METHOD FOR MEASURING OF THE FLOW RATE OF A PUMP

Abstract

A method for estimating the output flow rate provided by a pump in a system including the pump, an upstream pipe and a downstream pipe, by using pressure information coming from a first downstream pressure sensor placed on the downstream pipe at a first distance from the pump and a second downstream pressure sensor placed on the downstream pipe at a second distance from the pump for calculating the output flow rate.

Description

TECHNICAL FIELD

This disclosure pertains to the field of pump systems where a pump, in particular a centrifugal pump, pumps a fluid from an upstream pipe to a downstream pipe.

BACKGROUND ART

Pump systems are used in various hydraulic applications. Such systems transport different kinds of fluid with different properties and densities e.g., from clean water to wastewater applications. During their operation, the different mechanical parts such as impeller, blades, wear-ring, diffuser, that compose the pump are subject to wear, and they can wear differently depending on the wear causes, e.g., cavitation, corrosion, abrasion, abnormal usage. The degradation of those parts generates internal losses and decreases the performance of the centrifugal pump. The losses can be quantified in terms of loss of flow rate and loss of total dynamic head capacity of the pump.

In certain cases, one pressure sensor located at the output of the pump is present and no flow meters are used since a flow meter is much more expensive than a pressure sensor. Without a flow rate sensor, it is difficult to monitor the system operation and drift in pump characteristics without having the flow rate information.

The estimation of the flow rate downwards from the pump may however be done by using pump curves provided by the pump manufacturer, i.e., power vs. flow rate and a measured or estimated power which allows to deduce the flow rate by extrapolating from the configured pump curve at the corresponding pump speed. This method is however not very accurate.

Document EP2726827B1 proposes a method using the generation of a transient fluid wave using a generator and two pressures at two locations on a pipe to calculate a wave speed of the fluid. Such method needing injection of a transient fluid wave and a generator is not a passive method and cannot be used in any working condition, transient or steady state of a pump without additional device and condition.

SUMMARY

The present disclosure improves the situation in proposing a new passive method to obtain a measurement of the flow rate of a pump.

More precisely, the present disclosure proposes a method for estimating the output flow rate provided by a pump in any working condition, transient or steady state, of said pump in a system comprising said pump, an upstream pipe and a downstream pipe, by using pressure information coming from a first downstream pressure sensor placed on the downstream pipe at a first distance from the pump and a second downstream pressure sensor placed on the downstream pipe at a second distance from the pump such that a known distance L separates said first and second pressure sensors, said method comprising estimating said output flow rate {circumflex over (Q)} with an iterative process using the downstream pipe characteristics, the distance between the first and the second sensors the pressures sensed with said pressure sensors and a flow rate estimator model E1 defined by the equations:

$\{\begin{array}{cc}\hat{Q}=K_p·\left(\Delta P_{\mathrm{measured}}-\right)+\widehat{Q_I}& \left(1\right)\\ \frac{d\widehat{Q_I}}{dt}=K_i·\left(\Delta P_{\mathrm{measured}}-\right)& \left(2\right)\end{array}$

and equations:

$\begin{array}{cc}=\frac{\left(\hat{F}·L·v^2·\rho \right)}{2·D}& \left(3\right)\end{array}$ $\mathrm{and}$ $\begin{array}{cc}v=\frac{\hat{Q}}{A}& \left(4\right)\end{array}$

Where {circumflex over (Q)} is the Estimated flow rate (m³/h), is the Estimated differential pressure (bar), ΔP_measured is the Measured differential pressure (bar), {circumflex over (F)} is the Estimated friction losses coefficient, L is the Pipe length between said first and second pressure sensors, D is the Pipe diameter, v is the Fluid flow velocity (m/s) and A is the section of the pipe (m²), ρ is the Fluid density (kg/m3), K_p is the Proportional gain of the flow estimator,

$K_i=\frac{K_p}{T_{iq}}$

in which T_iq is the Integrator time constant(s) in the flow estimator.

In the present disclosure, thanks to the additional downstream pressure sensor at a defined distance from the first downstream pressure sensor which itself is located remote from the pump, the flow in the system may be estimated with an estimator model, or observatory, by knowing two downstream pressure information and the pipe characteristics for identification of the flow rate in a defined pipe section.

In a first embodiment, the friction loss coefficient {circumflex over (F)} may be a fixed constant.In an improved realization mode, the friction loss coefficient {circumflex over (F)} may be calculated based on a friction loss coefficient estimator model E2 defined by the equations:

$\{\begin{array}{cc}\hat{F}=K_1·\left(1-\hat{X}\right)+{\hat{F}}_I& \left(5\right)\\ \frac{d{\hat{F}}_I}{dt}=K_2·\left(1-\hat{X}\right)& \left(6\right)\\ \hat{X}=-2\times \sqrt{\hat{F}}\times \log \left(\frac{2.51}{R_e\times \sqrt{\hat{F}}}+\frac{nu}{3.71\times D}\right)& \left(7\right)\end{array}$ $\begin{array}{cc}{K}_1=1;K_2=\frac{K_1}{T_i}=\frac{K_1}{T_{\mathrm{iq}/2}}& \left(8\right)\end{array}$

In which {circumflex over (F)} is a dimensionless coefficient, K₁ is a dimensionless proportional gain, K₂ unit is s⁻¹ and where:

$\begin{array}{cc}{R}_e=\frac{\rho ·v·D}{\mu }& \left(9\right)\end{array}$

when the Reynolds coefficient R_e of the flow in the downstream pipe is greater or equal than 2300;The method may also comprise a friction loss coefficient {circumflex over (F)} calculation where

$\begin{array}{cc}\hat{F}=\frac{64}{R_e}& \left(10\right)\end{array}$

when the Reynolds coefficient R_e of the flow in the downstream pipe is smaller than 2300.The method may comprise measuring a pump speed and power information coming from a command unit of said pump to compare the estimated output flow rate and the flow rate calculated with the pump curves of the pump to detect wear of the pump.The pump may be a centrifugal pump.The present disclosure proposes further a computer program comprising instructions to implement the method according to any one of the preceding claims when the software is executed by a processor.

The present disclosure proposes also a computer-readable non-transient recording medium on which the computer program is registered to implement the method when such computer program is executed by a processor.

BRIEF DESCRIPTION OF DRAWINGS

Other features, details and advantages will be shown in the following detailed description and on the figures, on which:

FIG. 1 is a schematic drawing of a pump and piping with pressure sensors and flow meter;

FIGS. 2A and 2B are respectively a Head versus flow rate curve and a Power versus flow rate curve of pump datasheets;

FIG. 3 is a schematic view of a pump and piping with additional downstream pressure sensor;

FIG. 4 is a schematic view of a flow rate estimation process;

FIG. 5 is a schematic view of a friction loss estimation process.

DESCRIPTION OF EMBODIMENTS

In the present disclosure the following notations are used in the equations hereunder:

Hpump                 Pump Total dynamic head (m)
Qpump                 Pump flow rate (m3/h)
Pwpump                Pump mechanical power (kW)
ω                     Pump mechanical speed (rpm)
ωn                    Pump nominal mechanical speed (rpm)
Qsystem               System flow rate (m3/h)
Q                     Flow rate (m3/h)
{circumflex over (Q)} Estimated flow rate (m3/h)
                      Estimated differential pressure (bar)
ΔPmeasured            Measured differential pressure (bar)
{circumflex over (F)} Estimated friction losses coefficient
L                     Pipe length (m)
D                     Pipe diameter (m)
v                     Fluid flow velocity (m/s)
ρ                     Fluid density (kg/m3)
Re                    Reynolds coefficient
μ                     Dynamic viscosity kg/(m · s)
nu                    Pipe rugosity (m)
Tiq                   Integrator time constant (s) of flow estimator
Ti                    Integrator time constant (s) of friction loss estimator
Kp                    Proportional gain of flow estimator
A                     section of the pipe

The unit of is kg·²·m⁻¹·s⁻².

The unit of {circumflex over (Q)}_I and {circumflex over (Q)} is m³·s⁻¹

The unit of K_p is then m⁴·s·kg⁻¹

In such system,

$v=\frac{Q}{A}$

where A is the section of the pipe and Q is the flow rate passing inside the pipe.

Pumping stations usually do not have flow meters to give the information of the flow rate outcoming from the pumps of such pumping stations because globally flow meters are complex to install depending on the pumping station and are more expensive than pressure sensors which are less complex to install on the pipes of such stations. Except the use of the power and manufacturer datasheet, there is no known method in the literature that allow to provide an accurate value of the flow rate outside the pump without using an external flow rate sensor. In addition, the use of the power and manufacturer datasheet gives only the flow rate inside the pump which is generally higher due to internal recirculation in the pump.

Traditionally, when using an upstream pressure sensor, a downstream pressure sensor to calculate the pump head, the pump Head vs. flow rate characteristic of the pump datasheet and the measured inlet and outlet pressure, the flow rate may be deduced from the pump curves provided by the manufacturer at the corresponding pump speed. This is translated with mathematical equations as follows:

The pump characteristics are identified by the following equations:

$H_{\mathrm{pump}}=x^2·F\left(Q_{\mathrm{pump}},x\right)$ ${\mathrm{Pw}}_{\mathrm{pump}}=x^3·G\left(Q_{\mathrm{pump}},x\right)$

Where: H_pump is the head of the pump, Q_pump is the pump flow rate,

$x=\frac{\omega }{{\omega }_n}$

where ω is the pump mechanical speed (rpm), ω_n the pump nominal mechanical speed (rpm) as in the list above and F and G are interpolation functions.

To identify the pump flow rate, the functions “F” and “G” need to be inversed.

When using the pump characteristics “Head vs. Flow rate”, as in FIG. 2A the equation is:

$Q_{\mathrm{pump}}=x·F^{-1}\left(H_{\mathrm{pump}},x^2\right)$

When using the pump characteristics “Power vs. Flow rate” as in FIG. 2B the equation is:

$Q_{\mathrm{pump}}=x·G^{-1}\left(P{w}_{\mathrm{pump}},x^2\right)$

In practice, the pump flow rate inside the pump is higher than the system flow rate that would be measured outside the pump due to the internal recirculation inside the pump:

$Q_{\mathrm{system}}=Q_{\mathrm{pump}}-\partial Q\left(\omega ,Q_{\mathrm{pump}}\right)$

Due to the pump ageing, the pump characteristics change, and do not provide a correct information of the flow rate downstream the pump.

The present disclosure proposes a solution to identify the flow rate outcoming from the pump which is different from the flow rate inside the pump due to internal recirculation. The invention consists of the identification of the pump outcoming flow rate without using a flow sensor but by using an additional pressure sensor information and known pipe characteristics.

FIG. 3 provides a schematic drawing of a present disclosure example using two pressure sensors 12, 14 placed at well-known distances d2 and d1+d2 on a downstream pipe and measuring a first pressure P1 at distance d2 from the pump and a second pressure P2 at distance d1+d2 from the pump to estimate the flow rate that pass through this pipe by estimating the pressure losses and comparing such to the measured differential pressure on this pipe.

The principle is to use an estimator of the flow rate passing through the section of the pipe between the two-pressure sensors using the following estimator model E1:

$E1:\{\begin{array}{cc}\hat{Q}=K_p·\left(\Delta P_{\mathrm{measured}}-\right)+\widehat{Q_I}& \left(1\right)\\ \frac{d{\hat{Q}}_I}{dt}=K_i·\left(\Delta P_{\mathrm{measured}}-\right)& \left(2\right)\end{array}$

and equations:

$\begin{array}{cc}=\frac{\left(\hat{F}·L·v^2·\rho \right)}{2·D}& \left(3\right)\end{array}$ $\mathrm{and}$ $\begin{array}{cc}v=\frac{\hat{Q}}{A}& \left(4\right)\end{array}$

where {circumflex over (Q)} is the Estimated flow rate (m³/h), is the Estimated differential pressure (bar), ΔP_measured is the Measured differential pressure (bar), {circumflex over (F)} is the Estimated friction losses coefficient, L is the Pipe length between said first and second pressure sensors, D is the Pipe diameter, v is the Fluid flow velocity (m/s) and A is the section of the pipe (m²), ρ is the Fluid density (kg/m3), K_p is the Proportional gain of the flow estimator,

$K_i=\frac{K_p}{T_{\mathrm{iq}}}$

in which T_iq is the Integrator time constant(s) in the flow estimator, the unit of ΔP and is kg·m⁻¹·s⁻², the unit of {circumflex over (Q)} et {circumflex over (Q)}_I is m³·s⁻¹, the unit of K_p is m⁴·s·kg⁻¹, the unit of K_i is m⁴·kg⁻¹.

K_p and

$K_i=\frac{K_p}{T_{\mathrm{iq}}}$

are configured depending on the identification of the characteristics of the system and the estimator model E1 is programmed in a computerized system having a processor programmed to execute iterative calculations based on the estimator to determine the estimated flow rate {circumflex over (Q)}.

The present disclosure principle is to use the pressures at two separate points downstream from the pump and the pipe characteristics to build an observer and estimator model permitting to estimate the fluid flow without any action on the pump or artifice such as transient in fluid flow or pressure. The estimated fluid flow is introduced in the ΔP calculation in order to obtain a convergence towards the fluid flow such as ΔP=Δ{circumflex over (P)}.

As shown in FIG. 4, to implement the estimator, a first step 100 comprises a calculation of ΔP_measured as P2−P1, calculation of equations (1), (2) with an initial ΔP_estimated value then calculation of equation (3) with known pipe characteristics 200 and equation (4) to obtain a new ΔP_estimated. The calculations are then reiterated to obtain convergence on an estimated flow rate {circumflex over (Q)}.

In this model {circumflex over (F)} may be a fixed value but to provide a more accurate estimation, {circumflex over (F)} is made dependent of the Reynolds coefficient R_e of the flow in the downstream pipe and calculated in another algorithm as depicted in FIG. 5. In such case, after entry of the pipe characteristics 200 and a test 210 on the value of R_e the calculation of {circumflex over (F)} becomes:

If R_e≥2300 at step 230 the calculation of {circumflex over (F)} is done with a second estimator model E2 hereunder:

$E2:\{\begin{array}{cc}\hat{F}=K_1·\left(1-\hat{X}\right)+{\hat{F}}_I& \left(5\right)\\ \frac{d\widehat{F_I}}{dt}=K_2·\left(1-\hat{X}\right)& \left(6\right)\\ \hat{X}=-2\times \sqrt{\hat{F}}\times \log \left(\frac{2.51}{R_e\times \sqrt{\hat{F}}}+\frac{nu}{3.71\times D}\right)& \left(7\right)\end{array}$ $\begin{array}{cc}{K}_1=1;K_2=\frac{K_1}{T_i}=\frac{K_1}{T_{\mathrm{iq}/2}}& \left(8\right)\end{array}$

In which {circumflex over (F)} is a dimensionless coefficient, K₁ is a dimensionless proportional gain, K₂ unit is s⁻¹ and where:

$\begin{array}{cc}{R}_e=\frac{p·v·D}{\mu }& \left(9\right)\end{array}$

Else if R_e<2300 at step 220,

$\begin{array}{cc}\hat{F}=\frac{64}{R_e}& \left(10\right)\end{array}$

In this second estimator, Ti_q the integrator time constant is chosen to have a greater dynamic than the physical pump system time constant and Ti, the integral time constant of the second estimator, is chosen smaller than Ti_q, e.g. Ti_q/2.

The calculated estimated friction losses coefficient {circumflex over (F)} is then entered in the first estimator E1.

Tiq integrator time constant(s) for the flow estimator, Kp proportional gain for the flow estimator and the needed pipe characteristics and fluid characteristics: L: Pipe length (m); D: Pipe diameter (m); v: Fluid flow velocity (m/s); ρ: Fluid density (kg/m3); R_e: Reynolds coefficient; μ: Dynamic viscosity kg/(m·s); nu: Pipe rugosity (m) are stored in a memory of the computerized system.

The computerized system may be an electronic control unit with a microcontroller having analog to digital conversion means and receiving the pressures P1 and P2 as inputs and comprising a program provided with the estimators algorithms and data storage for the needed constants or may be part of a command unit 4 as shown in FIG. 3 such as a variable speed drive for the pump such command unit comprising the power control 41 for the pump motor and a processor system 42 to implement the drive command software and the above process software.

In this regard, the process may comprise obtaining the pump speed N and power P information coming from the variable speed drive of the pump to compare the estimated output flow rate and the flow rate calculated with the pump curves of the pump to detect wear of the pump.

The method is particularly suitable if the pump is a centrifugal pump.

INDUSTRIAL APPLICABILITY

The present disclosure avoids the use of a flow meter which is more expensive than a pressure sensor and more complicated to install on an existing station. The solution will provide the information of the flow given by the centrifugal pump in the system by using only the information of the two-pressure sensors installed on the upstream pipe and downstream pipes. the benefit of the solution is huge because it simplifies the installation and provide the information of flow by pump for different applications: control, protection, monitoring, pump wear monitoring and for predictive maintenance.

The invention is not limited to the description above and the invention object of the attached claims may be used in a remote survey system or a local fault detection program.

Claims

1. A method for estimating an output flow rate provided by a pump in any working condition, transient or steady state, of said pump in a system comprising said pump, an upstream pipe and a downstream pipe, by using pressure information coming from a first downstream pressure sensor placed on the downstream pipe at a first distance from the pump and a second downstream pressure sensor placed on the downstream pipe at a second distance from the pump such that a known distance L separates said first and second pressure sensors, said method comprising estimating said output flow rate {circumflex over (Q)} with an iterative process using the downstream pipe characteristics, the distance between the first and the second sensors the pressures sensed with said pressure sensors and a flow rate estimator model E1 defined by the equations:

2. The method according to claim 1 wherein the friction loss coefficient {circumflex over (F)} is a fixed constant.

3. The method according to claim 1 comprising a friction loss coefficient {circumflex over (F)} calculation based on a friction loss coefficient estimator model E2 defined by the equations:

4. The method according to claim 1 comprising a friction loss coefficient {circumflex over (F)} calculation where

5. The method according to claim 1 comprising measuring a pump speed and power information coming from a command unit of said pump to compare the estimated output flow rate and the flow rate calculated with the pump curves of the pump to detect wear of the pump.

6. The method according to claim 1 wherein said pump is a centrifugal pump.

7- (canceled)

8. A computer program product comprising a non-transitory processor-readable recording medium on which a computer program comprising processor-executable instructions is stored to implement the method of claim 1 when the computer program is executed by a processor.