JP3387667B2 - Estimation method of pollutant diffusion state in distribution pipe network and display method of estimation result - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention displays a method of estimating the diffusion state of pollutants and a result of the estimation in order to devise effective countermeasures when red water pollution occurs in the water distribution network of waterworks. On how to do.

[0002]

2. Description of the Related Art As a first conventional technique for estimating the state of diffusion of pollutants of this type, there is a method of estimating from the flow direction of contaminated water obtained from past experience and the result of pipe network calculation at the time of water distribution network planning. is there. As a second conventional technique, the distribution of pollutants in the water distribution network over time is assumed to be based on the traveling distance of the pollutants in the pipeline, assuming that the pollutants are completely mixed at the nodes. There is a method of estimating the pollutant concentration only at each node in the water pipe network (hereinafter, referred to as a pollutant concentration if necessary) (see Japanese Patent Application No. 5-234214 by the same applicant).

In the second prior art, the flow rate of the pipeline required for obtaining the traveling distance of the pollutant is obtained by the pipe network calculation, and the fluctuation of the demand amount of the water distribution pipe network is generally the time of each demand point. It is assumed that the demand amount at each demand point is different and that the temporal change ratio shows the same change at all demand points, though it is considered as a total change rather than a large change. That is, the flow rate of each pipeline is calculated by multiplying the flow rate of each pipeline calculated in the initial state by a coefficient of temporal variation.

When the valve is operated, the pipe network model is manually changed corresponding to the valve operation at predetermined calculation time intervals, and the pipe network is calculated to calculate the flow rate in the initial state. Then, the above estimation calculation was performed again.
Then, the estimation result is displayed by a water quality contour map as shown in FIG. 11 in which the pollution concentrations of only the nodes are connected.

[0005]

Generally, in the network calculation, whether or not the pressure at each node at the time of maximum / minimum demand and at the time of emergency such as fire is appropriate at the planning stage of the water distribution network is appropriate. I'm calculating. For this reason, the water distribution network targeted for calculation is for normal operation, and once contamination occurs and valve operation is performed, the water distribution network will become mesh-like and will not be experienced or planned at the planning stage. In some cases, the flow direction and flow rate of the obtained water may differ greatly. Therefore, it is necessary to recalculate the diffusion state of pollutants after valve operation, reflecting the influence after the change of the flow direction and flow rate of water.

Even if the pollution concentration at each node is estimated by the second conventional technique, these pollution concentrations are not related to the pollution progress situation at any point in the pipeline connecting the nodes. Extremely speaking, it is impossible to analyze the situation in which the pollutant stays in the pipeline connecting the upstream node where the pollutant has already passed and the downstream node where the pollutant has not yet reached.

Further, in the second prior art, in order to estimate the diffusion state of the pollutant when the valve operation is performed, the pipe network model corresponding to the valve operation is manually changed one by one to calculate the pipe network. It is necessary to perform the calculation to estimate the diffusion state of pollutants again, and it is not possible to immediately reflect the examination result on the display, so it is possible to consider valve operation while watching the display of the diffusion state progress. Can not.

Further, even if the diffusion state is displayed, since the pollution concentration in the pipeline cannot be analyzed, the water quality contour map, which is constructed by connecting the pollution concentrations only at the nodes, has to be drawn. Since the display is stationary and discontinuous, there is a problem in that it is difficult to visually appeal the diffusion state of pollutants and the progress of the pollutants.

The present invention has been made in order to solve the above problems, and its purpose is to determine the state of diffusion of pollutants not only at the nodes but also in the entire distribution network including the pipes connecting these nodes. It is possible to estimate and display, and to eliminate the need for manual input of the pipe network model after valve operation, and to immediately reflect the effect of valve operation on the diffusion of pollutants in the water distribution network. Another object of the present invention is to provide a method of estimating the diffusion state of pollutants, which enables continuous and dynamic display of the progress status, and a method of displaying the estimation result.

[0010]

[Means and Actions for Solving the Problems] The movement itself of water plays a central role in the diffusion of pollutants in the water distribution network. Therefore, in the estimation method of the present invention, a dynamic demand network calculation is performed in which a demand demand at a node is set by giving a varying demand amount at a predetermined time interval, and a pipe network calculation is performed each time the demand amount is calculated. To do. Then, it was decided to determine how the contaminated area spreads from the point where the pollution occurred by following the movement of water containing pollutants.

The method of calculating the contamination concentration, which is the main part of the first invention, will be described in detail below. In the present invention, in order to represent not only the pollution concentration at each node as in the second conventional technique but also the pollution concentration at any point on the conduit between the nodes, a pipe having a length L as shown in FIG. The road is divided into n pieces at equal intervals for calculation. Assuming that the water in the pipe flows in the positive direction (direction from 0 to n in FIG. 4), the diffusion equation of the pollutant can be expressed by Equation 1.

[0012]

## EQU1 ## V (dC _i / dt) =-KVC _i + Q (C _i-1 -C _i ).

Where L is the length of the pipeline, Q is the flow rate of the pipeline,
C _i : contamination concentration of the i-th portion (i-th divided portion) of the divided pipeline, K: reduction coefficient proportional to the contamination concentration,
V: The capacity of the divided portion of the pipeline. It should be noted that the capacity V is obtained by Equation 2 based on the inner diameter D of the conduit and the length ΔL (= L / n) of the divided portion.

[0014]

[Formula 2] V = (π / 4) D ² ΔL

Here, unlike the residual chlorine, the pollutant does not decrease in the pipe, so K = 0 in the equation (1). In the above formula 1, C _i = C _i (t) and C _i ′ = C _i (t−
When it is differentiated as Δt), it becomes as shown in Expression 3. Note that Δt is a calculation time interval.

[0016]

[Number 3] _{C i = C i '+ Δt} (Q / V) (C i-1' -C i ')

For all the pipelines in the water distribution network, if the direction of water flow is positive, Equation 3 is calculated sequentially from i = 0 to n + 1. In general, the water distribution network has a complicated mesh shape, and there are many branching and joining points. Assuming that the pollutants are completely mixed at the confluence point where a plurality of inflow conduits merge, the pollution concentration at the confluence point is calculated based on the pollution concentration at the lowest point of each upstream conduit.

For example, assuming that C ₀ (t) is the contamination concentration at the time t at the confluence point, this C ₀ (t) can be expressed by Equation 4. In Expression 4, k is the total number of conduits that join at the merge point.

[0019]

[Equation 4]

Assuming that the direction of water flow is negative (the direction from n to 0 in FIG. 4), the contaminant diffusion equation can be expressed as Equation 5, and the reduction coefficient K is the same as above. When Equation 5 is differentiated with = 0, Equation 6 is obtained.

[0021]

V (dC _i / dt) = − KVC _i −Q (C _{i + 1} −C _i )

[0022]

[6] _{C i = C i '-Δt (} Q / V) (C i + 1' -C i ')

If the flow direction is negative for all the pipelines in the water distribution network, Equation 6 is calculated sequentially from i = n + 1 to 0. The number of divisions n when dividing each pipeline at equal intervals is
It is necessary to satisfy the condition of Expression 7 from the stable condition of calculation.

[0024]

(7) n ≦ T / Δt

Therefore, the pipeline division number n is set to the maximum integer that satisfies the following formula 8 when Δt is set to a certain constant value. In Equations 7 and 8, T: time during which contamination remains in the divided portion of the pipeline, T _min is the minimum retention time in the divided portion, and Equation 9 is based on the maximum flow rate Q _max of the pipeline. Ask from. However, when T _min / Δt <1, n = 0. That is, in this case, the pollution concentration C ₀ at the upstream side node and the pollution concentration C _{1 at the} downstream side node of the pipe having the length L are always equal to each other.

[0026]

[Equation 8] n ≦ T _min / Δt

[0027]

[Equation 9] T _min = (π / 4) D ² L / Q _max

As shown in the equation (8), the number n of divided pipes depends on the minimum residence time T _{min and} thus the maximum flow rate Q _max of the equation (9). If the valve is operated when pollution occurs, the flow rate of each pipeline after the operation is recalculated, so that the maximum flow rate after the operation may be larger than the maximum flow rate before the operation. At this time, if the number of pipeline divisions before the valve operation is calculated as it is, since n is the maximum integer that satisfies Expression 8, the stability condition of Expression 7 may not be satisfied, and the calculation may become unstable. .

To prevent this, the number of divisions n may be reduced or the calculation time interval Δt may be reduced so as to satisfy the stability condition of Expression 7. If the number of pipeline divisions n is reduced, the calculation results will be thinned (that is, the division within the pipeline will become rough), so the calculation time interval Δt will be shortened here. Therefore, such a pipeline, that is, a pipeline in which the maximum flow rate after the valve operation is larger than the maximum flow rate before the operation is searched for, and the calculation time interval Δt is shortened after the valve operation only in these pipelines. Then, the calculation of the contamination concentration is repeated according to Formula 3, Formula 6, and Formula 4.

[0030] For example, the minimum residence time in the pipe by a valve operation 'and changed to (T _min' T _min from _{T min = a · T min (} 0 <a <1)). As a result, T _{min in} Formula 8 is _replaced with T _min ′, and satisfying Formula 10 is a condition for stable calculation.

[0031]

[Equation 10] n ≦ T _min '/ Δt = a · T _min / Δt

Since 0 <a <1, the calculation time interval Δt may be set to Δt ′ (Δt ′ ≦ a · Δt) in order to satisfy Expression 9 without changing the number of divisions n before and after operating the valve. .
Therefore, only in this pipeline, the calculation time interval after valve operation is changed to Δt ′ in the following formula 11, and formula 3 or formula 6,
Formula 4 is calculated. In Expression 11, m is m ≧
1 / a = T _min / T _min ′ is the smallest integer that satisfies the condition.

[0033]

[Expression 11] Δt ′ = (1 / m) · Δt

The flow rate Q of each pipeline used for the calculation of the residence time T of the pollutant is obtained by using dynamic pipe network calculation. This dynamic pipe network calculation is performed in correspondence with the time each time the demand volume at each demand point fluctuates, unless measures such as water cut are taken. In addition, when measures such as water interruption are taken, valve operation is performed using an input screen (valve opening change screen) that simulates valve opening operation as described later, and operation is performed using the changed pipe network model. Perform a dynamic network calculation. It is possible to calculate the flow direction and flow rate of each pipeline at each time after valve operation, and
If the pollution concentration is calculated based on the flow rate by the mathematical formulas 3 and 6, the influence of the valve operation on the diffusion of pollutants in the water distribution network can be reflected.

In the second invention, the pollution concentration of each portion of the water distribution network estimated by the first invention is displayed on the network diagram by a color or gradation corresponding to the pollution concentration over time, and this display is shown. While displaying the valve opening change screen for changing the valve operation amount input as a result of examination based on
By displaying the pollutant diffusion state after the valve operation again, the influence of the valve operation on the diffusion of the pollutant can be visually recognized.

In the third invention, the pollution concentration of each part of the distribution pipe network estimated by the first invention is continuously displayed on the pipe network diagram with a color or gradation according to the pollution concentration with the passage of time. The diffusion status or progress status of pollution is dynamically displayed, and the time scale of this dynamic display can be arbitrarily set with respect to real time.

[0037]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the configuration and processing flow of a contaminant diffusion state estimation / display device used in the first to third embodiments of the invention. With this device, information about pipe network model (pipe length, pipe inner diameter, connection relationship, etc.), time fluctuation of demand (actual / predicted demand), pollution occurrence such as red water (pollution occurrence point, time, concentration) ) And the operation amount (pipe network operation amount) during valve operation, the operation unit 10 such as a computer calculates and estimates the diffusion state of pollutants.

Then, the estimation result is displayed on the display device 20 such as a color display by color-coding the pollution concentrations of the pipelines (including nodes and confluences) on the network diagram (indicating the pollution concentration in the pipeline). Also, the time variation of the contamination concentration is displayed in a graph or the like (contamination concentration time variation chart). Further, the operator determines the valve operation amount by looking at the pollution concentration display in the pipe network, and reflects it as the pipe network operation amount in the dynamic pipe network calculation by the arithmetic unit 10.

As a method of displaying the estimation result of the pollution diffusion state, as in the second aspect of the present invention, a measure such as valve operation is interactively performed so that the result can be confirmed at every calculation time interval. There are a method of displaying the change each time and a method of continuously dynamically displaying the change of the pollution diffusion state calculated in advance as in the third aspect of the invention.

Next, the embodiment of the first and second inventions is shown in FIG.
It will be described based on. First, by setting the demand amount of the node based on the actual / predicted demand amount at each time (S1) and calculating the pipeline flow rate based on the original pipe network model (S2), the well-known dynamic pipe network calculation Create a pipeline flow rate file for each time. Note that this dynamic network calculation is repeated every time the demand amount changes.

The pipeline flow rate at each time is read from the pipeline flow rate file (S3), and the above equation 9 is applied to all pipelines.
Calculate the minimum residence time T _min from the maximum flow rate Q _{max according} to
The number n of divided pipes is determined by Expression 8 (S4).

Contamination occurrence information (contamination occurrence point, time, concentration) is set from the network diagram (S8) displayed on the display device 20 (color display) (S5), and each conduit, node, The contamination concentration at the confluence is calculated by the above-mentioned formula 3 or formula 4 and formula 6 (S6, S7).

Colors corresponding to the calculated contamination concentrations of the respective pipelines, nodes, and junctions are displayed on the pipeline network diagram of the display device 20 (S9). If the valve is not operated, the specified time interval Δ
At t, the processes from step S3 onward are repeated.

As a result of examining the time course of the display screen by the operator, if it becomes necessary to operate the valve, the valve operation amount (the valve opening operation (Amount), the pipeline flow rate calculation is performed again based on the changed pipeline network model (S2), and the pipeline flow rate file at each time after the operation is changed.

Only when the valve operation is performed, the pipeline flow rate file is read again, and the calculation after step S4 is repeated at a predetermined time interval under the pipeline flow rate at each time. At this time, when the maximum flow rate after valve operation becomes larger than the maximum flow rate before valve operation and there is a possibility that the stability condition of Equation 7 may not be satisfied, the calculation time interval Δt ′ obtained by Equation 11 described above is used. Calculation of the contamination concentration such as Equation 3 is performed.

Next, the embodiments of the first and third inventions are shown in FIG.
It will be described based on. Nodal demand setting (S11) and pipeline flow rate calculation (S1
2) is substantially the same as steps S1 and S2 in FIG. 2, and a pipeline flow rate file at each time is created by these dynamic pipeline network calculations.

The pipeline flow rate at each time is read from the pipeline flow rate file (S13), the minimum residence time T _min is calculated from the maximum flow rate Q _max by the above equation 9 for all the pipelines, and the pipeline division number is calculated by the equation 8. n is determined (S14).
These processes are also similar to steps S3 and S4 in FIG.

Further, similarly to step S5 in FIG. 2, the pollution occurrence information is set from the network diagram (S18) displayed on the color display (S15), and based on this, the pipelines, nodes, and confluence points are identified. The pollutant concentration is calculated by the above equations 3 or 4 and 6 (S16, S17). These calculations are repeatedly executed at a predetermined time interval Δt.

After the pollutant concentration is calculated over the entire time, the pollutant concentration is displayed on the pipe network diagram by adding a color corresponding to the concentration of the calculated result to the pipeline in the pipe network diagram (S19). ). Then, at each display time interval set in advance by the timer (S20), the color is changed to the color of the contamination density of the next display time, and this process is continuously repeated at the predetermined time interval. Therefore, the state in which the pollution concentration of each part in the network diagram changes is displayed as a continuous change in color. The time scale of this dynamic display can be arbitrarily set with respect to the real time.

5 to 10 show display screens of the display device 20 for explaining the simulation result according to the present invention. FIG. 5 is a pipe network model diagram for estimating the pollutant diffusion state and displaying the estimation result. The pipe network diagram display unit 21, the message display unit 22, and the pollution concentration displayed in the pipe network diagram are shown in FIG. Contamination concentration legend 23 displayed in different colors
It has a display magnification display section 24, a display time display section 25, a screen scroll operation section 26, and a processing button operation section 27 for selecting start / next display, display stop, and end processing.

Here, the pipe network diagram is composed of nodes, pipes between the nodes, and valves to which appropriate symbols are attached. Further, the pollution concentration legend portion 23 is color-coded such that the pollution concentration increases from light blue to yellow and red, for example. In addition,
The level of the pollution concentration may be displayed by changing the gradation of a single color. The display time and the display magnification can be arbitrarily set with a keyboard or the like, and the display magnification can be changed by moving the volume knob 24a with a cursor for mouse operation.

FIG. 6 shows that the pollution at the point A is 0.1 [m
[g / l] for 2 hours, and shows the state of diffusion of contamination after 2 hours when continuously generated. Pipe network diagram display unit 21
Then, according to the legend of the pollution concentration legend section 23, the pollution concentrations of the pipelines and nodes are displayed in different colors. In the attached drawings,
The higher the pollution concentration is, the darker the color is displayed. Needless to say, the pollution concentration of each part on the network diagram is calculated according to the first invention, and is represented by the color corresponding to the density of each part by the display program.

FIG. 7 shows the state 3 hours after the pollution occurred at the point A, and it is possible to directly visually grasp how the pollutants gradually move in the pipe network. The water quality contour map of FIG. 11 illustrated above shows the state of pollution diffusion 3 hours after the occurrence of pollution under the same conditions according to the second conventional technique. Comparing FIG. 7 and FIG. 11, it is obvious that contaminants are accumulated in the pipe line B25 in FIG. 7, for example, but the accumulated state cannot be displayed in the pipe line B25 in FIG.

This is because the points F and E, which are the nodes upstream and downstream of the pipeline B25 in FIG. 11, are not polluted, so the points F and E are plotted in the water quality contour map calculated by calculating the pollution concentration at only the nodes. This is because the contamination state of the pipe line B25 connecting the lines does not appear. This also applies to the pipelines B26 and B27. As described above, in the present invention, by estimating the pollution concentration at any point in the pipeline, it is possible to display the retention of pollutants that could not be expressed in the past.

FIG. 8 is a pollution concentration change screen 28 showing the temporal change of the pollution concentration at the point B (pipe B37) in FIG.
Is displayed on the contamination concentration display screen (pipe network diagram), and is a screen obtained by clicking the pipeline B37 in FIG. 6 or the like. On the pollution concentration change screen 28, a change in the pollution concentration within a fixed time from the occurrence of pollution is displayed in the form of a graph, and at the same time, the pipe length of the pipe B37, the pipe inner diameter,
Friction coefficient, cross-sectional area of pipe, flow rate of pipe, etc. are displayed. It should be noted that the curve of the graph of the contamination concentration can also be displayed in different colors according to the contamination concentration.

The arrival time of the pollutant at each point in the pipe network can be read from the pollution concentration change screen 28 of FIG. Since there are a plurality of arrival routes from the pollution occurrence point A to the point B, and the arrival times of the pollutants via the respective routes are different, the duration of pollution is longer than 2 hours at the occurrence point A. It is also found that the contaminated concentration fluctuates with time due to the mixing of contaminated water and non-polluted water. These matters cannot be displayed or recognized by conventional techniques, or are difficult.

FIG. 9 shows a state after the valve at the point C was fully closed to fully opened 3 hours after the occurrence of pollution, and 0.5 hours later, that is, the pollution diffusion after 3.5 hours from the pollution occurrence. It shows the state. Since the flow rate of the conduit B52 was 0 [m ³ / s] when the valve was closed, as shown in FIG. 7, the pollutant did not proceed to the point C, but according to FIG. 9, the valve was fully opened. It can be seen that the pollutant entered from point D after turning on.

Note that FIG. 10 shows a state in which the valve opening change screen 29 for performing the above-mentioned valve operation is displayed in an overlapping manner on the pollution concentration display screen. Similar to the actual valve operation, this screen 29 continues to indicate the push button 29a called "open" with a mouse operation cursor when instructing valve opening, and "close" when instructing valve closing. Push button 2
Continue pointing at 9a. This allows the volume knob 2
As 9b moves in the corresponding direction, the numerical display continuously changes, and the desired valve opening can be set. Further, even if the volume knob 29b is directly operated with a mouse or the like, a desired valve opening degree can be set in the same manner.

The pipe network model is changed as described above according to the valve operation amount on the valve opening change screen 29. Then, the flow direction and flow rate of each pipeline at each time after operation are calculated by the dynamic pipe network calculation based on this pipe network model, and the pollution concentration of each part is calculated. When returned, the effect of valve actuation on contaminant diffusion can be immediately recognized.

[0060]

As described above, according to the present invention, it is possible to estimate and display the pollutant diffusion state of the entire water distribution network including not only the nodes as in the conventional case but also the pipeline connecting the nodes. Therefore, it becomes possible to analyze the diffusion state of pollutants with high accuracy, and it is possible to accurately know the place and time at which countermeasures should be taken when planning countermeasures when pollution occurs. Therefore, it is possible to prevent the expansion of contaminated areas.

Further, since the manual input of the pipe network model after valve operation is not required, the labor of the operator can be greatly reduced, and the effect of the valve operation on the diffusion of pollutants can be immediately reflected, so that the measure should be taken. It can be easily examined. Further, since the diffusion state of the pollutant can be dynamically displayed moment by moment, the diffusion state can be easily recognized and there is no risk of misidentification.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration and processing flow of a contaminant diffusion state estimation / display device used in an embodiment of the present invention.

FIG. 2 is a flow chart showing an embodiment of the first and second inventions.

FIG. 3 is a flow chart showing an embodiment of the first and third inventions.

FIG. 4 is a model diagram of one pipeline.

FIG. 5 is an explanatory diagram of a display screen of a pipe network model used for simulation.

FIG. 6 is an explanatory diagram of a contamination concentration display screen showing a state when two hours have elapsed from the occurrence of contamination.

FIG. 7 is an explanatory diagram of a contamination concentration display screen showing a state when 3 hours have elapsed from the occurrence of contamination.

FIG. 8 is an explanatory diagram of a case where a pollution concentration change screen is superimposed and displayed on a pollution concentration display screen.

FIG. 9 is an explanatory diagram of a contamination concentration display screen showing a state when the valve at the point C is fully closed to fully open 3 hours after the occurrence of contamination and 0.5 hour has elapsed.

FIG. 10 is an explanatory diagram of a case where a valve opening change screen is displayed in an overlapping manner on a pollution concentration display screen.

FIG. 11 is a diagram showing an example of a water quality contour map.

[Explanation of symbols]

10 arithmetic unit 20 display 21 Pipe network diagram display section 22 Message display 23 Contamination concentration legend 24 Display magnification display section 24a Volume knob 25 Display time display 26 Screen scroll operation section 27 Processing button operation unit 28 Contamination concentration change screen 29 Valve opening change screen 29a push button 29b Volume knob

─────────────────────────────────────────────────── --Continued from the front page (56) References JP-A-7-62714 (JP, A) JP-A-4-245508 (JP, A) JP-A-4-205176 (JP, A) JP-A-5- 280076 (JP, A) Masakazu Kubota, Kenichi Kuroya, Masanori Morimoto, Analysis of Pollutant Diffusion State in Water Distribution Network, Automatic Measurement and Control of Environmental Systems Domestic Works Workshop, pp.176-179 (58) Field (Int.Cl. ⁷ , DB name) E03B 1/00 E03F 1/00

Claims (3)

(57) [Claims] 1. A method for estimating a diffusion state of a pollutant when water is polluted at a certain point in a water distribution network of water supply, considering a water network model in consideration of fluctuations in water demand. seeking a conduit flow at each time by the dynamic pipe network calculation, this flow rate
Based on the number of divisions calculated from the residence time of pollution based on each, divide each pipeline into equal intervals,
Estimate the pollution concentration in each pipe by calculating the pollution concentration in each divided part at a predetermined time interval based on the diffusion equation according to the flow direction of water using the pollution generation information such as the generated concentration. The pollution concentration at the upstream and downstream nodes of the road,
At the confluence where multiple pipes meet, it is assumed that the pollutants are completely mixed, and the pollution concentration at that confluence is estimated, and the flow direction and flow rate of water are changed by valve operation in the pipe network, and the pipe network model When it is changed, the above process is repeated based on the pipe flow rate at each time calculated for the changed pipe network model, and the pollution diffusion state is estimated from the pollution concentration of each part of the water distribution network. Method for Estimating the Diffusion State of Pollutants in a Water Distribution Network. 2. The pollution concentration of each part of the distribution pipe network estimated by the estimation method according to claim 1 is displayed on a pipe network diagram with a color or gradation according to the pollution concentration over time, and examination based on this display is performed. A pollutant characterized by displaying a valve opening change screen for changing the valve operation amount input as a result and displaying the pollutant diffusion state by the estimation method according to claim 1 after valve operation again. How to display the diffusion estimation result. 3. The pollution concentration of each part of the distribution pipe network estimated by the estimation method according to claim 1 is displayed continuously on a pipe network diagram with a color or gradation according to the pollution concentration over time. A method of displaying the estimation result of the pollutant diffusion state, characterized in that the diffusion status is dynamically displayed and the time scale of this dynamic display can be arbitrarily set with respect to real time.