1. Fundamental Principles

The mathematical models used in the design of gas transmission lines are based on algorithms derived from the fundamental principles of thermodynamics and fluid flow. The system to be modeled can be characterized as a control volume of fixed identity, open to the flow of matter, subject to the following definitions:

  1. The flow of matter is one-dimensional.

  2. The mass flow rate through the control volume does not vary with time.

  3. The change in fluid properties at a point in the control volume does not vary with time.

1.1. System Mass Balance

The principle of conservation of mass states that the total mass of the system is constant. For an open system, this requires that the mass entering the system must equal the mass leaving the system. A schematic illustration of the flow of mass through the control volume is given below. As Δt approaches zero, the change in mass in Region I can be considered to represent the mass flowing out of Region I and into the control volume (Region II). Correspondingly, the change in mass in Region III represents the mass flowing out of the control volume and into Region III. Since the space occupied by Region II is equivalent the space occupied by the given mass, the change in mass which is resident in Region II over the entire span can be considered to represent the change in mass of the control volume.

1.2. System Energy Balance

The principle of conservation of energy requires that the overall energy of the system remains constant. However, as long as energy is conserved, there can be a transfer of energy among different energy forms. This energy transfer is defined by the first law of thermodynamics : any work which is performed on the system by external forces is equal to the heat absorbed by the system less the increase in the energy of the system. The development of the system energy balance is analogous to that of the mass balance. At some time, t, a given mass occupies the control volume. This control mass consists of the sum of the masses in Regions I and II. At some time, t + Δt, some of the control mass will have moved into Region III. Heat and work interactions may also have occurred during the time span Δt. The change in energy for Region I can be considered to represent the flow of energy out of Region I and into Region II. The potential energy depends upon the position of the fluid in the gravitational force field. Since only a net change of position along the z-axis will affect the gravitational pull a change in potential energy requires a change in the elevation of the gas. The elevation change is caused by a force acting upon the system. The change in potential energy is equal to the work (force exerted over a distance dz) required to change the elevation of the gas from a reference elevation.

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