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Optimisation of fuel consumption in natural-gas compressor stations using spread sheets.

Abstract: For the purpose of natural gas transmission in compressor stations, a considerable amount of natural gas is normally consumed to overcome the frictional pressure loss. In this paper, using spread sheets, the steady state, isothermal one dimensional and compressible flow in pipes is simulated with the equations for the operation of centrifugal compressor. In the second stage, the fuel consumption of the generator (Gas Turbine) is optimised with non-linear programming based on General Reduced Gradient. Finally, a case study is conducted, in which a turbine's fuel consumption in appropriate boundary conditions is minimised.

Key words: Compressor Station, Fuel Consumption, Optimization, Spread Sheets, General Reduced Gradient.

1. INTRODUCTION

In compressor stations, about 3 to 5 percent of transitive gas is consumed in turbines to create required pressure gradient and prepare the necessary mass flow rate at the delivery point. Therefore, it seems necessary to propose a proper mathematical model to minimize the fuel consumption by finding the proper decision variables. A number of research projects have been conducted to find a way to optimise the process of gas transmission, focusing on the most complex part of transmission system, i.e. compressor stations. Andrus for the first time used spread sheets to simulate the steady state gas transmission system by assuming constant value for the compression ratio in the whole transmission system (Samuel J. Andrus 1994). This method was used again by Ian Cameron to analyse both steady state and transient flows in Excel sheets (Ian Cameron 1999). Later on, optimisation in the performance of station was considered for non-isothermal and unsteady condition by choosing the speed of compressor as decision variable (Chapman & Abbaspour 2005).

In this paper we extend the pervious studies by assigning special spread sheet for each part of the gas pipeline system (main pipe, connecting pipe, dividing and combining junction, compressor, and turbine). Moreover, in this study the compression ratio is not constant and is determined in a form of an additive. Also, the possibility of optimising turbine's fuel consumption is analysed by the use of General Reduced Gradient (GRG) method. Finally, the optimisation process is applied in a case study.

2. RELATIONS AND EQUATIONS

Flow rate and pressure changing in the pipes are calculated using the AGA equation 1 in isothermal, steady state, single phase conditions and assuming no elevation. There is an attempt to keep transmission systems in turbulence regime. In different Reynolds Numbers, the equation gives us various results and some of the outcomes have too much difference from the local measurements. Hence, by changing the coefficients ([a.sub.1] to [a.sub.5]), according to table 1, it will be compatible for various restrictions.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Fanning factor (f) is one of the most important parameters to determine the pressure loss in the flow equation. Since the deviation from the modified Colebrook-White equation (in both cases of smooth and rough pipes and for the Re<2000 * 108) is less than 0.068 percent, using the trial and error method in spread sheets, the following equation for calculating fanning factor, which gives a precise answer in Moody's diagram, is extracted:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

In fact, the compressibility factor (Z) determines the amount of deviation from the behaviour of real flow rate, considering the behaviour of ideal flow rate. Z is calculated using the iterative and numerical Newton-Rophson method, introduced by Dranchuk & Kassem in 1975, and also in Standing-Katez chart in spread sheet's environment:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The reduced density, temperature and pressure parameters are calculated through the equations 4, 5 and 6:

[[rho].sub.r] = 0.27[P.sub.r]/[ZT.sub.r] (4)

Pr = P/[P.sub.c] (5)

[T.sub.r] = T/[T.sub.c]

3. MODELING OF COMPRESSOR AND GAS TURBINE

To build a mathematical model for the centrifugal compressor, we defined the Head/[[omega].sup.2], [Q.sub.ac]/[omega] and [eta], parameters by using the least square numerical method on digitized value of compressor map (Fig.1). The coefficients in equations 7 and 8 were finally derived from the specific spread sheet.

[FIGURE 1 OMITTED]

Head/[[omega].sup.2] = [A.sub.h] + [B.sub.h] ([q.sub.ac/[omega]) + [C.sub.h] [([q.sub.ac/[omega]).sup.2 (7)

[eta] = [A.sub.e] + [B.sub.e] ([q.sub.ac/[omega]) + [C.sub.e] [([q.sub.ac/[omega]).sup.2] (8)

Compressor head was dynamically calculated from equation 9 in an appropriate spread sheet. Also, by changing [omega], the amount of [eta] and consequently the required compressor power was determined from equation 10:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

PWR = W x Head x BPWR/[eta] x [[eta].sub./mech] + Al

Providing the summation of required compressor power and axial loads is equal to the power of gas turbine, the amount of fuel consumption of gas turbines in different operational conditions can be calculated. Fuel consumption of gas turbine is determined according to the following relations, where SFC is specific fuel consumption and HV is heating value of the gas:

[[eta].sub.D] = [[eta].sub.R]/([A.sub.DE] + [B.sub.DE] x FAP + [C.sub.DE] x [FAP.sup.2]) (11)

SFC = 1/([[eta].sub.D] x HV) (12)

FC = SFC x PWR (13)

4. OPTIMISATION

We used equation 13 as our objective function. Considering the equality of created power in gas turbines with the required power in the compressor, and respecting all the constraints of the system, equation 14 was calculated changing speed as our decision variable:

min [[??].sub.f] = min [n.summation over (i=1)] FC([x.sub.i]) = min [n.summation over (i=1)] [PWR.sub.i]/[[eta].sub.Di] x HV (14)

[[omega].sub.i] is considered as rotational speed in compressor i in the station. In this situation, min [[omega].sub.i], max [[omega].sub.i], min [q.sub.ac,i] and max [q.sub.ac,i] are the limitation of rotational speed and volumetric flow rate of compressor [[??].sub.min] is another constraint of system and shows the minimum necessary mass flow rate at delivery point. [[??].sub.f,] which was obtained from equation 14 is our objective function equal to the amount of gas turbine fuel consumption in compressor stations.

5. A CASE STUDY

As a case study, the parameters of the best operational point in a compressor station with minimum rate of fuel consumption were established. In this experiment, the natural gas with the relative density of 0.6, molecular weight of 17.382 lbm/lbm.mol at 80[degrees]F and 104.6 bar.a pressure flowed through a 192-mile pipeline. The diameter of pipe is 20 inch through the length and relative roughness is 0.0007 inch .In the middle of the pipe, there is a station, including 2+1 identically parallel centrifugal compressor with the same configuration. The type of gas turbine is Centaur40 with nominal power of 3500kw. Minimum and maximum operational speeds of the centrifugal were 6000 and 14300 rpm respectively, while the real volumetric flow rate is bounded between 21.57 and 133.10 [ft.sup.3]/sec. The discharge pressure and mass flow rate at delivery point are 56.8 bar.a and 92 lbm/sec and the inlet volumetric flow rate in standard condition is 4050.92 [ft.sup.3]/sec. Table2 indicates the result of the optimisation process:

6. CONCLOUSION

Fuel consumption in compressor stations has an important role in the costs associated with the natural gas transmission. In this paper following the modelling of the major parts in pipeline systems using spread sheets, we optimised the fuel consumption in a compressor station. Following activities can be considered for further works:

* Instead of a single station, the fuel consumption of the network, as a whole, can also be optimised.

* All other configurations can be also optimised.

* It is possible to change decision variables in some other cases to obtain more efficient results.

7. REFRENCES

Andrus, S. (1994). Steady State Simulation of Pipeline Networks Using A Spreadsheet Model. 26th PSIG conference, 1989, California.

Chapman & Mohammed Abbaspour (2005). Non-isothermal Compressor Station Transient Modeling. Avaiable from: http://www.osti.gov Accessed: 2007-1-16.

Dranchuk, P.M & Abou-Kassem, J.H.(1975). Calculation of Z factors for natural gases using equations of state. JCPT, 14(3),(July 1975) 34-36.

Howard, G. & Murphy, Jr.(1989). Compressor Performance Modeling to Improve Efficiency and the Quality of Optimization Decisions. 21st PSIG conference, Oct., 1989, Texas.

Ian, Cameron (1999).Using an Excel-Based Model for Steady-State and Transient Simulation. 31st PSIG conference, Oct. 1999, Missouri.

Walsh (2004). Gas Turbine Performance, ASME Press, USA.
Table 1. Coefficients of AGA Equation in USCS

Equation [a.sub.1] [a.sub.2] [a.sub.3] [a.sub.4] [a.sub.5]

Panhandle 435.7 1.078 0.539 0.460 2.618
IGT 434.2 1.111 0.556 0.444 2.666
Weymouth 433.5 1.000 0.500 0.500 2.666

Table 2. Initial value & result of fuel consumption optimisation

 Initial Value After Optimisation

1st Comp. Speed 13200 rpm 12850 rpm
1st Comp. Efficiency 82.46 83.23
2ed Comp. Speed 13200 12580
2ed Comp. Efficiency 82.46 83.23
Mass Flow Rate 5527.50 lbm/min 5527.95 lbm/min
Fuel Consumption 15.0371*2 14.8729*2 SCF/sec
 SCF/sce 2.570 MMSCFD
 2 5984 MMSCFD
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Author:Molaei, Reza; Sanaye, Sepehr; Fahimnia, Behnam; Eskandari, Khodadad
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2007
Words:1558
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