手法を比較

	マッケイブ・チーレ法	トロンプ曲線	ウォッシャビリティ分析
分野	鉱山工学	鉱山工学	鉱山工学
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1925	1937	1950
提唱者	Warren L. McCabe and Ernest W. Thiele	K. Tromp	Mining Industry Practice (1930s-1960s)
種類	Graphical design method for distillation columns	Empirical model for size classifier performance	Separation analysis by density fractionation
原典	McCabe, W. L., & Thiele, E. W. (1925). Graphical design of fractionating columns. Transactions of the American Institute of Chemical Engineers, 21, 30-60.	Tromp, K. (1937). Separation of fine particles from slurries by hydrocyclone. Colliery Guardian, 155(4), 251-256.	McCullough, R. B. (1963). The theoretical basis and practical application of coal washability studies. Transactions of the Society of Mining Engineers, 226, 13-26.
別名	McCabe-Thiele Diagram, Graphical Distillation Method	Partition Curve, Classification Efficiency Curve, Grade Recovery Curve	Coal Washability, Density Separation Analysis, Float-Sink Analysis
関連	3	3	3
概要	The McCabe-Thiele Method, introduced by Warren L. McCabe and Ernest W. Thiele in 1925, is a graphical technique for designing and analyzing distillation columns. It predicts the number of theoretical plates (stages) needed to achieve a desired separation between light and heavy components. While primarily a chemical engineering tool, it applies to liquid-vapor separation problems in mining operations such as mercury recovery and rare earth element refining.	The Tromp Curve, introduced by K. Tromp in 1937, is an empirical model that quantifies the performance of size classifiers (cyclones, screens, jigs) by showing the fraction of particles at each size that report to the target stream (overflow or underflow). It is universally used in mineral processing to evaluate classifier performance, design circuits, and diagnose operational problems.	Washability analysis is a laboratory method that determines the feasibility and efficiency of density-based separation for coal or mineral beneficiation. By fractionating ore or coal into density bins using sink-float tests and assaying each fraction, engineers can optimize design of separation plants (dense-medium cyclones, jigs, spirals) and predict clean product quality. Washability curves are essential tools for pre-feasibility and detailed design studies.