drying kinetics and moisture diffusivity in r

To determine drying kinetics and moisture diffusivity in R, you can use the package NMOF (Numerical Methods and Optimization in Finance). This package provides functions for optimization, including non-linear least squares parameter estimation.

Here is a step-by-step guide on how to perform drying kinetics and moisture diffusivity analysis in R:

  1. Install the NMOF package (if not already installed):
install.packages("NMOF")

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  1. Load the NMOF library:
library(NMOF)

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  1. Define your drying model function. This function should take the input parameters as arguments and return the predicted moisture content at a given time:
model <- function(params, t) {
  # Define the drying model equation
  # You need to specify a suitable drying model equation depending on your specific case
  # For example, for a simple exponential drying model: 
  # MC = MC0 * exp(-k * t)
  # where MC is the moisture content, MC0 is the initial moisture content, k is the drying rate constant, and t is time
  
  # Extract the parameters
  MC0 <- params[1]
  k <- params[2]
  
  # Calculate the predicted moisture content at each time point
  MC <- MC0 * exp(-k * t)
  
  return(MC)
}

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  1. Prepare the data for fitting. Create vectors for time points (t) and observed moisture content (MC_obs), representing the experimental data:
t <- c(0, 1, 2, 3, 4, 5) # example time points
MC_obs <- c(10, 8, 6, 4, 2, 1) # example observed moisture content

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  1. Define the objective function for parameter estimation. In this case, we want to minimize the sum of squared differences between the observed and predicted moisture content values:
objective <- function(params) {
  MC_pred <- model(params, t)
  resid <- MC_obs - MC_pred
  return(sum(resid^2))
}

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  1. Perform parameter estimation using the solnp function from the NMOF package:
# Specify the initial parameter values (MC0 and k)
params_init <- c(10, 0.5)

# Perform parameter estimation
result <- solnp(pars = params_init, fun = objective, LB = 0, UB = Inf)

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Note: In the above code, LB = 0 and UB = Inf set lower and upper bounds on the parameter values to ensure positive values for MC0 and k.

  1. Extract the estimated parameter values:
MC0_est <- result$pars[1]
k_est <- result$pars[2]

# Print the estimated parameter values
cat("Estimated MC0:", MC0_est, "\n")
cat("Estimated k:", k_est, "\n")

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  1. Calculate the moisture diffusivity:
# Assuming a simplified drying model equation with diffusivity parameter (D):
# D = k^2 / (2 * L^2), where L is the characteristic length (e.g., thickness)

L <- 0.01 # example characteristic length (e.g., thickness)
D_est <- k_est^2 / (2 * L^2)

# Print the estimated moisture diffusivity
cat("Estimated moisture diffusivity:", D_est, "\n")

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That's it! You have now obtained the estimated parameter values for the drying model and calculated the moisture diffusivity. Remember to adjust the drying model equation and any other parameters according to your specific experiment and needs.

Tags: drying kinetics, moisture diffusivity, parameter estimation, non-linear least squares, optimization, R

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