This paper proposes a correction method, which corrects the actual compressor performance in real
operating conditions to the equivalent performance under specified reference condition. The purpose is to
make fair comparisons between actual performance against design performance or reference maps under
the same operating conditions. Then the abnormal operating conditions or early failure indications can be
identified through condition monitoring, which helps to avoid mandatory shutdown and reduces
maintenance costs. The corrections are based on an iterative scheme, which simultaneously correct the
main performance parameters known as the polytropic head, the gas power, and the polytropic efficiency.
The excellent performance of the method is demonstrated by performing the corrections over real industrial
measurements.
Automatic Structural Optimization of Engine Components Using HCF and TMF Fail...IDES Editor
Modern combustion methods and the constant wish
for an increase in the specific performance results in high
thermal and mechanical loads in modern combustion engines.
In order to shorten the development time, an interactive,
simultaneous execution of design (CAD) and calculation
activities (CAE) is necessary. In this the product must be looked
at in detail and be optimized in various disciplines and in a
harmonized way of procedure to the development progress. In
the initial proactive phase the efficiency of virtual CAEmethods
is high and quickly decreases in the second half of the
development, which shows strongly reactive features. Therefore
a combined HCF (High-Cycle-Fatigue) Failure Analysis and
Optimization and TMF (Thermo-Mechanical-Fatigue) Failure
Analysis and Optimization model is discussed in this paper for
the reduction in the analysis time.
An approach to evaluate the heat exchanger retrofit for installed industrial ...eSAT Journals
Abstract This paper is the first part of a two-part study aiming to introduce a new integrated approach to evaluate the techno-economic value of recuperator retrofit on existing gas turbine engines. The original gas turbines are designed for combined cycles so that the pressure ratios are moderate to secure suitable exhaust temperatures. One way to enhance the thermal efficiency of some gas turbines is by using recuperation to recover some of the exhaust heat. In this part, the developed model is described and implemented for two gas turbine engines so the obtained characteristics are evaluated against the actual data. The new approach will assist users to select the suitable gas turbine models with favorable recuperator characteristics based on a technical and economic prospective. Besides, the performance results are used to design an appropriate shell and tube heat exchanger. Moreover, a new technique has been established to define the typical heat exchanger parameters in order to ensure the highest possible improvements over the original cycles. One of the main features of this method is that it depends only on the velocity of hot and cold heat exchanger streams from which the rest of the heat exchanger design and performance characteristics were derived. Key Words: integrated approach, techno-economic value, recuperation, shell and tube heat exchanger, velocity
Production Optimization using nodal analysis. The nodal systems analysis approach is a very flexible method
that can be used to improve the performance of many well
systems. The nodal systems analysis approach may be used to analyze
many producing oil and gas well problems. The procedure can
be applied to both flowing and artificial
Project Objectives:
To build a representative network model for one OGM(Oil Gathering Manifold) in H Field consists of 4 wells using PIPESIM software.
To match the network model with the field data.
To display & analyze the results after building the model.
Control System Based on Fuzzy Logic in Nutmeg Oil Distillation ProcessTELKOMNIKA JOURNAL
The focus of this research is the application of electronic control on the distillation boiler of
nutmeg oil. The control system is based on fuzzy logic and as the input parameter is temperature and
vapor pressure. The temperature parameters are set in the range 80-120ºC, and the vapor pressure
parameters are set in the range of 1-2.5 atmospheres. The output parameter is the time required in the
distillation process. The optimal values of these input and output parameters are embedded in
microcontroller based control. The control responds to the temperature and vapor pressure to select the
gas flow rate at the distillation boiler. This experiment was conducted on a distillation system with a
capacity of 25 kg of crushed dried nutmeg, manually and with control based on fuzzy logic. Conventional
testing requires 6.90 kg of gas and applying fuzzy logic based control requires 5.50 kg of gas. The yield of
nutmeg oil from the distillation process is 2.5 kg conventionally and 2.63 kg with fuzzy logic control. Based
on the optimal time of 16 hours distillation process, there was a decrease of gas consumption by 20.3%.
Automatic Structural Optimization of Engine Components Using HCF and TMF Fail...IDES Editor
Modern combustion methods and the constant wish
for an increase in the specific performance results in high
thermal and mechanical loads in modern combustion engines.
In order to shorten the development time, an interactive,
simultaneous execution of design (CAD) and calculation
activities (CAE) is necessary. In this the product must be looked
at in detail and be optimized in various disciplines and in a
harmonized way of procedure to the development progress. In
the initial proactive phase the efficiency of virtual CAEmethods
is high and quickly decreases in the second half of the
development, which shows strongly reactive features. Therefore
a combined HCF (High-Cycle-Fatigue) Failure Analysis and
Optimization and TMF (Thermo-Mechanical-Fatigue) Failure
Analysis and Optimization model is discussed in this paper for
the reduction in the analysis time.
An approach to evaluate the heat exchanger retrofit for installed industrial ...eSAT Journals
Abstract This paper is the first part of a two-part study aiming to introduce a new integrated approach to evaluate the techno-economic value of recuperator retrofit on existing gas turbine engines. The original gas turbines are designed for combined cycles so that the pressure ratios are moderate to secure suitable exhaust temperatures. One way to enhance the thermal efficiency of some gas turbines is by using recuperation to recover some of the exhaust heat. In this part, the developed model is described and implemented for two gas turbine engines so the obtained characteristics are evaluated against the actual data. The new approach will assist users to select the suitable gas turbine models with favorable recuperator characteristics based on a technical and economic prospective. Besides, the performance results are used to design an appropriate shell and tube heat exchanger. Moreover, a new technique has been established to define the typical heat exchanger parameters in order to ensure the highest possible improvements over the original cycles. One of the main features of this method is that it depends only on the velocity of hot and cold heat exchanger streams from which the rest of the heat exchanger design and performance characteristics were derived. Key Words: integrated approach, techno-economic value, recuperation, shell and tube heat exchanger, velocity
Production Optimization using nodal analysis. The nodal systems analysis approach is a very flexible method
that can be used to improve the performance of many well
systems. The nodal systems analysis approach may be used to analyze
many producing oil and gas well problems. The procedure can
be applied to both flowing and artificial
Project Objectives:
To build a representative network model for one OGM(Oil Gathering Manifold) in H Field consists of 4 wells using PIPESIM software.
To match the network model with the field data.
To display & analyze the results after building the model.
Control System Based on Fuzzy Logic in Nutmeg Oil Distillation ProcessTELKOMNIKA JOURNAL
The focus of this research is the application of electronic control on the distillation boiler of
nutmeg oil. The control system is based on fuzzy logic and as the input parameter is temperature and
vapor pressure. The temperature parameters are set in the range 80-120ºC, and the vapor pressure
parameters are set in the range of 1-2.5 atmospheres. The output parameter is the time required in the
distillation process. The optimal values of these input and output parameters are embedded in
microcontroller based control. The control responds to the temperature and vapor pressure to select the
gas flow rate at the distillation boiler. This experiment was conducted on a distillation system with a
capacity of 25 kg of crushed dried nutmeg, manually and with control based on fuzzy logic. Conventional
testing requires 6.90 kg of gas and applying fuzzy logic based control requires 5.50 kg of gas. The yield of
nutmeg oil from the distillation process is 2.5 kg conventionally and 2.63 kg with fuzzy logic control. Based
on the optimal time of 16 hours distillation process, there was a decrease of gas consumption by 20.3%.
The mean key variable to control the burner performance for safe and efficient operations is the amount of excess air or oxygen which flow to react with fuel. In accordance with Typical Draft Profile in a Natural Draft furnace the numerical results of computing fluid dynamics model of the air flow from the environment to the burner by adjusting the area of air box prototype openings will give the necessary information to adjust the performance of burner as optimum. The model of air box prototype is useful tool in applying similarity theory on another burners̕ designs which depends the air box tools to calibrate the quantity of combustion air flow to the burner.
Key Thermo-Physical Properties of Light Crude OilsVijay Sarathy
Process facilities are equipped with protection measures, such as pressure safety valves (PSV) & as a minimum, PSVs are sized for a fire case. To do so for a pressure vessel containing crude oil a key parameter is the Latent heat of Vaporization [Hv].
For pure components, the Joback’s Method can be employed which uses basic structural information of the chemical molecule to estimate thermo-physical data. However it can be complex for equipment that contains crude oil because the plus fractions [C7+] can contain thousands of straight chain, cyclic & functional groups. Therefore by splitting and lumping the crude fractions, a smaller number of components are arrived at, to characterize and be able to apply Equation of State (EoS) correlations to estimate the fraction’s thermo-physical properties.
Empirical Approach to Hydrate Formation in Natural Gas PipelinesVijay Sarathy
Natural Gas Pipelines often suffer from production losses due to hydrate plugging. For an effective hydrate plug to form, factors can vary from pipeline operating pressure and temperature, presence of water below its dew point, extreme winter conditions & Joule Thomson cooling. In the event hydrates form in the pipeline section, their consequence depends on how well the hydrates agglomerate to grow and form a column. If the pipeline section temperature is only at par with the hydrate formation temperature, the particles do no agglomerate; instead they have to cross the metastable region which is of the order of 50C to 60C, before hydrate formation accelerates to block the pipeline.
Although engineering softwares exist to estimate pipeline process conditions and also generate a P-T hydrate curve, the following tutorial provides a guidance summary to estimate the expected pipeline temperature profile and the associated hydrate formation temperatures.
2008 IFAC World Congress: Oil and gas production optimization - lost potentia...Steinar Elgsæter
The information content in measurements of offshore oil and gas production is often low, and when a production model is fitted to such data, uncertainty may result. If production is optimized with an uncertain model, some potential production profit may be lost. The costs and risks of introducing additional excitation are typically large and cannot be justified unless the potential increase in profits are quantified. In previous work it is discussed how bootstrapping can be used to estimate uncertainty resulting from fitting production models to data with low information content. In this paper we propose how lost potential resulting from estimated uncertainty can be estimated using Monte-Carlo analysis. Based on a conservative formulation of the production optimization problem, a potential for production optimization in excess of 2% and lost potential due to the form of uncertainty considered in excess of 0.5% was identified using field data from a North Sea field.
Numerical Simulation of Flow in a Solid Rocket Motor: Combustion Coupled Pres...inventionjournals
Acomputational study is performed for the simulation of reactive fluid flow in a solid rocket motor chamber with pressure dependent propellant burning surface regression. The model geometry consists of a 2D end burning lab-scale motor. Complete conservation equations of mass, momentum, energy and species are solved with finite rate chemistry. The pressure dependent regressive boundary in the combustion chamber is treated by use of remeshing techniques. Hydrogen and propane combustion processes are examined. Time dependent pressure and burning rate variations are illustrated comprehensively. Temperature and species mass fraction variations are given within the flame zone. Temperature, velocity and density distributions are compared for both constant burning rate and pressure dependent burning rate simulations.
An Update on my Gas Modelling Tools: Addition of New Shale Diagnostics, Gas S...Colin Jordan
In addition to other tools, I have coded a Gas Modelling & Analytics tools (for reservoir engineering) which now includes more/new Shale Decline Models, as well as introduction of non-linear permeability due to gas slippage, stress, or both (i.e coupled models).
Investigation of Significant Process Parameter in Manganese Phosphating of Pi...IJERA Editor
The aim of this study is to determine the most significant parameter such as phosphating bath temperature,
phosphating time,accelerator level on the fatigue life of piston pin material such as 40NiCr4Mo3 by analysis of
variance (ANOVA).The selected three imput parameters were studied at three different level by conducting nine
experiments based on L9 orthogonal array of Taguchi’s methodology.Phosphating bath temperature has
significant effect on fatigue strength followed by phosphating time and accelerator level.
Piping systems associated with production, transporting oil & gas, water/gas injection into reservoirs, experience wear & tear with time & operations. There would be metal loss due to erosion, erosion-corrosion and cavitation to name a few. The presence of corrosion defects provides a means for localized fractures to propagate causing pipe ruptures & leakages. This also reduces the pipe/pipeline maximum allowable operating pressure [MAOP].
The following document covers methods by DNV standards to quantitatively estimate the erosion rate for ductile pipes and bends due to the presence of sand. It is to be noted that corrosion can occur in many other scenarios such as pipe dimensioning, flow rate limitations, pipe performance such as pressure drop, vibrations, noise, insulation, hydrate formation and removal, severe slug flow, terrain slugging and also upheaval buckling. However these aspects are not covered in this document.
Based on the erosional rates of pipes and bends, the Maximum Safe Pressure/Revised MAOP is evaluated based on a Level 1 Assessment procedure for the remaining strength of the pipeline. The Level 1 procedures taken up in this tutorial are RSTRENG 085dL method, DNVGL RP F-101 (Part-B) and PETROBRAS’s PB Equation.
The mean key variable to control the burner performance for safe and efficient operations is the amount of excess air or oxygen which flow to react with fuel. In accordance with Typical Draft Profile in a Natural Draft furnace the numerical results of computing fluid dynamics model of the air flow from the environment to the burner by adjusting the area of air box prototype openings will give the necessary information to adjust the performance of burner as optimum. The model of air box prototype is useful tool in applying similarity theory on another burners̕ designs which depends the air box tools to calibrate the quantity of combustion air flow to the burner.
Key Thermo-Physical Properties of Light Crude OilsVijay Sarathy
Process facilities are equipped with protection measures, such as pressure safety valves (PSV) & as a minimum, PSVs are sized for a fire case. To do so for a pressure vessel containing crude oil a key parameter is the Latent heat of Vaporization [Hv].
For pure components, the Joback’s Method can be employed which uses basic structural information of the chemical molecule to estimate thermo-physical data. However it can be complex for equipment that contains crude oil because the plus fractions [C7+] can contain thousands of straight chain, cyclic & functional groups. Therefore by splitting and lumping the crude fractions, a smaller number of components are arrived at, to characterize and be able to apply Equation of State (EoS) correlations to estimate the fraction’s thermo-physical properties.
Empirical Approach to Hydrate Formation in Natural Gas PipelinesVijay Sarathy
Natural Gas Pipelines often suffer from production losses due to hydrate plugging. For an effective hydrate plug to form, factors can vary from pipeline operating pressure and temperature, presence of water below its dew point, extreme winter conditions & Joule Thomson cooling. In the event hydrates form in the pipeline section, their consequence depends on how well the hydrates agglomerate to grow and form a column. If the pipeline section temperature is only at par with the hydrate formation temperature, the particles do no agglomerate; instead they have to cross the metastable region which is of the order of 50C to 60C, before hydrate formation accelerates to block the pipeline.
Although engineering softwares exist to estimate pipeline process conditions and also generate a P-T hydrate curve, the following tutorial provides a guidance summary to estimate the expected pipeline temperature profile and the associated hydrate formation temperatures.
2008 IFAC World Congress: Oil and gas production optimization - lost potentia...Steinar Elgsæter
The information content in measurements of offshore oil and gas production is often low, and when a production model is fitted to such data, uncertainty may result. If production is optimized with an uncertain model, some potential production profit may be lost. The costs and risks of introducing additional excitation are typically large and cannot be justified unless the potential increase in profits are quantified. In previous work it is discussed how bootstrapping can be used to estimate uncertainty resulting from fitting production models to data with low information content. In this paper we propose how lost potential resulting from estimated uncertainty can be estimated using Monte-Carlo analysis. Based on a conservative formulation of the production optimization problem, a potential for production optimization in excess of 2% and lost potential due to the form of uncertainty considered in excess of 0.5% was identified using field data from a North Sea field.
Numerical Simulation of Flow in a Solid Rocket Motor: Combustion Coupled Pres...inventionjournals
Acomputational study is performed for the simulation of reactive fluid flow in a solid rocket motor chamber with pressure dependent propellant burning surface regression. The model geometry consists of a 2D end burning lab-scale motor. Complete conservation equations of mass, momentum, energy and species are solved with finite rate chemistry. The pressure dependent regressive boundary in the combustion chamber is treated by use of remeshing techniques. Hydrogen and propane combustion processes are examined. Time dependent pressure and burning rate variations are illustrated comprehensively. Temperature and species mass fraction variations are given within the flame zone. Temperature, velocity and density distributions are compared for both constant burning rate and pressure dependent burning rate simulations.
An Update on my Gas Modelling Tools: Addition of New Shale Diagnostics, Gas S...Colin Jordan
In addition to other tools, I have coded a Gas Modelling & Analytics tools (for reservoir engineering) which now includes more/new Shale Decline Models, as well as introduction of non-linear permeability due to gas slippage, stress, or both (i.e coupled models).
Investigation of Significant Process Parameter in Manganese Phosphating of Pi...IJERA Editor
The aim of this study is to determine the most significant parameter such as phosphating bath temperature,
phosphating time,accelerator level on the fatigue life of piston pin material such as 40NiCr4Mo3 by analysis of
variance (ANOVA).The selected three imput parameters were studied at three different level by conducting nine
experiments based on L9 orthogonal array of Taguchi’s methodology.Phosphating bath temperature has
significant effect on fatigue strength followed by phosphating time and accelerator level.
Piping systems associated with production, transporting oil & gas, water/gas injection into reservoirs, experience wear & tear with time & operations. There would be metal loss due to erosion, erosion-corrosion and cavitation to name a few. The presence of corrosion defects provides a means for localized fractures to propagate causing pipe ruptures & leakages. This also reduces the pipe/pipeline maximum allowable operating pressure [MAOP].
The following document covers methods by DNV standards to quantitatively estimate the erosion rate for ductile pipes and bends due to the presence of sand. It is to be noted that corrosion can occur in many other scenarios such as pipe dimensioning, flow rate limitations, pipe performance such as pressure drop, vibrations, noise, insulation, hydrate formation and removal, severe slug flow, terrain slugging and also upheaval buckling. However these aspects are not covered in this document.
Based on the erosional rates of pipes and bends, the Maximum Safe Pressure/Revised MAOP is evaluated based on a Level 1 Assessment procedure for the remaining strength of the pipeline. The Level 1 procedures taken up in this tutorial are RSTRENG 085dL method, DNVGL RP F-101 (Part-B) and PETROBRAS’s PB Equation.
www.vogeldenisenewsome.net
Είδες ΓΟΥΪΛΙ LYNCH ΕΡΧΕΤΑΙ στη χώρα σας; Ρωτήστε τον πρόεδρο Μπαράκ Ομπάμα, ο ίδιος και η εβραϊκή τους ομολόγους του είναι πολύ εξοικειωμένοι με τον Willie LYNCH! Γιατί νομίζετε ότι ο Μπαράκ Ομπάμα και η Μισέλ Ομπάμα τέθηκαν στις Ηνωμένες Πολιτείες ΛΕΥΚΑ σπίτι; Για να ωθήσει το ΓΟΥΪΛΙ LYNCH ΑΤΖΕΝΤΑ!
Our clothing is designed for adults and children (of all ages).
Wild Fun Wear was created with the goal of encouraging environmental and wildlife appreciation through art and fun. Wild Fun Wear shows nature and wildlife living uninhibited, wild and free in imagined self-expression.
“Our aim is to brighten spirits and amuse through the international language of laughter."
Teraz
Irigasi dan Drainase. Bagian 2 Bahan kuliah irigasi bab 5-7 Prodi AgroteknologiPurwandaru Widyasunu
Irigasi dan Drainase. Bagian 2 Bahan Kuliah Irigasi dan Drainase Bab 5-7 Prodi Agroteknologi Faperta Unsoed. Ditulis oleh Bondansari dan Purwandaru Widyasunu. Untuk keperluan pendidikan (For education purpose only). Bahan-bahan kuliah diambilkan dari berbagai buku, data jurnal, Peraturan Pemerintah R.I., dan foto/gambar dan data asal internet tentang Irigasi. Boleh download untuk mahasiswa dan kalangan yang tertarik untuk belajar tentang irigasi dan drainase. Salam Indonesia Raya, Humanisme dunia internasional, dan keselamatan planet bumi "our mother heart".
Similar to An Iterative Method Applied to Correct the Actual Compressor Performance to the Equivalent Performance Under the Specified Reference Conditions
OPTIMIZATION OF AN OPEN CYCLE GAS TURBINE POWER PLANT USING EXERGOECONOMICSijmech
The purpose of current study is to analyze the performance of an open cycle gas turbine power plant using
the concepts of exergoeconomics. Exergoeconomic technique involves the use of Second law of
thermodynamics and assigns monetary values to the thermodynamic quantity known as exergy. Analyses
based on exergoeconomic criteria are done for the open cycle gas turbine power plant turbine. The
methodology is illustrated using the example of a 25 MW open cycle gas turbine power plant. Optimization
has been done for the open cycle gas turbine power plant as tradeoffs between the unit product cost of the
compressor and combustion chamber as functions of compressor pressure ratio and unit product costs of
combustion chamber and gas turbine as functions of turbine inlet temperature.
PERFORMANCE ANALYSIS OF A COMBINED CYCLE GAS TURBINE UNDER VARYING OPERATING ...meijjournal
The combined cycle gas turbine integrates the Brayton cycle as topping cycle and the steam turbine
Rankine cycle as bottoming cycle in order to achieve higher thermal efficiency and proper utilization of
energy by minimizing the energy loss to a minimum. In this work, the effect of various operating
parameters such as maximum temperature and pressure of Rankine cycle, turbine inlet temperature and
pressure ratio of Brayton cycle on the net output work and thermal efficiency of the combine cycle are
investigated. The outcome of this work can be utilized in order to facilitate the design of a combined cycle
with higher efficiency and output work. A MATLAB simulation has been carried out to study the effects and
influences of the above mentioned parameters on the efficiency and work output.
Thermodynamic modeling and Exergy Analysis of Gas Turbine Cycle for Different...IJPEDS-IAES
In this study an exergy analysis of 88.71 MW 13D2 gas turbine (GT) topping
cycle is carried out. Exergy analysis based on second law was applied to the
gas cycle and individual components through a modeling approach. The
analysis shows that the highest exergy destruction occurs in the combustion
chamber (CC). In addition, the effects of the gas turbine load and
performance variations with ambient temperature, compression ratio and
turbine inlet temperature (TIT) are investigated to analyse the change in
system behavior. The analysis shows that the gas turbine is significantly
affected by the ambient temperature and with increase there is decrease in
GT power output. The results of the load variation of the gas turbine show
that a reduction in gas turbine load results in a decrease in the exergy
efficiency of the cycle as well as all the components. The compressor has the
largest exergy efficiency of 92.84% compared to the other component of the
GT and combustion chamber is the highest source of exergy destruction of
109.89 MW at 100 % load condition. With increase in ambient temperature
both exergy destruction rate and exergy efficiency decreases.
Robust control of speed and temperature in a power plant gas turbineISA Interchange
In this paper, an H∞ robust controller has been designed for an identified model of MONTAZER GHAEM power plant gas turbine (GE9001E). In design phase, a linear model (ARX model) which is obtained using real data has been applied. Since the turbine has been used in a combined cycle power plant, its speed and also the exhaust gas temperature should be adjusted simultaneously by controlling fuel signals and compressor inlet guide vane (IGV) position. Considering the limitations on the system inputs, the aim of the control is to maintain the turbine speed and the exhaust gas temperature within desired interval under uncertainties and load demand disturbances. Simulation results of applying the proposed robust controller on the nonlinear model of the system (NARX model), fairly fulfilled the predefined aims. Simulations also show the improvement in the performance compared to MPC and PID controllers for the same conditions.
COMPARATIVE STUDY OF DIFFERENT COMBINED CYCLE POWER PLANT SCHEMESijmech
Combined Cycle Power Plants (CCPPs) are imperative for power generation with the capability for
deciphering power shortage during peak and off peak hours. To perk up the recital of the plant, foremost
locations of exergy losses are to be identified and analyzed. In the present work, exergetic analysis of a
CCPP is carried out using the computer programming tool Engineering Equation Solver (EES). The effects
of overall pressure ratio and turbine inlet temperature on the exergy destruction in the CPR are
investigated. The results obtained are compared with that of simple gas turbine cycle power plant. During
real time operation of CCPP exergy destruction in different components is associated with change in
overall pressure ratio and turbine inlet temperature (TIT). Out of the total exergy destruction in the cycle it
is the combustion chamber (CC) which is responsible for the maximum exergy destruction. Nearly 60% of
the total exergy is destroyed in CC. Results clearly show that with increase in complicacy of the power
plant structure, irreversibility of the processes can be improved.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Thermal analysis of cooling effect on gas turbine bladeeSAT Journals
Abstract Performance of a gas turbine is mainly depends on various parameters e.g. ambient temperature, compressor pressure ratio, turbine inlet temperature etc. The most important parameter to increase the life of the turbine blade is the cooling of the blade, which is necessary after reaching a certain temperature of the gases passing through the blades. Various types of cooling models are available for a turbine blade cooling. The power output of a gas turbine depends on the mass flow rate through it. This is precisely the reason why on hot days, when air is less dense, power output falls off. This paper is to analyze the film cooling technique that was developed to cool gases in the initial stages of the turbine blades, where temperature is very high (>1122 K). It is found that the thermal efficiency of a cooled gas turbine is less as compare to the uncooled gas turbine for the same input conditions. The reason is that the temperature at the inlet of the turbine is decreased due to cooling and the work produced by the turbine is slightly decreased. It is also found that the power consumption of the cool inlet air is of considerable concern since it decreases the net power output of gas turbine. In addition, net power decreases on increasing the overall pressure ratio. Furthermore, the reviewed works revealed that the efficiency of the cooled gas turbine largely depends on the inlet temperature of the turbine and previous research said that the temperature above 1123K, require cooling of the blade. Keywords: Gas turbine, Turbine blade cooling, film cooling technique, Thermal Efficiency
Reactivity Feedback Effect on the Reactor Behaviour during SBLOCA in a 4-loop...IJMREMJournal
The reactivity coefficient is a very important parameter for safety and Stability of reactors operation. To provide
the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary
because it is related to the reactor operation. The objective is to study the effect of the temperature reactivity
coefficients of fuel and moderator of the PWR core, as well as the moderator density and boron concentration on
fluid density, reactivity, void fraction. peak fuel clad temperature and time to core uncover were found for two
feedback cases. This paper focuses on the effect of the Reactivity feedback, of the 6" (6-inch) Cold Leg
SBLOCA sequences in a 4-loop PWR Westinghouse nuclear power plant with a scram for various feedback,
moderator density coefficient, MDC, moderator temperature coefficient, MTC, the fuel temperature coefficient,
FTC, and boron concentrations. Dragon neutronic code is used for calculating reactivity's coefficient which is
used in RELAP5 thermal hydraulic computer code to simulate the effect of Reactivity feedback during Cold
Leg SBLOCA. The plant nodalization consists of two loops; the first one represents the broken loop and the
second one represents the other three intact loops. In the present analysis two models in RELAP5 code for
computation of the reactivity feedback, separable and tabular models are used. The 6-inch break size was chosen
because the previous work [1], showed that it was the worst size break in a 4-loop PWR Westinghouse. The
results show that the neglecting of the reactivity feed-back effect causes overheating of the clad and that the
importance of the reactivity feed-back on calculating the power (reactivity) which the key parameter that
controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core
uncover and fuel damage where the fuel temperature, clad temperature and core water level are in the range.
An approach to evaluate the heat exchanger retrofit for installed industrial ...eSAT Journals
Abstract This is part 2 of the conducted study to develop a new systematic method to evaluate the heat exchanger retrofit on existing industrial gas turbines. A new approach has been introduced and validated in the first part comparing with the measured data. This method was used to optimize the obtained cycle performance characteristics and the generated heat exchanger design options based on technical prospective to attain the highest possible improvement on the simple cycle performance. However, it is essential to consider the economic viability of using the recuperative cycle which will be investigated in thispaper. Although that there are several tools which can be used to achieve that objective, this study uses the Net Present Value (NPV) method due to its simplicity and accuracy. The established technique has been applied for the same described gas turbine cycles in the previous part. Based on the stated assumptions, it was found that by applying the recuperation in the first engine,W6BRC, and at full load and 100% utilization factor conditions, the payback period has increased by one year by applying over that of simple cycle. Moreover, at the end of the project life, the recuperative cycle of this engine is expected to achieve an increase of $11M in the NPV over that of simple cycle. This difference between the two cycles becomes greater in the case of the second engine, W7FA, which is ranging between $33.9M and $46.8M.However, the drop in the availability of the overall recuperative gas turbine by about 18% over the simple cycle gas turbine causes the NPV of both cycles to be equal. Moreover, this paper includes a sensitivity study to investigate the effects of utilization factor and recuperator effectiveness and pressure drop on the cumulative discounted cash flow. KeyWords:new systematic method,economic viability, Net Present Value, utilization factor,availability
Similar to An Iterative Method Applied to Correct the Actual Compressor Performance to the Equivalent Performance Under the Specified Reference Conditions (20)
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
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An Iterative Method Applied to Correct the Actual Compressor Performance to the Equivalent Performance Under the Specified Reference Conditions
1. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
DOI : 10.5121/ijctcm.2013.3501 1
AN ITERATIVE METHOD APPLIED TO CORRECT
THE ACTUAL COMPRESSOR PERFORMANCE TO THE
EQUIVALENT PERFORMANCE UNDER THE
SPECIFIED REFERENCE CONDITIONS
Yuanyuan Ma, Harald Fretheim, Erik Persson, and Trond Haugen
Department of Product and Technology for Oil, Gas, and Petrochemicals,
Division of Process Automation, ABB, Oslo, Norway
ABSTRACT
This paper proposes a correction method, which corrects the actual compressor performance in real
operating conditions to the equivalent performance under specified reference condition. The purpose is to
make fair comparisons between actual performance against design performance or reference maps under
the same operating conditions. Then the abnormal operating conditions or early failure indications can be
identified through condition monitoring, which helps to avoid mandatory shutdown and reduces
maintenance costs. The corrections are based on an iterative scheme, which simultaneously correct the
main performance parameters known as the polytropic head, the gas power, and the polytropic efficiency.
The excellent performance of the method is demonstrated by performing the corrections over real industrial
measurements.
KEYWORDS
Corrections, Actual Operating Conditions, Reference Operating Conditions, Reference Map, Compressor
Performance, Corrected Performance, Expected Performance
1. INTRODUCTION
Compressor performance is dependent on many external process conditions such as pressures,
temperatures, and gas compositions [1, 2]. Monitoring the compressor performance can identify
abnormal compressor performance and problems at an early stage so that failures or mandatory
shut down can be avoided, which significantly reduces maintenance cost and is essential for daily
operation actions [3].
One main challenge in condition monitoring is how to fully utilize the monitored performance
parameters in further analysis and troubleshooting [4]. When comparing the actual performance
against design/reference performance, the comparisons must be fairly and taken under the same
operating conditions. The design performance or reference maps are often conducted under
certain specific inlet pressure, temperature, and gas composition, which are known as reference
conditions. In contract, the actual performance is only valid for their real operating conditions,
which varies for each operating point. To compare these performances under the same operating
conditions, one solution is to transform the actual performance in real conditions to the equivalent
performance valid for the reference conditions. This task is known as corrections and is the main
focus of the paper.
2. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
2
To the best of the authors' knowledge, such corrections have been presented so far only in [5] for
validating a new centrifugal compressor's compliance to the guarantee conditions after it is built.
To check whether the compressor will meet the specified duty, the performance achieved from a
shop test needs to be compared with specifications provided by a manufacturer. However, due to
practical difficulties, the test gas conditions are usually different with the specific gas conditions
used previously by a manufacturer. To compare the performance equivalently, the rules for
correlating the results obtained with the test gas to that with the design specifications were
proposed in [5].
Although three different testing cases have been discussed in [5], they are only categorized by
various testing gas conditions. The reference conditions can be characterized not only by the gas
conditions but also by pressures and temperatures. Unfortunately, the correction method in [5]
does not work for a more general case and definitely limits the applications of the method.
Moreover, the existing correction method requires a big set of parameters and meter readings to
complete the whole correction process. In reality, rather than in a test, full access of all these
information is not practical. Such a method cannot fulfil basic applications in condition
monitoring such as presenting actual compressor performance in a reference map.
To eliminate all limitations mentioned above and extend the applications of the corrections, we
propose a new and practical correction method for real gas. The method can correct actual
compressor performance to more practical reference conditions, which are specified not only by
the gas composition, but also by the inlet pressure and temperature. The method is based on an
iterative scheme, which simultaneously corrects the main performance parameters including the
polytropic head, the gas power, and the polytropic efficiency. The report `ASME PTC-10' [5]
only presents the instructions how to carry out the corrections. In our paper, we also validate the
proposed method by performing the corrections over the real operating points sampled from our
industrial gas processing pump pilot. It will be shown experimentally that the corrected
performance are very close to the expected values obtained directly from a given reference map.
It is also interesting to mention that since our new method requires less information to carry out
the corrections, it is very easy to compare two sets of historical data by correcting them to pre-
defined reference conditions.
The paper is organized as follows. Section 2 describes the general procedure of the corrections.
The principle regarding how to correct an individual operating point under the real conditions to
the specific reference conditions is introduced in Section 3. The verification of the correction
methods is discussed in Section 4. Results for demonstrating the accuracy of the proposed method
are presented in Section 5. Finally, some concluding remarks are given in Section 6.
2. GENERAL PROCEDURE OF CORRECTIONS
Section 2 describes the general procedure and the basic assumptions that applied to the
corrections.
Figure 1 explains the idea regarding how to correct an individual operating point under the real
conditions to the specific reference conditions:
1) The first step is to transform the real operating conditions, i.e., the inlet & discharge pressures,
temperatures, and gas composition, to the specific reference conditions. As shown in Fig. 1,
the inlet pressure and temperature of the operating point after corrections are considered to be
the same as the reference inlet ones. The gas composition for the operating point is also
changed from the real one to the reference gas composition.
3. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
3
2) The second step of the correction is to find out, under certain constraints, what the equivalent
discharge pressure and temperature are when the real inlet conditions change to the reference
conditions.
Figure 1 Interpretation of Correction Principle.
3) Finally, recalculate the polytropic head, gas power, and polytropic efficiency based on the
corrected gas composition as well as the corrected inlet & discharge pressures and
temperatures. The new values calculated under the reference conditions are referred to
corrected performance.
The constraints mentioned in Step 2 are known as follows:
1) The polytropic efficiency is constant before and after the corrections;
2) The ratio of the volumetric flow at inlet to the flow at outlet remains the same before and
after the corrections.
The first assumption comes from the fact that the polytropic efficiency is independent on the
thermodynamic state such as the temperature and the pressure [6]. The purpose of the second
assumption is to have similar flow conditions before and after the corrections. It indicates that the
density ratio before and after the corrections remains the same.
3. CORRECTION METHODOLOGY
As discussed in Section 2, the corrected inlet conditions of operating points are assumed to be
equal to the given reference conditions. The remaining problem is how to determine the corrected
discharge conditions based on the known pressures, temperatures, and gas compositions. This is
the most challenge part in the corrections.
Reference Conditions
Conditions for Operating
Point before Corrections
Inlet pressure: ܲଵ
Inlet temperature: ܶଵ
Discharge pressure: ܲଶ
Discharge temperature:
ܶଶ
Gas composition: real
gas composition
Reference inlet pressure: ܲଵ
Reference inlet temperature:
ܶଵ
Gas composition: reference
gas composition
Perform
Corrections
Step
1
Conditions for Operating
Point after Corrections
Step
2
Step
3
Inlet pressure: ܲଵ
= ܲଵ
Inlet temperature: ܶଵ
= ܶଵ
Gas composition: reference
gas composition
Discharge pressure: ܲଶ
Discharge temperature: ܶଶ
Corrected polytropic head
Corrected gas power
Corrected polytropic
efficiency
4. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
4
The procedure to determine the corrected discharge values and the corrected performance can be
summarized as follows:
1) Calculate the average physical gas properties of the original operating points including:
average polytropic exponent n , average specific heat ratio k , average additional function X
and Y , which are given by
1 2
,
2
n n
n
+
=
1 2
,
2
k k
k
+
=
1 2
,
2
X X
X
+
=
1 2
.
2
Y Y
Y
+
=
Here, the symbols 1 1 1,k , ,n X and 1Y denote the polytropic exponent, specific heat ratio, and
additional functions at inlet, while the four parameters at discharge are represented by 2 2 2,k , ,n X
and 2Y . The two additional functions mentioned here are used to supplement the compressibility
factor calculated under real-gas conditions [7].
These parameters can be calculated by the function 'ExponentCalc' introduced in Appendix A for
real gas. The required inputs for using this function are the relevant pressure, temperature, and
gas composition.
2) Calculate the corrected inlet polytropic exponent and the specific heat ratio.
Since the inlet pressure and temperature have been changed to the reference ones after the
corrections, the physical gas properties at inlet, known as the corrected inlet polytropic exponent
1
c
n , corrected specific heat ratio 1
c
k , and two corrected additional functions 1
c
X , and 1
c
Y , need to
be recalculated. The procedure and equations can be found in Appendix A.
3) Calculate the corrected discharge pressure, temperature, and average polytropic exponent.
The first assumption indicates that the corrected polytropic efficiency ( c
η ) equals to the
uncorrected polytropic efficiency (η ), i.e.,
.c
η η=
According to the definition of the polytropic exponent for real-gas conditions [7], the polytropic
efficiency can be written as:
(1 )
.
(1 ) ( )
Y n k
k X Y n k X
η
⋅ ⋅ −
=
⋅ + − ⋅ ⋅ +
Substituting (6) and the similar expression for the corrected polytropic efficiency in eq. (5) yields
the relationship (7), which is presented at the bottom of this page.
(6)
(5)
(4)
(3)
(2)
(1)
5. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
5
(1 ) (1 )
.
(1 ) ( ) (1 ) ( )
c c c
c c c c c c
Y n k Y n k
k X Y n k X k X Y n k X
⋅ ⋅ − ⋅ ⋅ −
=
⋅ + − ⋅ ⋅ + ⋅ + − ⋅ ⋅ +
The symbols c
X , c
Y , and
c
k , in (7) represent the two average corrected additional functions and
the average corrected specific heat ratio. The corrected polytropic exponent c
n can then be
deduced from (7) and expressed in the form as shown in (8).
(1 ) (1 )
.
[ (1 ) ( )] (1 ) (1 ) ( )
c c
c
c c c c c
Y n k k X
n
k X Y n k X Y k Y n k Y k X
⋅ ⋅ − ⋅ ⋅ +
=
⋅ + − ⋅ ⋅ + ⋅ ⋅ − + ⋅ ⋅ − ⋅ ⋅ +
Since these average corrected values c
X , c
Y , and c
k , on the right side of equation (7) are
unknown and their calculations depend on the value for
c
n , equation (8) cannot be solved.
Our solution is to replace these average corrected parameters ( c
X , c
Y , )c
k , in (8) by the
parameters 1( c
X , 1Yc
, 1k )c
at inlet. Then we use the new obtained value, denoted by
c
initialn (see
(9)), as the initial value and calculate the corrected polytropic exponent
c
n through the following
iterative scheme:
1 1
1 1 1 1 1
(1 ) (1 )
.
[ (1 ) ( )] (1 ) (1 ) ( )
c c
c
initial c c c c c
Y n k k X
n
k X Y n k X Y k Y n k Y k X
⋅ ⋅ − ⋅ ⋅ +
=
⋅ + − ⋅ ⋅ + ⋅ ⋅ − + ⋅ ⋅ − ⋅ ⋅ +
Step 0: Set the initial value
c
initialn as the corrected polytropic exponent, i.e.,
.c c
initialn n=
Step 1: Calculate the corrected discharge pressure and temperature.
According to Appendix B, the corrected pressure and temperature are given by
2
2 1
1
,
c
n
n
c c P
P P
P
= ⋅
1
1
2
2 1
1
.
c
n
n
c c T
T T
T
−
−
= ⋅
Step 2: Calculate the corrected discharge compressibility factor 2
c
z , enthalpy 2
c
h , specific heat
capacity 2
c
pc and molecular weight c
MW for the corrected operating points. The physical
properties can be computed according to the expressions presented in [8].
Step 3: Calculate the corrected polytropic exponent at discharge, which is expressed as
(12)
(11)
(10)
(9)
(8)
(7)
6. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
6
2
2
2 2
2
1
.
1 1 1
1
c
c
c c
c c c
X
n
Y X
k η η
+
=
⋅ ⋅ + − −
Here, 2
c
X , 2Yc
, and 2kc
can be computed according to the function 'ExponentCalc
2 2 2 2( , , , ,c c c c c
pP T c z η , reference gas composition)’ presented in Appendix B.
Step 4: Calculate the overall corrected polytropic exponent by averaging the corrected
polytropic exponents at inlet and discharge, i.e.,
1 2
.
2
c c
c n n
n
+
=
Step 5: Repeat Steps 1-4 for 100 times. The values obtained after the iterations for 2 ,c
P 2 ,c
T
and c
n are considered as the corrected discharge pressure, temperature, and polytropic
exponent.
4) Calculate the Schultz factor f by the equation below [5,7]
2 1
2 2 1 1
( 1) ( )
,
( / / )
c c c
s s
c c c c c c c
s s s s
k h h
f
k z R T MW z R T MW
− ⋅ −
=
⋅ ⋅ ⋅ − ⋅ ⋅
Where
1 2
1 2
1
,
2
c c
c
s c c
k k
k
Y Y
= ⋅ +
denotes the corrected isentropic exponent. In (15), 3
8314.3 / / ,R Pa m kmol K= 1 ,c
h and 1
c
z
are the gas constant, corrected enthalpy, and corrected compressibility at inlet. The values for 1 ,c
h
and 1
c
z can be calculated by the theory introduced in [8]. The symbols with subscript's' denote the
parameters of isentropic process.
5) Calculate the corrected polytropic head c
pH [9]:
2 2 1 1
1
( ).
1
c
c c c c c
p c c
n
H f z R T z R T
n MW
= ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ ⋅
−
6) Correct the speed and the mass flow according to the fan law [10, 12]:
,
c
pc
p
H
N N
H
= ⋅
(14)
(15)
(16)
(17)
(18)
(13)
7. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
7
.c cN
m m
N
= ⋅
In (18), ,c
N N and Hp are known as the corrected compressor speed, compressor speed, and
polytropic head. The calculations for the polytropic head can be found in [6]. In (19), the symbols
c
m and m are corrected mass flow and original mass flow.
7) Calculate the corrected gas power [6]
.
c
pc c
c
H
PWR m
η
= ⋅
4. VERIFICATION OF THE CORRECTION METHODOLOGY
The accuracy of the correction method can be verified by the relative difference between the
corrected performance and the expected performance. The interest performance parameters for
verifications are polytropic head and gas power. The expected performance are the output values
predicted directly from the given compressor performance maps. If the performance has been
corrected to the reference conditions properly, the corrected performance is supposed to be close
to the expected one.
The deviation of the corrected polytropic head or gas power from the expected one are defined by
100%,p
c e
p p
H c
p
H H
H
δ
−
= ×
100%.
c e
PWR c
PWR PWR
PWR
δ
−
= ×
In the equations above, the symbol e
pH and e
PWR denote the expected polytropic head and gas
power. The expected performance can be determined by locating the expected operating point
from a given reference map. The location of the point can be found by first mapping the given
mass flow to the performance characteristic curved curve at specified compressor speed. Then,
the expected value can be determined by mapping the expected operating point to the y-axis
describing the performance parameter, e.g., the corrected polytropic head.
5. RESULTS
As To verify the correctness of the proposed correction method, the deviation of the corrected
performance from the expected performance predicted in a reference map will be studied. The
measurements used in verifications are real industry gas processing pump data, which record the
compressor actions for the past three years.
If a reference map is already given, one just needs to follow the procedure introduced in Section 3
to carry out the corrections for all real operating points. Then, determine the expected
performance as discussed in Section 4. Otherwise, if the reference map is not available, which is
the case for this paper, a reference map needs to be generated from certain amount of the real
(20)
(21)
(22)
(19)
8. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
8
operating points. First correct certain operating points to some pre-set reference conditions. Then
apply the third polynomial curve fitting technique to generate the reference map.
In our case, the operating points sampled at 2011 were used to generate the reference map. The
reference inlet pressure and temperature were set to 1 76.5ref
P = bar and 1 299.5 .ref
T K=
Figures 2-4 illustrate the deviations between the corrected polytropic head and the expected one
for different operating period.
Figure 2 shows the correction results performed on the operating points from 2011. These
operating points are the same data as the one used to generate the reference map. Due to this fact,
the obtained deviations are supposed to approach to zero. This is illustrated by the results
presented in Fig. 2. As can be seen, the deviations are very small and the average deviation is less
than 1%.
Figure 2 Corrected Polytropic Head Deviations for Operating Data from 2011.
Figures 3 and 4 present the correction results for operating points sampled at 2009 and 2012.
Even the operating conditions especially the real gas composition is different with the reference
one, the correction method still works and returns acceptable results. The average deviation is
3.67% when correcting the operating data at 2009 and the average deviation is 3.53% when the
correcting data at 2012
9. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
9
Figure 3 Corrected Polytropic Head Deviations for Operating Data from 2009
Figure 4 Corrected Polytropic Head Deviations for Operating Data from 2012.
Some peak values exist in Figs. 3 and 4, which indicate that large deviations exist in the
corrections. There are two reasons for getting such peak values. One reason is that for some data
points, their operating conditions are quite different with the reference conditions. It is already
beyond the correction capability. Then big deviations occur. The conditions here can be the inlet
(discharge) temperatures, pressures, and gas composition. For example, in our further study, we
find that when the inlet pressure or the discharge pressure is 10% away from the reference
pressure, the average deviation exceeds 10%. The other factor causing large deviations comes
from the accuracy and the valid range of the reference map. In our paper, the reference map is not
a standard one provided by manufactures. It is generated by applying the polynomial fitting
10. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
10
techniques on a certain amount of the operating points. Then, the accuracy of the fitting
techniques directly influences the accuracy of the map. Moreover, since the reference map is
generated based on a limit number of the operating points. The map has its own valid range. If the
operating points after the corrections are already out of the valid range, the expected performance
obtained from the map is not accurate. This leads to severe deviations from the corrected values.
Here, since they are beyond the scope of the paper, we will not discuss more in the paper. In
general, the correction method is efficient in correcting operating points with all kinds of
conditions. Even counting these peak values and the factors which bring inaccuracy in evaluating
the correction method, the average deviation is still low.
Figures 5-7 show the corrected gas power deviations for the operating points sampled at 2009,
2011, and 2012. The average deviations are 2.08%, 0.68%, 2.6%, respectively. The average
deviations for the corrected gas power are even smaller than the deviations for the corrected
polytropic head. More important, all figures presented above verify that the correction method
performs well when simultaneously correcting the two main performance parameters: the
polytropic head and the gas power. In addition, in corrections, we assume the polytropic
efficiency remains the same before and after corrections, the deviations for corrected efficiency
are always zero.
Figure 5 Corrected Gas Power for Operating Data from 2009.
11. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
11
Figure 6 Corrected Gas Power for Operating Data from 2011.
Figure 7 Corrected Gas Power for Operating Data from 2012.
6. CONCLUSIONS
In this paper, we have proposed an iterative method, which enables to correct the actual
compressor performance under the real operating conditions to the equivalent performance valid
for the given reference conditions. The general procedures and detailed theory of the corrections
have been described. The accuracy of the method has been demonstrated by comparing the
12. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
12
deviations between the corrected performance data and the expected values obtained from a
reference map.
The corrections have been performed on three year measurements from real industry gas
processing pump. The obtained average deviations of the corrected polytropic head from the
expected one are: 3.67%, 0.97%, and 3.5% for the years 2009, 2011, and 2012. The obtained
average deviations for the corrected gas power for these three years are: 2.08%, 0.68%, 2.6%.
It can be concluded that the correction method is practical and performs well over real industry
data. The method returns very small deviations when simultaneously correcting the polytropic
head, the gas power, and the polytropic efficiency.
The proposed correction procedure and theory enable to compare the actual compressor
performance from different operating period fairly. In addition, it also allows comparing real
performance with the reference values provided by compressor manufactures. With the helps
from the corrections, the abnormal compressor performance and potential problems can be
identified at an early stage so that failures or mandatory shutdown can be avoided, which
therefore significantly reduces maintenance costs.
APPENDIX
A. Calculations of the Polytropic Exponent and Specific Heat Ratio for Real-Gas Conditions
This appendix explains how to calculate the polytropic exponent and the specific heat ratio.
The first step is to calculate the thermodynamic properties from the given operating conditions,
i.e., the given pressure P , temperatureT , and gas composition. The compressibility factor z and
the heat capacity pc are the necessary thermodynamic properties needed for the purpose of this
appendix and can be calculated according to [8]. The second step is to compute the required
partial derivatives. The mathematic details of these partial derivatives can be found in [8, 11].
As can be seen in [7] the polytropic exponent for real-gas conditions is given by
1
,
1 1 1
1
X
n
Y X
k η η
+
=
⋅ ⋅ + − −
Where
,
T z
X
z T
∂
= ⋅
∂
1 ,
P z
Y
z P
∂
= − ⋅
∂
represent the two additional functions. These two functions are used to supplement the
compressibility factor calculated under real-gas conditions. The expressions for the partial
derivatives /z T∂ ∂ and /z P∂ ∂ in (A.2) and (A.3) can be found in [11].
The exponent
1 p
p
c
k
P v
c T
T T
= −
∂ ∂
− ⋅ ⋅
∂ ∂
(A.1)
(A.2)
(A.3)
(A.4)
13. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
13
denotes the specific heat ratio, and pc is known as the heat capacity of hydrocarbon mixtures. The
expressions for the partial derivatives /P T∂ ∂ and /v T∂ ∂ can be found in [8].
For convenience, we denote the calculations of these exponents by the function 'ExponentCalc',
i.e., ( , , , ) ( , , , , ,pX Y k n ExponentCalc P T c z η= Gas composition).
It has to be mentioned that the expressions presented in this appendix can be used to calculate the
polytropic exponent and specific heat ratio either at inlet or discharge, one just need to
substituting the relevant required parameters from inlet or discharge.
B. Prof of Equations (11) and (12)
Based on the deductions in [p.180, 6], the ratio of the volumetric flow at inlet to the flow at
discharge, denoted by ,rν can be written as
1
2
1
.
n
v
P
r
P
=
Similarly, the ratio of the corrected volumetric flow at inlet to the corrected flow at discharge is
given by
1
2
1
.
cc n
c
v c
P
r
P
=
The second assumption made in Section 2 indicates that the ratio of the volumetric flow ratio at
inlet and discharge remains the same before and after corrections, i.e.,
.c
v vr r=
Then, the corrected discharge pressure can be derived from equations (B.1) and (B.2) and
expressed as
2
2 1
1
,
c
n
n
c c P
P P
P
= ⋅
Starting from the relation between volumetric flow and temperature presented in [p.180, 6],
equation (12) can be obtained.
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(B.1)
(B.2)
(B.3)
(B.4)
14. International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.3, No.4/5, September 2013
14
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