Henderson Pabis ModelEdit
The Henderson-Pabis model is a simple, widely used empirical tool for describing how moisture leaves foods and other agricultural products during drying. It is valued for its minimal parameter set, ease of fitting to experimental data, and usefulness as a first-step descriptor in drying studies. The model captures the overall rate at which a sample loses water under relatively steady drying conditions, making it a staple in food engineering and processing research.
In practice, the model expresses the moisture ratio (MR) as a function of time (t) in the exponential form MR = a exp(-kt). Here MR is defined as MR = (M_t − M_e)/(M_0 − M_e) or, under common simplifying assumptions, MR ≈ M_t/M_0, where M_t is the moisture content at time t, M_0 is the initial moisture content, and M_e is the equilibrium moisture content. The constants a and k are empirical parameters determined by fitting the model to drying data using nonlinear regression. The quantity k is often interpreted as a rate constant that reflects the intensity of moisture removal under the given conditions, while a serves as a scaling factor that accounts for geometry and measurement conventions. See also Moisture ratio for the standard way researchers express drying progress, and Nonlinear regression for the typical method used to estimate the model parameters.
Model formulation
The Henderson-Pabis equation can be written succinctly as MR = a exp(-kt). The time variable t is measured in the drying experiment from the start of drying, and the parameters a and k are obtained by fitting the observed MR values over time. The model is dimensionally simple, requiring only two adjustable constants, and it is particularly convenient when rapid screening of drying behavior is required or when a process engineer needs a tractable, interpretable descriptor of drying kinetics. For general reference to the theoretical underpinnings of moisture movement and drying, see Drying (food science) and Diffusion.
Calibration, validation, and interpretation
Parameter estimation for the Henderson-Pabis model relies on nonlinear regression, and researchers commonly assess fit quality with metrics such as the coefficient of determination and error measures like RMSE. In many cases, the two-parameter Henderson-Pabis model gives an adequate description of the early to mid-stages of drying, after which deviations often appear as the process transitions to diffusion-limited or multi-stage behavior. Consequently, practitioners frequently compare Henderson-Pabis fits to more flexible models, such as the Page model or the Logarithmic drying model, to determine whether additional terms improve accuracy. The model remains a valuable starting point because it is easy to implement and interpret, providing a benchmark against which more complex models can be evaluated.
Applications and scope
The Henderson-Pabis model has been applied across a wide range of food and agricultural materials, including fruits, vegetables, grains, and dried products where the drying conditions are reasonably constant (stable air temperature, humidity, and velocity). Its simplicity makes it attractive for quick assessments of drying rate, process optimization, and preliminary design of dryer equipment. In many studies, the model serves as a baseline against which more mechanistic descriptions—such as diffusion-based models that explicitly account for internal moisture transport—are compared. Related concepts and models appear in Fick's laws and in discussions of Moisture content dynamics during drying.
Limitations and alternatives
As an empirical model, the Henderson-Pabis form does not derive directly from physical transport laws. It often assumes constant drying conditions and homogeneous samples, and it generally neglects sample shrinkage, internal diffusion variations, and multi-stage drying behavior. When conditions change during the process or when the geometry and internal moisture gradients become significant, the two-parameter form may fail to capture late-stage kinetics, prompting use of multi-term variants (e.g., a sum of exponentials) or more physically grounded models. For those reasons, researchers frequently compare Henderson-Pabis fits with models such as the Page model or the Logarithmic drying model, and may invoke diffusion-based treatments rooted in Fick's laws to gain a more mechanistic understanding of moisture transport.