Performance characteristics of deterministic leak detection systems

The pillars of deterministic leak detection (LD) and leak location (LL) for pipelines are: measuring technology, communication and SCADA technology, and the application of hydraulic and thermodynamic laws. Any leak detection system that uses process data – no matter if based on deterministic or statistic methods – faces the same limits with respect to the achievable performance characteristics. Sensitivity, response time and cumulated leakage volume are the most important performance characteristics to be discussed here. The focus of this paper is on liquid pipelines.

An important advantage of deterministic methods for leak detection and leak location (LDL) for pipelines compared to statistic and other methods is the possibility to predict the performance characteristics of the deterministic LDL system already before its implementation. This will be demonstrated by three examples of predicted results compared to data obtained from field experiments. Vice versa the deterministic approach enables us to specify the requirements of the instrumentation, communication system and SCADA components to obtain the requested sensitivity and accuracy of the LDL system. This is last but not least an important aspect for choosing an economically feasible solution for each pipeline.

1 Requirements & performance characteristics

Following the demands of the German technical rules for cross country pipelines (Technische Regel für Rohrfernleitungen TRFL) the equipment for leak detection (LD) and leak location (LL) should be implemented as a continually operating monitoring system. Depending on the transported medium and its hazard potential the requirements are graded. The performance characteristics for a pipeline are individually specified in coordination with the authorities. In general, all operation modes from downtime over steady-state to transient flow situations should be fully covered. In all these situations reliable detection and location of a leak should be possible. The performance characteristics of a LDL system are:

• detection thresholds (sensitivity)
• response time
• cumulated leakage volume (cumulated loss until leak alarm)
• location accuracy
• low false alarm rate (reliability)
• fail safety (recognition of missing or erroneous input data)

It’s an engineering task to select and combine the optimal set of instruments, SCADA components, and different LDL methods for each particular pipeline to comply with the demands of operational safety and environmental protection.

2 Direct detection methods

When a leak arises in a pipeline section, flow and pressure will respond to that in a characteristic manner. Direct methods work fine for steady-state pipeline operation as well as during downtime. However, due to its dimension, line content, and other conditions every pipeline section responds with an individual hydraulic behaviour. On the basis of a detailed and well-calibrated pipeline model we can simulate the hydraulic behaviour for all operation modes. These simulation results are used for planning and testing the LDL system.

2.1 Flow/pressure monitoring

When a leak arises in a pipeline section, the pressure there will typically drop as sketched in Figure 1.

At the same time the flow will rise in the counter-flow direction and will drop in the flow direction. These effects can be detected by continual recording of all pressure and flow readings. An algorithm is used to filter out any significant variation in a recorded value from its noisy measurement signal. Such variations, however, can also be induced by the usual operational interventions. Therefore, all events detected by direct methods should be checked for plausibility. If pressure drops while no operational changes or control action have been executed, this event is likely to be caused by a leak.

The time span Ä t mentioned in Figure 1 has to be chosen according to the hydraulic response of the pipeline (section) and the scenario to be monitored. For steady-state operation (i.e. constant flow and pressure) the time slot Ä t is normally just some seconds. During downtime it can be stretched out up to minutes or even hours (cf. 2.3).

Another application for pressure drop detection is time tagging of pressure wave fronts when they pass the metering stations next to the leak (cf. 2.4). These time tags are then used to locate the leak.

2.2 Flow or volume balance

Balancing the line pack of a pipeline section by simply comparing what flows out and what flows in is another direct leak detection method (Figure 2). Its accuracy, however, is frequently not acceptable for large pipelines. During transient flow situations this simple balance is “blind”. The larger the pipeline volume and the elasticity of the medium the longer will last the transient periods.

While operating a pipeline in steady-state mode this balance yields a constant difference level – not necessarily zero. Any change (of appropriate sign) in this level without executing operational interventions or control action might indicate a leak.

2.3 Downtime pressure monitoring

Downtime Pressure Monitoring is a topic of special interest, because it is a sensitive LD method and is separately mentioned in the demands of the TRFL. A requirement to achieve high sensitivity with this LD method is a hydraulically sealed off pipeline section (e.g. double block and bleed). If this is the case, there is a tight relation between line pack and line pressure. While pressure drops as a quadratic function with time t:

p(t) = p_i ⋅ [1 - (Χ ⋅ (Q_i / p_i) ⋅ t]²                   (1)

the corresponding decrease of leak rate is linear:

Q(t) = Q_i ⋅ [1 - (Χ ⋅ (Q_i / p_i) ⋅ t]                  (2)

The factor Χ in eqs. 1 and 2 is specific for each sealed off and packed pipeline section in combination with its line content. It can be calculated from basic pipeline and fluid data. Both functions are shown in Figure 3. It depends on Χ, the initial leak rate Q_i , and the initial pressure p_i, when the quadratic contribution in equation 1 becomes significant.

If the algorithm that is used to detect pressure drops (cf. 2.1) provides a reliable detection threshold of Δp, the response time of the Downtime Pressure Monitoring is given by:

t_resp = (1/Χ) ⋅ (p_i/Q_i) ⋅ [1 - √1 - (Δp/p_i)] ≈ (Δp/2ΧQ_i)               (3)

Figure 4 shows the typical relation between response time and leak rate. Small leaks take more time to be detected than large ones. The initial pressure is not important for Downtime Pressure Monitoring as long as the line is pressurized above vapour pressure.

The total leakage volume that accumulates until the leak can be detected is calculated by integrating the leak rate within the response time:

V_leak = ₀∫^t_resp Q(t) ⋅ dt = Q_i ⋅ t_resp ⋅ [1 - (Χ/2) ⋅ (Q_i/p_i) ⋅ t_resp]             (4)

Comparison with field data recorded during leak experiments using orifices of different cross section area lead to a relation between leak width and leak rate for the particular pipeline section.

For tiny leak rates the results of the Downtime Pressure Monitoring must be checked against a possible pressure drop that might be caused by decreasing pipeline temperature (broken curve in Figure 5).

2.4 Pressure wave detection

If a leak arises abruptly, two pressure wave fronts are generated which propagate along the pipeline in opposite direction with a defined wave speed c. In oil pipelines the wave speed is around c = 1000 m/s. The exact value can directly be measured or calculated from the oil density, the pipeline material, its diameter, and wall thickness. Pressure waves which might be related to a leak show negative amplitude. If such a wave is detected and time tagged, the leak position between two adjacent metering stations at distance L can be calculated (cf. Figure 6):

x_leak = ½ (L ⋅ ±c ⋅ (t₂-t₁))               (5)

There are two aspects related to the performance characteristics of this LL method: “sensitivity” and “location accuracy”.

Sensitivity: The detection threshold for pressure drop Ä p is the limiting factor for sensitivity. For larger distances the inevitable attenuation of pressure waves has to be considered. Depending on the distance between the leak and the metering station the minimum required pressure drop Δp* is larger than the detection threshold (Δp < Δp* ) itself. Therefore, the sensitivity is best for a leak in the middle between two metering stations and worst if the leak is near one of the adjacent stations. The minimum pressure wave amplitude that is necessary to be detectable is related to the minimum (initial) leak rate by the Joukowski relation:

Q_min > (A ⋅ Δp*) / (ρ ⋅ c)      (6)

Simulation of pressure surges on the basis of a detailed and calibrated pipeline model yields the attenuation characteristics.

Location accuracy: Because the wave speed in oil pipelines is about 1000 m/s, the accuracy of time tagging is very important to obtain acceptable location accuracy. Precise time tagging requires a common time basis across all stations. The tagging precision depends on synchronization and cycle time of the pressure measurements. If the synchronisation and cycle time are both within 100 ms and the algorithm that recognises pressure drops is able to tag the onset of a pressure drop with an uncertainty of two cycles, the predictable location accuracy is less than or up to 500 m. Real leak tests on a 47 km section of an 18 inch crude oil pipeline found deviations from the true leak position between 30 and 320 m (location accuracy). The leak position was near the middle of the section, the leak rates were 37-45 m³/h, and the pressure drop detection threshold was 0.25 bar (sensitivity).

The accuracy and homogeneity of the wave speed |δc|/c along the line and the accuracy of time tagging |δt| contribute to the total location accuracy δx_leak, which is given by the next equation.

δx_leak = (c/2) ⋅ [(|δc| / c) ⋅ |t₂ + t₁| + (2 ⋅ |δt|)]      (7)

Both, the sensitivity and the location accuracy turn out to be best in the middle between two stations.

3 Model based detection methods

A leak detection and leak location system, which is based on or assisted by a well-calibrated hydraulic model, is sensitive and provides reliable results even during non-steadystate operation. Parallel to the operation of the pipeline its hydraulic behaviour is calculated in real time. Deviations are continually monitored and analysed, whether they could be caused by a leak.

3.2 Dynamic mass balance

A standard method of model based leak detection is the Dynamic Mass Balance. The principle of the Dynamic Mass Balance (DMB) is similar to the simple Volume Balance discussed in . The deciding improvement is that the line pack is calculated in real time and included in the Dynamic Mass Balance (Figure 7).

The periodically calculated result of the DMB is the (negative) potential leak rate, which should normally be zero.

The first two terms of the above equation are direct process values of the volume metering stations (if necessary, beforehand integrated from flow to volume and further converted to standard volume). The third term is provided by the Real Time Hydraulic Simulation (RTHS) as sketched in Figure 8.

The analysis of the performance characteristics of the Dynamic Mass Balance is definitely more complicated than that for the direct methods. A general calculation of errors is lengthy but straight forward. Such a calculation has been done for an 18 inch crude oil pipeline operated at about 1000 m³/h. Considering the accuracy of the volume metering of that pipeline and all the other contributions the expected average error for steady-state operation was found to be about 3.5 m³/h, which is very well in agreement with daily experience there as shown in Figure 9.

During transient operation modes the curves of the Dynamic Mass Balance show larger deviations. Within a period of 72 days of continual crude oil batch operation 8 deviations of more than 5 m³/h (including 3 deviations of more than 10 m³/h) have been reported. In average, this is less than such large deviation per week. All these events, however, could definitely be assigned to abrupt operational intervention.

3.2 Real time hydraulic simulation & deviation monitoring

A basic requirement for a reliable hydraulic simulation is a complete and well-calibrated pipeline model. The pipeline can be roughly divided into pipeline sections and pipeline stations. The main attributes of the pipeline sections are their dimensions and the profiles of altitude, wall thickness, etc. The stations have to be modelled in detail as well. The next step is to parameterise all elements of the stations. Finally, the whole hydraulic model has to be calibrated until the simulation results coincide with the measured process data. The software package SIR 3S (shown in Figure 10 and Figure 11) is a powerful tool for this task.

For transient operation modes it is frequently necessary to do the simulation on time steps of one second or even less. All control loops and their hydraulic feedback is fully included. With a well-calibrated hydraulic model it is possible to simulate all operational modes very close to reality and this is the solid basis for what we call Deviation Monitoring. Two instances of the same simulation are configured differently and complementary. One is based on real time process data like pressure, flow, etc., and the other is based on control variables, setpoints, and status information of the valves. Both instances are operated simultaneously and are synchronised. Their results are continually compared to each other. The principle of Deviation Monitoring is sketched in Figure 12.

The two simulation results are displayed by the so called Hydraulic Profile and refreshed in real time. Parallel to the Hydraulic Profile the result of the Deviation Monitoring is displayed as shown in Figure 13.

In this way any deviation is directly visible. If its magnitude exceeds a defined limit, the operator can easily see where the problem is located and can take action for remedy.

4 Summary

To fully cover all operational modes from downtime over steady-state operation to transient flow the presented methods for leak detection and leak location must be implemented as a cooperating system. Three examples have been chosen to demonstrate the influence of the accuracy of the measured input data and the performance characteristics of the data acquisition on the achievable accuracy of a Deterministic Leak Detection and Leak Location System. Comparison to field data shows that it is possible to predict the performance characteristics. For steady-state pipeline operation these error calculations can be done analytically. For the non-steady-state case this is only possible, if a complete and well-calibrated pipeline model is used.