# Modeling the beating degree of wheat straw biochemical mechanical pulp using multifactorial equations

## TL;DR

This study creates a reliable model to predict the beating degree of wheat straw pulp using three key factors, improving efficiency and reducing resource waste.

## Contribution

The study introduces a novel application of Box-Behnken Design for modeling pulp beating degree without extreme conditions.

## Key findings

- A quadratic polynomial model with high R² values (0.9899) accurately predicts the beating degree.
- The model demonstrates strong predictive ability with a signal-to-noise ratio of 29.2395.
- The model avoids extreme conditions, making it safer and more practical than traditional methods.

## Abstract

In traditional pulp beating processes, the “produce-test-adjust” cycle is commonly employed, often resulting in unnecessary consumption of energy and chemicals. To address this issue, this study integrated single-factor experiments with a Plackett-Burman (PB) design to identify three key parameters—refiner gap, KOH dosage, and enzyme dosage—that significantly influence the beating degree of wheat straw biochemical mechanical pulp, selected from ten potential factors. On this basis, the Box-Behnken Design (BBD) response surface methodology (RSM) was employed to establish a quadratic polynomial predictive model between the beating degree and the aforementioned three factors. For this quadratic polynomial predictive model, the coefficient of determination (R²) is 0.9899, the adjusted R² is 0.9768, and the predicted R² is 0.8723. The adjusted R² is close to R², and the predicted R² is close to the adjusted R² with both values being relatively high, indicating the reliability and practicality of the model. The standard deviation is 0.44, the coefficient of variation is 1.13%, and the signal-to-noise ratio of the model reaches 29.2395, suggesting its strong predictive ability and excellent robustness. Methodologically, this study innovatively applied BBD to the prediction of beating degree. Compared with the traditional Central Composite Design (CCD) model, the proposed model does not require extreme operating conditions, and all 17 experimental points fall within a safe operation range. The establishment of this model provides a predictable and controllable optimization tool for the wheat straw bio-pulping process.