(Not Applicable)
Control valves play a major role in the operating efficiency of power generating systems. Such control valves must be capable of regulating the flow of fluid under extreme thermodynamic conditions. High-temperature fluid flowing through the control valve may be under high pressure and may be flowing at a high velocity. Control valves must be capable of regulating the flow of single-phase fluid where the fluid is in a gaseous state. Control valves must also be capable of regulating the flow of two-phase fluid wherein a liquid phase of the fluid at the valve inlet flashes into a mixture of liquid and steam at the valve outlet. Regardless of the form of the fluid passing through the control valve, tight shutoff of the control valve must be maintained in order to minimize valve leakage such that operating costs and maintenance intervals of the power generating system may be kept to a minimum.
Valve leakage may be caused by a significant pressure gradient across the valve seat of the control valve which can lead to cavitation. Cavitation results in the formation of vapor bubbles in the liquid flow which can cause pitting of the valve seat as well as damage downstream components. The pitting of the valve seat may result in leak paths that may increase in size over time due to erosion. Erosion may also occur as a result of fluid flowing past the valve seat of the control valve when in an open position. Excessive valve leakage may require the temporary isolation of the portion of the fluid circuit containing the leaking control valve so that the control valve may be serviced. In extreme cases, excess valve leakage may necessitate that the power generating system be taken off line in order to replace the leaking valve. Excessive leakage may also have a significant economic impact in that it may drive up the operating costs of the power generating system.
For example, in a nuclear power plant, damage to a series of control valves as a result of steam cutting along the leakage path may reduce the circumference of the valve seat of the control valves by 30%. The resulting leakage path for each one of the control valves may be about 0.19 in2 for a total leakage area of only about 1.5 in2. With a steam inlet pressure of 1100 psi at a temperature of 560° F., the steam leakage flow rate translates to over 100,000 lb/hr of lost steam. At a steam flow rate of 13,500 lb/hr/Megawatt for nuclear power plants, the loss represented by the leakage is 7.4 Megawatts of lost electrical power output. At a fuel cost of $1.00/MegaBtu, the annualized cost of the steam leakage through the control valve is over $500,000 in lost revenue. As can be seen, such a small leak may have a tremendous impact on the costs of operating the power generating system.
By monitoring the flow rate of fluid through a valve, valve leakage may be detected at an early stage such that the risk of extensive damage to the control valve and to downstream components may be minimized. Furthermore, early detection of valve leakage may help to maintain the efficiency and performance of the power generating system such that the operational costs thereof may be kept to a minimum. Thus, there exists a need for a method of monitoring valves such that valve leakage may be quantified.
The present invention addresses the above-described leakage quantification problem by providing a method for determining valve leakage based upon temperature measurements recorded upstream and downstream of the valve. More specifically, the present invention provides a method for determining the flow rate of valve leakage by correlating the heat loss of the fluid across the valve to the change in enthalpy of the fluid across the valve. The change in enthalpy is then correlated to the flow rate of valve leakage.
The present invention provides a method for determining valve leakage across a valve for single-phase flow and for two-phase flow. In single-phase flow, fluid is in the form of steam or gas at an inlet of the valve and at a temperature that is above ambient temperature. In two-phase flow, the fluid is in liquid form at the inlet of the valve that subsequently flashes to a mixture of liquid and vapor at an outlet of the valve. Flashing is the sudden vaporization of the liquid caused by a pressure drop across the valve wherein the temperature of the mixture drops to its saturation temperature corresponding to its pressure. Under single-phase flow and two-phase flow conditions, the flow rate of valve leakage may be ascertained by measuring the temperature of bare pipe at locations adjacent the inlet and outlet of the valve. For single phase flow, the temperature of the bare pipe is measured at two locations downstream of the valve. For two-phase flow, the temperature of insulated pipe is measured at the inlet and the outlet of the valve.
In single-phase flow across the valve, the underlying principle upon which the leakage flow may be determined is that the heat loss across a length of bare pipe causes a drop in the temperature of the leakage flow. Thus, in measuring the leakage across a valve with single-phase flow, a section of the piping immediately downstream of the valve is provided in a bare or uninsulated state. The surface temperature of the bare pipe is measured immediately adjacent the valve outlet. The surface temperature of the bare pipe is also measured at a downstream end of the bare pipe. The temperature differential across the length of the bare pipe corresponds to a loss in enthalpy across the length. The loss in enthalpy is representative of the heat loss in the length of bare pipe.
The heat loss in the uninsulated portion of the bare pipe is the result of a combination of convective and radiative heat loss. Convective heat loss occurs as a result of the temperature differential between the outer surface of the bare pipe and the relatively cooler ambient air. Radiative heat loss occurs as a result of the electromagnetic radiation of heat from the outer surface of the bare pipe to relatively cooler objects surrounding the bare pipe. The radiative heat loss of the bare pipe is dependent on the thermal emissivity of the bare pipe outer surface. By using input parameters of the ambient air temperature as well as the temperature differential across the length of bare pipe as representative of the heat loss, the flow rate of valve leakage, if any, may be calculated for a bare pipe configuration of a given length, diameter and thermal emissivity.
In two-phase flow across the valve, the underlying principle upon which the leakage flow may be determined is based upon the condition that the liquid at the inlet of the valve (i.e., upstream of the valve) flashes to a mixture of liquid and vapor at the outlet of the valve (i.e., downstream of the valve). Under this condition, the flow downstream of the valve is at saturation temperature for its pressure. The underlying principle for determining valve leakage under such a condition is that any leakage of the valve will cause an increase in the pressure on the downstream side of the valve because of frictional resistance to flow in the downstream piping.
The increased pressure of the flow downstream of the valve corresponds to a higher temperature as compared to the temperature at the same location when there is no leakage. The temperature of insulated pipe upstream and downstream of the valve is representative of the respective temperatures of the flow across the valve. The respective temperatures may be measured at the outer surface of the insulated pipe. By using input parameters of actual and predicted temperature differential for conditions of no leakage at the valve outlet, the flow rate of valve leakage, if any, may be calculated for a given piping configuration.
These as well as other features of the present invention will become more apparent upon reference to the drawings wherein:
Referring now to the drawings wherein the showings are for purposes of illustrating preferred embodiments of the present invention only, and not for purposes of limiting the same,
The piping system 10 of
In
In addition to comparing T2-1 and T2-L in order to detect leakage of the closed valve 12, T2-L may also be compared to ambient temperature Tamb of the air surrounding the piping system 10. Substantially equal values for Tamb and T2-L may also indicate an absence of leakage in the valve 12. For example, in the case where the valve 12 in
For single-phase flow, the leakage flow rate Wleak of the valve 12 may be calculated in a method of the present invention wherein a temperature differential across the length L of the second pipe section 20 is correlated to a loss in enthalpy of the fluid flowing therethrough. The loss in enthalpy is then correlated to the leakage flow rate Wleak of the valve 12.
The correlation of loss in enthalpy to the leakage flow rate Wleak may be mathematically described wherein h0-1 is representative of enthalpy h0-1 of the fluid at a fluid source (not shown) of the piping system 10. At the fluid source, the enthalpy h0-1 of the fluid corresponds to a temperature T0-1 and known pressure P0-1 of the fluid. At the second end 24 of the second pipe section 20, the enthalpy h2-L of the fluid corresponds to the temperature T2-L of the surface of the second pipe section 20 at the second end 24. Because throttling of the valve 12 is an is enthalpic process, the loss in enthalpy of the fluid in the second pipe section 20 is equivalent to the heat loss in the second pipe section 20. The loss in enthalpy in the second pipe section 20 may be expressed as:
Δh=(h0-1−h2-L) (1)
The loss in enthalpy or heat loss in the second pipe section 20 is the result of a combination of convective heat loss Qc and radiative heat loss Qr. Convective heat loss Qc occurs as a result of the temperature differential between the surface of the second pipe section 20 and the relatively cooler ambient air. Radiative heat loss Qr occurs as a result of the electromagnetic radiation of heat from the surface of the second pipe section 20 to relatively cooler objects surrounding the second pipe section 20. The radiative heat loss Qr of the second pipe section 20 is dependent on the thermal emissivity ε of the outer surface thereof. The convective heat loss Qc may be mathematically expressed as follows:
Qc=hAout(T2,avg−Tamb) (2)
where h is a heat transfer coefficient, Aout is a surface area of the outer surface along length L of the uninsulated second pipe section 20, T2,avg is an average of temperatures T2-L and T2-1, and Tamb is the ambient temperature of the air surrounding the second pipe section 20. Radiative heat loss Qr may be mathematically expressed as follows:
Qr=εσ[∫(T2-x4−Tamb4)·dAout] (3)
where ε and σ are thermal emissivity of the bare second pipe section 20 and Stefan-Boltzmann constant, respectively, and T2-x is a temperature of the surface of the second pipe section 20 at a predetermined distance x downstream of the first end 22. T2-x may also be represented as a function of the predetermined distance x in order to improve accuracy while keeping integration simple. Examples of functions suitable for such representation of T2-x, are 2nd order (or higher) polynomials and exponential decay types of equations such as the following:
T2-x=(T2-1)(e−kx) and T2-x=T2-1+k1x+k2x2
wherein T2-1 is the temperature of the surface of the second pipe section 20, e is the base of the natural logarithms and is approximately equal to 2.71828, x is the distance downstream of the first end 22, and k is a constant that is representative of heat loss Qflow of the fluid in the second pipe section 20 as a result of a combination of convective heat loss Qc and radiative heat loss Qr.
The heat loss Qflow of the fluid in the second pipe section 20 with leakage flow rate Wleak may be mathematically expressed as follows:
Qflow=Wleak(h0-1−h2-L) (4)
where Δh=(h0-1−h2-L), as recited in Equation (1).
In heat transfer theory, heat loss Δh in a system may be generally expressed as follows:
Δh=Cp(ΔT) (5)
where Cp is an average specific heat of a fluid flowing through the system and ΔT is a temperature differential of the fluid measured at two locations in the system. In the piping system 10 of
Qflow=WleakCp(T2-1−T2-L) (6)
wherein Qflow is the heat loss of the second pipe section 20. As was mentioned earlier, the heat loss Qflow of the second pipe section 20 is the sum of the convective heat loss Qc and the radiative heat loss Qr and may be written as follows:
Qflow=Qc+Qr (7)
Therefore, by combining Equations (2), (3) and (6), the leakage flow rate Wleak can be determined by the following expression:
WleakCp(T21−T2n)=hcAout(T2,avg−Tamb)+εσ[∫(T2x4−Tamb4)·dAout] (8)
wherein the heat transfer coefficient hc may be determined by the following heat transfer equation:
NuD=hcDout/k (9)
wherein NuD is a dimensionless Nusselt Number, k is the thermal conductivity of air, and Dout is an outer diameter of the second pipe section 20. In heat transfer theory, the Nusselt Number is a ratio of total heat transfer of a system to conductive heat transfer of the same system. For convective heat loss in horizontally disposed cylinders, NuD may be determined from the following correlation:
NuD=[0.60+0.387[RaD/{1+(0.559/Pr)9/16}16/9]1/6]2 (10)
wherein RaD is the Rayleigh Number and Pr is the Prandtl Number for a given configuration of the second pipe section 20. The Prandtl Number Pr is equivalent to [ν/μ]. The Rayleigh Number RaD is equivalent to the following expression:
RaD=g(ΔT/Tamb)Dout3/[v α] (11)
wherein g is a gravitational constant, ΔT is a temperature difference between T2,avg and Tamb, Dout is an outer diameter of the length L of the second pipe section 20, ν is a kinematic viscosity of air at Tamb, and α is a thermal diffusivity of air at Tamb. By solving Equation (3) for radiative heat loss Qr of the second pipe section 20 and by substituting a resultant of Equation (3) as well as substituting Equations (10) and (11) into Equation (8), Wleak may be expressed by the following Equation (12):
wherein Dout is the outer diameter of the length L of the uninsulated portion of the second pipe section 20, ν is the kinematic viscosity of air at Tamb, α is the thermal diffusivity of air at Tamb, Cp is the specific heat of air at Tamb, ε is the thermal emissivity of the surface of the second pipe section 20, σ is the Stefan-Boltzmann constant given as 5.67×10−8 W/m2K4, and g is the gravitational constant given as 9.8 m/sec2.
Utilizing Equation (12), the leakage flow rate Wleak for single-phase flow through the valve 12 may be measured in a method wherein fluid is initially moved through the second pipe section 20. The temperature T2-1 is then measured at the surface of the second pipe section 20 at the first end 22. The temperature T2-L at the surface of the second pipe section 20 at the second end 24 is also measured. The temperature T2-x of the surface of the second pipe section 20 at a predetermined distance x downstream of the first end 22 is measured or determined as a function of the predetermined distance x in a manner as was earlier mentioned. In addition, the ambient temperature Tamb of air surrounding the second pipe section 20 is also measured. The leakage flow rate Wleak is then calculated according to Equation (12).
The temperatures T2-1 and T2-L may be respectively measured by a first temperature sensor and a second temperature sensor mounted on the surface of the second pipe section 20 at respective ones of the first and second ends 22, 24. The first and second temperature sensors are operative to generate a first temperature signal and a second temperature signal, respectively. The first and second temperature signals are representative of temperatures T2-1 and T2-L, respectively. In addition, the temperature T2-x may be measured by a third temperature sensor mounted on the surface of the second pipe section 20 at the predetermined distance x downstream of the first end 22. The third temperature sensor is operative to generate a third temperature signal representative of T2-x.
By configuring the piping system 10 of
Turning now to
Turning now to
As was mentioned earlier, the underlying principle upon which the leakage flow rate Wleak may be determined for two-phase flow is that any leakage of the valve 12 will cause an increase in the pressure on the downstream side of the valve 12 because of frictional resistance to flow in the downstream piping. The increased pressure of the flow downstream of the valve 12 corresponds to a higher temperature of the surface of the second pipe section 20 as compared to the temperature of the second pipe section 20 when there is no leakage of the valve 12. In this regard, temperatures T1, T2 of respective ones of the first and second pipe sections 18, 20 are representative of the flow and, hence, the leakage across the valve 12.
In a method of detecting leakage of the valve 12 for two-phase flow, the pressure P2 of the fluid is measured or known. Because saturation pressure of a fluid is a function of temperature of the fluid, the saturation pressure P2s at the valve outlet is determined by correlating P2s to T2 using steam properties commonly available in steam tables. The corresponding density ρ2-0 of the two-phase flow is determined for P2s. Assuming constant enthalpy of the fluid upstream of the vessel 26, the saturation pressure P2s is compared to the pressure P2. If there is a pressure differential ΔP between P2s and P2, then there is leakage in the valve 12. The pressure differential ΔP may be expressed as follows:
ΔP=(P2s−P2) (13)
The relationship between ΔP and leakage of the valve 12 is given by:
ΔP=(K)(1/2)(ρ2-0V2-02) (14)
where K is the piping resistance factor for a given piping configuration, V2-0 is a velocity of the flow through the second pipe section 20, and ρ2-0 is the corresponding density of the two-phase flow through the second pipe section 20. For a given piping system 10 configuration, K is representative of the total resistance to the flow. K includes frictional loss factors for individual pipe sections [(f(L/D)] and loss factors (Kf) for individual fittings in the line. In general, for pipe sections, the loss factors for friction are a function of the length and corresponding inner diameter of the pipe section. For a given piping system, K may be expressed as follows:
K=(Σ·Kf)+Σ(fL/D) (15)
Because ρ2-0 and ΔP are determined from measurements, and because K is determined from the specific piping system 10 configuration, the velocity V2−0 of the two-phase flow may be estimated from Equation (14). In
Wleak=ρ2-0AinV2-0 (16)
Referring still to the piping system 10 arrangement of
The method of measuring the leakage flow rate Wleak of the valve 12 comprises the steps of initially moving fluid from the first pipe section 18 into the inlet 14 of the valve 12. Due to leakage of the valve 12, the fluid exits at the outlet 16. The fluid is moved through the second pipe section 20 and into the vessel 26. The temperature T1 of the surface of the first pipe section 18 is measured. As shown in
wherein Din is the inner diameter of the second pipe section 20.
For piping systems including at least one additional downstream pipe section (not shown) located upstream of the vessel 26, frictional losses Kpx of the downstream pipe sections are incorporated into Equation (17) for calculating the leakage flow rate Wleak according to the following formula:
For piping system 10 configurations including at least one pipe fitting (not shown) located upstream of the vessel 26, the method of calculating the leakage flow rate Wleak comprises the additional steps of determining frictional losses Kf for the pipe fitting and calculating the leakage flow rate Wleak according to the following formula:
A first and second temperature sensor may be mounted on respective ones of the first and second pipe sections 20. The first and second temperature sensors are operative to generate first and second temperature sensor signals representative of T1 and T2, respectively. Furthermore, a pressure sensor may be mounted on the vessel 26 for measuring pressure P2 of the vessel 26. The pressure sensor is operative to generate a first pressure signal representative of P2. The piping system 10 shown in
Turning now to
Additional modifications and improvements of the present invention may also be apparent to those of ordinary skill in the art. Thus, the particular combination of parts described and illustrated herein is intended to represent only certain embodiments of the present invention, and is not intended to serve as limitations of alternative devices within the spirit and scope of the invention.
This application claims priority to U.S. Provisional Application No. 60/465,309, filed Apr. 25, 2003.
Number | Name | Date | Kind |
---|---|---|---|
4308746 | Covington | Jan 1982 | A |
4336708 | Hobgood et al. | Jun 1982 | A |
5067094 | Hayes | Nov 1991 | A |
20020116986 | Pompa et al. | Aug 2002 | A1 |
Number | Date | Country | |
---|---|---|---|
20040225458 A1 | Nov 2004 | US |
Number | Date | Country | |
---|---|---|---|
60465309 | Apr 2003 | US |