2. Materials and Methods
The temperature, pressure and velocity measurements in the diagram in
Figure 2 were carried out according to the methods approved in the Eurasian Economic Union. However, the authors were also guided by the recommendations of the European Union in the field of measurement uncertainty and the methodology used. Measuring devices that were installed in the experimental boiler room according to
Figure 2: pressure gauges showing in place and electric contact, Karat-520 water flow meter (produced by the limited liability company “Uraltechnologiya”, a member of the NPO KARAT group of companies, Yekaterinburg City, Russia), Petroll fuel meter (“Petroll” company, Moscow, Russia), thermocouples for measuring the temperature of steam and gases in different parts of the coils, testo-320 gas analyzer (German Corporation Testo SE & Co. KGaA, Lenzkirch, Germany) for analyzing the composition of flue gases. With the help of the above devices, the main parameters were measured for steam (pressure and temperature), water and fuel consumption, as well as the main indicators for flue gases (temperature, O
2).
During operational testing, the MTPB was operated in two modes to compare the results. A schematic diagram of the MTPB is shown in
Figure 2. The first mode represents the operation of one boiler (in
Figure 2, Symbols 1 and 2) and feed pumps (in
Figure 2, 21, 22 and 17, 18) in turn.
The development of the experimental research methodology is based on the estimation of the uncertainty arising from each of its sources. For example, the diagram in
Figure 2 shows devices for measuring flow, temperature, and pressure. To determine the total uncertainty, you need to define each one separately, and then use the formulas for the constructed model.
In the case of the authors’ research, the method itself contributes to the uncertainty, so this contribution can be expressed as a value that affects the final result. In this case, the uncertainty of the parameter is expressed directly in units of y, and the sensitivity coefficient ∂y/∂x = 1.
The result of the steam velocity measurements—the arithmetic mean of 4.147 m/s is characterized by a standard deviation of 0.04 m/s. The standard uncertainty u(y) associated with precision under these conditions is 0.04 m/s. The model of this measurement in this case can be expressed by the formula y = (calculated result) + ε, where ε reflects all random effects under the given measurement conditions, with the sensitivity coefficient ∂y/∂x = 1.
Calculate the arithmetic mean of the steam velocity from all measurements at a given point:
After calculations using Equation (1), we get the value w = 4.147 m/s.
For sources of random uncertainty, we calculate the uncertainty by type A:
Calculations using Equation (2) gave the result .
For sources of systematic uncertainty (instrument error) calculating the uncertainty by type B:
Calculations using Equation (3) gave the value of
Calculate the total standard uncertainty:
Using Equation (5), we get the value
For the confidence probability (coverage probability) P = 0.95 (it is recommended in the Manual calculation of uncertainty) setting the coverage factor k = 2 and calculate the extended measurement uncertainty:
Finally, the total value of the extended uncertainty is. The total value of the extended uncertainty is in case of k = 2. The purpose of using u is to show the confidence interval of the uncertainty band near the pressure measurement result, within which one can expect to find most of the distribution of pressure values that could reasonably be attributed to the measured value.
According to the Guidelines for measurements and their uncertainties in the countries of the Eurasian Economic Union, a maximum value of 5% is accepted for experimental data, so the results obtained fall into the confidence interval.
The found uncertainty value is subject to revision only in the process of revalidation of the analysis methodology. Validation of the measurement method was carried out during repeated tests of the boiler unit in the conditions of operation at the oil and gas field in the far north. To ensure that the performance indicators obtained during the development of the methodology are achieved with its specific application, the methodology is validated. In the case of the author’s research, the technique was conducted in an interlaboratory study, which resulted in additional data on the effectiveness.
At this stage, we know the distribution functions of all the parameters of the model, so, assuming that the parameters correspond to the distribution functions, we calculated the validation error shown in
Figure 3 and
Figure 4, and Error = 895.5186 (Normal), Error = 177.7951 (Lognormal). Charts are made using MatLab (MathWorks developer, Natick, MA, USA).
Similarly, the uncertainty of other variables, such as temperature and pressure, was evaluated. The calculated value of the correction introduced in the measurement result, necessary to take into account the influence of the heat sink on the thermometer body and the thermal resistance between the sensor element of the thermometer and the channel wall, is 0.025 °C. The uncertainty of the correction value using thermal modeling lies in the range from 0.005 to minus 0.005 °C. There are reasons to assume that the probability density of uncertainty has a uniform distribution. The certificate of verification of the used measuring device indicates its confidence error is equal to 0.01 °C with probability 0.95 (2σ).
Thus, we consider the case of direct measurements, which does not require the representation of the measured value in the form of a functional dependence. In this case, the uncertainty of the measurement result can be represented as the sum of the uncertainties caused by the influence of various factors, which can be determined on the basis of all available information. At the same time, it can be assumed that all the components of uncertainty are not correlated. The following sources of uncertainty of the measurement result can be determined from the experimental condition:
- (1)
Random component of the thermometer reading Ti, caused by a random change in all possible effects affecting the measurement result.
- (2)
Inaccuracy of the method for estimating the correction introduced to account for the effect of the heat sink effect on the thermometer body.
- (3)
The probabilistic nature of the estimation of the error of the thermometer. Total standard uncertainty
of temperature measurement can be described by the following relation:
where
—estimation of the random component of the total uncertainty of the temperature measurement result, estimated by type A;
—estimation of the uncertainty component of the temperature measurement result due to the uncertainty of the correction introduced to account for the heat sink effect on the thermometer body;
—estimation of the uncertainty component of the temperature measurement result due to the uncertainty of the thermometer error estimation.
The random component of the uncertainty of the measurement result of the temperature measured by the type A.
We determine the estimate of the result of temperature measurements in the channel of the metal block as the arithmetic mean of the results of 30 observations:
Getting the value
Defining the standard uncertainty
by type A rating T:
Getting the value
The correction that takes into account the presence of a heat sink is added to the arithmetic mean of the temperature: .
Estimates of standard measurement result uncertainties caused by the uncertainties of the correction introduced to account for the heat sink effect and the thermometer error are determined by type B.
Estimation of uncertainty
correction introduced to account for the effect of the heat sink on the thermometer body. From the general reasoning and the experimental data obtained, it is known that the uncertainty of the correction value lies within the limits of ±0.005 °C. That is, the upper bound b+ the distribution of the correction is a plus value 0.005 °C, and the bottom one, b
− is the value of −0.005 °C. In this case, the standard uncertainty of the correction is
can be determined from the relation:
Getting the value = .
Estimation of uncertainty measurement result caused by the probabilistic nature of the thermometer error estimation. In the certificate of verification of the thermometer, its confidence error is indicated, equal to 0.01 °C with probability 0.95, which corresponds to the Student’s coefficient equal to 1.96. It follows that the standard uncertainty of the thermometer is u(δ) equal to = 0.01/1.96 = 0.005 °C, where 1.96—Student’s coefficient, corresponding to 95% the confidence level for a normal distribution.
The total standard uncertainty is calculated using Equation (6).
The total value of the extended uncertainty is in case of k = 2. The purpose of using u is to show the confidence interval of the uncertainty band near the temperature measurement result, within which one can expect to find most of the distribution of temperature values that could reasonably be attributed to the measured value.
The calculated value of the correction introduced into the measurement result, which is necessary to account for the influence between the pressure gauge sensor element and the channel wall, is 0.05 MPa. The uncertainty of the correction value using thermal modeling lies in the range from 0.01 to minus 0.01 MPa. There are reasons to assume that the probability density of uncertainty has a uniform distribution. The certificate of verification of the used measuring device indicates its confidence error equal to 0.02 MPa with the probability of 0.95 (2σ).
Thus, we consider the case of direct measurements, which does not require the representation of the measured value in the form of a functional dependence. In this case, the uncertainty of the measurement result can be represented as the sum of the uncertainties caused by the influence of various factors, which can be determined on the basis of all available information. At the same time, it can be assumed that all the components of uncertainty are not correlated. The following sources of uncertainty of the measurement result can be determined from the problem condition:
- (1)
The random component of the pressure gauge readings caused by a random change in all possible effects affecting the measurement result.
- (2)
The probabilistic nature of the estimation of the error of the pressure gauge. Total standard uncertainty
of temperature measurement can be described by the following relation:
where
—estimation of the random component of the total uncertainty of the pressure measurement result, estimated by type A;
—estimation of the uncertainty component of the pressure measurement result due to the uncertainty of the type B thermometer error estimation.
Uncertainty of the random component of the measurement result of the pressure gauge, estimated by type A.
We determine the estimate of the result of pressure measurements in the channel of the metal block as the arithmetic mean of the results of 30 observations:
Getting the value
Defining the standard uncertainty
by type A rating p:
Getting the value
Estimates of standard measurement result uncertainties caused by the uncertainties of the correction introduced to account for the error of the pressure gauge are determined by type B.
Estimation of uncertainty the measurement result caused by the probabilistic nature of the thermometer error estimation. In the certificate of verification of the thermometer, its confidence error is indicated, equal to 0.02 MPa with probability 0.95, = 0.01 MPa.
The total standard uncertainty is calculated using Equation (10):
Finally, the total value of the extended uncertainty is in case of k = 2. The purpose of using u is to show the confidence interval of the uncertainty band near the pressure measurement result, within which one can expect to find most of the distribution of pressure values that could reasonably be attributed to the measured value.
Experiments were carried out on direct-flow coil-type boilers to measure the length of the torch, in particular, its initial section, as well as the height of the intense combustion zone. During the experiments, the methods approved for operation and measurement of parameters in high-temperature installations were used, for example, errors of primary and secondary measuring devices were multiplied. The discrepancy between the results on measuring the temperature and length of the torch of the theoretical and experimental studies tended to 3%, which could be explained by some error when conducting experiments at high temperatures in boiler installations, for example, re-emission and high dust content of the torch in the furnace space. Our novel boiler plant proposal, which includes coil-type steam boilers, is characterized by an increased heat transfer coefficient in the convective part, consisting of two coaxial cylinders (
Figure 5), which makes it possible to turbulize the flue gas flow.
This also intensifies heat transfer in an annular channel with a variable cross section, reducing the temperature of the gases at the outlet. A distinctive feature of the boiler unit is the ratio of the geometric dimensions of the boiler—the height of the furnace H
F, the diameters of the coaxial cylinders of the coils D
1 and D
2, which are defined as H
F = (2…2.1)·D
1, H
F = (1.7…1.9)·D
2, moreover, similar characteristics are presented by Kuznetsov [
24] for industrial medium pressure boilers and Lummi [
25] for low pressure boilers.
The intensification of heat transfer in the boiler is achieved by using coils of different diameters. Flue gases move along an annular channel with a variable cross section. With this arrangement, the total heat exchange surface is increased. The first coil has a larger diameter, which allows the coolant to obtain more heat and accelerate the vaporization process due to the amount of heat received and the narrowing of the flow area. An additional area of heat exchange is provided by a spiral coil installed on the ceiling of the boiler, this is stipulated in the work of Sidelkovsky and Yurenev [
26].
Flue gas velocity was measured in laboratory conditions using an experimental stand. The aerodynamic characteristics of the fan were controlled by a frequency drive of the electric motor. The experiment was carried out with different diameters of the flue gas duct formed by the coils. The flue gas velocity is calculated from the pressure difference measured at the inlet and outlet of the flue gas duct, more information about this can be found in the work of Trembovlya et al. [
27]. Based on the results of the experiment, we chose the optimal ratio between the aerodynamic drag of the gas-air duct and the maximum value of the flue gas velocity. The increased flue gas velocity and increased heat transfer area increased the convection heat transfer coefficient, increasing the heat transfer coefficient (6):
where
is the beam thermal efficiency coefficient;
and
are the heat transfer coefficients by convection and radiation in the convective part, respectively.
The average logarithmic temperature head of the built-in air heater increases due to the difference between cold (T
c.a.) and hot air (T
h.a.). In addition, the temperature difference
is increased due to the upper supply of the air flow movement when using the fan compared to the lower supply, without additional power consumption for the fan drive. With an increase in ΔT by 120%, the air flow rate in the fan-boiler section increases by 122%. Under the same conditions, electricity costs increase by 0.80–0.90%. The thermal stress of the boiler decreases due to the heating of the air passing through the built-in air heater. Zykov [
28] offered a variety of air heating options and Lipov et al. [
29] showed the need to use air heating for low-pressure boiler units.
Next, we present the results of studies of the aerodynamic characteristics of the torch, as well as measurements on the aerodynamic stand. The length L
f and the temperature of the torch on the length of the torch L
f during the operation of the steam generator of the coil type. The data are given depending on the steam capacity of the boiler unit. Rated load of the boiler D
nom of steam per second. In addition, the data are provided when burning crude oil (
Table 1).
4. Experimental Data
In December 2020, the authors tested a similar installation at an oil and gas field in the far north. The data obtained during these experiments agree very well with the calculated data, so the authors decided to present these data in
Table 2 and
Figure 7. The calculations for the coolant velocity based on experimental and theoretical calculations using mathematical modeling are presented in
Table 2.
When constructing a mathematical model of the vaporization process, the theory of boiling and vaporization modes in coils was confirmed. However, the study showed that there is a high probability changes of the last mode dispersion when near a wall is formed a steam film, the conductivity decreases and the burnout of the tube wall, if not reduce the heat flux density applied to the coil. The amount of heat that is released into the environment in the presence of external and internal factors: poor quality of the coolant, intense combustion, wear of pipes, can serve as a catalyst and cause serious damage to the coils of the considered direct-flow boiler.
Mode 1. Experimental values of boiler operation 1 and 2, feed pumps 17, 18 and 21, 22, respectively,
Figure 2 (
Table 3 and
Table 4).
The correlation coefficient showing the relationship between the steam temperature and the fuel consumption for steam boiler No. 1 (
Figure 8a) is 0.948, which indicates a strong relationship between these values. A positive correlation close to unity allows us to assert that an increase in one value affects the growth of the second, what is mentioned in the work of Pustylnik [
30]. The correlation coefficient showing the relationship between the steam pressure and the fuel consumption of boiler No. 1 (
Figure 8b) is also 0.948. A similar conclusion about the relationship between the steam temperature and the fuel consumption was taken to be valid for these values.
The correlation coefficient showing the relationship between the steam temperature and the fuel consumption for steam boiler No. 2 is 0.89, which indicates a sufficient relationship of these values. A positive correlation indicates that an increase in one value contributes to an increase in another,
Figure 9.
The correlation coefficient showing the relationship between steam pressure and fuel consumption of boiler 2 is also 0.89. The above conclusion for the considered relationship between steam temperature and fuel consumption is also accepted for these parameters,
Table 4.
Mode 2. Simultaneous operation of two boilers with the inclusion of two feed pumps,
Table 5.
Both boilers and feed pumps are switched on to increase the steam output. All systems were working at full power.
Table 5 shows the results of the experiment.
Figure 10 shows the relationship between temperature, steam pressure, and fuel consumption in the first boiler, respectively.
The correlation coefficient showing the relationship between steam temperature and fuel consumption, as well as the relationship between steam pressure and fuel consumption for steam boiler 1 in the second mode is 0.2306 and 0.2352, respectively. Points 1 and 3 illustrate that with a large difference in vapor pressure, the fuel consumption changed by a small value ΔB = 0.00006 kg/s. A small drop in fuel consumption is associated with a sharp increase in the temperature of the feed water, Δt = 8 °C (18). The increase in the temperature of the feed water reduced the boiler’s need for higher fuel consumption to maintain steam parameters (27):
where
is fuel consumption, kg/s;
is steam capacity, kg/s;
is the enthalpy of steam and feed water, MJ/kg;
is net calorific value of fuel, MJ;
is boiler efficiency, %.
The experimental data also show that the feed water consumption at point 3 increased, which resulted in a sharp jump in all steam parameters at the boiler outlet. In connection with the analyzed corrections for the experimental values of temperature and feed water consumption, the smaller relationship between steam parameters and fuel consumption is explained.
Figure 11 shows the relationship between temperature, steam pressure, and fuel consumption at the first boiler, respectively.
The correlation coefficient calculated to study the relationship between temperature, steam pressure, and fuel consumption on boiler 2 was 0.6895 and 0.6888, respectively. The experiment on the second boiler was carried out with a gradual increase in all parameters of the coolant; therefore, a stronger relationship is traced between temperature, steam pressure, and fuel consumption.
Thus, the analysis of the dependences of steam parameters and fuel consumption showed that the low storage capacity of once-through boilers is reflected in the temperature and pressure of the steam with changes in fuel consumption. Depending on the operating factors, the heating surface of the superheating zone changes. To maintain constant parameters of the coolant, it is necessary to maintain the ratio of the flow rate of feed water and fuel. In an earlier work, [
31] the authors Osintsev et al. of the article proved a similar effect. In their work [
31], the authors investigated a new design of a boiler unit that was part of an energy technology complex based on renewable energy sources. When conducting experimental tests, the authors proved that in direct-flow boilers, the working point (the ratio of parameters: temperature and pressure), at which the vaporization process begins, does not have a constant place (as it happens in boilers with drums), which in turn affects fuel consumption (you need to constantly monitor the flame). Therefore, the process is “floating”. With the help of graphs and calculations based on the data collected during the commissioning tests, the researchers were able to find a good ratio between fuel consumption and feed water to stabilize the boiler operation. The work described [
31] was not only applied in nature, but in the patent for the invention, the authors were able to justify the efficiency of the boiler unit in “floating” modes.
Fuel consumption value is a dynamic characteristic for a once-through boiler. In a direct-flow boiler, the water–fuel ratio is regulated through the temperature and amount of feed water, by returning condensate, and installing a control valve. With low storage capacity, changes in the flow rate, quantity, and temperature of feed water affect the values , which affects the instantaneous change in the fuel consumption value .
Mode 3 (
Table 3) for the first boiler and Mode 4 for the second are recorded in the performance-adjustment chart. In this mode, the outlet coolant is supplied with maximum parameters in terms of temperature and pressure at optimal fuel consumption for each boiler.
The coil-type boiler model has no drum. The vaporization process ends in a separator, which is installed outside the boiler. This has a positive effect on the quality of pipes during operation, deposits in the boiler elements form more slowly over time, thereby increasing the service life and reducing economic costs.
In their early works, the authors of the article presented the results of research on the operation of boiler units and heat and power equipment. For example, in [
32] Toropov et al. presented new methods for studying the operation of boiler units, and in [
33] E.V. Toropov et al. showed the possibility of organizing new methods in a new methodological framework. In addition, in [
34], Toropov et al. proposed to use the results of [
33] for low-and medium-pressure thermal power equipment. It should be noted that the paper by Osintsev et al. [
35] shows the possibility of using the results of the work [
33] in order to organize neural network control of combustion processes, including natural gas combustion. Thus, the methodological basis of the article was laid by the authors earlier in the work [
33]. When introducing a new boiler unit to the drilling site, the operating company studied the thermal diagram of the entire production and the indicators of the coolant in each block. This examination confirmed the presence of heat losses to the environment on the lines and the absence of pressure gauges and thermometers. In addition, they confirmed that the connection of the pipelines did not provide the proper volume of the coolant when returning the condensate, which increased the consumption of make-up water. Analysis confirmed the need for modernization of the heating lines. Improvements to the scheme included changing the system of pipelines for returning condensate to the boiler room from the blocks, installing new instrumentation on the lines, insulating the pipelines, and installing an additional insulated tank for collecting condensate.