3.2.1 Wells 28
3.2.2 Pumps 29
Figure 5: Gear, Lobe, Rotary Vane and Screw Pumps
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10 Pipe System Domain Models
A pump displaces a volume by physical or mechanical action. A positive displacement pump causes a fluid to move by trapping a fixed amount of it and then forcing (displacing) that trapped volume into the discharge pipe. Positive displacement pumps, unlike centrifu-gal or roto-dynamic pumps, will in theory produce the same flow at a given speed (RPM) no matter what the discharge pressure. Thus, positive displacement pumps are ”constant flow machines”. However due to a slight increase in internal leakage as the pressure in-creases, a truly constant flow rate cannot be achieved. A positive displacement pump must not be operated against a closed valve on the discharge side of the pump, because it has no shut-off head like centrifugal pumps.
The power imparted into a fluid will increase the energy of the fluid per unit volume.
Thus the power relationship is between the conversion of the mechanical energy of the pump mechanism and the fluid elements within the pump. In general, this is governed by a series of simultaneous differential equations, known as the Navier-Stokes equations.
However a more simple equation relating only the different energies in the fluid, known as Bernoulli’s equation can be used. Hence the power, P, required by the pump:
P = ∆P Q η
where ∆P is the change in total pressure between the inlet and outlet (in Pa), and Q, the fluid flowrate is given in m3/s. The total pressure may have gravitational, static pressure and kinetic energy components; i.e. energy is distributed between change in the fluid’s gravitational potential energy (going up or down hill), change in velocity, or change in static pressure. η is the pump efficiency, and may be given by the manufacturer’s information, such as in the form of a pump curve, and is typically derived from either fluid dynamics simulation (i.e. solutions to the Navier-stokes for the particular pump geometry), or by testing. The efficiency of the pump will depend upon the pump’s configuration and operating conditions (such as rotational speed, fluid density and viscosity etc.).
∆P = v22−v12
2 + ∆zg+∆pstatic ρ
∆P is the difference, P2 −P1, between the outlet and the inlet. v2 and v1 are the respective velocities.
For a typical ”pumping” configuration, the work is imparted on the fluid, and is thus positive. For the fluid imparting the work on the pump (i.e. a turbine), the work is negative power required to drive the pump is determined by dividing the output power by the pump efficiency. Furthermore, this definition encompasses pumps with no moving parts, such as a siphon.
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Examples of Informal and Formal Descriptions 11 Main Applications ISO 13709 / API 610 type BB1,
Heavy duty pump for upstream and downstream petroleum, petrochemical, and power generation applications
Maximum Speed of rotation 5,000 rpm
Discharge sizes 150mm to 750mm (6 to 30 inches) Capacity up to 10,200 m3/h (up to 45,000 usgpm)
Head up to 500 m (up to 1,650 ft) Maximum pressure up to 125 bar (up to 1,800 psi)
Materials API 610 Material Classes:
S-4, S-5, S-6, S-8, C-6, A-8, D-1, D-2, 317L Bearing Options Ball/Ball, Sleeve/Ball, Sleeve/Pivot Shoe
Lubrication Ring oil, optional purge mist, pure mist or pressure fed Temperatures -29 - 205oC (-20 - 400oF)
3.2.3 Compressors 32
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Figure 6: Gas Compressor
3.2.4 Pipes 34
Oil pipelines are made from steel or plastic tubes with inner diameter typically from 4 to 48 inches (100 to 1,200 mm); most pipelines are typically buried at a depth of about 3 to 6 feet (0.91 to 1.8 m); the oil is kept in motion by pump stations along the pipeline, and usually flows at speed of about 1 to 6 metres per second (3.3 to 20 ft/s). 35
For natural gas, pipelines are constructed of carbon steel and vary in size from 2 to 36
60 inches (51 to 1,500 mm) in diameter, depending on the type of pipeline. The gas is pressurized by compressor stations and is odourless unless mixed with a mercaptan odorant where required by a regulating authority.
3.2.5 Valves 37
There are basically two kinds of valves: block valve and regulator stations.
12 Pipe System Domain Models
Figure 7: Pipes
Block valve stations These are the first line of protection for pipelines. With these valves the operator can isolate any segment of the line for maintenance work or isolate a rupture or leak. Block valve stations are usually located every 20 to 30 miles (48 km), depending on the type of pipeline. Even though it is not a design rule, it is a very usual practice in liquid pipelines. The location of these stations depends exclusively on the nature of the product being transported, the trajectory of the pipeline and/or the operational conditions of the line.
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Figure 8: Block Valve Stations
Regulator stations: This is a special type of valve station, where the operator can release some of the pressure from the line. Regulators are usually located at the downhill side of a peak.
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Examples of Informal and Formal Descriptions 13
3.2.6 Forks 40
3.2.7 Joins 41
3.2.8 Sinks 42
Sinks are final delivery stations. They are known also as outlet stations or terminals, and is where the product will be distributed to the consumer. It could be a tank terminal for liquid pipelines or a connection to a distribution network for gas pipelines.
4 A Preliminary Analysis
434.1 Parts
We informally analyse further attributes of pipeline units.
4.1.1 Unique Unit Identifiers
In order to distinguish among the many well, pipe, pump. valve, fork, join and sink units we endow each with a unique identity, π : Π. However we otherwise formalise the pipeline units we say that we can observe the unique unit identifier from units. We do not mandate any representation of these unique unit identifiers.
4.1.2 Connectors 44
Connectors can be thought of as non-physical in the sense that they do not “occupy” space ! We then see that wells and sinks have one output, respectively one input connector; pipes, valves, and pumps each have both an input and an output connector; forks have one input connector and two output connectors; and joins have two input connectors and one output connector. Connections are seen as pairs of connectors. Connectors and connections are 45 distinct kinds of concepts. Connectors and connections are not considered to be physically existing parts. We choose to represent connectors by the pipeline unit to which they are
“associated”. And we choose to represent connections by pairs of connectors, that is, by pairs of unique unit identifiers, one is the output connector of one unit, the other is the input connector.
4.1.3 Routes of Nets 46
Pipeline systems are created, by liquid or gaseous material companies, in order to trans-port liquid or gaseous materials over usually great distances. Therefore pipeline units are connected such as to form routes from wells to sinks. A route is any connected sequence of zero or more adjacent units. We define routes so as to allow circular, but, in fact, undesirable routes. We then constrain nets to not contain circular routes.
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4.1.4 Wellformedness of Nets 47
The way in which we describe how units form nets require that we express a number of constraints on the attributes of pipeline units.
4.1.5 Part Attributes 48
Pipeline units have attributes. One attribute is a unique unit identifier. Each unit has its own distinct, hence unique unit identifier. Another attribute prescribe how units are connected. And then there are the unit properties. There are the geometrical properties of units. Then there are the cadestral properties of units: their absolute location in some spatial system: an (X, Y, Z) or a spherical coordinate system (r, θ, φ). And there are the flow and leak properties of units. There may be many additional properties such as we shall see next.
4.1.6 Flows and Leaks 49
The whole purpose of a pipeline system is to ‘flow’ liquid or gaseous material from one point to another. Each unit participates in this flow. So flow characteristics, laminar and turbulent, static and dynamic, of units are properties of these. So are leaks of liquid or gaseous material from a unit: the maximum allowable normal leakage, a quantity expected to be well below the laminar flow; the laminar flow (maximum); the minimum flow that causes turbulence; etcetera.