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#' @title Koble-Carrigan Isotherm Nonlinear Analysis
#' @name koblecarrigananalysis
#' @description It is three-parameter isotherm model equation that incorporates
#' both Freundlich and Langmuir isotherms for representing equilibrium adsorption
#' data. Koble-Corrigan isotherm model appeared to have advantages over both the
#' Langmuir and Freundlich equations in that it expresses adsorption data over
#' very wide ranges of pressures and temperatures.
#' @param Ce the numerical value for the equilibrium capacity
#' @param Qe the numerical value for the adsorbed capacity
#' @import nls2
#' @import Metrics
#' @import stats
#' @import ggplot2
#' @return the nonlinear regression, parameters for Koble-Carrigan isotherm, and
#' model error analysis
#' @examples Ce <- c(0.01353, 0.04648, 0.13239, 0.27714, 0.41600, 0.63607, 0.80435, 1.10327, 1.58223)
#' @examples Qe <- c(0.03409, 0.06025, 0.10622, 0.12842, 0.15299, 0.15379, 0.15735, 0.15735, 0.16607)
#' @examples koblecarrigananalysis(Ce, Qe)
#' @author Keith T. Ostan
#' @author Chester C. Deocaris
#' @references Corrigan, T. E., and Koble, R. A.(1952) <doi:10.1021/ie50506a049> Adsorption isotherms for
#' pure hydrocarbons Ind. Eng. Chem. 44 383-387.
#' @export
# Building the Koble-Corrigan isotherm nonlinear form
koblecarrigananalysis <- function(Ce,Qe){
x <- Ce
y <- Qe
data <- data.frame(x, y)
# Koble-Corrigan isotherm nonlinear equation
fit1 <- y ~ (Ak*(x^p))/(1 + Bk*(x^p))
# Setting of starting values
start1 <- list(Ak = 1, Bk = 1, p = 1)
# Fitting of the Koble-Corrigan isotherm via nls2
fit2 <- nls2::nls2(fit1, start = start1, data=data,
control = nls.control(maxiter =50 , warnOnly = TRUE),
algorithm = "port")
print("Koble-Carrigan Isotherm Nonlinear Analysis")
print(summary(fit2))
AIC <- AIC(fit2)
print("Aikake Information Criterion")
print(AIC)
BIC <- BIC(fit2)
print("Bayesian Information Criterion")
print(BIC)
# Error analysis of the Koble-Corrigan isotherm model
errors <- function(y) {
rmse <- Metrics::rmse(y, predict(fit2))
mae <- Metrics::mae(y, predict(fit2))
mse <- Metrics::mse(y, predict(fit2))
rae <- Metrics::rae(y, predict(fit2))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit2))^2)/(N-2))
colnames(y) <- rownames(y) <- colnames(y)
list("Relative Mean squared Error" = rmse,
"Mean Absolute Error" = mae,
"Mean Squared Error" = mse,
"Relative Absolute Error" = rae,
"Standard Error for the Regression S" = SE)
}
a <- errors(y)
print(a)
rsqq <- lm(Qe~predict(fit2))
print(summary(rsqq))
# Graphical representation of the Koble-Corrigan isotherm model
### Predicted parameter values
parskobleC <- as.vector(coefficients(fit2))
pars_Ak <- parskobleC[1L];
pars_Bk <- parskobleC[2L];
pars_p <- parskobleC[3L]
rhs <- function(x){((pars_Ak*(x^pars_p))/(1 + pars_Bk*(x^pars_p)))}
#### Plot details
ggplot2::theme_set(ggplot2::theme_bw(10))
ggplot2::ggplot(data, ggplot2::aes(x = x, y = y)) + ggplot2::geom_point(color ="#3498DB" ) +
ggplot2::geom_function(color = "#D35400", fun = rhs ) +
ggplot2::labs(x = "Ce",
y = "Qe",
title = "Koble-Corrigan Isotherm Nonlinear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
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