Steam generator and method for generating steam
09671106 ยท 2017-06-06
Assignee
Inventors
Cpc classification
F22B35/102
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/48
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22D5/26
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/10
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
C02F2303/22
CHEMISTRY; METALLURGY
F22B29/067
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B29/061
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/50
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
International classification
F22B35/10
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22D1/02
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/50
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/10
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B37/48
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F22B29/06
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
A steam generator apparatus for generating steam from a feedwater inlet stream including impurities is disclosed. The apparatus includes a tubing circuit in communication with an inlet for receiving the feedwater stream, the tubing circuit having a substantially unrifled bore defined by a metal wall, and a heat source operable to deliver a heat flux to the feedwater stream through the metal wall of the tubing circuit, the heat flux being operable to cause evaporation of feedwater within the tubing circuit and to produce an outlet stream at an outlet of the tubing circuit, the outlet stream includes a steam portion and liquid phase portion, the steam portion being greater than about 80% of the outlet stream by mass, the steam portion providing sufficient cooling of the metal wall to maintain a wall temperature at less than a threshold temperature associated with safe operation of the steam generator apparatus.
Claims
1. A steam generator apparatus for generating steam from a feedwater inlet stream including impurities, the apparatus comprising: a tubing circuit in communication with an inlet for receiving the feedwater stream, the tubing circuit having an unrifled bore defined by a metal wall; a heat source operable to deliver a heat flux to the feedwater stream through the metal wall of the tubing circuit, the heat flux being operable to cause evaporation of feedwater within the tubing circuit and to produce an outlet stream at an outlet of the tubing circuit, the outlet stream comprising a steam portion and liquid phase portion, the steam portion being greater than about 80% of the outlet stream by mass, the steam portion providing sufficient cooling of the metal wall to maintain a wall temperature at less than a threshold temperature associated with safe operation of the steam generator apparatus; and a controller operably configured to control at least one of a flow rate of the feedwater stream and the heat flux to cause the outlet stream to have the steam portion greater than about 80% of the outlet stream by mass.
2. The apparatus of claim 1, wherein the tubing circuit comprises an economizer section for heating the feedwater within the tubing circuit and an evaporator section for causing evaporation of the feedwater stream to generate the outlet stream, and the heat source is disposed to deliver heat flux along at least a portion of the economizer section and at least a portion of the evaporator section.
3. The apparatus of claim 1, wherein the heat source is configured to deliver sufficient heat flux to cause a substantial portion of the impurities present in the feedwater stream to be entrained in the liquid phase portion of the outlet stream and discharged as part of the outlet stream thereby reducing scaling of the bore of the tubing circuit.
4. The apparatus of claim 1, wherein the controller is operably configured to control at least one of a flow rate of the feedwater stream and the heat flux to cause the outlet steam to have the steam portion greater than about 90% of the outlet stream by mass.
5. The apparatus of claim 1, wherein the controller is operably configured to control at least one of a flow rate of the feedwater stream and the heat flux to cause the outlet steam to have the steam portion greater than about 92% of the outlet stream by mass.
6. The apparatus of claim 1, wherein the controller is operably configured to control at least one of a flow rate of the feedwater stream and the heat flux to cause the outlet steam to have the steam portion greater than about 95% of the outlet stream by mass.
7. The apparatus of claim 1, wherein the unrifled bore of the tubing circuit comprises a substantially un-contoured wall.
8. The apparatus of claim 1, wherein the unrifled bore of the tubing circuit comprises a generally smooth wall.
9. The apparatus of claim 1, further comprising a chamber housing the tubing circuit and wherein the heat source is configured deliver heat to the chamber and the chamber is operably configured to cause heat to be directed to the metal wall of the tubing circuit for delivering the heat flux.
10. The apparatus of claim 1, further comprising a chamber housing at least a first portion of the tubing circuit, and wherein the heat source is configured to generate a radiant heat flux within the chamber and wherein a second portion of the tubing circuit is disposed outside the chamber for receiving a convective heat transfer from the chamber.
11. The apparatus of claim 1, wherein the tubing circuit comprises an economizer section for heating the feedwater within the tubing circuit and an evaporator section for causing evaporation of the feedwater stream to generate the outlet stream, and wherein the heat source produces a heated gas flow that is received at the evaporator section and directed to the economizer section.
12. The apparatus of claim 1, wherein the metal wall of at least a portion of the tubing circuit comprises a material selected to withstand operating stresses due to a pressure associated with the feedwater stream at elevated wall temperatures caused by delivery of the heat flux to the feedwater stream.
13. The apparatus of claim 12, wherein the metal wall of the portion of the tubing circuit comprises tubing that complies with ASTM A 335 P22 specification.
14. The apparatus of claim 1, further comprising an outlet flow nozzle in communication with the outlet, the flow nozzle being operable to cause a pressure drop across the nozzle to facilitate measurement of at least one of: a steam quality associated with the outlet stream; and a mass flow rate of steam vapor in the outlet stream.
15. The apparatus of claim 1, further comprising a controller operably configured to receive signals representing pressures and temperatures for determining at least one of: a steam quality associated with the outlet stream; a mass flow rate of the feedwater stream; and a mass flow rate of steam vapor in the outlet stream.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) In drawings which illustrate embodiments of the invention,
(2)
(3)
(4)
(5)
(6)
(7)
(8)
DETAILED DESCRIPTION
(9) Referring to
(10) In one example embodiment the feedwater inlet stream may have a total suspended solids (TSS), total oil & grease (TOG), total organic carbon (TOC), total dissolved solids (TDS), silicate (Si), total alkalinity (Alk), and total hardness (calcium carbonate) content, each of which may fall within a certain range typical of the hydrocarbon recovery industry. For example the feedwater stream may have one or more properties such as, a total alkalinity (e.g., M-Alk) of at least about 200 mg/l (e.g., measured using methyl orange as a pH indicator), a total suspended solids concentration of at least about 2 mg/l, a total dissolved solids concentration of at least about 500 mg/l, a silicate concentration of at least about 10 mg/l, and a hardness of at least about 0.1 mg/l. In other embodiments, different impurities may be present in the feedwater stream.
(11) The steam generator 100 also includes a tubing circuit 104 in communication with the inlet 102. The tubing circuit 104 is housed within a chamber 108 and in this embodiment the tubing circuit 104 comprises plurality of tubing sections 110 coupled together by tubing bends 112 to provide a folded tubing circuit extending through the chamber to an outlet 106. In other embodiments, the tubing circuit 104 may include more than one tubing circuit extending between the inlet 102 and outlet 106 for providing a greater steam generating capacity. Commonly in embodiments where the tubing circuit 104 includes multiple parallel tubing circuits, the tubing circuits may be housed in a common chamber and a single heat source, such as the heat source 120 may deliver the heat flux to each of the tubing circuits. The tubing sections 110 and tubing bends 112 have metal walls 116 that define a substantially un-rifled bore 118 for carrying the feedwater stream through the steam generator 100. The tubing circuit 104 is in thermal communication with a heat source 120 that delivers a heat flux 122 to the feedwater stream through the metal wall 116 of the tubing circuit to generate steam by causing evaporation of feedwater within the tubing circuit. Un-rifled tubing is usually supplied as seamless steel tubing generally having an un-contoured bore, which may have some surface roughness introduced during fabrication, but may otherwise be described as having a smooth bore.
(12) Rifled bore tubing operates in a generally similar manner to the rifling in gun barrels in that the grooves have a twist that imparts a spin to the fluids passing though the tubing. Ribs or other contours may produce similar effects to rifling grooves. As noted above, the use of rifled bore tubing has been suggested for steam generation from feedwater including impurities and particularly for generation of high steam quality from such a feedwater. However incorporation of rifled tubing in the tubing circuit 104 is associated with substantial additional cost. Importantly, the inventors have discovered that the use of rifled or ribbed tubing is not required for cooling the tubing circuit 104 and for reducing precipitation of impurities on the metal walls 116 of the tubing circuit. From the standpoint of tube cooling, which is commonly believed to require wall wetting by a liquid portion of the feedwater stream, the inventors have discovered that multi-phase fluid and not just the liquid phase portion will help cool the tube even at high steam qualities, and accordingly, saturated steam itself can act as a cooling fluid, for example, when the tube temperature exceeds the temperature of the steam. Accordingly, it is the steam and water mixture which absorbs and transports the heat from the tube wall and not just the water (liquid phase) portion as was previously believed.
(13) In the embodiment shown, the steam generator 100 also includes a controller 124 for controlling operation of the steam generator. The controller 124 includes an output 126 for producing a control signal for controlling a firing rate of the heat source 120, thereby controlling the heat flux 122 delivered to the feedwater stream. The controller 124 also includes an output 128 in communication with a flow controller 130 for controlling a flow rate of the feedwater inlet stream received at the inlet 102. The flow controller 130 may control flow by controlling a pump rate of a pump (not shown) in communication with a storage tank holding feedwater, for example.
(14) In one embodiment, the controller 124 is configured to control at least one of a flow rate of the feedwater stream and the heat flux 122 to cause generation of an outlet stream at the outlet 106 that includes a steam portion and liquid phase portion such that the liquid phase portion is less than about 20% of the outlet stream by mass. Increasing the heat flux 122 by increasing a firing rate of the heat source 120 has a generally similar effect to reducing the flow rate of the feedwater inlet stream, which both have the effect of reducing the proportion of the liquid phase portion that remains in the outlet stream. The controller 124 thus causes the steam generator 100 to generate an outlet stream having a steam quality of greater than 80%. Advantageously, a substantial portion of the impurities present in the feedwater stream received at the inlet 102 are entrained in the liquid phase portion of the outlet stream and are discharged as part of the outlet stream at the outlet 106. This has the advantage of reducing scaling of the bore 118 of the tubing circuit 104.
(15) The inventors have discovered that even when the steam quality at the outlet exceeds 90%, the temperature rise in the metal walls 116 of the tubing circuit 104 is modest and generally remains below a threshold temperature T.sub.t associated with safe operation of the steam generator 100. For example, for a typical ASTM SA106B/C high pressure seamless steel tube the carbonization temperature limit is about 427 C., above which carbonization of the tube walls may occur leading to a reduction of the wall stresses that the tube can withstand. Accordingly, operating above this carbonization temperature limit would lead to a greater likelihood of failure of the tubing circuit 104. The applicable threshold temperature may thus be a temperature that is lower than the carbonization temperature limit for the tubing circuit 104, to provide an operating margin. In another embodiment the tubing circuit 104 may include tubing that complies with ASTM A 335 P22 specification, which is able to withstand high operating stress at temperatures of up to about 454 C. before allowable stresses begin to reduce with increasing temperatures above 454 C.
(16) In the embodiment shown in
(17) The conditions at the walls 116 of the tubing circuit 104 that permit generation of an elevated steam quality outlet stream at the outlet 106 are described further with reference to
(18) In this example the bore 118 is shown having a layer of scale 204 that has accumulated on the bore. The constitution of the scale layer 204 depends on the actual impurities and combinations of impurities in the feedwater inlet stream and may also generally vary in thickness and constitution along the tubing circuit 104, with some portions of the tubing circuit being more susceptible to scale accumulation due to the conditions to which these specific tubing portions are subjected.
(19) A temperature profile associated with the wall portion 200 is shown graphically at 210 and represents temperature values T taken at various locations x through the wall taken along the cross section line A-A. Equivalent thermal resistances associated with the heat flux 122 in flowing through the wall portion 200 are shown at 220.
(20) The highest temperature T.sub.wo is the outside wall temperature (in this example the effect of outside wall fouling has been omitted) and the wall 116 may be represented as a thermal resistance R.sub.w. The inside wall temperature T.sub.wi at the bore 118 is thus lower than the temperature T.sub.wo due to the resistance R.sub.w of the metal wall 116. The effect of the scale layer 204 is to add thermal resistance R.sub.s which further lowers the temperature T.sub.si at the inside portion of the scale layer in communication with the feedwater stream 202. The scale layer 204, if present, would thus have the effect of increasing the required outside wall temperature T.sub.wo for a desired steam quality level and may increase T.sub.wo beyond the temperature threshold T.sub.t as described above.
(21) A final resistance to the heat flux is the internal convective heat transfer coefficient between the scale layer 204 and the feedwater, which is represented by a resistance R.sub.f in
(22) The effect of the resistance R.sub.s due to the scale layer 204 is thus an important factor in safe operation of a steam generator 100 in an operating range such that the outside wall temperature T.sub.wo remains below the threshold temperature T.sub.t. The actual thermal resistance R.sub.s for any particular scale layer 204 is difficult to predict and generally depends on the thickness of the layer, the constituents of the scaling materials, and the porosity of the scale accumulation, for example.
(23) It is widely held that scale accumulation is significantly accelerated at high steam quality, since impurities are concentrated in any remaining liquid phase portion of the stream and it is believed that such impurities precipitate out onto the wall surfaces. While steam generation using carefully treated feedwater may avoid such scale accumulation due to elimination of impurities, in practice elimination of impurities is impractical and costly. Steam generation using feedwater having significant levels of impurity is more common, particularly in hydrocarbon recovery operations where regulations require use of brackish water and recycled water and limit fresh water use.
(24) Scale accumulation has been thus far believed to be a limiting factor in production of high quality steam in a steam generator, unless costly measures to avoid scaling and/or reduce wall temperature are implemented (see for example Berruti US Patent publication 2011/0017449).
(25) In contrast, the inventors have established that no such significant acceleration of scale accumulation occurs at steam qualities higher than 80%, and that ribbed or rifled tubing is not required for operation of the steam generator 100 to produce elevated steam qualities above 80% and more particularly 90% and beyond. Importantly, the incorporation of rifled tubing in the tubing circuit 104 would represent a significant added cost to the steam generator 100 and such rifling may also present an impediment to pigging of the tubing circuit, in which a tool is launched through the tubing circuit to clear potential blockages. In the embodiments disclosed herein rifled or ribbed tubing is not required to provide for contaminant concentration in the liquid phase portion of the stream.
(26) Furthermore, in contrast to another widely held view that wetting of the bore 118 of the tubing circuit 104 by the liquid portion is essential (see for example Berruti referenced above), the inventors have established that even under conditions where portions of the bore 118 of the steam generator 100 are dry or substantially dry (i.e. steam quality at or approaching 100%), the threshold wall temperature T.sub.t would generally not be exceeded simply by operating the steam generator 100 at such elevated steam quality levels. The inventors have established that operating the steam generator 100 at elevated steam quality levels at worst results in a moderate increase in outside wall temperature T.sub.wo of a few degrees, which generally remains well within the threshold temperature T.sub.t over an operating period of interest. Such an operating period may be defined in terms of a periodic maintenance schedule, for example and may extend over months or even years.
(27) Referring to
(28) Steam Generating System
(29) A simplified steam generating system embodiment for use in a SAGD in situ hydrocarbon thermal recovery operation is shown in schematic view in
(30) Referring to
(31) The cooled produced water stream from the heat exchanger 404 is received at an inlet of a skim tank 406. The skim tank 406 provides a sufficient volume to permit a residence time in the skim tank that facilitates further cooling of the produced water to meet pipeline temperature specifications. The skim tank 406 may also facilitate separation of some of the residual hydrocarbons by skimming. The skim tank 406 may also have an inlet for receiving other water streams, such as may be recovered during further processing of the produced hydrocarbon stream by the separator 402 for example.
(32) The skim tank 406 includes an outlet for drawing off the produced water stream, which is then directed to an inlet of a filter 408. The filter 408 may include an induced static flotation filtration stage and an oil removal filtration stage, for example. The filter 408 produces a filtered produced water stream at an outlet, which is then transported to an inlet of a conditioning tank 410.
(33) In one embodiment the conditioning tank 410 may be a warm lime softening tank that facilitates removal of constituents such as calcium, magnesium, and silicate to reduce the hardness of the produced water stream while the water stream is still at elevated temperature (i.e. at about 50 C. to 60 C.). In this embodiment the conditioning tank 410 includes an additive inlet for facilitating introduction of additives. In general additives to be introduced into the produced water may be selected on the basis of the constitution of the produced water stream, and may include lime, magnesium oxide, and polymers, for example.
(34) For some in situ thermal flood recovery operations, a pH of the feedwater stream will generally be between 8 and 10. In embodiments, where the produced water has a low pH, conditioning may involve increasing the pH of the produced water. For example, if the produced water has a pH of less than 9, the produced water in the conditioning tank 410 may be conditioned to increase the pH to a pH of at least about 9 to prevent precipitation of impurities from the liquid phase portion during steam generation.
(35) A conditioned produced water stream is drawn off from an outlet of the conditioning tank 410, and transported to a feedwater tank 412, which has inlets 414 for receiving various water streams that make up the feedwater stream for the generation of steam. In the embodiment shown in
(36) In the embodiment shown in
(37) A second steam generator 450 is configured as a heat recovery steam generator (HRSG) and includes an inlet 452 for receiving a heated gaseous flow discharged as an exhaust gas produced through conversion of a primary fuel source to provide energy for other processes, such as generation of electricity for example. The HRSG 450 includes an economizer section 454 for heating the feedwater in a tubing circuit 456 and an evaporator section 458 for causing evaporation of the feedwater stream to generate an outlet stream of high steam quality. In other embodiments, the second steam generator may be otherwise configured to the steam generator 450 shown in
(38) The tubing circuit 436 of the OTSG 428 and the tubing circuit 456 of the HSRG 450 may be configured and operated generally as described above in connection with the embodiment shown in
(39) Advantageously, generating high quality steam in the OTSG 428 or HRSG 450 has one or more of the following advantages of reducing feedwater treating costs, generating less disposal water, lowering CO.sub.2 emissions, improving water recycle ratio, and lowering required make up water.
(40) Steam Quality Measurement
(41) When operating a steam generator such as the steam generator 428 shown in
(42) Referring to
(43) The measuring system 500 also includes a pressure sensor 512 for measuring the feedwater pressure P.sub.2 at the outlet 446 of the OTSG steam generator 428, an outlet flow nozzle or orifice plate 514 and associated differential pressure sensor 516 for measuring the pressure drop P.sub.2 across the nozzle, and a temperature sensor 518 for measuring the temperature T.sub.2 of the outlet stream at the outlet 446. The sensors 512, 516, and 518 are also each in communication with the controller 510.
(44) Referring to
(45) At block 606, the feedwater mass flow rate is determined. The feedwater inlet stream is a single phase liquid stream having a mass flow rate in {dot over (m)}.sub.FW, which for a nozzle such as the nozzle 514 may be written as:
{dot over (m)}.sub.FW=k.sub.1{square root over (.sub.1.sub.1)};Eqn 1
where k.sub.1 is a constant associated with the inlet flow nozzle for the liquid feedwater stream. In general k.sub.1 is dependent on a constitution of the fluid flowing through the nozzle and may be given by:
k.sub.1=C.Math.A.Math.Y{square root over (2)}.Eqn 2
(46) In Eqn 2, C is the flow coefficient, A is the area of the nozzle 504, and Y is the compressibility factor. In other embodiments, an alternative flow meter such as a coriolis flow meter, which provides mass flow rate and density of a fluid flowing through the tube, may be used to determine the mass flow rate of the feedwater.
(47) Through conservation of mass, the mass flow rate of the feedwater {dot over (m)}.sub.FW at the inlet 444 and the mass flow rate of the outlet stream {dot over (m)}.sub.OS at the outlet 446 should be equivalent, i.e.:
{dot over (m)}.sub.OS={dot over (m)}.sub.FW=k.sub.2{square root over (.sub.mP.sub.2)};Eqn 3
where k.sub.2 is a constant for the outlet flow nozzle 514 and is associated with the constitution of the outlet stream, which includes liquid and vapor phase portions, and .sub.m is the effective density of the mixture of liquid and vapor phases. Again, in other embodiments, an alternative flow meter such as a coriolis flow meter may be used to provide the flow rate.
(48) Eqn 3 may be rewritten as:
(49)
(50) The density .sub.m of the mixture of liquid and vapor phases is a function of steam quality x and depends on the flow regimen, which for high steam quality may be assumed to be an annular mist flow. Assuming homogenous flow and no slip (i.e. different flow velocities) between the vapor and liquid phases in the outlet stream:
(51)
where .sub.g is the density of saturated vapor in the outlet stream, and .sub.L is the density of saturated liquid in the outlet stream, which may be determined from a correlation or from steam tables. At block 608 of the process 600 estimates for .sub.g and .sub.L are produced from correlations or from steam tables. For example, .sub.g and .sub.L are both functions of pressure and may be determined by steam tables, tabulations or other correlations.
(52) Substituting the expression for .sub.m from Eqn 4 in Eqn 5 yields:
(53)
where: x is the estimated steam quality; C.sub.f is a correction factor; and {dot over (m)}*.sub.st is the mass flow rate of dry steam vapor at assumed quality of x=100% given by:
{dot over (m)}*.sub.st=k.sub.2{square root over (.sub.gP.sub.2)}.Eqn 7
(54) The correction factor C.sub.f may be used as a calibration factor for adjusting the value of x to be in agreement with steam quality measurements provided by other measurements such as a conductivity measurement, for example. In general C.sub.f would be close to unity and use of the constant C.sub.f in equation 7 may also be omitted if no independent calibration is to be performed.
(55) At block 610, the steam quality x is determined from the values of .sub.g and .sub.L above and the demined mass flow rates of the feedwater inlet stream and the dry steam vapor in accordance with Eqn 6 above.
(56) In other embodiments, where it is desirable to take the slip ratio between the liquid and gas phases into account, an alternative to Eqn 6 may be written as follows:
(57)
where S is the slip ratio between phases (i.e., the ratio of the velocity of the gas phase to the velocity of the liquid phase). Various correlations from published literature or empirical correlations from actual operating data can be used for the slip ratio S. However, in general, at high steam quality the slip ratio S between phases is close to unity and thus Eqn 8 and Eqn 6 should provide substantially similar results under high steam quality conditions.
(58) Advantageously, the online steam quality measuring system 500 provides a continuously updated quality measurement that should be sufficiently precise for monitoring high steam quality levels in the output stream produced by the steam generator 428 at the outlet 446. The steam quality measuring system 500 may be similarly implemented on the HRSG 450 shown in
(59) Referring to
Alternative Steam Quality Measurement Embodiments
(60) Selection of the correction factor C.sub.f in Eqn 6 above may provide reasonable steam quality results in a narrow range. The correction factor may be selected to provide accurate results for a steam generation flow at a specific temperature and steam quality. For example, the correction factor may be selected to provide an accurate steam quality at an 80% steam quality level for a steam generation flow having the following characteristics: about 335000 pounds/hour and a temperature of about 310 C. For operation at 90% actual steam quality, the results provided by Eqn 6 may be in error by about 3.7% and for operation at a steam quality of 95% the error may be about 6%.
(61) Various calculation methods that may be used to implement block 610 of the process 600 (shown in
(62) Method I
(63) Substituting Eqn 7 in Eqn 6, and applying the correction factor only to a first term of the equation yields the following alternative steam calculation embodiment:
(64)
(65) For the steam generation flow example above, at 90% actual steam quality the results provided by Eqn 9 may still be in error by about 3.6% and at 95% actual steam quality the error may be about 5.8%.
(66) Method II
(67) In another embodiment the correction factor C.sub.f in Eqn 6 is replaced by a correction factor that is dependent on steam quality x. From Eqn 6, replacing the correction factor C.sub.f with a correction factor (1+A(1x)) yields:
(68)
where the term in square brackets in Eqn 10 is obtained by substituting Eqn 7 in Eqn 6 and simplifying. For the steam generation flow example above, at 90% actual steam quality the results provided by Eqn 10 reduce the error to about 0.06% and at 95% actual steam quality to about 0.05%.
Method III
(69) As an alternative, a correction to the k.sub.2 term may also be used in place of the correction factor C.sub.f in Eqn 9 above. An alternative steam calculation embodiment based on Eqns 6 and 7 may be expressed as follows:
(70)
where A is an alternative correction factor and the constant k.sub.2 for the outlet flow nozzle 514 is modified and is now written as a function of steam quality x. Rewriting Eqn 11 yields:
(71)
(72) From Eqn 12, writing:
(73)
and substituting Eqns 13-15 in Eqn 12 yields:
y=.sub.1.sub.2k.sub.2.sup.22.sub.2k.sub.2Ay.sub.2A.sup.2y.sup.2.Eqn 16
(74) Rearranging Eqn 16, and setting y=0 yields the following quadratic in y:
0=.sub.2A.sup.2y.sup.2+(2.sub.2k.sub.2A+1)y+.sub.2k.sub.2.sup.2.sub.1;Eqn 17
which has roots:
(75)
and thus yields the following expression for x:
(76)
(77) The correction factor A may be determined from Eqn 19 for an instantaneous set of actual operating conditions and by determining an actual co-incident steam quality by analytical methods, such as by comparing the ion content of collected condensate to the ion content of the feedwater, for example. The actual co-incident steam quality value for x, along with the set of actual operating conditions provides the necessary information for determining A from Eqn 19.
(78) For the steam generation flow example above, at 90% actual steam quality the results provided by Eqn 19 reduce the error to about 0.005% and at 95% actual steam quality the error is reduced below 0.005%.
(79) In an alternative embodiment, the correction factor A may be calculated for a plurality of different values of steam quality x and an approximate correction factor A may be used for a particular range of steam quality x.
(80) In yet another embodiment the correction factor A may be expressed as a function of temperature T:
A=Af(T);Eqn 20
(81) For example, A may be adjusted on a linear basis to account for changes in Temperature
A=9.0254T;Eqn 21
where T is the change in temperature from a reference temperature associated with a reference set of operating points for the outlet flow nozzle or orifice plate 514 and A is the resulting temperature correction to the correction factor A. Alternatively, the correction factor A may be adjusted based on a polynomial, for example:
A=a.sub.1T+a.sub.2T.sup.2;Eqn 22
where a.sub.1 is a linear coefficient (for example, 9.0254 as in Eqn 21), and a.sub.2 is a coefficient for the higher order temperature correction term in T.sup.2. Similar equations to Eqn 21 and Eqn 22 may also be written for providing a correction to A on the basis of pressure, or steam quality, for example.
(82) While specific embodiments of the invention have been described and illustrated, such embodiments should be considered illustrative of the invention only and not as limiting the invention as construed in accordance with the accompanying claims.