ratio being two for rectangular openings and three for circular openings. Grain angularity and shape do not materially affect the opening size for a stable bridge,but do increase the range of bridging. In mixtures of two grain sizes of either spherical or angular grains, the bridging influence of the larger grain is great in relation to the amount present. One rule of thumb that is used is to determine the size of the slot opening or screen opening for screen only type completions is to make the opening less than or equal to the D10 of the formation sand as determined using a standard sieve analysis. This allows bridging of the larger particles to occur on the slotted liner or screen. The smaller particles in the sand distribution will then start bridging on the larger particles.
In 1972, Saucier2 suggested that the median gravel diameter for a gravel pack should fall within a range of five to six times the formation particle diameter at the median point of the sieve analysis (D50). Saucier’s work was focused on the absolute stoppage of the formation sands, and it has now become the industry standard. Saucier’s work showed formation sand would flow through the pack relatively unrestrained at a median pack to formation grain size ratio of approximately 14. In addition, his work showed that reduced pack permeability occurs in the ratio range of 6 to 14.
Where sands are generally more uniform in size and roundness, such as on the US Gulf Coast,slots equal to the 10 to 15 percentile point on a sieve analysis have been used.3
In order to apply the above and many other size selection criteria, it is necessary to determine accurate particle size distribution of the formation sand. All the above theories are based on the assumption that the analysed formation sand sample is truly representative ofthe formation particle size distribution. If this assumption is true then the other factor that many of the analysts tend to neglect is the method of particle size distribution analysis. All the above theories can be theoretically and practically applied only if the particle size distribution is accurate.

Various ways of measuring particle size distribution include the following:

Sieves Analysis
The sieve analysis procedure determines the relative grain size of solids such as sands, gravels proppants, and aggregates. Dry sample material passes through a specific set of sieves. The weight percentage of the sieved sample retained in each sieve is recorded. This is the traditional way of measuring particle size distribution. This technique is not onlyeconomicalbut is a readily usable technique for formation sand when a higher quantity of formation sand is considered for analysis.

Limitations: Cohesive and agglomerated materials such as clays are difficult to measure. A true weight distribution is not produced as the method relies on measuring the second smallest dimension of the particle.

Microscopic Images
This is an excellent technique that allows direct examination of the particles. However, the limitation of this technique is thatsince relatively few particles are examined, there is a real danger of unrepresentative sampling and if weight distribution is measured results are magnified. Sample preparation for electron microscopy is laborious and slow, and for manual methods fewer particles are examined.

Laser Particle Size Analysers ( LPSA)
Laser particle size analysers have been developed to meet the industry's growing need for global comparability of results, traceability, regulatory compliance, and efficiency in the laboratory. The analysers come with anaccuracy of ± 1 per cent. Software-driven operating conditions eliminate user variability and enable global method transfer. They come with a broad measuring range from 0.02 to 2000µm. These instruments are designed to handle a wide range of sample types.They can be used in dry or wet conditions depending upon the sample type and available quantities. The only limitation to oil industry use is that the amount of sample analysed in one test is very low. For dry analysis ~ 25 gm of sand sample is required whereas wet analysis requires ~ 10 gm of sample. In the following sections the discussion is for this widely used LPSA technique.
Limitation on data reporting using LPSA: Since the instrument for laser particle size analysis is easy to operate and many samples can be analysed in a shorter time, this is the most preferred method in the oil industry. However, formation sand obtained from an oil well may contain clays and fines along with the bigger formation sand. Fluid used for wet dispersion may have an effect on the particle size distribution readings.
The general assumption is that if the formation sand contains clays, using fresh water for dispersing the particles may causeswelling of the particles. Also, if some of the particles are light or very small then a surfactant would be required to get them into suspension so that they can be measured. In order to evaluate the effects of the clays and fines with different dispersion media a series of experiments were performed.
Analysis of pure sand:

Particle size distribution analysis of pure sand was performed. Assumption was made that this sand represents a major portion of the formation sand. As shown in the Figure (1) there was no difference in the particle size distribution in various dispersion media. This confirmed repeatability of the LPSA instrument in evaluating the particle size distribution.

Table (1) shows different d values obtained after the analysis. Since, pure sand (quartz) is inert to most of the carrier media,no difference in the particle size distribution was observed.
Analysis of pure fines:
Since fines or migrating clays are usually present in most formation sands, similar tests were performed with samples containing fines with different carrier fluids. It was observed that there was negligible interaction of fines with the carrier fluid as was the case with pure sand and no significant difference was observed in the particle size distribution.

Analysis of pure swelling clays:
Swelling clays were analysed for their particle size distribution using the same carrier fluids as used in the previous analysis. The common perception is that swelling clays would swell when they come in contact with water or brine and would result in higher particle size reading. This would result in an increase in overall d values. However, it was observed that overall particle size and distribution was decreased when swelling clays came in contact with other carrier fluids as compared to air.
When the equipment was observed closely, it was noted that some big chunks of the clays were formed during the experiment and were settled at the bottom of the measuring instrument and some chunks were stuck to the wall of the instrument. This resulted in reduced overall d values. Instead of larger d values we observed lower d values of swelling clays in presence of water as compared to dry analysis.
Analysis of sand+ fines +swelling clays mixture:
Since formation sand consists mostly of sand, fines and clays, a sand mixture was prepared simulating formation sand with the major part being inert or pure sand and some portion consisting of fines or migrating clays and swelling clays. Three conditions were considered for further analysis. (90/8/2):90 per cent sand+ 8 per cent fines + 2 per cent swelling clays; (90/5/5):90 per cent sand + 5 per cent fines + 5 per cent swelling clays and (80/10/10): 80 per cent sand + 10 per cent fines +10 per cent swelling clays. Results obtained from the analysis are summarised in the Table (4)
From the above results it is very clear that the sand mixture consisting of swelling and migrating clays behaved unpredictably. Based on mathematical interpolation, different d values for the sand mixture should have been as shown in the Table (5) (assuming dry dispersion is the most accurate way since there is no fluid interaction with sand grains)

Table (5) various d values calculated after interpolation for various sand mixtures Per cent differences in different d values of the mixture calculated numerically and observed experimentally are shown in the Table (6).
Assume that 10 per cent error is acceptable as an experimental error and human error. From the above data it is very clear that as clay content increases, deviation in the results increases. When swelling clay content was 2 per cent , there was error in only three points. As swelling clay content was increased deviation occurred in five different d values. It was observed that error points increased to seven in the last sand mixture when the clay content was highest for the present analysis.Almost all the points were deviating from the interpolated values.

1. LPSA technique can provide accurate particle size distribution for the clay free sand by using any dispersion media.
2. As clay content in the formation sand increases, results obtained from the LPSA analysis vary tremendously. This is true even when the dry dispersion method is used.
3. Interpolation of the particle size distribution of individual component in the sand sample can predict the particle size distribution of the mixture.