Modeling Cement Hydration Kinetics Using the Equivalent Age Concept Xueyu Pang 1 , Dale P. Bentz 2 , Christian Meyer 1 1: Dept. of Civil Engineering and Engineering Mechanics, Columbia University, USA 2: Engineering Laboratory, National Institute of Standards and Technology, USA In this study the hydration kinetics of four different types of cements during early ages were investigated by both chemical shrinkage and isothermal calorimetry tests. Chemical shrinkage tests were performed at both different temperatures and pressures while isothermal calorimetry tests were conducted only at different temperatures. The hydration kinetics curves at different curing conditions were found to converge reasonably well if properly transformed with a set of scaling factors. Therefore, the experimental hydration kinetics curve at one curing condition can be used to predict that of another curing condition using a single scale factor. The scale factor is similar to the coefficient used to compute the equivalent age of a specified curing condition when applying the maturity method to estimate concrete strength. Its dependence on curing temperature and curing pressure can be modeled by the activation energy and the activation volume of the cement, respectively. Keywords: hydration kinetics, temperature, pressure, chemical shrinkage, heat evolution, oil well cement 1 Introduction Cement hydration is a complex chemical process that involves a number of different reactions. Although many detailed features of the process are still not clearly understood today, the general hydration kinetics can be approximately represented by the overall degree of hydration as a function of time. This overall degree of cement hydration, defined as the total weight fraction of cement reacted, is directly related to many different physical and mechanical properties of cement-based materials, such as viscosity [1], setting time [2-4], autogenous shrinkage [5], compressive strength [6, 7], tensile strength [8], and modulus of elasticity [5, 8]. It is arguably the most important parameter that can be used to model the time-dependent characteristics of cement-based materials [9]. Since Portland cement mainly consists of four clinker phases, its overall degree of hydration can be written as [10]:      3 3 2 2 3 3 4 4 CS CS CS CS CA CA C AF C AF t p t p t p t p t          (1) where p i is the original weight fraction of Phase i in the anhydrous cement and α i (t) is the degree of hydration of Phase i at time t. Direct determination of α i (t) can be made by using quantitative X-ray diffraction analysis [10, 11], but the method is rarely used in practice due to complex test procedures and high equipment cost. Some properties of a hydrating cement paste, such as the cumulative heat evolution, the total chemical shrinkage, and the non-evaporable water content, have been shown to have approximately linear relationships with each other and the overall degree of hydration [4, 10, 12, 13]. Measuring these properties serves as alternative ways of determining α, i.e. the so-called indirect methods. As a matter of fact,  is more commonly determined by these indirect methods due to their simplicity. The following equation may be used to convert experimental results (obtained from indirect methods) to the degree of hydration of cement, α(t): 0 0 0 ) ( ) ( ) ( ) ( n n w t w CS t CS H t H t     (2) where H(t) and H 0 are the amounts of cumulative heat evolution at time t and at complete hydration, respectively (typically in J/g cement); CS(t) and CS 0 are the amounts of chemical shrinkage at time t and at complete hydration, respectively (typically in mL/g cement); while