Standalone screen (SAS) design conventionally relies on particle size distribution (PSD) of the reservoir sands. The sand control systems generally use D-values, which are certain points on the PSD curve. The D-values are usually determined by a linear interpretation between adjacent measured points on the PSD curve. However, the linear interpretation could result in a significant error in the D-value estimation, particularly when measured PSD points are limited and the uniformity coefficient is high. Using the mathematical representation of the PSD is an efficient method to mitigate these errors. The aim of this paper is to assess the performance of different mathematical models to find the most suitable equation that can describe a given PSD.
The study collected a large databank of PSDs from published SPE papers and historical drilling reports. These data indicate significant variations in the PSD for different reservoirs and geographical areas. The literature review identified more than 30 mathematical equations that have been developed and used to represent the PSD curves. Different statistical comparators, namely, adjusted R-squared, Akaike's Information Criterion (AIC), Geometric Mean Error Ratio, and Adjusted Root Mean Square Error were used to evaluate the match between the measured PSD data with the calculated PSD from the formulae. The curve fit performance of the equations for the overall data set as well as PSD measurement techniques were studied. A particular attention was paid towards investigating the effect of fines content on the match quality for the calculated versus measured curves.
It was found that certain equations are better suited for the PSD database used in this investigation. In particular, Modified Logestic Growth, Fredlund, Sigmoid and Weibull models show the best performance for a larger number of cases (highest adjusted R-squared, lowest Sum of Squared of Errors predictions (SSE), and very low AIC). Some of the models show superior performance for limited number of PSDs. Additionally, the performance of PSD parameterized models is affected by soil texture: For higher fines content, the performance of equations tends to deteriorate. Moreover, it appears the PSD measurement techenique can influence the performance of the equations. Since the majority of the PSD resources used here did not mention their method of measurement, the effect of measurement technique could only be tested for a limited data, which indicates the measurement technique may impact the match quality.
Fitting of parameterized models to measured PSD curves, although well known in sedimentology and soil sciences, is a relatively unexplored area in petroleum applications. Mathematical representation of the PSD curve improves the accuracy of D-values determination, hence, the sand control design. This mathematical representation could result in a more scientific classification of the PSDs for sand control design and sand control testing purposes.