Synthesis of work exchange networks for gas processing applications 3

In order to provide refrigeration at warm condition, high pressure superheated propane is cooled and condensed at ambient temperature using cooling water.. High pressure MR stream exitin

system, is introduced which has higher train capacity than the well known C3MR process Due to energy intensive nature of this relatively new technology a process optimization approach is presented in the following sections to minimize compressor power requirement

3.1 Technical Background of the AP-X TM Technology

dominant NG liquefaction system utilized by LNG producers around the world This enhancement was motivated by the demand for greater LNG production capacity and cost savings associated with economies of scale With the increasing environmental pressure towards cleaner burning fuels such as NG, there had been an unprecedented surge in the demand for LNG With such high demands, greater LNG production rate is high on the

priority list in any plant construction or expansion plan The current C3MR technology is only rated up to a maximum of 5 million ton per annum (mta) due to equipment

the unproven size, performance, and reliability zones of refrigerant compressors Parallel trains are costly and do not benefit from economies of scale The use of parallel equipments such as parallel compression faces problems of flow imbalances which poses unacceptable operational and safety concerns Heat exchanger size and capacity also

train capacity of 7.8 mta, which is approximately 50% greater than the largest C3MR

while maintaining C3MR’s industry leading high efficiency levels Figure 3.1 illustrates

on

TM

MR cooler

P 1,MR

MR Cycle

PR Cycle

T SW

P 1,PR

T SW

NG Precooler NG

LNG

MCHE

T MR

N2-N2 Heat Exchanger

Sub-cooler

N2 Cycle

P 1,N2

P 2,N2

As mentioned earlier, the AP-XTM system is an evolution of the C3MR process,

classical C3MR process In order to provide refrigeration at warm condition, high pressure superheated propane is cooled and condensed at ambient temperature using cooling water The saturated liquid propane is then throttled through a Joule-Thompson (JT) valve, producing two phase flow at reduced temperature and pressure The liquid-vapor mixture of propane is completely vaporized as it passes through evaporators to cool the NG feed from ambient temperature down to approximately 240 K Moreover, the C3 loop also provides pre-cooling to the MR loop Note that the lowest pressure of PR stream in PR cycle is maintained at or above atmospheric pressure to avoid air leakage

High pressure MR stream exiting from compressor is cooled using cooling water Then it is pre-cooled by the C3 loop This produces partially condensed MR which is further cooled and liquefied by low pressure and temperature MR stream in the main cryogenic heat exchanger (MCHE) The exiting stream is then let down in pressure resulting in partial flashing and a reduction in temperature According to technical publications by Air Products, a three or four staged pressure let down system is usually implemented to provide pre-cooling refrigeration at several pre-determined temperature levels, analogous to the cascade design This, in theory, provides greater matching of the hot and cold streams in the heat exchangers and therefore, improves cycle efficiency This cold MR stream is subsequently passed through the shell side of the MCHE, vaporizing itself to provide refrigeration for liquefying and sub-cooling the NG feed An optimally adjusted MR composition whose evaporation curve closely mimics the cooling

curve of the NG feed will enhance thermodynamic efficiency (greater reversibility) of the system and therefore, reduce compressor power requirements

In the classical C3MR process, the MR loop is responsible for sub-cooling the NG feed down to approximately 111 K, producing LNG However, further increases in production capacity could not be accommodated as the refrigerant compressors are already at their size and performance limits On the other hand, the refrigeration loads of the C3 and MR cycle are reduced by shifting the sub-cooling refrigeration duty away

production level while still utilizing proven equipment sizes similar to that of C3MR

approximately 165 K before entering another Spiral Wound Heat Exchanger (SWHE) which sub-cools it down to 111 K utilizing the final N2 refrigeration cycle

pressure and cooled to ambient temperature using cooling water Further cooling is

to the compressors after providing sub-cooling duty to feed stream in SWHE It is then let down in pressure through an expander (turbine) which further lowers the temperature

drive refrigerant compressor and/or a generator to produce electricity The exiting cold nitrogen stream from valve is then used to provide sub-cooling duty to the feed stream

is capable of producing up to 7.8 mta of LNG Further increases in capacity to 8-10 mta may be possible by incorporating Air Products’ new proprietary technology such as the

Split-MRTM compressor-turbine configuration33 and split propane casing arrangement32 However, such enhancements will not be considered in this work and its incorporation may be included in future extensions of the current model

3.2 Problem Statement

The objective of this work is to formulate a mathematical model for the generalized

AP-XTM refrigeration system for a given refrigeration load that is able to optimally distribute compressor load among different cycles to minimize total compressor power demanded

by all the three refrigerant cycles over different operation scenarios such as different feed composition, MR composition, and cooling water temperature Each scenario produces a set of optimal operating conditions of each cycle and is able to guide the operators to optimally response by changing operating conditions to shift compressor load among different cycles at different environmental and process conditions

NG As NG passes through each of the cycles, we consider no pressure drop After

temperature T feed_4 and pressure P feed Note that it fixes overall feed cooling, liquefaction,

and refrigeration duty q_feed_total provided by the entire refrigeration system; however,

feed cooling duty provided by each cycle may vary with their operating conditions, cooling water supply, MR composition, and refrigerants’ mass flow rate

3.3 NLP Formulation

As the objective of this work is to obtain optimal operating condition for the latest

Components and energy balance involved in the process force the model to be non-linear Therefore, we develop a non linear programming (NLP) that optimally distribute load among different cycles to minimize total compressor power consumption The exact

restriction by Air Products Hence, we use a generic flow diagram for this process Figure

nomenclature at each node that is the basis of this optimization study Each section of this basic schematic is described wherever it is applicable Note that we will use the same nomenclature for temperatures and pressures in our model formulation indicated in Figure 3.2

Figure 3.2 Basic Schematic of the AP-XTM Refrigeration System

As AP-XTM process uses three different cycles consecutively to sub-cool and

liquefy NG, energy balance among feed and refrigerants tells us,

2

q feed total q feed pr q feed mr q feed N   (3.1)

the model for feed stream exchanging energy with three different refrigeration cycles

Second, we formulate model for PR cycle Third, we formulate model for MR cycle

that includes compressor load of each of the abovementioned cycles

3.3.1 Feed Stream

First, NG enters PR refrigeration pre-cooler LNG-101 where it is pre-cooled to

temperature T feed_2 We can calculate the enthalpy change, ∆H feed_pr of the feed stream as

it passes through PR loop as follows

_ 2 _1

0

feed feed

feed pr T feed feed feed

where, the first term (heat capacity) indicates the ideal enthalpy change of the feed stream

and the remaining part accounts deviation from ideality called residual property Value of

capacity correlations incorporating mixing rule and the generalized second virial

reduced pressure, reduced temperature, and critical temperature of component p Note

that residual property approach is slightly less precise than compressibility approach at

as very high pressure is not expected in AP-XTM system Let m feed is the mass flow rate of

feed NG Hence, feed cooling duty provided by propane is,

  q feed pr m_ _  feedH feed pr_   (3.3)

liquefaction Hence, the feed temperature after propane cooler remains above its dew

point T feed_dew which is a known constant as per definition

feed feed dew

Moreover, to ensure heat exchange compliance with minimum temperature

approach between feed and PR streams, we define the following constraints

_1 _ 4 min

feed pr

at entrance to or exit from heat exchange However, these constraints do not ensure

feasible heat exchange among cold and hot streams because of nonlinear nature of cold

exchange

Next, the MR stream liquefies pre-cooled NG in an MCHE LNG-102 where NG

converts into two phases Due to multi-component nature of feed NG, its H-T curve is

highly non-linear To avoid this complexity, we utilize a back calculation method through

the overall energy balance of the feed stream As we are directly calculating the cooling

optimizer to calculate not only the cooling duty by MR, but also the inlet and outlet

temperature of feed stream to MR cycle indirectly To ensure feasible heat exchange in

liquid NG to its target / storage temperature coming from MCHE This enables the LNG

to be stored and transported in liquid state by special tankers The enthalpy change of the

liquid feed NG can be calculated as follows

T feed N T L feed

Correction term that accounts for deviation from ideality is not mandatory for

liquid stream as pressure has negligible effect on liquid properties; hence, the omission of

the correction term should not result any significant deviation with respect to reality

temperature which does not include predicted process conditions and thus, is not utilized

in this work To circumvent this problem, the following empirical method is utilized

Enthalpy data is collected from Aspen HYSYS 7.1 for a certain range of process

condition of liquid feed stream Then, the following enthalpy-temperature correlation is

regressed from the collected data utilizing MATLAB’s curve fitting tool

condition is expressed as follows

Now, we model PR cycle which is the simplest refrigeration cycle among threes It only

pre-cools feed and MR stream but not liquefies due to the fact that below 230 K its vapor

pressure is less than atmospheric pressure Overall energy balance in PR cycle tells us,

  q comp pr q evap pr q cooler pr q valve pr_ _  _ _  _ _  _ _ (3.13)

where, q_comp_pr and q_evap_pr indicate energy consumed by propane through

compressor and evaporator, whereas q_cooler_pr and q_valve_pr indicate energy lost by

propane through water cooled heat exchanger and valve in PR cycle In this work, we

assume only a single stage compressor K-100 to compress propane to its optimized value

The actual power demanded by compressor shaft is calculated as follows

capacity-temperature and correlation of residual enthalpy can be adopted from Perry’s Chemical

expansion through valve in PR cycle Assuming adiabatic compression,

temperature-pressure correlation across compressor tells us,

1 _1

_ 2

pr pr pr

example, a worked example showed that the discharge temperature can deviate as much

has a detrimental effect on enthalpy and power calculation which can be calculated as

follows36

_ 6 _ 5 _ 6 _ 5

0

01.99

pr pr pr pr

T pr T

pr T

pr T

Besides this, liquid damages compressor; hence, temperature and pressure of incoming

propane must be greater than saturation temperature or less than saturation pressure to avoid such adverse condition The following vapor pressure correlation avoids liquid formation through compressor

_ 2 _1

Next, the saturated propane stream passes through a valve, VLV-100 when it undergoes abrupt decrease in pressure resulting adiabatic flash evaporation and auto-refrigeration of

a portion of liquid stream This throttling process occurs at constant enthalpy and thus, the enthalpy change across the valve is zero

Finally, propane enters two evaporators LNG-100 and LNG-101 to pre-cool feed gas and MR respectively by evaporating itself As flash calculation of liquid propane through valve increases complexity of formulation, the following back calculation is used

to calculate propane cooling duty in LNG-101

  q evap pr q feed_ _  _ _ pr q pc mr _ _   (3.22)

where, q_pc_mr indicates cooling duty in LNG-101 supplied by PR cycle To enforce

feasible temperature approach,

3.3.3 MR Cycle

refrigeration system The multi-component nature of MR stream results in highly linear enthalpy curves and thus, requires more complex formulation In this work, we consider that MR cycle has two compressor stages K-101 and K-102 with one water cooled heat exchanger E-102 between them Moreover, a water cooler heat exchanger E-

non-101 after final compression, a throttle valve VLV-non-101, a propane cooler LNG-non-101, and

an MCHE is present in the cycle Energy enters the loop via compressors and MCHE while leaves via cooler and inter-cooler Hence, overall energy balance in MR cycle tells

us,

q comp mr q mche mr q cooler mr q pc mr q valve mr      (3.25)

where, q_comp_mr and q_mche_mr indicate energy consumed by compressors and MCHE while q_cooler_mr, q_pc_mr, and q_valve_mr indicate energy lost by MR

through water coolers, propane cooler, and valve accordingly In this work, we included two compressor stages in MR cycle due to lack of information on actual number of compressor stages in public domain as more compressor stages with inter-cooler reduce total power consumption by compressors and increase efficiency More compressor stages can be added while a holistic cost analysis must be performed Compressors total power demand is calculated as follows

capacity ratio is calculated as follows

_ 1 _ 1 1 _ 7

_ 6

mr mr mr

_ 8

mr mr mr

_ 2 _ 1

position Let H mr_2 , H mr_3 , H mr_4 , H mr_5 , and H mr_6 are the enthalpy of MR stream before

propane pre-cooler, before MCHE, before valve, after valve, and after MCHE accordingly Calculation of the aforementioned enthalpy in two phase regions enables us accurate energy balance across each of the units; however, it makes the formulation highly non-linear and complex to solve Hence, some simplification is carried out while formulating the process

We write a generalized mass and energy balance equations for the abovementioned

nodes Let q (q = 2, 3, …, 6) denotes the position /node of MR stream in MR cycle Note

that this formulation can be used for the whole MR cycle but it unnecessarily increases model complexity and thus, it is only applied to this two phase regions in MR cycle Let

composition of MR stream where r is the component of MR stream Then, mass and

component balance tell us,

  m z mr r x L rq qy V rq q x L rq q1y V rq q1  (3.37)

and vapor compositions are dependent on MR composition, temperature, and pressure Complex vapor liquid calculations involving the use of fugacity and its coefficients which is highly non-linear and overly complicated An alternative solution is to use an empirical correlation, equilibrium ratio that specifies component balance in two phases

Equilibrium ratio K is related to vapor and liquid composition of each stream as follows

However, K value for different MR composition is not available in the literature It

is found that the effect of composition on K value is relatively small as compared to

temperature and pressure Besides this, empirical correlation found in the literature is only valid for a certain range of temperature and pressure Usage of these ranges will

certainly lead to erroneous value due to its highly non-linear nature Hence, all K values

used in this work are self-regressed via MATLAB using data gathered from Aspen

HYSYS As K values are dependent on pressure and temperature, a 3D surface regression

is utilized; however, due to high non-linear nature of this correlation, even the fifth order equation is unable to accurately represent the whole temperature and pressure range required in this work Hence, the relation is developed for two pressure ranges that fit with the real data This two pressure ranges are applied safely without introducing any additional binary variable It is possible because MR cycle has two pressure conditions higher and lower pressure side before and after the valve while utilizing this approach

= 6 are same and in lower pressure side Note that the aforementioned constant value also varies for different components Moreover, the summation of component mole fraction in any one of the phases must be one

x  y 

Peng Robinson’s equation of state which is applicable to all fluid properties

As the same set of equation is applicable for both vapor and liquid streams, we only describe formulation for vapor stream Enthalpy of any MR vapor stream comprises of

three terms: ideal heat of formation H f v , ideal gas enthalpy H id v, and departure function

property is different for vapor and liquid stream

,

_

mr q TR

mr q l

With these equations it is now possible to calculate MR enthalpy at any position; however, we only use this approach to calculate properties in two phase regions to avoid complexity and non-linearity Now, we write specific energy balance for propane pre-cooler LNG-101 and MCHE LNG-102 The pre-cooler acts to further lower the temperature of the MR stream after it exits the water cooled heat exchanger This indirectly lowers the heat load on MCHE and thus, reduces compressors’ power requirement This condition to which MR stream is pre-cooled to, results in two phase flow Therefore, energy balance across LNG-101 tells us,

bubble point As the throttling process through valve is adiabatic, enthalpy of MR before and after valve is same Therefore, energy balance across LNG-102 tells us,

highly efficient for low temperature processes32 Its relative simplicity of being a pure gas stream throughout the whole cycle makes formulation a much more easier and straightforward In this work, we consider three compressor stages K-103, K-104, and K-

105 with one inter-cooler E-104 as real design is unknown This facilitates lower compressor load; however, cost analysis need to be performed to verify the feasibility of

heat exchanger (SWHE) LNG-103 to sub-cool NG Energy enters the cycle through compressors and SWHE, while leaves through expander and water cooled heat exchangers Therefore, energy balance of N2 loop tells us,

  q comp N_ _ 2q feed N_ _ 2 q cooler N_ _ 2q_ exp_N2  (3.56)

write energy balance equation for each of the unit Power consumed by all compressors

in N2 cycle is calculated as follows

_ 9 2

0

N N

2

1 _ 7

_ 6

N N N

2

1 _ 8

_ 7

N N N

2

1 _10

_ 9

N N N

_ 6 2

0 _1

N N N N

T

pr T

pr T

_ 7 2

0

1.99

N N N N

T pr T

pr T

in exchangers is calculated as follows

_ 2 2

_ 1 2

_ 8 2

0

N N

N N

0

N N

utilize energy This cools the feed NG to cryogenic temperature to provide sub-cooling to liquid NG This expander is well known as a compander in this process In this work, this compander is coupled with any one of the compressors shaft to utilize extracted energy and thus, is a potential source to save total energy demanded by the process The major difference in an expander compared to a valve is that the internal energy of the expanding stream is extracted in the form of shaft work resulting in decrease in enthalpy across the

expander Hence, the amount of energy that can be extracted from the expander can be calculated as follows

_ 3 2

2

1 _ 4

_ 3

N N N

_ 3 2

0 _ 4

N N N N

T

pr T

pr T

The SWHE is much simpler than MCHE as it comprises only two streams where

consider a simple counter-current heat exchange in this unit

_ 4 2

The objective of this work is to distribute compressor load in different cycles in such a

way that total compressors load in the whole system is minimized Let η represents

efficiency of compressors in each cycle Therefore,

It is prudent to reiterate that the objective of this work is to develop a generalized model to select operational parameters in such a way that it can optimally distribute

Products to provide refrigeration to NG However, the potential of this model to optimize

proprietary operational data As a consequence, the following case studies are demonstrated to illustrate the model’s ability to handle and optimize different operational scenarios using fictitious data The first case study illustrates the effect of feed composition, second one illustrates the effect of MR composition, and the final one illustrates the effect of cooling water (environment) temperature on compressor loads

among different cycles Though fictitious data is used to verify the ability of this model,

it successfully handles different case scenario which is an admirable indication of its potential effectiveness in the field

As for feed inlet temperatures, it is assumed to be a high equatorial temperature of 30°C to simulate maximum cooling requirements in the model This temperature is chosen because it approximates the lowest temperature that a water-cooled heat exchanger can achieve using sea-water On the other end, the NG outlet temperature is considered to be 111K to approximate the normal boiling point of methane which is the major constituent of LNG Such low temperature is required as the LNG must remain liquid while being transported under atmospheric pressure conditions in LNG tankers However, recent research has indicated the possibility of transporting LNG at higher pressures (condition of NG coming from NG processing unit), thus reducing the amount

The NG mass flow rate is set at 250 kg/s for all the following case studies, which approximates to 7.88 mta, assuming continuous year round operations This assumption

mta

Besides this, compressor and expander efficiencies are dependent on a number of factors including equipment type, operating conditions, and even vendor specific Without knowledge on the actual specifications, all efficiencies have been set at 85% for simplicity, although both higher and lower values have been reported in compressor handbooks, specification data booklets and technical publications from established compressor and turbo-expander manufacturers For instance, modern centrifugal and