Experimental pressure-driven pig mechanics

neqsim.process.equipment.pipeline.PigMotion supplies the mechanical part of a rigid pig model. It advances position and velocity under a prescribed pressure difference, gravity, and explicitly supplied static and kinetic friction forces. It resolves a stop inside a time step before deciding whether the pig remains stationary or reverses. No friction coefficient is fitted or supplied by default.

This is an experimental building block for the flowline roadmap. It is not yet coupled to TwoFluidPipe and cannot predict fluid-driven pig arrival, upstream pressure buildup, bypass, swept liquid, receiver surges or a safe operating pressure. A prescribed pressure schedule is an input assumption, not a solution of the pipeline hydraulics. Mechanical restart of the pig is distinct from the shutdown/cooldown/restart of a multiphase flowline.

Model and units

The axial coordinate increases in the direction the user chooses. Inclination is positive uphill. All inputs are SI; pressure differences are Pa, not bar.

\[F=A\Delta p-mg\sin\theta\]

For a moving pig:

\[m\frac{dv}{dt}=F-F_k\operatorname{sign}(v),\qquad\frac{dx}{dt}=v\]

Here $m$ is pig mass in kg, $A$ is the effective pressure area in m², $\Delta p=p_{upstream}-p_{downstream}$ in Pa, $\theta$ is inclination in radians, $x$ is axial position in m, and $v$ is velocity in m/s. $g=9.80665$ m/s². $F_s$ and $F_k$ are the supplied static and kinetic resistance forces in N, with $F_s\geq F_k\geq0$. At rest the pig remains stationary when $|F|\leq F_s$, including equality. Otherwise it starts in the direction of $F$. A moving pig uses $F_k$, even when the driving force is below the static breakaway threshold.

For each constant-input interval the acceleration is constant until velocity reaches zero. The solver integrates exactly to that event and resolves the remaining interval with the appropriate resting or reverse-motion branch. There is no velocity clipping or artificial near-zero velocity threshold. Divide the schedule at every imposed input change. Inclination in simulate is a prescribed time history; spatial terrain/diameter crossings and receiver contact are not applied automatically by simulate.

Executable start, stop and restart example

The following method-body fragment uses PigMotion from the package above. PigMotionTest.documentedStartStopRestartSchedule compiles and executes this exact fragment, compares its text with this guide, and checks the endpoints.

PigMotion pig = new PigMotion(100.0, 0.01, 100.0, 50.0);
PigMotion.Trajectory result = pig.simulate(0.0, 0.0,
    new double[] {2.0, 10.0, 1.0},
    new double[] {20000.0, 0.0, 25000.0},
    new double[] {0.0, 0.0, 0.0});

The input pig mass is 100 kg, effective pressure area 0.01 m², breakaway force 100 N and moving resistance 50 N. These are synthetic example parameters. The three horizontal intervals apply +20,000 Pa for 2 s, zero differential pressure for 10 s, then +25,000 Pa for 1 s.

Elapsed time (s) Position (m) Velocity (m/s) Interpretation
0 0 0 Initial rest
2 3 3 Acceleration at 1.5 m/s²
12 12 0 Stops at elapsed 8 s, then remains stationary
13 13 2 Restarts at 2 m/s²

getTimesSeconds, getPositionsM and getVelocitiesMps return defensive arrays containing the initial state and interval endpoints. getSteps returns immutable interval ledgers. Java/JPype callers can use the same constructor and advance/simulate signatures; no separate Python implementation is needed.

Work ledger and numerical evidence

Each step exposes pressure work, gravity work, nonnegative friction heat, kinetic energy change, travelled distance, moving time and the first stop time. getStopTimeSeconds is relative to the interval start; -1 means no moving-to-rest event. An initially stationary pig does not itself count as a stop event.

\[\Delta K=A\Delta p\,\Delta x-mg\sin\theta\,\Delta x-F_k\int|v|\,dt\]

The friction term uses total travelled distance, including both legs of a reversal, rather than the absolute net displacement. getEnergyResidualJ returns kinetic energy change minus pressure and gravity work plus friction heat. Its roundoff-level value verifies this mechanical model only; it is not a fluid or combined fluid/pig energy balance. Friction heat is reported but not deposited into a fluid or pipe wall.

Tests cover analytical acceleration and stopping distance, threshold equality, reverse motion, vertical gravity balance, frictionless motion, zero-duration identity, invalid/overflow inputs, serialization and deterministic replay. A fixed 200-case force/velocity/inclination matrix compares one 7 s interval with 70 intervals of 0.1 s and checks sign symmetry and the work balance. This is analytical and numerical verification, not validation against pigging experiments or a commercial simulator.

Public sensor-timing evidence

PigMotionPositionEventTest.limaPublicSensorTimingBenchmark reproduces the published event arithmetic from Lima et al., Sensors 17 (2017) 2119, doi:10.3390/s17092119. The article and its figures are available under CC BY 4.0. The reported pressure-sensor spacing is 5.90 m and the pressure-event separation is 272 samples at 50 ms, or 13.6 s. The executable test advances 272 prescribed 50 ms intervals, verifies that the sensor position is first reached at sample 272, and compares the endpoint with one 13.6 s interval to retain the existing partition-invariance contract. Its sample detector permits only 1e-12 m of accumulated floating-point roundoff, more than ten orders of magnitude below one sample’s travel.

The derived supervisory speed is 5.90 m / 13.6 s = 0.4338 m/s, reported as 0.43 m/s. The paper’s odometer values are 5.70 m in 12.53 s, or 0.4549 m/s, reported as 0.45 m/s. The test retains the publication’s two-decimal reporting and its stated 4.44% difference between 0.43 and 0.45 m/s. The 50 ms sample period is the timing resolution; it is not a fitted mechanics parameter.

This evidence validates sampled-trajectory arithmetic and timing interpretation only. A frictionless prescribed-velocity case is used deliberately because the publication does not provide a redistributable pressure-force/bypass time series suitable for fitting this model. The test therefore does not qualify pressure-force closure, seal friction, gas or liquid bypass, swept-liquid slug, receiver surge, or coupled two-fluid pigging.

Integration and remaining qualification

Public sources for subsequent coupled-model qualification include Hendrix et al., Experiments and modeling of by-pass pigging under low-pressure conditions, and Transient pigging dynamics in gas pipelines: Models, experiments, and simulations. No experimental dataset from these publications is included or claimed passed by the current mechanics tests.