Pipelines operations are inherently transient processes. Inlet and outlet flows change, pumps and compressors start and stop, control setpoints change, different products and compositions move down the line, and temperatures change with changing ambient conditions. These facts would seem to indicate that a useful pipeline flow model should be a transient model, that is, it should solve the time-dependent flow equations. However, steady-state models are widely used to design pipelines, and to estimate the flow and line pack. Succession-of-steady-states (SSS) solutions corresponding to sequences of boundary conditions, control setpoints, equipment statuses, and interface positions are used for tracking or estimating the movement of products through pipelines. This paper addresses the two types of models and their suitability for various purposes.

Purposes of Pipeline Flow Models

The appropriateness of a particular type of flow model depends on the use to be made of the model results. Pipeline flow models are used for the following purposes:

  1. Product Tracking - Batches of different products, composition, quality, cost, origin, and ownership can be tracked through a pipeline. The objective for offline product tracking models is usually to estimate schedules. For real-time models the objective is usually to estimate interface arrival times. Product tracking may also be used to estimate allocations of ownership and specific (as opposed to average) transmission costs. For both real-time and offline models knowledge of interface locations is necessary for accurate hydraulic calculations.

  2. Line Balance - The net flow in and out of the pipeline, by batch or over time intervals, is a check on the integrity of the pipeline and/or the metering process. A flow model permits the calculation of more accurate line balances by estimating the change in line pack.

  3. Line Pack Distribution - Flow models are used to estimate the distribution of product in the pipeline as an aid to managing the product inventory temporarily stored in the pipeline.

  4. Pressure Monitoring - Flow models provide estimates of the maximum/minimum pressures at points between pressure sensors.

  5. Deliverability - The maximum achievable delivery flow rates at specified points can be estimated with flow models.

  6. Pump/Compressor Performance Monitoring - By comparing model estimates of current performance with manufacturer's specifications, changes in the performance of pump or compressor stations and individual units can be detected.

Fundamental Differences Between Transient and SSS Models

The underlying difference between transient and steady state models lies in the equations of motion. The transient equations contain terms for the rates of change with time of the dynamic variables: pressure, temperature, density, and velocity. By setting these rates of change equal to zero, which is the mathematical expression of the steadystate condition, the steady-state equations of motion are obtained. However, in considering the suitability of transient vs. SSS for various purposes, differences in the results are of more interest than differences in the equations. The results of the two approaches have in common the production of spatial arrays of the dynamic variables at successive points in time.

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