Due to uncertainty of fluid volume with different parameters of crude oil and gas viz.
viscosity, temperature, the oil and gas sector uses a reciprocating air compressor together
with disc, reed or ring valves while centrifugal compressor is good for fixed volume of fluid.
Keeping this in view, a comprehensive study has been suggested to examine important
parameters of reciprocating compressor with mathematical modelling.
Reciprocating compressors are driven by the engine itself through a proper belt driven
arrangement. A well designed compressor will consume less power and deliver the
maximum flow of air and thereby improving the power output of internal combustion
engine. It indirectly reduces the fuel consumption of the engine and consequently the
emission of pollutants.
Mathematical numerical model will be a compelling apparatus in compressor design plan
and for analysing the impact of different physical and working parameters on compressor
execution parameters like power required and volumetric efficiency. Examinations on the
procedures of reciprocating compressors utilizing mathematical models is a viable
instrument with the improvement of processing and computing method by which
complicated problems may be solved with a minimum number of simplifying assumptions
The numerical model will also be be helpful in developing new reciprocating compressors to
give the maximum volumetric efficiency with least power utilization.
The designer will be in a position to know the outcome at the initial stage of the proposed
work and thereby reducing time and cost of work during manufacturing. A number of
previous works has been employed in the mathematical formulation, modelling and
simulation. Most of the researchers have focused their attention on radial or centrifugal
compressors and have not dealt with the impact on compression varying index and
expansion which have a significant effect on the prediction of power required to run the
reciprocating compressor.
A few analysts have developed numerical mathematical model for hermetic compressors.
The previous works in this field are dealt only with compressor having disc or plate valves.
Earlier work used basic equations to determine the mass flow rate of air through discharge
or suction valves.
The objective of the present work is to construct a numerical mathematical model which is
easy to understand and recognize mistakes during the time spent building a model and
simple to register numerical arrangement and solutions,. The work presents a simple
effective mathematical model for the estimation of reciprocating compressor performance.
A software code will be developed for model analysis using C++. The model will be
developed with minimum number of assumptions in the ideal reciprocating compressor. All
the assumptions in the analysis of the ideal compressor will be grouped and as a first
approach a numerical mathematical model of an ideal reciprocating compressor will be
developed. The model will be developed for obtaining the cylinder temperature, cylinder
pressure, valve lift and free air delivered and indicated power of the reciprocating
compressor. Predicted results from the model will be compared with experimental results.
Experimental results thus obtained from multiple compressors will validate the developed
model performance. The effect of various physical and mechanical parameters like,
clearance volume, connecting rod length, cylinder diameter, crank radius and valve lift and
operating parameters like compressor speed and discharge pressure on the thermodynamic
behaviour of reciprocating compressor in working condition will be analysed.
UNIQUE FEATURES OF A COMPRESSOR MODELLING
A well designed compressor will consume less engine power with good volumetric efficiency
and operating life. The engineers at the design stage will try to analyse the outcome of their
work related to performance and life at various operating and physical conditions.
Mathematical model is an effective tool to predict the performance of a compressor at any
working condition. The designer will be in a position to know the outcome at the initial
stage of the proposed work and thereby reducing the time and cost of experimental work.
The model can accommodate any modification of physical and operating parameters in the
existing compressor or in the compressor to be developed.
Modelling concepts
A mathematical model uses mathematical language to describe a system. The process of
developing a mathematical model is termed mathematical modelling and is widely used in
all engineering and sciences for performance prediction. Eykhoff (1974) defined a
mathematical model as a representation of the essential aspects of an existing system (or a
system to be constructed) which presents knowledge of that system in usable form.
Mathematical modelling problems are often classified into black box or white box models,
according to how much a priori information is available of the system. A black-box model is
a system in which there is no a prior information available. A white-box model (also called
glass box or clear box) is a system where all necessary information is available. Practically all
systems are somewhere between the black-box and white-box models, so this concept only
works as an intuitive guide for approach. Usually it is preferable to use as much a priori
information as possible to make the model more accurate. Therefore the white-box models
are usually considered easier, because if the information is used correctly, then the model
will give results accurately.
Conventionally, mathematical modelling is defined as process of designing a numerical
model of a real system and conducting experiments with it for the purpose of understanding
the behaviour of the system. Numerical models can take many forms, including but not
limited to statistical models, differential equations, dynamical systems, or game theoretic
models. These and other different models can overlap, with a given model involving a
variety of parameters with abstract structures. Often when engineers or expert analyze a
framework to optimised be controlled, they use a numerical mathematical model. In
analysis, experts can build a descriptive model of the system as a hypothesis of how the
system (framework) could function, or try to estimate how an unforeseeable event could
affect the system. Similarly, in the control of a system, experts can try out various control
approaches in simulations. Mathematical models in general can be classified following ways:
Linear vs. nonlinear: Mathematical models are usually composed by variables, which are
abstractions of quantities of interest in the described systems, and operators that act on
these variables, which can be algebraic operators, functions, differential operators, etc. If all
the operators in a mathematical model exhibit linearity, the resulting mathematical model is
defined as linear. A model is considered to be nonlinear otherwise. The question of linearity
and nonlinearity is dependent on the context, and linear models may have nonlinear
expressions in them. For example, in a statistical linear model, it is assumed that a
relationship is linear in the parameters, but it may be nonlinear in the predictor variables.
Similarly, a differential equation is said to be linear if it is written with linear differential
operators, but itcan still have nonlinear expressions in it. In a mathematical programming
model, if the objective functions and constraints are represented entirely by linear
equations, then the model is regarded as a linear model. If one or more of the objective
functions or constraints are represented with a nonlinear equation, then the model is
known as a nonlinear model. Nonlinearity, even in fairly simple systems, is often associated
with phenomena such as chaos and irreversibility. Although there are exceptions, nonlinear
systems and models tend to be more difficult to study than linear ones. A common
approach to nonlinear problems is linearisation, but this can be problematic for studying the
effect such as irreversibility, which are strongly tied to nonlinearity.
Deterministic vs. probabilistic (stochastic): A deterministic model is the one in which every
set of variable states is uniquely determined by parameters in the model and by sets of
previous states of these variables. Therefore, deterministic models perform the same way
for a given set of initial conditions. Conversely, in a stochastic model, randomness is
present, and variable states are not described by unique values, but rather by probability
distributions.
Static vs. Dynamic: A static model does not account for the element of time, while a
dynamic model does. Dynamic models typically are represented with difference equations
or differential equations.
Lumped vs. distributed parameters: If the model is heterogeneous (varying state within the
system) the parameters are distributed. If the model is homogeneous (consistent state
throughout the entire system), then the parameters are lumped. Distributed parameters are
typically represented with partial differential equations.
OBJECTIVES OF THE PRESENT WORK
The volumetric efficiency of reciprocating compressor is more than centrifugal compressor
but due to different losses overall efficiency of reciprocating compressor is less than
centrifugal compressor.
The losses due to wear and tear with change in field parameters like leaking the packaging
due to liner material, piston rings valves occurs. Packaging with high thermal efficiency is
required but due to leakage it is not possible.
The failure consequences and reason behind these losses will be identified due to change in
parameters of gas and gas hydrates. Compressor consumes certain amount of gas from a
suction pressure to a discharge pressure and high isentropic eff efficiency of the compressor
including all parasite losses.
The future prediction will be presented by modelling so that preventive measure can be
taken after 5 or more years to increase the efficiency of the system. Due to change in early
suction pressure of gas, compression ratio is increased and thus due to increase
compression ratio reciprocating compressor is best suited for the purpose. Performance
parameter of the compressor and its driver those are important for the economic evaluation
will be studied.
Predicting the power loss of reciprocating compressor manifolds and development of a
theoretical basis for oil consumption in reciprocating cylinders is also among prime
objectives.
Where small compressors are employed , large number of spare compressors can be used
at break down but in oil and gas fields having so many reserve compressors is not feasible
and cost effective and replacement with new compressors may take duration of 2 months
or more, so losses due to break down is more (high capital intensive) so preventive
measures for maintenance with wearing life by mathematical modelling will be suggested.
The objective of the present study is to develop a model for the steady state performance of
a reciprocating compressor with least cycle cost (LCC). The mathematical model equations
will be composed of analytical equations based on simple mass and energy balances in
addition to simple relations developed from experimental data. If the model equations will
be simple in form, they will easily be solved sequentially yielding the reasonable numerical
results to predict the performance of reciprocating compressor at different operating
conditions. Furthermore, the basic analytical equations contained physical parameters
which can be varied to provide simulations of various reciprocating compressor geometries.
The constants appeared in the empirical relations will be obtained from the analysis of
experimental data. The experimental data will be used for parameter estimation. The
algorithm of modelling will be presented will easily be extended to other reciprocating
compressors with a minimal amount of experimental data. Furthermore, the algorithm will
be capable of establishing a mathematical model that is accurate over a broad range of
working conditions. The objective of this study is to compare the model's performance by
comparison of modelling and simulation results with experimental data. The objective of
present work is to develop effective and simple model of a reciprocating air compressor for
investigating its thermodynamic behaviour. various inputs and outputs of the mathematical
model is given below.