Leak identification in a mass transport network
A method and system method to detect a leak within a pipeline network include measuring pressure at each of a plurality of sensors distributed along the pipeline network as a time-varying pressure signal. Tuning a model is based on gas mass conservation law in the absence of the leak, the tuning including obtaining the time-varying pressure signal from each of the plurality of sensors, and monitoring the time-varying pressure signals is done to detect the leak based on the model.
1. A method of identifying a leak within a pipeline network, the method comprising:
measuring pressure at each of a plurality of sensors distributed along the pipeline network as a time-varying pressure signal;
tuning, using a processor, a model based on gas mass conservation law in the absence of the leak, the tuning including obtaining the time-varying pressure signal from each of the plurality of sensors;
monitoring, using the processor, the time-varying pressure signals to detect the leak based on the model, wherein the tuning the model includes tuning a numerical minimization model of:
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US refers to upstream sensors among the plurality of sensors, DS refers to downstream sensors among the plurality of sensors, t strt to t end is a selected time interval with a delay Δt i specific to each of the upstream sensors or the downstream sensors, t strt and t end are selected to capture an entire cycle of mass flow, and Q(t) is isothermal mass flow rate, and the selected time interval is a same duration for every one of the upstream sensors and the downstream sensors;
comparing, using the processor, the numerical minimization model with a predetermined threshold value; and
identifying a leak within the pipeline network when the numerical minimization model is greater than the predetermined threshold value.
2. The method according to claim 1 , wherein the tuning the model includes determining Q(t) for each sensor as being proportional to:
p i ( t ) f i ( t ), where
p(t) is pressure and f(t) is flow rate.
3. The method according to claim 2 , wherein the determining Q(t) includes determining pressure and flow rate based on affine mapping according to:
f i =α i {circumflex over (f)} i +β i and p i =a i {circumflex over (p)} i +b i , where
{circumflex over (f)} and {circumflex over (p)} are measured flow rate and measured pressure values, respectively, and a i , b i , α i , and β i are determined based on tuning the numerical minimization model.
4. The method according to claim 3 , further comprising obtaining flow rate from the time-varying pressure signal of each of the plurality of sensors based on:
f j ( t )∝α p input ( t )− p j , where
p input refers to pressure at an input of the pipeline network.
5. The method according to claim 3 , wherein the tuning includes determining minimum values of Δt i , a i , b i , α i and β i to solve the numerical minimization model in the absence of the leak, solving including one of the numerical minimization model values being below a threshold value.
6. A system to identify a leak within a pipeline network, the system comprising:
a plurality of sensors distributed along the pipeline network, each sensor configured to measure pressure as a time-varying pressure signal; and
a processor configured to tune a model based on gas mass conservation law in the absence of the leak based on the time-varying pressure signal from each of the plurality of sensors, and monitor the time-varying pressure signals to detect the leak based on the model, wherein the model is a numerical minimization model of:
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US refers to upstream sensors among the plurality of sensors, DS refers to downstream sensors among the plurality of sensors, t strt to t end is a selected time interval with a delay Δt i specific to each of the upstream sensors or the downstream sensors, t strt and t end are selected to capture an entire cycle of mass flow, and Q(t) is isothermal mass flow rate, the selected time interval is a same duration for every one of the upstream sensors and the downstream sensors, compare the numerical minimization model with a predetermined threshold value, and identify a leak within the pipeline network when the numerical minimization model is greater than the predetermined threshold value.
7. The system according to claim 6 , wherein Q(t) is determined for each sensor i as being proportional to:
p i ( t ) f i ( t ), where
p(t) is pressure and f(t) is flow rate.
8. The system according to claim 7 , wherein the processor determines pressure and flow rate based on affine mapping according to:
f i =α i {circumflex over (f)} i +β i and p i =a i {circumflex over (p)} i +b i , where
{circumflex over (f)} and {circumflex over (p)} are measured flow rate and measured pressure values, respectively, and a i , b i , α i , and β i are determined based on tuning the numerical minimization model.
9. The method according to claim 8 , further comprising obtaining flow rate from the time-varying pressure signal of each of the plurality of sensors based on:
f j ( t )∝α p input ( t )− p j , where
p input refers to pressure at an input of the pipeline network.
10. The method according to claim 8 , wherein the tuning includes determining minimum values of Δt i , a i , b i , α i and β i to solve the numerical minimization model in the absence of the leak, solving including one of the numerical minimization model values being below a threshold value.
11. A computer program product for identifying a leak in a pipeline network, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to perform a method comprising:
receiving pressure values measured at each of a plurality of sensors distributed along the pipeline network as a time-varying pressure signals;
tuning a model based on gas mass conservation law in the absence of the leak, the tuning including obtaining the time-varying pressure signal from each of the plurality of sensors; and
monitoring the time-varying pressure signals to detect the leak based on the model, wherein the tuning the model includes tuning a numerical minimization model of:
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US refers to upstream sensors among the plurality of sensors, DS refers to downstream sensors among the plurality of sensors, t strt to t end is a selected time interval with a delay Δt i specific to each of the upstream sensors or the downstream sensors, t strt and t end are selected to capture an entire cycle of mass flow, and Q(t) is isothermal mass flow rate, and the selected time interval is a same duration for every one of the upstream sensors and the downstream sensors;
comparing, using the processor, the numerical minimization model with a predetermined threshold value; and
identifying a leak within the pipeline network when the numerical minimization model is greater than the predetermined threshold value.
12. The computer program product according to claim 11 , wherein the tuning the model includes determining Q(t) for each sensor as being proportional to:
p i ( t ) f i ( t ), where
p(t) is pressure and f(t) is flow rate.
13. The computer program product according to claim 12 , wherein the determining Q(t) includes determining pressure and flow rate based on affine mapping according to:
f i =α i {circumflex over (f)} i +β i and p i =a i {circumflex over (p)} i +b i , where
{circumflex over (f)} and {circumflex over (p)} are measured flow rate and measured pressure values, respectively, and a i , b i , α i , and β i are determined based on tuning the numerical minimization model.
14. The computer program product according to claim 13 , wherein the tuning includes determining minimum values of Δt i , a i , b i , α i and β i to solve the numerical minimization model in the absence of the leak, solving including one of the numerical minimization model values being below a threshold value.
15. The method according to claim 1 , wherein the monitoring the time-varying pressure signals includes performing pattern detection to detect an increase in the pressure.
16. The system according to claim 6 , wherein the processor performs pattern detection on the time-varying pressure signals to detect an increase in the pressure.
17. The computer program product according to claim 11 , wherein the monitoring the time-varying pressure signals includes performing pattern detection to detect an increase in the pressure.