Pigging is a common operation in the oil and gas industry. Because of the compressibility of the gas, starting up a pipeline inspection gauge (pig) from a stoppage can generate a very high speed of the pig, which is dangerous to the pipe and the pig itself. Understanding the maximum speed a pig achieves in the restarting process would contribute to pig design and safe pigging. This paper presents the modeling of a pig restarting from a stoppage in gas pipeline. In the model, the transient equations of gas flow are solved by method of characteristics (MOC). Runge-Kutta method is used for solving the pig speed equation. The process of a pig restarting from a stoppage in a horizontal gas pipe is simulated. The results indicate that the maximum speed a pig achieves from a stoppage is primarily determined by the pressure of the pipe and the pressure change caused by the obstructions. Furthermore, response surface methodology (RSM) is used to study the maximum speed of pig. An empirical formula is present to predict the maximum speed of a pig restarting from a stoppage in gas pipeline.
To date, a large variety of pigs have evolved to perform operations such as locating obstructions, cleaning out debris and deposits, liquid removal, and inspection for corrosion spots or damage in pipes [
In pigging operations for the horizontal gas pipeline, there are occasions that the pig stops at some positions in the pipelines, which can be identified by the increase of upstream pressure or the decrease of downstream pressure [
Currently, the release of a pig from a stoppage can be divided into two ways: forward push and backward push. The forward push means the release of a pig from a stoppage by increasing the upstream pressure and/or decreasing the downstream pressure. If the forward push is failed, backward push can be considered in some cases, i.e., increasing the downstream pressure and/or decreasing the upstream pressure to push the pig out of the pipeline through the inlet. In these situations, the pig can easily reach a very high speed that would be dangerous for the pipe and the pig itself [
To understand the dynamic behavior of the pig, the pig dynamic equation must be solved together with the governing equations of flows [
A literature survey reveals that very few papers pay attention to the maximum speed of pig as it restarts from a stoppage in gas pipeline. This paper deals with the dynamic model of the process of a normal pig restarting from a stoppage in horizontal gas pipeline. The equations for unsteady gas flow in pipe are solved by MOC. Then the differential pressure between pig tail and nose is gotten from MOC results. Thus the pig dynamic equation is solved by Runge-Kutta method. The process of a pig restarting from a stoppage in gas pipeline is simulated. The results indicate that the maximum speed a pig achieves from a stoppage is primarily determined by the pressure of the pipe and the pressure change caused by the obstructions. Furthermore, RSM is used to study the maximum speed of pig. Based on the results of the RSM simulations, an empirical formula is present to predict the maximum speed of a pig restarting from a stoppage in gas pipeline.
Figure
Schematic diagram of a pig moving in a pipeline.
The driving force
The following assumptions are adopted to simplify the model:
(1) The gas is ideal gas.
(2) The fluid in the pipeline is a single-phase gas.
(3) The gas flow is quasi-steady heat flow.
(4) The stiffness of the pipeline is large enough to keep the diameter unchanged during pigging.
The transient flow dynamics can be modeled based on the continuity equation, momentum equation, and energy equation, respectively, as follows [
Equation (
For each pair of
By writing (
Figure
Characteristic lines using in MOC.
According to the characteristic lines in Figure
According to (
The sampling time,
To analyze the restarting process of a pig in horizontal gas pipeline, we made the following assumption: the pig stopped in the pipeline and the gas stopped flowing. It means at the initial moment, the gas velocity is zero and the pressure is equal everywhere.
It is assumed that the upstream and downstream gas flows are fully coupled to the pig. Therefore, the velocity of gas at the tail and nose of the pig is equal to that of the pig [
Three kinds of boundary conditions are used: (1) constant inlet flow rate and constant pressure at the outlet, simulating the releasing of a stuck pig by increasing upstream pressure; (2) constant inlet pressure and constant flow rate at the outlet, simulating the releasing of a stuck pig by pressure relief of downstream; (3) constant inlet flow rate and the outlet pressure to decrease in the rate of inlet pressure increase, which simulates the unstuck pig in the way of inlet pressurization together with outlet relief.
To simulate the pigging process in gas pipeline, the pipe is divided into two sections: one behind the pig and the other in front of it. Figure
Computational scheme for solving the coupling process of pigging.
As the pig moves across one or more grids during time step
In this section, a 6 km horizontal gas pipeline is used for the simulation of pig restarting from a stoppage. Values of the parameters adopted are shown in Table
Numerical values for simulation.
Parameter | Unit | Value | Parameter | Unit | Value |
---|---|---|---|---|---|
| bar | 50 | | bar | 0.3 |
| kg/m3 | 35.2 | | bar | 5 |
| m2/s | 3.47 × 10−7 | | m3/s | 0.98 |
| - | 1.44 | | mm | 0.03 |
| m | 0.5 | | kg | 200 |
Figure
Pig speed variation due to different pressure strategies to release the pig from the stoppage.
Pressure on the nose and tail of the pig in the three conditions is shown in Figure
Pressure on the nose and tail of the pig. (a) Pig is released by increasing upstream pressure; (b) pig is released by decreasing downstream pressure; (c) pig is unlocked in the way of inlet pressurization together with outlet relief.
The distributions of gas parameters are shown in Figure
Distributions of gas parameters. (a), (b), and (c) are gas density, pressure, and velocity during the time the pig was unstuck by increasing upstream pressure, respectively; (d), (e), and (f) are gas density, pressure, and velocity during the time the pig was unstuck by decreasing downstream pressure, respectively; (g), (h), and (i) are gas density, pressure, and velocity during the time the pig was unstuck by inlet pressurization together with outlet relief, respectively.
Parametric sensitivity analysis of pig restarting from a stoppage in a horizontal gas pipeline is then carried out. To release a pig from a stoppage in the way of increasing upstream pressure of decreasing downstream pressure is discussed. As shown in Figures
Parametric sensitivity analysis of pig restarting from a stoppage by increasing upstream pressure. (a) Change of pig mass, (b) change of pipe diameter, (c) change of the stuck position, (d) change of pipe length, (e) change of obstruction force, and (f) change of gas pressure.
Parametric sensitivity analysis of pig restarting from a stoppage by decreasing downstream pressure. (a) Change of pig mass, (b) change of pipe diameter, (c) change of the stuck position, (d) change of pipe length, (e) change of obstruction force, and (f) change of gas pressure.
Examining Figure
Response surface methodology (RSM) is a statistical experimental method for optimizing stochastic processes. The objective is to find out the quantitative law between the experimental index and each factor and to find the best combination of each factor level [
Simulations of the maximum speed of pig restarting from a stoppage using RSM.
Run number | Gas pressure [bar] | Obstruction [bar] | Maximum pig speeds of restarting it in different ways [m/s] | ||
---|---|---|---|---|---|
By increasing inlet pressure | By decreasing outlet pressure | By increasing inlet pressure together with decreasing outlet pressure | |||
1 | 80 | 2 | 4.53 | 4.65 | 4.57 |
2 | 20 | 8 | 53.80 | 73.60 | 65.72 |
3 | 20 | 2 | 16.78 | 18.02 | 17.30 |
4 | 80 | 5 | 11.15 | 11.55 | 11.42 |
5 | 50 | 2 | 7.33 | 7.58 | 7.12 |
6 | 80 | 8 | 16.60 | 16.90 | 16.82 |
7 | 20 | 5 | 37.50 | 45.00 | 41.41 |
8 | 50 | 5 | 17.15 | 18.50 | 17.83 |
9 | 50 | 8 | 25.85 | 28.88 | 27.65 |
The results show that the maximum velocity obtained by inlet pressurization is close to that obtained by outlet depressurization. Moreover, the maximum speed a pig reaches, in the way of inlet pressurization together with outlet relief, is generally between the maximum speed corresponding to the inlet pressurization and that of outlet relief. Hence, an empirical formula for estimating the maximum speed a pig achieves from a restarting process, obtained from the average of the three results of the RSM simulations, is as follows.
In this equation,
Residuals versus run. (a) Pig restarts in the way of inlet pressurization together with outlet relief, (b) pig restarts from a stoppage by increasing upstream pressure, and (c) pig restarts from a stoppage by decreasing downstream pressure.
Compared with (
Model graphs of the obtained formulas are shown in Figure
Model graph of the obtained formula.
A calculation scheme using MOC to solve the equations of gas flow for estimating the pig dynamics has been shown. The process of a pig restarting from a stoppage in gas pipeline was simulated. The maximum speed a pig achieved from a stoppage was studied using RSM.
The results of the parametric sensitivity analysis of the start-up process indicate that the maximum speed a pig achieves from a stoppage is primarily determined by the pressure of the pipe and the pressure change caused by the obstructions.
An empirical formula for estimating the maximum speed of a pig restarting from a stoppage in gas pipeline is obtained from the results of the RSM simulations. The maximum speed of pig restarting from a stoppage in horizontal gas pipeline can be predicted based on the gas pressure and the pressure change of upstream and/or downstream. The empirical formulas obtained would contribute to pig design and safe pigging.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This research was supported by the Graduate Innovation Foundation of School of Mechatronic Engineering of SWPU (CX2014BY09).