Nothing
#' @title Koble-Carrigan Isotherm Linear Analysis
#' @name koblecarrigan.LM
#' @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 linear 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 koblecarrigan.LM(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 Sips isotherm linear form
koblecarrigan.LM <- function(Ce,Qe) {
x1 <- Ce
y1 <- Qe
data <- data.frame(x1, y1)
# Koble-Corrigan isotherm nonlinear equation
fit1 <- y1 ~ (Akc*(x1^Nkc))/(1 + Bkc*(x1^Nkc))
# Setting of starting values
start1 <- list(Akc = 1, Bkc = 1, Nkc = 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")
param <- summary(fit2)
expModel <- param$coefficients[3]
# Establishing Koble-Corrigan isotherm linear form
x <- 1/(Ce^expModel)
y <- 1/Qe
rhs <- function (x, Bkc, Akc) {
(Bkc/Akc) + (1/Akc*x)
}
# Koble-Corrigan isotherm linear fitting
fit3 <- lm(y~x)
print("Koble-Corrigan Isotherm Linear Analysis")
print(summary(fit3))
### y = a + bx
c <- (summary(fit3))
a <- c$coefficients[1]
b <- c$coefficients[2]
### Parameter values calculation
Akc <- b^-1
print("Akc")
print(Akc)
Bkc <- a*Akc
print("Bkc")
print(Bkc)
Nkc <- expModel
print("Nkc")
print(Nkc)
# -------------------------------------
AIC <- AIC(fit3)
print("Aikake Information Criterion")
print(AIC)
BIC <- BIC(fit3)
print("Bayesian Information Criterion")
print(BIC)
# Error analysis of the Koble-Corrigan isotherm linear model
errors <- function(y) {
rmse <- Metrics::rmse(y, predict(fit3))
mae <- Metrics::mae(y, predict(fit3))
mse <- Metrics::mse(y, predict(fit3))
rae <- Metrics::rae(y, predict(fit3))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit3))^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)
# Graphical representation of the Koble-Corrigan isotherm linear model
#### 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_smooth(formula = y ~ x, method = "lm", se = F, color = "#D35400" ) +
ggplot2::labs(x = expression(paste("1"/"Ce"^"Nkc")),
y = "1/Qe",
title = "Koble-Corrigan Isotherm Linear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.