Chapter 5.7, Problem 13P

(A)

Interpretation Introduction

Interpretation:

The flow rate of the supercritical methane entering the flash chamber.

Concept Introduction:

The energy balance with an initial mass flow rate of supercritical stream is,

${\dot{m}}_{in}={\dot{m}}_{liq}+{\dot{m}}_{vap}$

Here, initial mass flow rate of supercritical stream is ${\dot{m}}_{in}$, mass flow rate of liquid stream is ${\dot{m}}_{liq}$, and mass flow rate of vapor stream is ${\dot{m}}_{vap}$

The energy balance equation for the system is,

${\dot{m}}_{in}{\widehat{H}}_{in}={\dot{m}}_{liq}{\widehat{H}}_{liq}+{\dot{m}}_{vap}{\widehat{H}}_{vap}$

Here, initial specific enthalpy of supercritical methane is ${\widehat{H}}_{in}$, specific enthalpy of liquid methane is ${\widehat{H}}_{liq}$, and specific enthalpy of vapor methane is ${\widehat{H}}_{vap}$.

(B)

Interpretation Introduction

Interpretation:

The work done for each of the two compressors.

Concept Introduction:

The expression to obtain the reversible work rate of shaft for the eversible compressor 1 with respect to mass flow rate $\left({\dot{W}}_{S,rev,c1}/\dot{m}\right)$ is,

${\dot{W}}_{S,rev,c1}/\dot{m}=\frac{{\widehat{H}}_{out,rev,c1}-{\widehat{H}}_{in,c1}}{\eta }$

Here, reversible work rate of shaft for the eversible compressor 1 is ${\dot{W}}_{S,rev,c1}$, mass flow rate is $\dot{m}$, and efficiency is $\eta$.

The expression to obtain the actual work $\left(W_1\right)$ for compressor 1 is,

$W_1=\left({\dot{W}}_{S,rev,c1}/\dot{m}\right)\left({\dot{m}}_{in}\right)$

The expression to obtain the reversible work rate of shaft for the eversible compressor 2 with respect to mass flow rate $\left({\dot{W}}_{S,rev,c2}/\dot{m}\right)$ is,

${\dot{W}}_{S,rev,c2}/\dot{m}=\frac{{\widehat{H}}_{out,rev,c2}-{\widehat{H}}_{in,c2}}{\eta }$

Here, reversible work rate of shaft for the eversible compressor 2 is ${\dot{W}}_{S,rev,c2}$.

The expression to obtain the actual work $\left(W_2\right)$ for compressor 2 is,

$W_2=\left({\dot{W}}_{S,rev,c2}/\dot{m}\right)\left({\dot{m}}_{in}\right)$

(C)

Interpretation Introduction

Interpretation:

The heat transfer for each of the four heat exchangers.

Concept Introduction:

The expression to obtain the actual initial specific enthalpy of entering methane for compressor 1 $\left({\widehat{H}}_{in,act,c1}\right)$ is,

${\widehat{H}}_{in,act,c1}={\widehat{H}}_{in,c1}+{\dot{W}}_{S,rev,c1}/\dot{m}$

The expression to obtain the actual final specific enthalpy of entering methane for compressor 2 $\left({\widehat{H}}_{out,act,c2}\right)$ is,

${\widehat{H}}_{out,act,c2}={\widehat{H}}_{in,c1}+{\dot{W}}_{S,rev,c1}/\dot{m}$

The energy balance equation for HX2 and HX3 is,

$\frac{\dot{Q}}{{\dot{m}}_{in}}={\widehat{H}}_{out}-{\widehat{H}}_{in}$

Here, rate of heat added or removed from the system is $\dot{Q}$, final specific enthalpy is ${\widehat{H}}_{out}$, and an initial specific enthalpy is ${\widehat{H}}_{in}$.