Chemical & Process Technology: Improved Manual Method for Settle Out Condition Estimation

Sunday, November 30, 2008

Improved Manual Method for Settle Out Condition Estimation

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In earlier discussion "Simple Manual Method for Settle Out Condition Estimation", a manual method has been can be considered without using any Process Simulator. This method basically utilising universal gas law (PV=znRT) with the following basis and assumption :

Vapor only system
No condensation during the process
Compressibility factor assumed same for condition before and after settle-out and assumed (z=1)
Limited fluid with molecular weight is similar range. Higher the different, higher the deviation

In this method (T x n method), the settle out temperature is calculated using this equation :

T_s = Sum (n₁ x T₁ + n₂ x T₂ + n₃ x T₃ +...) / n_s

This method (T x n method) has a particular known issue where it does not considered the impact of Molecular Weight (MW). In the event molecular weight of each sections are different, the calculated settle temperature will not change with molecular weight. In this post, an improved method is introduced to use same derivation per T x n method, however it includes MW as part the calculation. It basically use mass (m) to replace mole (n) which simply name as T x m method.

Derivation
A system consists of n-section with pressure (P_i, kPag), temperature (Ti, K), Molecular weight (MW_i), physical volume (V_i, m3) for i-section.

Number of mass in each i-section (before settle-out),

m_i = (P_i x V_i x MW_i) / (z_i x R x T_i).....[1]

Total mass (after settle-out),

m_s = Sum (m₁ + m₂ + m₃...).....[2]

Total volume (after settle-out),

V_s = Sum (V₁ + V₂ + V₃...).....[3]

Volume at normal condition (P_i,n = 1.01325 bar & Ti,_n = 273.15 K) for each i-section (before settle-out)

V_i,n = (P_i x V_i / T_i) /(P_i,n / T_i,n)......[4]

Total volume at normal condition (after settle-out)

V_s,n = Sum (V_1,n + V_2,n + V_3,n...).....[5]

m_i x T_i for each i-section (before settle-out),

m_i x T_i = (P_i x V_i x MW_i) / (z_i x R).....[6]

Total m_s x T_s (after settle-out),

m_s x T_s = Sum (m₁ x T₁ + m₂ x T₂ + m₃ x T₃ +...).....[7]

Thus, From [7] and [2],
Settle-out temperature (T_s),

T_s = Sum (m₁ x T₁ + m₂ x T₂ + m₃ x T₃ +...) / m_s .....[8]

Settle-out pressure (P_s),

P_s = (1.01325) x (V_s,n/ V_s) x (T_s / 273.15)......[9]

Case Study
There are five sets of system with each system has 3 section will be settled-out. The five set of fluid will have same pressure and temperature prior to settle out, however the composition of each section will be difference as follow :

Composition Set 1 :
Section 1 : Methane : 100%
Section 2 : Methane : 100%
Section 3 : Methane : 100%

Composition Set 2 :
Section 1 : Ethane : 100%
Section 2 : Methane : 100%
Section 3 : Methane : 100%

Composition Set 3 :
Section 1 : Ethane : 100%
Section 2 : Methane : 100%
Section 3 : Methane : 50%, Ethane : 20%, Propane : 30%

Composition Set 4 :
Section 1 : Propane : 100%
Section 2 : Propane : 100%
Section 3 : Methane : 50%, Ethane : 20%, Propane : 30%

Composition Set 5 :
Section 1 : Propane : 100%
Section 2 : Propane : 100%
Section 3 : Ethane : 40%, Propane : 60%

Image below display the results of HYSYS Settle-out using method in "Simple Method For Compressor Settle Out (Vapor Only) Using HYSYS", T x n and T x m methods.

Above results show
i) Settle-out pressure and temperature will not change with composition.
ii) if the composition are close between each sections, both T x n and T x m may be used.
iii) Accuracy for T x m are typically higher than T x n methods.

Related Topic

Labels: Compressor