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Fix notation of flow rates in docs
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Changes the symbol for flow rates from F to Q in the section on unit
operation networks.
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sleweke committed Oct 12, 2020
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4 changes: 2 additions & 2 deletions doc/tex/docs/models.tex
Original file line number Diff line number Diff line change
Expand Up @@ -47,9 +47,9 @@ \section{Network of unit operation models}\label{sec:MUOPNetwork}
While $N_{\text{port},\text{in},n}$ denotes the number of inlet ports of unit operation $n$, the number of outlet ports is given by $N_{\text{port},\text{out},n}$.
The connection variables $c_{\text{con},n,k,i}$ collect all inflows of component $i$ into port $k$ of unit operation $n$:
\begin{align}
c_{\text{con},n,k,i} &= \frac{\sum_{m=1}^{N_{\text{units}}} \sum_{\ell = 1}^{N_{\text{port},\text{out},n}} \sum_{j = 1}^{N_{\text{comp},m}} S_{(n,k,i),(m,\ell,j)} F_{m,\ell} c_{\text{out},m,\ell,j}}{\sum_{m=1}^{N_{\text{units}}} \sum_{\ell=1}^{N_{\text{port},\text{out},m}} \hat{S}_{(n,k),(m,\ell)} F_{m,\ell} }, \label{eq:NetworkConnection}
c_{\text{con},n,k,i} &= \frac{\sum_{m=1}^{N_{\text{units}}} \sum_{\ell = 1}^{N_{\text{port},\text{out},n}} \sum_{j = 1}^{N_{\text{comp},m}} S_{(n,k,i),(m,\ell,j)} Q_{m,\ell} c_{\text{out},m,\ell,j}}{\sum_{m=1}^{N_{\text{units}}} \sum_{\ell=1}^{N_{\text{port},\text{out},m}} \hat{S}_{(n,k),(m,\ell)} Q_{m,\ell} }, \label{eq:NetworkConnection}
\end{align}
where $F_{m,\ell}$ denotes the volumetric flow rate from outlet port $\ell$ of unit operation $m$, $S_{(n,k,i),(m,\ell,j)} \in \{0, 1\}$ is a connection matrix indicating whether component $i$ at outlet port $k$ of unit operation $n$ is connected to component $j$ at inlet port $\ell$ of unit operation $m$, and $\hat{S}_{(n,k),(m,\ell)} \in \{0, 1\}$ is another connection matrix indicating whether outlet port $k$ of unit operation $n$ is connected to inlet port $\ell$ of unit operation $m$, that is
where $Q_{m,\ell}$ denotes the volumetric flow rate from outlet port $\ell$ of unit operation $m$, $S_{(n,k,i),(m,\ell,j)} \in \{0, 1\}$ is a connection matrix indicating whether component $i$ at outlet port $k$ of unit operation $n$ is connected to component $j$ at inlet port $\ell$ of unit operation $m$, and $\hat{S}_{(n,k),(m,\ell)} \in \{0, 1\}$ is another connection matrix indicating whether outlet port $k$ of unit operation $n$ is connected to inlet port $\ell$ of unit operation $m$, that is
\begin{align*}
\hat{S}_{(n,k),(m,\ell)} = \begin{cases}
1 & \text{if } \sum_{i = 1}^{N_{\text{comp},n}} \sum_{j = 1}^{N_{\text{comp},m}} S_{(n,k,i),(m,\ell,j)} \geq 1, \\
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