Recall LHS of Eq(\ref{mass})
\begin{multline}\label{mass_L}
\overbrace{\nabla\cdot\bar{\bar{k}}X_c\xi_o\lambda_o\left(\nabla P_o-\gamma_o\nabla D\right)}^{OilTerm}
+\overbrace{\nabla\cdot\bar{\bar{k}}Y_c\xi_g\lambda_g\left(\nabla P_g-\gamma_g\nabla D\right)}^{GasTerm}
\\
+\underbrace{\nabla\cdot\bar{\bar{k}}W_c\xi_w\lambda_w\left(\nabla P_w-\gamma_w\nabla D\right)}_{WaterTerm}
+\underbrace{\left(X_c\xi_o\hat{q_o}+Y_c\xi_g\hat{q_g}+W_c\xi_w\hat{q_w}\right)}_{sink/sourceTerm}
\end{multline}
Multiply both sides of Eq(\ref{mass_L}) by $V_R=\left(\Delta x\Delta y\Delta z\right)_i$ and Discretized it in for 1D problem term by term.\\
Let's define unit conversion factor $\alpha=0.006328$
\begin{itemize}
	\item Oil Term
		\begin{multline}\label{LHS_o}
		\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(X_c\xi_o\lambda_o\right)^n_{i+\frac{1}{2}}\left(P^{n+1}_{o,i+1}-P^{n+1}_{o,i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(X_c\xi_o\lambda_o\right)^n_{i-\frac{1}{2}}\left(P^{n+1}_{o,i}-P^{n+1}_{o,i-1}\right)\right]\\
		-\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(X_c\xi_o\lambda_o\gamma_o\right)^n_{i+\frac{1}{2}}\left(D_{i+1}-D_{i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(X_c\xi_o\lambda_o\gamma_o\right)^n_{i-\frac{1}{2}}\left(D_{i}-D_{i-1}\right)\right]
		\end{multline}
	\item Gas Term
		\begin{multline}\label{LHS_g}
		\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(Y_c\xi_g\lambda_g\right)^n_{i+\frac{1}{2}}\left(P^{n+1}_{o,i+1}-P^{n+1}_{o,i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(Y_c\xi_g\lambda_g\right)^n_{i-\frac{1}{2}}\left(P^{n+1}_{o,i}-P^{n+1}_{o,i-1}\right)\right]\\
		+\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(Y_c\xi_g\lambda_g\right)^n_{i+\frac{1}{2}}\left(P^{n}_{cgo,i+1}-P^{n}_{cgo,i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(Y_c\xi_g\lambda_g\right)^n_{i-\frac{1}{2}}\left(P^{n}_{cgo,i}-P^{n}_{cgo,i-1}\right)\right]\\
		-\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(Y_c\xi_g\lambda_g\gamma_g\right)^n_{i+\frac{1}{2}}\left(D_{i+1}-D_{i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(Y_c\xi_g\lambda_g\gamma_g\right)^n_{i-\frac{1}{2}}\left(D_{i}-D_{i-1}\right)\right]
		\end{multline}
	\item Water Term
	{\small{
		\begin{multline}\label{LHS_w}
		\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(W_c\xi_w\lambda_w\right)^n_{i+\frac{1}{2}}\left(P^{n+1}_{o,i+1}-P^{n+1}_{o,i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(W_c\xi_w\lambda_w\right)^n_{i-\frac{1}{2}}\left(P^{n+1}_{o,i}-P^{n+1}_{o,i-1}\right)\right]\\
		-\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(W_c\xi_w\lambda_w\right)^n_{i+\frac{1}{2}}\left(P^{n}_{cow,i+1}-P^{n}_{cow,i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(W_c\xi_w\lambda_w\right)^n_{i-\frac{1}{2}}\left(P^{n}_{cow,i}-P^{n}_{cow,i-1}\right)\right]\\
		-\alpha\left[\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i+\frac{1}{2}}}k_{xx,i+\frac{1}{2}}\left(W_c\xi_w\lambda_w\gamma_w\right)^n_{i+\frac{1}{2}}\left(D_{i+1}-D_{i}\right)-\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i-\frac{1}{2}}}k_{xx,i-\frac{1}{2}}\left(W_c\xi_w\lambda_w\gamma_w\right)^n_{i-\frac{1}{2}}\left(D_{i}-D_{i-1}\right)\right]
		\end{multline}
	\item Sink/Source Term
		\begin{equation}\label{LHS_q}
			\left(X_c\xi_oq_o+Y_c\xi_gq_g+W_c\xi_wq_w\right)
		\end{equation}}}
\end{itemize}

Let's define

$$T^{n}_{xoc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(X_c\xi_o\lambda_o\right)^n_{i\pm\frac{1}{2}}$$

$$(T\gamma)^{n}_{xoc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(X_c\xi_o\lambda_o\gamma_o\right)^n_{i\pm\frac{1}{2}}$$

$$T^{n}_{xgc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(Y_c\xi_g\lambda_g\right)^n_{i\pm\frac{1}{2}}$$

$$(T\gamma)^{n}_{xgc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(Y_c\xi_g\lambda_g\gamma_g\right)^n_{i\pm\frac{1}{2}}$$

$$T^{n}_{xwc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(W_c\xi_w\lambda_w\right)^n_{i\pm\frac{1}{2}}$$

$$(T\gamma)^{n}_{xwc,{i\pm\frac{1}{2}}}=\alpha\frac{\Delta y_{i}\Delta z_{i}}{\Delta x_{i\pm\frac{1}{2}}}k_{xx,i\pm\frac{1}{2}}\left(W_c\xi_w\lambda_w\gamma_w\right)^n_{i\pm\frac{1}{2}}$$

We can substitute Eq(\ref{LHS_o}),(\ref{LHS_g}),(\ref{LHS_w}), and (\ref{LHS_w}) into (\ref{mass_L}), we get the general form of Left-Hand-Side for Eq(\ref{mass}). This form can be applied for every component

\begin{multline}\label{mass_LH}
	\left[\begin{array}{cc}\left(T^{n}_{xoc,{i+\frac{1}{2}}}+T^{n}_{xgc,{i+\frac{1}{2}}}+T^{n}_{xwc,{i+\frac{1}{2}}}\right)\left(P^{n+1}_{o,i+1}-P^{n+1}_{o,i}\right)\\
	-\left(T^{n}_{xoc,{i-\frac{1}{2}}}+T^{n}_{xgc,{i-\frac{1}{2}}}+T^{n}_{xwc,{i-\frac{1}{2}}}\right)\left(P^{n+1}_{o,i}-P^{n+1}_{o,i-1}\right)\end{array}\right]\\
	+\left[T^{n}_{xgc,{i+\frac{1}{2}}}\left(P^{n}_{cgo,i+1}-P^{n}_{cgo,i}\right)-T^{n}_{xgc,{i-\frac{1}{2}}}\left(P^{n}_{cgo,i}-P^{n}_{cgo,i-1}\right)\right]\\
	-\left[T^{n}_{xoc,{i+\frac{1}{2}}}\left(P^{n}_{cow,i+1}-P^{n}_{cow,i}\right)-T^{n}_{xoc,{i-\frac{1}{2}}}\left(P^{n}_{cow,i}-P^{n}_{cow,i-1}\right)\right]\\
	-\left[\begin{array}{cc}\left((T\gamma)^{n}_{xoc,{i+\frac{1}{2}}}+(T\gamma)^{n}_{xgc,{i+\frac{1}{2}}}+(T\gamma)^{n}_{xwc,{i+\frac{1}{2}}}\right)\left(D_{i+1}-D_{i}\right)\\
	-\left((T\gamma)^{n}_{xoc,{i-\frac{1}{2}}}+(T\gamma)^{n}_{xgc,{i-\frac{1}{2}}}+(T\gamma)^{n}_{xwc,{i-\frac{1}{2}}}\right)\left(D_{i}-D_{i-1}\right)\end{array}\right]\\
	+\left(X_c\xi_oq_o+Y_c\xi_gq_g+W_c\xi_wq_w\right)^n	
\end{multline}

Define $P_o^{n+1}=P_o^l+\delta P_o$ and substitute into Eq (\ref{mass_LH}) we get

\begin{multline}\label{mass_LHS}
	\left[\begin{array}{cc}\left(T^{n}_{xoc,{i+\frac{1}{2}}}+T^{n}_{xgc,{i+\frac{1}{2}}}+T^{n}_{xwc,{i+\frac{1}{2}}}\right)\left(\delta P_{o,i+1}-\delta P_{o,i}\right)\\
	-\left(T^{n}_{xoc,{i-\frac{1}{2}}}+T^{n}_{xgc,{i-\frac{1}{2}}}+T^{n}_{xwc,{i-\frac{1}{2}}}\right)\left(\delta P_{o,i}-\delta P_{o,i-1}\right)\end{array}\right]\\
	+\left[\begin{array}{cc}\left(T^{n}_{xoc,{i+\frac{1}{2}}}+T^{n}_{xgc,{i+\frac{1}{2}}}+T^{n}_{xwc,{i+\frac{1}{2}}}\right)\left(P^{l}_{o,i+1}-P^{l}_{o,i}\right)\\
	-\left(T^{n}_{xoc,{i-\frac{1}{2}}}+T^{n}_{xgc,{i-\frac{1}{2}}}+T^{n}_{xwc,{i-\frac{1}{2}}}\right)\left(P^{l}_{o,i}-P^{l}_{o,i-1}\right)\end{array}\right]\\
	+\left[T^{n}_{xgc,{i+\frac{1}{2}}}\left(P^{n}_{cgo,i+1}-P^{n}_{cgo,i}\right)-T^{n}_{xgc,{i-\frac{1}{2}}}\left(P^{n}_{cgo,i}-P^{n}_{cgo,i-1}\right)\right]\\
	-\left[T^{n}_{xwc,{i+\frac{1}{2}}}\left(P^{n}_{cow,i+1}-P^{n}_{cow,i}\right)-T^{n}_{xwc,{i-\frac{1}{2}}}\left(P^{n}_{cow,i}-P^{n}_{cow,i-1}\right)\right]\\
	-\left[\begin{array}{cc}\left((T\gamma)^{n}_{xoc,{i+\frac{1}{2}}}+(T\gamma)^{n}_{xgc,{i+\frac{1}{2}}}+(T\gamma)^{n}_{xwc,{i+\frac{1}{2}}}\right)\left(D_{i+1}-D_{i}\right)\\
	-\left((T\gamma)^{n}_{xoc,{i-\frac{1}{2}}}+(T\gamma)^{n}_{xgc,{i-\frac{1}{2}}}+(T\gamma)^{n}_{xwc,{i-\frac{1}{2}}}\right)\left(D_{i}-D_{i-1}\right)\end{array}\right]\\
	+\left(X_c\xi_oq_o+Y_c\xi_gq_g+W_c\xi_wq_w\right)^n	
\end{multline}

Note here that, value of $X_c$, $Y_c$, and $W_c$ for the equation of each component is shown in Table(\ref{tab:compv})

\begin{table}[htbp]
	\centering
	\caption{$X_c$, $Y_c$, and $W_c$ value for each component}
	\label{tab:compv}
\begin{tabular}{ccccc} 
\hline
Component No. & Description & $X_c$	& $Y_c$	& $W_c$ \\[1.0ex]
\hline \hline
1 & $CH_4$									& $X_1$	& $Y_1$	& 0	\\ [1.0ex]
2 & $n-C_4H_{10}$ 					& $X_2$	& $Y_2$	& 0\\ [1.0ex]
3 & $n-C_{10}H_{20}$				&	$X_3$	& $Y_3$	& 0 \\ [1.0ex]
4 & $H_2O$ 									&	$0$		& $0$		& 1\\ 
\hline %inserts single line
\end{tabular}
\end{table}