In the current work, we utilize a recently developed staged Livengood-Wu (L-W) correlation to evaluate and predict the two-stage ignition behaviors of different primary reference fuels (PRFs) under homogeneous reciprocating engine conditions, to demonstrate its capability in capturing detailed ignition kinetics in combustion simulation. Based on the understandings of the global and detailed kinetics of low-temperature chemistry, simplified Arrhenius-based global expressions were developed for both ignition stages, and a linear correlation was applied for the cool flame temperature rise at the end of the first stage, for PRFs with various octane number (ON) 0, 20, 60 and 87 under constant volume conditions. For their performance under homogeneous charge compression ignition (HCCI) conditions, it is shown that for the same engine speed, the inlet temperature range allowing for two-stage ignition shrinks with increased ON numbers, and eventually two-stage ignition turns into single-stage ignition with sufficiently high ON numbers. Based on the ignition database, the combustion phasing for all PRFs under a wide HCCI operation range are predicted with the staged L-W integral method with satisfactory accuracy, including the first-and second-stage ignition timing as well as the cool flame temperature rise. The sensitivities of each of the engine operation parameters are successfully captured, further demonstrating the applicability of the staged L-W method for realistic fuels with low temperature chemistry and its potential applications for engine combustion control. This study also provides an alternative approach of accommodating low temperature ignition kinetics in combustion simulation, especially useful for those under variable thermodynamic conditions. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.