Gas Objects

1. Network (GNET)

The main factor that facilitates the movement of any gas mixture within a network is pressure. To ensure a balance between capacity and costs, networks maintain elevated pressure levels. As gas flows through the pipeline, pressure decreases, typically by about 0.1 bar per kilometer, primarily due to friction against the pipe’s inner surface. To counteract these pressure losses, compressor stations are strategically placed approximately every 150-200 kilometers along the pipelines. These compressors boost the inlet pressure from the "from" node to a higher outlet pressure at the "to" node. When natural gas reaches consumption areas through pipelines, it is either directly supplied to large customers, such as gas-fired power plants and major industrial users, or distributed to local gas distribution networks that serve smaller customers, including households, businesses, and public facilities. In both scenarios, the network’s output pressure and flow are monitored and managed by pressure reduction and metering stations, which are equipped with valves, regulators (also known as control valves), and other related devices.

SAInt uses three types of core variables to characterize the physical behavior of a gas pipeline network. These "primitive" variables that cannot be derived from other variables are summarized in Table 1. In addition to these core variables, there are a number of parameters that are defined on the network level and are used across different object types which are described in Table 2. Furthermore, SAInt uses specific parameters to define simplification strategies (e.g., assume to use isothermal conditions or disregard node elevation) or specific general properties (e.g., which equation to use for the compressibility factor). Those parameters are described in Table 3.

The unofficial unit of measure "sm3" indicates "cubic meter at standard condition" in all following sections. SAInt uses the expression "standard condition" to indicate the conditions defined by the reference temperature (Tn) and the reference pressure (Pn), and must not be confused with the wording and values defined in the international standard LST EN ISO 13443. SAInt sets by default Tn equal to zero degrees Celsius (i.e., 273.15 degrees Kelvin) and Pn equal to 101.325 kilopascal (i.e., 1.01325 bar or 1 standard atmosphere). Using the wording of the ISO standard, such conditions define the so-called "normal conditions". The ISO standard uses the expression "standard conditions" when the temperature is set to 15 degrees Celsius (i.e., 288.15 degrees Kelvin) and the pressure to 101.325 kilopascal.

Table 1. Core variables in a gas network model. None of them can be derived.
Symbol Extension Description Unit

P

P

Gas pressure.

bar-g

T

T

Gas temperature.

K

Q

Q

Volumetric flow rate at standard conditions.

ksm3/h

Table 2. Numerical parameters in a gas network model. They are defined on the network level and are used across different objects.
Symbol Extension Description Unit

PN

Pn

Pressure of the standard condition.

bar

Pamb

PAMB

Ambient pressure. Used for converting between absolute pressure and gauge pressure.

bar

TN

Tn

Temperature of the standard condition.

K

Tamb

TAMB

Ambient temperature. Default value TAMBDEF can be set on the network level. TAMBDEF can be overwritten through a TAMB event for the network, sub network or a pipe. Used for calculating the line pack in case of isothermal conditions or for calculating the heat exchange between the pipe and its surroundings in non-isothermal conditions.

K

μ

VISC

Dynamic gas viscosity. Used for calculating the Reynolds number.

kg/(m s)

κ

Kappa

Isentropic exponent. Ratio between isobaric and isochoric heat capacity. Used for calculating the adiabatic head of the gas compression process in a gas compressor station.

-

Table 3. Parameters of a gas network model for general features leading to different simplifications and for the different types of equations, such as the equations for the friction factor and the compressibility factor.
Symbol Extension Description Unit

-

QTOFF

Network event to disable gas quality tracking for hydraulic simulations. By default, gas quality tracking is performed in hydraulic simulation scenarios unless a QTOFF event is defined.

-

-

HTON

Network event to enable temperature tracking. By default, gas temperature tracking is disabled in hydraulic simulation scenarios unless a HTON event is defined.

-

-

H

Network event to neglect the effects of nodal elevation differences in hydraulic simulation scenarios.

-

-

RO

Network event to define a constant inner pipe roughness for all pipes.

-

-

VISCEQN

Network property to select the type of equation to be used for computing the dynamic viscosity. Up to the present release only the option constant ("CNST") is available. This option cannot be changed by the user.

-

LAMEQN

Network property to select the type of equation to be used for computing the friction factor. Up to the present release the available options are: "HOFER", "AGA", "NIKURADZE", "ZANKE", "COLEBROOK", "mCOLEBROOK" or "CNST".

-

-

ZEQN

Network property to select the type of equation to be used for computing the compressibility factor. Up to the present release the available options are: "PAPAY", "AGA", "TOM", "CUSTOM", "AGA8DC92", or "GERG2008".

-

-

Pz_b

Constant term in the custom equation for compressibility factor.

bar

-

Z_1

Coefficient of linear term in the custom equation for compressibility factor.

-

-

Z_2

Coefficient of quadratic term in the custom equation for compressibility factor.

-

2. Branch (GBR)

In SAInt, a gas branch object (GBR) is responsible for transporting gas between nodes. The platform distinguishes between two types of "passive" branches, which include pipes and resistors, and three types of "active" branches, comprising valves, control valves, and compressor stations. While "passive" branches have their operational behavior solely defined by their pressure drop equations, "active" branches are controlled components that can adjust their operational state and modify control set points throughout the simulation. For instance, a set point may be altered to prevent breaches of operational constraints. There are several derived variables associated with a gas branch that provide additional insights into its functionality. Table 4 describes the derived variables of a branch.

Table 4. Some derived variables for a gas branch.
Symbol Extension Description Unit

Qvol

QVOL

Volumetric gas flow rate of a gas in a branch direction. If negative actual flow direction is opposite to prescribed branch direction.

m3/s

V

V

Gas flow velocity in a branch direction. If negative actual flow direction is opposite to prescribed branch direction.

m/s

ΔP

PD

Difference between pressures at the "from" and the "to" nodes.

bar

Pfr

PI

Gas pressure at the "from" node.

bar-g

Pto

PO

Gas pressure at the "to" node.

bar-g

Π

PR

Ratio between pressures at "from" and "to" nodes.

-

2.1. Pipe (GPI)

A pipe object (GPI) models the gas flow inside a conduit connecting node A to node B. The parameters and derived variables used in modeling a pipeline are presented in the tables from Table 5 to Table 6.

Table 5. Parameters of a gas pipeline. They cannot be modified by events. Heat related properties are only used when the option for "temperature tracking" is turned on.
Symbol Extension Description Unit

Dwall

WTH

Thickness of wall of a pipeline. Currently not used in calculations.

mm

L

L

User-specified pipeline length.

km

rpipe

RO

Roughness of the inner surface of a pipeline.

mm

ηpipe

Eff

Pipeline efficiency. Accounts for pressure losses due to pipeline curvature and shape.

-

D

D

Inner pipeline diameter. The outer diameter is calculated as D+2Dwall.

mm

h

HTC

Heat transfer coefficient through the wall of a pipeline. Currently not used in calculations.

W/(m2 K)

The gas flow within pipelines is a key factor in defining the dynamic behavior of a gas network. Due to the variation in pipeline lengths and possible input-output configurations, different segments of the pipeline can exhibit unique flow rates. Additionally, the ability to compress gas allows lengthy pipelines to act as temporary storage, with linepack significantly influencing the network’s behavior. As a result, constructing a mathematical model for pipelines in a dynamic simulation necessitates a thoughtful approach to these factors, distinguishing it from the models used for other branch types.

Table 6. More derived variables of a gas pipeline.
Symbol Extension Description Unit

Tave

T

Average gas temperature.

K

Pave

P

Average gas pressure.

bar-g

Zave

Z

Compressibility factor based on average gas pressure and average gas temperature.

-

cave

c

Speed of sound based on average gas temperature and compressibility factor.

m/s

λ

LAM

Friction factor.

-

m

-

Mass flow rate.

kg/s

ν

-

Kinematic viscosity.

m2/s

μ

-

Dynamic viscosity.

kg/(m s)

Re

REY

Reynolds number.

-

ΔH

DH

Elevation difference between "from" and "to" node.

m

RF

RF

Resistance Factor, coefficient of the quadratic term for the flow rate in the pressure drop equation.

(bar2 s2)/m6

V

V

Average gas flow velocity.

m/s

2.1.1. Partial differential equations describing the gas flow in a pipeline

Figure 1 provides a graphical representation of the forces acting on an infinitesimal control volume (CV) of gas within a general pipeline with constant cross-sectional area A and an infinitesimal length dx.

pipe segment
Figure 1. Illustration of forces acting on a pipe segment in a gas pipe.

Assuming that the parameters describing the gas flow along the pipeline coordinate x are averaged over A, it is possible to describe the forces by a set of three partial differential equations (PDEs) based on the law of mass conservation, Newton’s second law of motion, and the first law of Thermodynamics. These equations can be expressed more explicitly as follows:

Equation 1

the continuity equation (Law of mass conservation):

Pt+(ρV)x=0
Equation 2

the momentum equation (Newton’s Second Law of Motion):

(ρV)t+(ρV2)x+Px+λρV|V|2D+ρgsinα=0
Equation 3

the energy equation (First Law of Thermodynamics):

t[(cvT+0.5V2)ρA]+x[(cvT+Pρ+0.5V2)ρVA]+ρVAgsinα=˙Ω

where cv is the isochoric heat capacity and ˙Ω is the heat exchange rate.

To describe the relationship between pressure, temperature, and density, the state equation (Real Gas Law) is used:

Pρ=ZRT

The following assumptions are generally accepted as reasonable approximations for the prevailing conditions in gas transportation:

  • Isothermal flow: The changes in gas temperature are negligible; therefore, we can assume isothermal flow, i.e., the gas temperature is constant in time and space and equal to the ground temperature.

  • Creeping motion: The influence of the convective term (ρV2)x is negligible compared to the other terms in the momentum equation, due to the typically low flow velocities in transport pipelines (i.e., the velocity is below 15 m/s).

Applying these two assumptions to eqn. 1, eqn. 2, eqn. 3, and eqn. 4 yields the following reduced set of hyperbolic PDEs:

Pt=ρNc2AQxPx=ρNAQtρN2c2λE2DA2P|Q|Qgsinαc2P

considering the equation for the mass flow rate m and speed of sound c:

m=ρNQ=ρVA
c2=dPdρ=ZRT

The gas density at standard conditions ρN is derived from the relative gas density ρr (also referred to as specific gravity) and the density of air at standard conditions ρair:

ρN=ρrρair

For dynamic simulation, the set of PDEs are discretized in space and time using an implicit finite difference method. The time step for the temporal discretization Δt is set by the user through the scenario time step property, while for the spatial discretization the pipe object is internally segmented into multiple pipe segments such that each segment Δx fulfills the following criteria:

LD30,000&ΔH200m

The number of segments a pipe object is divided into for the dynamic simulation can be obtained from the pipe property J.

For steady state simulations, the time derivatives in eqn. 5 are equal to zero, and the equations can be simplified to a set of ordinary differential equations (ODEs):

dQdx=0dP2dx=ρN2c2λEDA2|Q|Q2gsinαc2P2

In steady state conditions the flow rate Q along the pipeline is constant and the pressure drop between the from node (fr) and to node (to) of a pipe can be expressed by:

P2frP2toes=Rf|Q|Q

where

s=2g(HtoHfr)c2,Rf=16ρ2Nc2λELeπ2D5,Le={L,Hfr=Htoes1s L,HfrHto

2.1.2. Friction Factor (λ)

The Darcy friction factor (λ) or simply friction factor, is a dimensionless number used in the Darcy-Weisbach relation. Its value depends on the gas flow velocity, the roughness of the inner surface, and the diameter.

To take pipe geometry and flow velocity into consideration, a dimensionless number, the Reynolds number, is usually used:

Re=Dρ|V|μ=D|V|ν

whose value is reset to 2300 if it is less than 2300. μ and ν are the dynamic viscosity and the kinematic viscosity of the gas, respectively. The hydraulic diameter of the branch should be used, and it is the inner diameter (D) if the branch is circular.

Once the friction factor is estimated, it is possible to derive the effective friction factor (λE), which considers the curvature and the shape of the pipe (ηpipe) into consideration. Its relationship with the friction factor is:

λE=λη2pipe

Six equations for the friction factor are implemented in SAInt (see Table 3):

Equation 1

For turbulent flow (typical flow condition in transport pipelines), the Colebrook-White equation for friction factor is usually used (option "COLEBROOK" for the network’s parameter LAMEQN):

1λ=2log10(2.51Reλ+rpipe3.71D)
Equation 2

HOFER equation for friction factor (option "HOFER" for the network’s parameter LAMEQN):

λ=[2log10(4.518Relog10(Re7)+rpipe3.71D)]2
Equation 3

AGA equation for friction factor (option "AGA" for the network’s parameter LAMEQN):

1λ=2log10(3.7Drpipe)
Equation 4

Nikuradze equation for friction factor (option "NIKURADZE" for the network’s parameter LAMEQN):

λ=1[2log10(D/rpipe)+1.138]2
Equation 5

Zanke equation for friction factor (option "ZANKE" for the network’s parameter LAMEQN):

λ=[2log10(2.7log10(Re1.2)Re+rpipe3.7D)]2
Equation 6

mColebrook equation for friction factor (option "mCOLEBROOK" for the network’s parameter LAMEQN):

1λ=2log10(rpipe3.7D+2.851Reλ)

2.1.3. Compressibility Factor (Z)

The compressibility factor is a variable that models the deviation of the compressibility behavior from that of an ideal gas. Its value depends on the pressure and the temperature. Different methodologies for deriving the compressibility factor have been developed in the scientific literature. SAInt allows the user to select among six different methods (as indicated in Table 3) which are explained below.

Method 1

The first method for the compressibility factor is the Papay equation (option "PAPAY" for the network’s parameter ZEQN):

Z=13.52Prexp(2.260Tr)+0.274(Pr)2exp(1.878Tr)

The two constants, Pr and Tr, represent the reduced pressure (Pr=P/PC) and the reduced temperature (Tr=T/TC), respectively. They are defined as the actual value divided by the value at the critical point.

Method 2

A second standard method is the AGA equation for the compressibility factor (option "AGA" for the network’s parameter ZEQN):

Z=1+0.257Pr0.533PrTr

which remains valid for natural gas up to 150 bar.

Method 3

An extension of the AGA equation has been proposed, incorporating a detailed molar-composition description into a virial-type equation. The method was introduced by Starling and Savidge (1992)[1] and described in the ISO standard 12213-2 (2006, part 2). The so-called AGA8-DC92 equation for the compressibility factor is (option "AGA8DC92" for the network’s parameter ZEQN):

Z=1+Bρmρr18n=13C*n+58n=13C*n(bncnknρknr)ρbnrexp(cnρknr)

where B is the second virial coefficient; ρm is the molar density; ρr is the reduced density; bn, cn, kn are constants (see table B.1 of the ISO standard 12213-2), and C*n are coefficients which are functions of temperature and composition. The reduced density and the molar density are calculated respectively as follows:

ρr=K3ρmρm=PabsZRUT

K is a mixture size parameter, and Pabs is the absolute pressure. For a detailed description of the model and the algorithm for solving the problem, the user is referred to the publication or to the ISO standard 12213-2.

Method 4

Kunz and Wagner (2008)[2] proposed an extended version of another thermodynamic model for the compressibility factor. This new reference equation of state was called GERG-2008 equation for the compressibility factor (option "GERG2008" for the network’s parameter ZEQN). The equation is based on a multi-fluid approximation explicit in the reduced Helmholtz free energy:

α(δ,τ,x)=α°(ρ,T,x)+αr(δ,τ,x)

where the first term α°(ρ,T,x) represents the properties of the ideal-gas mixture at a given mixture density, temperature T, and molar composition (here in vector format), and the second term is the residual part of the reduced Helmholtz free energy of the mixture. The first term is estimated as follows:

α°(ρ,T,x)=Ni=1xi[α°0i(δ,τ)+lnxi)]

The second term is computed as:

αr(δ,τ,x)=Ni=1xiαr0i(δ,τ)+N1i=1Nj=i+1xixjFijαrij(δ,τ)

Here, δ and τ indicate the reduced mixture density and the inverse reduced mixture temperature, respectively, and are expressed as follows:

δ=ρρr(x)τ=Tr(x)T

They depend only on the composition of the mixture. For a detailed model description, users can refer to the publication or to the ISO standard 20765-2.

Method 5

An alternative formulation of the compressibility factor is proposed by van der Hoeven (2004)[3] and described in chapter 10 of his book. This formulation is known as the Hoeven equation for the compressibility factor (option "TOM" for the network’s parameter ZEQN). The equation is based on temperature, density, and quality-related data and uses an implicit cubic formulation:

Z3Z2+bPZbP2P1=0

and the two terms:

b=Z2CZCPCP1ZC=1Pexp(4.91+0.0135T1.15ρ0.048H0.02C)

where P1 and PC are reference pressure values equal to 450 bar and 55 bar, respectively, and H and C are the molar concentration of hydrogen and carbon dioxide in the gas stream.

This implicit cubic formulation can be solved by an iterative scheme based on the following:

Zi+i=2Z3iZ2i+C3Z2i2Zi+B

where B is equal to bP, and C is bP2/P1.

A maximum of seven iterations are sufficient to reach machine accuracy.

Method 6

SAInt provides a custom formulation of the compressibility factor (option "CUSTOM" for the network’s parameter ZEQN). This variant is based on the formula:

Z=1+Z1+Z2((PPbase)2P2base)

Pbase, Z1, and Z2 are user-defined custom parameters for a reference base pressure and coefficients (defined as properties of a network object GNET with Pz_b, Z_1, and Z_2, respectively).

==== Linepack (LP) The amount of gas stored in a gas pipe, also referred to as linepack, can be calculated using the following equation:

LP=AρNc2x=Lx=0P dx=PaveρNZRTVgeo

where Vgeo is the geometric pipe volume and Pave the average pipe pressure, which is defined as a function of the inlet and outlet pressures P1 and P2 as follows:

Pave=23P2fr+PfrPto+P2toPfr+Pto

2.1.4. Volumetric Flow (Qvol)

The volumetric flow rate (Qvol) is defined as the volume of gas flowing through a pipe per unit time. It is calculated as:

Qvol=VA=ρNc2QNP

The volumetric flow rate depends on the pipeline pressure, thus, it changes along the pipeline as the pipeline pressure drops in flow direction. The volumetric flow rate at the inlet Qvol,fr, outlet Qvol,to and the average volumetric flowrate Qvol,ave are computed by replacing P with the inlet pressure Pfr, outlet pressure Pto and average pressure Pave, respectively.

2.1.5. Flow Velocity (V)

The flow velocity V can be obtained by dividing the volumetric flow Qvol by the cross-sectional area of the pipe A:

V=QvolA=ρNc2QNAP

The flow velocity at the inlet Vfr, outlet Vto and the average flow velocity Vave are computed by replacing P with the inlet pressure Pfr, outlet pressure Pto and average pressure Pave, respectively.

2.2. Compressor station (GCS)

A compressor station object (GCS) models the compression of the gas stream from a lower pressure at the inlet (suction pressure) to a higher pressure at the outlet (discharge pressure). Three parameters and eight constraints are required to describe a compressor, which are summarized in Table 7 and Table 8, respectively. Note that the pipeline inner diameter (D) is essential to relate the flow rate and the velocity.

Table 7. Parameters of a gas compressor object. D is only used to relate flow rate and flow velocity, just like that for gas pipeline. This parameter is also the same for control valves, valves, and resistors.
Symbol Extension Description Unit

ηH

EFFHDEF

Default average adiabatic efficiency of the compression process. Can be changed in a scenario by defining an EFFH event.

-

ηM

EFFMDEF

Default average mechanical efficiency of the driver. Can be changed in a scenario by defining an EFFM event.

-

D

D

Equivalent diameter of the inner surface of a gas branch.

mm

Table 8. Constraints of active gas branches. They can be changed by events.
Symbol Extension Description Unit

Vmax

VMAX

Maximum flow velocity.

m/s

Qvol, max

QVOLMAX

Maximum volumetric flow rate.

m3/s

Qmax

QMAX

Maximum volumetric flow rate at standard conditions.

ksm3/h

Pmax, out

POMAX

Maximum discharge pressure.

bar-g

Pmin, in

PIMIN

Minimum suction pressure.

bar-g

Πmax

PRMAX

Maximum compression ratio.

-

Wdriver, max

POWDMAX

Maximum driver power.

MW

Wshaft, max

POWSMAX

Maximum shaft power.

MW

Table 9. More derived variables of a gas compressor object. They have corresponding set-point events.
Symbol Extension Description Unit

Wshaft

POWS

Power required by the compressor’s shaft to increase the pressure of a gas.

MW

Wdriver

POWD

Power required by the driver to propel the shaft of the compressor.

MW

Qfuel

FUEL

Fuel consumption rate required by the driver to propel the compressor.

ksm3/h

In addition to those in Table 4, Table 9 presents three new derived variables for active gas branch. A compressor can control these eight derived variables, including Q, through set-point events, which will be discussed in depth in a dedicated on set point events, which is in preparation.

The set of constraints for a compressor are presented in the following two subsections.

2.2.1. Constraints for Pressure and Flow

There are three main constraints for pressure in a compressor station:

Pmin, inPfrPtofor the inlet pressure
PfrPtoPmax, outfor the outlet pressure
1Pto/PfrΠmaxfor the pressure ratio

There are four constraints related to the gas flow in a compressor station:

0QQmaxfor the flow rate
0QvolQvol, maxfor the volumetric flow rate
0VVmaxfor the flow velocity

Some of these constraints are the same for other object type like control valves and valves.

2.2.2. Power and Fuel

The relationships between parameters and variables of a compressor are described here. The adiabatic head, with base unit [m2/s2], can be expressed as:

HH=κκ1ZfrTfrR[(PtoPfr)κ1κ1]

Based on the adiabatic head, constraints for power consumption of shaft are:

Wshaft=ρNηHQHH0WshaftWshaft, max

Based on the power consumption of shaft, constraints for power consumption of driver are:

Wdriver=WshaftηM0WdriverWdriver, max

The equation for volumetric fuel consumption is (see Table 9 and Table 20):

Qfuel=WdriverEGHV

2.2.3. Become Resistor or Bypass

An active branch can be turned into a passive branch (a resistor object, a bypass, or a non-return bypass) via three particular event types. The equation for the resistor is in Section 2.5. A bypass connects two gas nodes and does not result in a pressure drop. In other words, a bypass can be considered as a resistor with a resistance value of zero. A non-return bypass is a bypass that allows gas to flow in the branch direction.

Based on the definitions, the bypass pressure equation describes a bypass or a non-return bypass:

Pfr=Pto

In addition, the flow constraint of non-return bypass makes sure gas flows in the branch direction:

Q0

2.3. Control Valve (GCV)

The control valve object (GCV) is an active branch type but cannot input power. So there are only six set-point events for five derived variables (see Table 4) and one core variable, Q. There is only one parameter, the inner diameter (D), mentioned in Table 5. There are four constraints for a control valve object (eqn. 6, eqn. 7, eqn. 9, and eqn. 11).

2.4. Valve (GVA)

Unlike a control value, a valve object (GVA) can only be completely closed or opened, which means there is no associated numerical event. Only one parameter, the inner diameter (D), is mentioned in Table 5. Besides, there is only one constraint: Vmax (Table 8).

2.5. Resistor (GRE)

A resistor object (GRE) models a device that causes a local pressure drop. The main difference between a pipeline and a resistor is that a pipeline has a linepack. For a resistor, SAInt requires the user to specify one parameter, the equivalent pipeline’s inner diameter (D) (Table 7), which relates the gas flow rate and the gas velocity. A resistor has one constant, the resistance factor of resistor (RRE, see Table 10), a non-dimensional quantity, used to express the degree of resistance to the flow.

The resistor pressure drop equation describes the relation between terminal pressures:

PfrPto=RREρ2|V|V
Table 10. List of the constants for a gas resistor.
Symbol Extension Description Unit

RRE

R

Resistance factor of a gas resistor.

-

3. Node (GNO)

A gas node object (GNO) is a joint for gas branches and gas externals. From a modeling perspective, a node is described by a set of core variables introduced in Table 1, and by a set of derived variables, parameters, and constants. The derived variables are presented in Table 11, and cover variables that can be obtained from the core set variables. Other parameters which events in a simulation cannot modify, are described in Table 12. Finally, constants for a node object are presented in Table 13 and define some general constraints on the pressure.

Table 11. Derived variables of a gas node.
Symbol Extension Description Unit

c

c

Speed of sound of a gas at a node.

m/s

ρ

RHO

Density of a gas at a node.

kg/m3

Qnode

Q

Total volumetric flow rate of a gas out of a node at standard conditions.

km3/h

Qnode, thermal

TQ

Total power of a gas flow out of a node.

MJ/h

Qnode, VOL

QVOL

Total volumetric flow rate of a gas out of a node.

m3/s

Table 12. Parameters of a gas node.
Symbol Extension Description Unit

Pmin

PMIN

Min pressure of gas at a node. Non-negative value.

bar-g

Pmax

PMAX

Max pressure of gas at a node. Non-negative value.

bar-g

Table 13. Constants of a gas node. They cannot be modified by event.
Symbol Extension Description Unit

Pmax

PMAX

Maximum pressure at a node.

bar

Pmin

PMIN

Minimum pressure at a node.

bar

3.1. Pressure Constraint

The node pressure is usually constrained:

Pmin<P<Pmax

4. External (GXT)

A gas external object (GXT) injects/withdraws gas into/from the network at some node. External are active elements in the network as events define their behavior. For any type of gas external, the user can set one of the two basic set-point events either for the gauge pressure (P) or for the volumetric flow rate (Q). Finally, external are also characterized by a set of constants summarized in Table 14.

Table 14. Common constants for gas external.
Symbol Extension Description Unit

Qmax

QMAX

Maximum volumetric flow rate of a gas injection/withdrawal object.

ksm3/h

Qmin

QMIN

Minimum volumetric flow rate of a gas injection/withdrawal object.

ksm3/h

T

T

Temperature of the gas injected into a gas network. There is no temperature for the gas withdrawal.

K

Cset

CTRLSET

Numerical value for the control mode.

-

4.1. Gas supply (GSUP)

The gas supply object (GSUP) models gas injection into the network. If the quality tracking feature is enabled, the quality of the gas injected must be specified. SAInt uses the default quality (i.e., pure methane) when a user-defined value is not provided. See Section 5.1 and Section 5.2 for more details on gas components and gas quality.

A gas injection constraint describes the ability to inject gas:

QminQQmax

The value of Qmin should not be smaller than zero to ensure that Q remains non-negative. The same constraint holds for any other external supplying gas to the network, such as gas storage or an LNG terminal.

4.2. Gas demand (GDEM)

The gas demand object (GDEM) models gas withdrawal from the network. Neither a parameter nor a gas quality is required for a demand external. Instead of the gas injection constraint (eqn. 14), a gas withdrawal constraint is applied as follows:

QminQQmax

with the constants having the same meaning. Note that Q is non-positive.

4.3. Gas storage (GSTR)

A gas storage object (GSTR) is a facility designed to temporarily store gas outside the network and utilize it when needed. Similarly, an LNG facility object (see Section 4.4) stores liquid gas temporarily outside the network, and converts it into its gaseous form before injection into the system. Due to the similarities between the two types of facilities, SAInt models gas storages and LNG terminals in a similarly.

The core parameters SAInt uses to model a gas storage object are described in Table 15. The parameter INVMAX is shared by both gas storage and LNG facility. Events cannot modify all these parameters during a simulation, but they are all user-defined values to be specified when adding a gas external object to the network.

Similar to a gas supply object, when quality tracking is enabled, SAInt expects the user to specify the quality of the gas withdrawn from gas storage (see Section 5.2). SAInt always assigns a default gas quality (i.e., the one of pure methane) to a newly created gas storage object, allowing the user to change the gas quality type at any moment.

Table 15. Core set of parameters of gas storage object. They cannot be modified by events. The first parameter INVMAX is shared with an LNG terminal object.
Symbol Extension Description Unit

Imax

INVMAX

Maximum weight of a gas in a storage (or LNG in onshore storage).

kg

QD, max

INJMAX

Maximum injection rate of a gas into storage (charging).

ksm3/h

QD, min

INJMIN

Maximum injection rate of a gas into storage (charging) at the maximum level of the inventory.

ksm3/h

ID, slope

INVINJ

Inventory level where the maximum injection rate starts to decrease because of the high inventory.

%

QG, max

WDRMAX

Maximum withdrawal rate of a gas from the storage (discharging).

ksm3/h

QG, min

WDRMIN

Maximum withdrawal rate of a gas from the storage (discharging) at the minimum level of the inventory.

ksm3/h

IG, slope

INVWDR

Inventory level where the maximum withdrawal rate starts to decrease because of the low inventory.

%

-

UGSTYPE

Type of storage. Choose "Depleted" for depleted gas field, "Salt" for salt cavern, or "Aquifer". This desriptive parameter does not affect the modlling of the gas storage object.

-

ηG

Efficiency for gas injection to discharge storage. Between 0 and 1.

-

ηD

Efficiency for gas withdrawal to charge storage. Between 0 and 1.

-

Table 16 describes three additional variables used in modeling a gas storage to track the weight of gas stored at different time steps, analogous to electric storage.

Table 16. Extra variables of gas storage. The value of either QG or QD is specified by the set-point event for Q.
Symbol Extension Description Unit

QG

-

Gas injection rate to discharge storage. Non-negative value.

ksm3/h

QD

-

Gas withdrawal rate to charge storage. Non-negative value.

ksm3/h

I

INV

State of charge. The weight of gas in the gas storage. Non-negative value.

kg

4.3.1. (Dis)Charging equation and constraints for a gas storage

When modeling gas storage, the efficiency for gas injection (ηG) or withdrawal (ηD) is derived based on the inventory level, the storage envelop, and the values of the parameters INVINJ and INVWDR. SAInt considers the following set of constraints:

Constraint 1

The (dis)charging equation of a gas storage describes the gas injection with two variables:

Qt=ηGQG, tQD, t
Constraint 2

The state of charge (SOC) constraint of gas storage describes the weight of the stored gas:

It=It1+Δt(ηDρN,tQD, tηGρsupplyQG, t)0ItImax

where the value of I at the initial time step is Iinit.

Constraint 3

Both the maximum charging rate and the maximum discharging rate depend on SOC. Six parameters in total describe such dependencies. Table 17 illustrates injection and withdrawal envelopes for typical gas storage types and values.

The discharging constraints of gas storage describe the rate of gas withdrawn from the storage or the rate of gas injection into the network:

QG<QG, maxQG<QG, min+QG, maxQG, minIslopeImaxItQG>0

The charging constraints of gas storage describe the rate of gas injected into the storage or the rate of gas withdrawal from the network:

QD<QD, maxQD<QD, maxIslopeQD, min1IslopeQG, maxQG, minImax(1Islope)ItQD>0

This equation is similar to eqn. 15.

Table 17. Typical values and illustrations for parameters for the withdrawal and injection of gas storages for depleted gas fields, aquifers and salt caverns.
withdrawal from storage injection into storage

depleted gas field

gstr envelops 1 1 tex
gstr envelops 1 2 tex

aquifer

gstr envelops 2 1 tex
gstr envelops 2 2 tex

salt cavern

gstr envelops 3 1 tex
gstr envelops 3 2 tex

4.4. LNG Regasification Terminal (LNG)

Docking LNG cargos and onshore storage tanks are modeled in an LNG terminal object (LNG). Two processes are considered simultaneously: on one side, the relocation of LNG from the arrived cargo to the onshore storage and, on the other, the conversion from the liquid to the gaseous form of natural gas and the injection into the network. The second process is the same as the one of gas storage.

SAInt requires a set of core parameters to model an LNG terminal. The parameters are described in Table 18. The parameter INVMAX is common with a gas storage object. Two variables, I and Ivessel, are used to track the weight of LNG in the onshore storage and the arrived cargo, respectively.

Table 18. Core set of parameters of an LNG terminal object. They cannot be derived from other variables.
Symbol Extension Description Unit

Imax

INVMAX

Maximum weight of LNG in the onshore storage (or gas in a gas storage).

kg

Iinit

INV

How much LNG is stored in the onshore storage of the terminal at the intial time step.

kg

dLNG

dLNG

Relative density of LNG to natural gas, at standard conditions.

-

Qvessel, max

VESMAX

Maximum storage size of any LNG cargo arriving at the terminal.

m3

QDIS

DIS

Default volumetric rate for relocating LNG from the cargo to the onshore storage. This is a non-negative number.

m3/s

QD

-

Volumetric rate for relocating LNG from the cargo to the onshore storage. This is a non-negative number.

ksm3/h

QG

-

Gas injection rate from the onshore storage to the network. This is a non-negative number.

ksm3/h

Ivessel

VOLVES

State of charge or inventory. The weight of LNG in arrived vessels. This is a non-negative number.

kg

I

INV

State of charge or inventory. The weight of LNG stored onshore. This is a non-negative number.

kg

During the regasification of LNG, SAInt assumes an active consumption of electricity. The discharging flow rate, QG, can also be called regasification rate, and its relationship with the electricity consumption is described using an ad hoc equation for a EDLNG object.

Table 19 describes two events for an LNG facility related to setting the initial inventory level of the onshore storage and to the size of the arriving cargo. Such events complement the events related to P and Q.

Table 19. Extra events types for LNG terminal.
Symbol Extension DisplayName Description Unit

Iinit

INV

inventory

Inventory (i.e., weight) of gas at reference conditions in the onshore storage at LNG terminal at initial time step.

kg

Qvessel, t

VESSEL

Arriving cargo size.

Volume of LNG in a newly arrived LNG cargo at a user-sepcified time step.

m3

4.4.1. Discharging equation and constraints for an LNG facility

When modeling an LNG facility, SAInt considers the following set of constraints:

Constraint 1

Since LNG can only be evaporated and injected into the network, it is not possible to withdraw gas, so the discharging equation is different from that for gas storage:

Qt=ηGQG, t
Constraint 2

The state of charge (SOC) constraints for LNG in vessels describe the total volume of LNG stored in vessels that have arrived at the LNG terminal:

Ivessel, t=Ivessel, t1+Δt(ρN, LNGQvesselρN, LNGQD, t)Ivessel00QvesselQvessel, max

The value of Ivessel at the initial time step is Ivessel, init.

Usually, LNG in vessels is relocated at the max rate possible. Thus, QD, t=QDIS whenever the resulting LNG in vessels is non-negative (Ivessel, t1+ΔtρN, LNGQvesselΔtρN, LNGQDIS0). Or else, QD, t=0.

The only constant is the arriving vessel size ( Qvessel), which represents the size of vessels that arrived during the first time step.

Constraint 3

Since the weight of LNG in the onshore storage is constrained, the relative density of LNG is used to relate the volume and the weight:

dLNG=ρN, LNGρN, NG

Similar to eqn. 15 for gas storage, the SOC constraints for onshore LNG describe the weight of LNG stored in the onshore storage:

It=It1+Δt(ρN, LNGηDQD, tρsupplyQG, t)0IImax

where the value of I at the initial time step is Iinit.

5. Other objects

5.1. Gas component (GCMP)

A gas component object (GCMP) is described by six basic parameters, whose values are either taken from the scientific literature (as in the built-in library of SAInt) or obtained as user-defined inputs. Events cannot modify these basic parameters. See Table 20 for the complete list and the details of each parameter.

Furthermore, SAInt calculates for each gas component three derived parameters. Details are provided in table Table 21. The equations used are:

  • the density at standard condition (ρN) is derived from the density of air and the density ratio as:

ρN=dρair
  • the Wobbe number (or Wobbe index) (Wobbe) of a gas component/mixture is derived from the density and the gross calorific values as:

Wobbe=EGCVd
  • the specific gas constant (R) of a gas component/mixture is defined as the universal gas constant divided by the molar mass:

R=RUM
Table 20. Literature or user-defined parameters to define a gas component. They cannot be modified by events.
Symbol Extension Description Unit

d

RHOr

Density of a gas at standard conditions relative to the density of air (at 273.15 K and 101.325 kPa).

-

EGCV

GCV

Gross calorific value, or higher heating value (HHV). Total amount of heat released when burning.

MJ/sm3

ENCV

NCV

Net calorific value, or lower heating value (LHV). Heat released in combustion, with water component in vapor state.

MJ/sm3

M

M

Mass per unit mole.

g/mol

PC

PC

Critical pressure. Pressure of the end point of the phase equilibrium curve.

bar

TC

TC

Critical temperature. Temperature of the end point of the phase equilibrium curve.

degree Celsius

Table 21. Extra parameters of gas component, derived from user-defined input parameters as described in table Table 20.
Symbol Extension Description Unit

Wobbe

WOB

Wobbe number, or Wobbe index. Indicator of the interchangeability of fuel gases.

MJ/sm3

ρN

RHOn

Density of a gas at standard conditions.

kg/sm3

R

R

Specific gas constant of a gas component or a gas mixture.

J/(K kg)

5.2. Gas quality (GQUAL)

In SAInt, a gas quality object (GQUAL) is a gas mixture of multiple pure substances. Because it is computationally expensive to implement nonlinear calculations for thermodynamic properties of a gas mixture, SAInt adopts a standard linear approximation assuming that:

  • a gas mixture can be defined using the same properties as any other pure gas component;

  • it is necessary to specify the molar fraction (X or MixtureFraction) of each pure gas component contributing to a gas mixture. The molar fraction is expressed as the molar proportion of the component in the gas quality. The sum of all molar fractions must be equal to one (or 100 % if the values are expressed as a percentage);

  • the mixing of two or more components is considered "perfect" so that the same set of essential parameters as for a component can be calculated based on the "perfect mixing equation" and the molar fractions.

In a gas model in SAInt, any external can supply a specific gas quality. If not otherwise specified by the user, SAInt assumes a default quality stream composed of only methane. The quality of a gas mixture remains unchanged in any branch but changes after perfect mixing at a node. The properties of the gas mixture are estimated by applying the perfect mixing equation, where the molar fraction and the mass flow of contributing flows to a node are combined.

As for a gas component, the properties of a gas quality cannot be changed by events.

The key points are summarized in table Table 23.

Table 22. User-input parameters to define a gas mixture. They cannot be modified by events.
Symbol Extension Description Unit

-

-

List of gas components involved.

-

-

Press to normalize "MixtureFraction"s of components, so that the sum is one.

-

-

Press to calculate properties of gas mixture based on "MixtureFraction"s.

-

X

Fraction of component in gas mix.

% Mol

Table 23. How MixtureFractions and parameters are obtained in three ways to specify gas mixture.
How MixtureFractions six parameters

composed of multiple gas components

user-input

weighted average based on MixtureFractions

the same way to define a gas component

-

user-input

mixing of gas mixture flows

See

As for how these ways are used, gas externals can supply different gas mixtures, the mixing of which later happens at nodes. So, if the supply from some external is different from the default gas mixture, either the first or the second way should be used to specify the new gas type. The properties of gas (parameters and MixtureFractions) remain unchanged in the gas branch, but change after perfect mixing at the node. The properties of the new mixture is calculated in the third way.


1. Starling, K.E., Savidge, J.L. "Compressibility Factors for Natural Gas and Other Related Hydrocarbon Gases", American Gas Association (AGA) Transmission Measurement Committee Report No. 8, American Petroleum Institute (API) MPMS, chapter 14.2, second edition, November 1992
2. Kunz, O., Wagner, W., The GERG-2008 wide-range equation of state for natural gases and other mixtures. An expansion of GERG-2004. J. Chem. Eng. Data 57 (2012), 3032-3091. https://doi.org/10.1021/je300655b
3. Hoeven, T.v.d., Math in Gas and the Art of Linearization.Netherlands: Energy Delta Institute. (2004). ISBN 9789036719902.