Statistical Study of the Crush Resistance Measurement for Ceramic Proppants
- Walter T. Stephens (Saint-Gobain Proppants) | Stephen K. Schubarth (Schubarth Inc.) | Deborah I. Rivera (Saint-Gobain Proppants) | E. Michael Snyder (Saint-Gobain Proppants) | Daniel Clare Herndon (Saint-Gobain Proppants)
- Document ID
- Society of Petroleum Engineers
- SPE Annual Technical Conference and Exhibition, 24-27 September, San Antonio, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2006. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 4.3.4 Scale, 4.1.2 Separation and Treating, 5.5.2 Core Analysis, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 2.5.2 Fracturing Materials (Fluids, Proppant), 5.3.4 Integration of geomechanics in models
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Crush resistance and size distribution are two measurements to select a proppant. While standard sieve analysis provides a good quantitative value for crush resistance, detailed size measurements can provide more understanding of proppant failure and the alteration of size distribution under load. The variance in proppant crush resistance is often larger than the typically reported accuracy of ±0.1%. In many cases, specimen handling and material retention upon sieves makes a real contribution towards measurement error.
This paper documents the variation in crush resistance measurements for proppants of similar size and size distribution at constant stress. Optical measurement of the size distribution can reveal more information about proppant failure under load. The paper discusses the sensitivity of the measurement with respect to manual versus automatic load application, loading rate, cell size, and specimen mass. The accuracy and precision of the test, along with the minimum sample size, are reported. The relationship between size distribution and crush resistance for different proppant materials is also presented.
The results of this paper address expanding the technical evaluation of proppants using new tools and analysis methods to provide a greater understanding of the crush resistance measurement. Operators will be able to select an appropriate proppant for their application with a practical understanding of measurement variation.
The American Petroleum Institute (API) defines the crush resistance test for proppants.1 A cylindrical cell holds a quantity of proppant and mechanical force compresses the proppant volume uniaxially at a specific rate to a desired pressure. After release of the mechanical force, the size distribution of the crushed proppant is measured. The definition of crush resistance is the weight percent of tested proppant that passes the smallest sieve of the originally specified size distribution. Several factors influence this measurement process and generate variance in the crush resistance value. The brittle materials comprising most proppants have a statistical rather than discrete mechanical strength. Each proppant will have a unique stress state that is a function of the local arrangement of proppants within the cell and this local arrangement will continuously change during compaction. Human factors, such as specimen handling and cell loading, can significantly affect the measurement process.
The crush resistance measurement must be a valid and reliable tool to quantify and compare proppant performance. Reducing sources of variance can improve the uniformity of the measured values. There are, however, many physical similarities between an actual propped fracture and the simulated proppant environment in a cell such that reduction of all variance could remove practical value from the results. The approach taken in this study is to characterize rather than eliminate the variance present in the process and then determine the validity of the test to evaluate proppants.
Characterizing the crush resistance requires statistical methods and tools to give an unbiased interpretation of the measurements and comparison between samples.2,3 Many methods describe a set of data using a confidence interval, which quantifies how close a point estimator is to the true population parameter for a specific certainty. For a desired confidence interval, a known or reasonably estimated standard deviation determines the required number of specimens to evaluate. Figure 1 shows the relationship between a 95% confidence interval and the number of specimens for a range of standard deviations. For a normally distributed process with a standard deviation is 0.5, 95% of the observed data ranges from -1 to +1 about the mean value. To determine the mean of this process with an accuracy of ±0.1, the required number of specimens to evaluate under identical test conditions is around 100.
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