transmission-system design

Transmission-System DesignAuthor(s): Peter LangSource: The Journal of the Operational Research Society, Vol. 39, No. 5 (May, 1988), pp. 459-466Published by: Palgrave Macmillan Journals on behalf of the Operational Research SocietyStable URL: http://www.jstor.org/stable/2582360 .

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J. Opl Res. Soc. Vol. 39, No. 5, pp. 459-466, 1988 0160-5682/88 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright ?) 1988 Operational Research Society Ltd

Transmission-System Design PETER LANG

Woodford Green, Essex

This paper describes some of the complexities of designing high-pressure gas-transmission systems. The contribution of OR to efficient gas-transmission-system design is discussed. A new network design program is described to illustrate the benefits of models to system design and plant selection.

Key words: modelling, network analysis

INTRODUCTION

The gas industry has been around for over a hundred years. Before the natural-gas era, the industry produced and sold what was commonly called town gas. Town gas was made from coal at or near the centres of demand, and distributed to the customers through local low-pressure networks. The arrival of natural gas has brought great changes. Gas is produced from gas fields hundreds or thousands of miles away from cities and towns, and is transported to market either in the liquid form or under high pressure. In the case of the UK, gas produced from under the North Sea is transmitted to on-shore reception terminals and delivered to the centres of demand through a network of high-pressure transmission pipelines. Natural gas is gaining popularity as a fuel because it is cleaner, safer and more efficient than town gas. Within the past 20 years a number of high-pressure transmission systems have been planned or built all over the world.

In the simplest terms, the design of a gas-transmission system is very straightforward. A supply of gas is available at a certain location, and there is demand for it at some other location. In most cases, it is a long distance away. What is then required is some form of link between the supply and demand.

In reality, there can be more than one source of supply, and each potential supply can be at a different location. The demand itself could be made up of varying proportions of domestic and industrial customers. The sizes, types and locations of both supplies and demands dictate what the transmission system looks like. It can range from a simple pipeline without any extra facilities, to a very complex network of pipelines requiring compression along the route and storage plant sited at strategic points to meet sudden variations in demand.

TRANSMISSION-SYSTEM DESIGN CONSIDERATIONS

Gas-transmission plant requires a lot of effort and time to design and is very expensive to build. For example, British Gas invest hundreds of millions of pounds every year on building and maintenance of plant.' Many complex issues, covering areas of engineering, economics and even politics, have to be resolved, and a large team of engineers, scientists and planners is needed to design a good transmission system.

Two important variables to be taken into account are the load profiles and load factors of supply/demand. The load factor is defined as the ratio between the average daily rate to the peak day rate, and is usually expressed as a percentage. The producers prefer to supply gas at a very high load-factor to maximize income. On the other hand, gas consumption is much higher in winter than in summer, resulting in a lower annual demand load-factor. As shown in Figure 1, the load profiles of supply and demand do not match, and it is apparent that the demand load-factor is also lower than that of the supply load-factor. In such cases consideration has to be given to whether extra transmisson capacity should be provided to meet peak demand in cold weather or whether extra storage facilities should be built. Provision for future development has also to be considered. Interaction with existing and future plant availability is another important factor since

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Journal of the Operational Research Society Vol. 39, No. 5

E

0 Supply profile

Demand profile

Jan Mar May Jul Sep Nov

Ti me

FIG. 1. Comparison of supply and demand load-profiles.

new plant does sometimes make existing facilities redundant. If the system is well designed, the redundant plant can be released for other uses rather than being left idle.

Man is essentially a day creature, preferring to use all services, including gas, for his convenience when he is awake. This creates a variation of usage that is higher during the day and lower at night. It is generally more economic to provide some storage to meet diurnal variation than to install larger-sized pipes to cope with peak hourly demand. A typical diurnal profile is shown in Figure 2. The type, size and siting of such plant has to be carefully selected.

Corrosion and cracking of pipes is another significant problem faced by pipeline engineers, as is the choice between compression and pipe reinforcement. It is out of the scope of this paper to describe in detail every aspect of transmission-system design. Some of the more important areas in terms of the OR contribution to transmission-system design are discussed below. These are:

(1) demand forecasting, (2) soil and temperature effects, (3) pipeline versus compressors, (4) gas storage, (5) risk analysis, (6) network modelling, and (7) an example of the use of the network model.

W - ---C---Average c-- g rate

E

a, ~\ 0~~~~~

I I I I I I

0600 1400 2200 0600

Time of day

FIG. 2. A typical diurnal demand-profile.

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P. Lang-Transmission-System Design

DEMAND FORECASTING

In industry, it is necessary to have a good estimate of the future demand so that production can be geared to the required amount. In the gas industry, transmission plant requires a number of years to design and build. Hence, it is essential to be able to forecast future demand so that the supply network can be properly developed to handle the correct demand level.

Forecasting occupies an important position in the design and optimization of a gas-transmission system. The main OR contribution here is in the development of forecasting models. A good long-term forecasting model provides information on load growth and changes in demand pattern. This enables the industry to plan and build the correct size of plant at the right location. Good forecasting results also ensure a reasonable supply/demand match, and reduce the requirement of seasonal storage.

Short-term within-day forecasting using a combination of time series and regression techniques is also important. It is needed to plan a proper operational strategy and reduce the amount of transmission plant required. Use of diurnal storage facilities can be optimized.

SOIL AND TEMPERATURE EFFECTS

The soil is a complex mixture. It consists of mineral particles, a certain proportion of decayed organic matter, soil water, a soil atmosphere and living organisms. Hence, the soil is not static but changes continuously, especially with the results of interactions of various biological processes. Both the physical and the chemical properties of a soil may change with time. Properties of a soil depend not only on the mineral and organic content but also on the amount of soil moisture, temperature and soil atmosphere.2

The soil is a corrosive environment. It is well known that dissolved carbon dioxide causes corrosion of steel pipes.3 Soil moisture is extremely significant in this connection, and in general, a dry, sandy soil will be less corrosive than a wet clay. Stress-corrosion cracking is defined as the crack initiation and growth in an alloy caused by the simultaneous action of corrosion and tensile stress. In particular, such corrosion can occur at the grain boundaries of steel. The exact mechanism of stress-corrosion cracking is not yet fully understood, but much research has been done on stress corrosion of buried pipes, and there is agreement that stress corrosion is related to temperature.4 The properties of a soil vary with the amount of soil moisture present. A soil can become thermally unstable as a result of moisture movement when it is subjected to thermal gradients due to the presence of heat transfer from a transmission line to the soil. OR simulation techniques work out how soil temperature may change with time. The frequency distribution of corrosion and cracking of different grades of pipe in various environments can be determined, and enables the design engineer to choose the correct type of pipe and the appropriate pipe protection for efficient operation.

PIPELINES VERSUS COMPRESSORS

The simplest transmission system is just a pipe linking a source of supply at one end and a demand or a number of demands at the other end of the pipe. Real transmission systems are more complicated, and in most cases one or more compressors form part of the system. Compressors are used to increase the capacity of a system and as an alternative to pipeline duplication.

When designing a high-pressure gas-transmission system, the location and appropriate type of compressor to be installed and the correct pipe size has to be determined. When selecting a compressor, the duration of operation and the fuel usage are important factors to be considered. Some compressors are specifically designed for continuous operation for a limited number of days in a year, whilst others are suitable for prolonged operation without incurring unacceptable maintenance or overhaul expenditure.

In cases where compressor usage is excessive, the capitalized fuel cost may be the deciding factor whether a compressor or a pipeline is installed. Although the unit cost of pipelines is higher, over a long period it may be more economic to increase transmission capacity by pipeline duplication

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rather than by installing additional compressors. A combination of network modelling and forecasting methods can determine the optimum compressor spacing and pipeline sizes.

GAS STORAGE

One of the main differences between gas and electricity is that gas can be stored much more easily than electricity on a large scale. Liquefied natural gas is a common form of storage.5 There is also an increasing tendency to store large volumes of gas underground.6

Storage has an important function in the gas supply industry.7 It encompasses the roles of:

(a) maximizing the capacity of the transmission system; (b) providing security of supply; (c) achieving an improved balance between supply and demand; (d) lowering the overall cost of gas supply.

Storage can be divided into seasonal, peak shaving and diurnal storage. Seasonal storage is necessary to even out variations in demand between summer and winter. It enables the transmission system to be better utilized during the summer. Peak shaving storage is required to provide extra gas needed during peak winter periods when demand exceeds pipeline level. Diurnal storage is needed to balance out the variation in demand throughout the day. During the day, the hourly demand is usually equal to, or above, the average hourly demand, and if the supply of gas is taken at a constant rate, then this is the period when gas is withdrawn from storage. During the night, when demand is below average, gas is put back into storage. Supply/demand modelling, network analysis and linear programming are methods to find optimum locations, estimate size and type of gas store and work out the economics of the level of storage provided.

RISK ANALYSIS

Most project development today is planned for completion time and budget by single value techniques. It is common to set a target date and a set amount of expenditure. Since project time and costs either are built into targets from the outset or automatically include rule-of-thumb contingency factors, they frequently fail to show the true time and cost.

When designing a transmission system, there are uncertainties relating to productivity, weather, environment etc. Under some circumstances, these uncertainties become important factors in the decision-making process, and risk/sensitivity analysis may be appropriate. Risk analysis offers the benefits of better contingency planning and selection of responses, and better feedback into the design and planning process. Hence, such analyses should be applied to demand forecasting, sizing of plant and long-term system development.

NETWORK MODELLING

Network modelling is a good example of the OR contribution to transmission-system design. There are two basic methods of approach to obtain the solution to network systems-either by trial and error or by mathematical models. In reality, even simple networks are difficult to solve manually. The usual method is to apply some form of iterative technique such as the Newton-Raphson procedure, and to use computers to carry out the calculations.

The balance of flow in a loop or network is governed by Kirchoff's Laws, which state that:

(1) at any point in a network, the quantity of gas flowing into that point equals the quantity flowing out of that point;

(2) the algebraic sum of the pressure drops along any paths equals zero.

Hence, for a given supply pressure, a fixed configuration of pipes with known demands will possess a unique value of flow and pressure in each section of pipe.

A number of commercial network programs are available.8 The source codes of these programs are commercial secrets and are not available in the open literature. By contrast, the programs described in published literature9"0o can be used for solving gas flow or pressure drop of a single

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pipeline, and cannot be used to solve networks. It is common to use steady-state methods for design-modelling purposes." Even for transient flow calculations it has been shown that steady- state equations produce results that agree well with actual field measurements.'

A SAMPLE SOLUTION

A new network modelling program which takes account of some of the principles and techniques of OR is described here. In this program, steady-state equations are used. This program is easy to operate. It requires very little computer storage. A brief description is given in Appendix A.

In the following example, the program was used to study the differences between compressor and pipeline reinforcement. A hypothetical system, consisting of a 42-in. diameter pipe, 300 miles long and with an initial pressure of a thousand pounds per square inch, was used. The number of compressors required versus miles of pipeline reinforcement (duplicate or triplicate) to transmit an increasing flow of gas through the system is given in Table 1. The horsepower requirement for an increasing gas flow is produced in Table 2. The results show that as the number of compressors increases along a transmission line, and the closer to each other they are spaced, so the marginal efficiency of each compressor decreases. For a 42-in. diameter pipeline, the optimum compressor spacing is between 80 and 100 miles, depending on the upstream and downstream pressure requirements and on the soil thermal properties.

TABLE I TABLE 2

Miles of pipe reinforcement Flow rate in Number of Total horsepower Flow rate in Number of in place of compressors m.c.fd.* compressors requirement m.c.f.d.* compressors (duplicate & triplicate)

1040 1 200 1040 1 20,000

1250 2 290 1250 2 50,000 1430 3 377 1560 4 26,000 1560 4 440 1560 4 1520,000 1660 5 500

*m c~f~d. = millions of cubic feet per day. *m.c.f.d. = millions of cubic feet per day. *m.c.f.d. = millions of cubic feet per day.

CONCLUSION

Transmission-system design is an essential and important part of the planning process in the gas and electricity industries. The application of a range of OR techniques can provide valuable benefits and insight in this subject. Methods such as forecasting, simulation, linear programming and risk analysis are needed to solve a whole range of problems in system design and related areas of business. The network program described above demonstrates that even a simple approach can be a big step towards a solution, although on its own it cannot supply a complete solution to a complex business problem.

APPENDIX

This model is written in standard GW-BASIC. Gas flow and pressure drop are calculated using the Panhandle equation'3 recommended by the AGA. When compressors are included in the network, the user can set a maximum horsepower limit, and if no limit is set, the program will automatically calculate the horsepower requirement. A global value for compressor inlet and outlet loss has to be specified to cover compressor-station piping pressure-loss, which can be significant. 14

There is a facility to set a global gas molecular weight, compressor efficiency, pipe efficiency and supercompressibility. Forecasting errors, compressor failures, supply failures and other incidents have to be considered in the design. Therefore, a flow margin'5 is included in the model and has to be defined. The user sets the mean pipeline and compressor outlet temperatures, maximum compression ratio and a maximum network-operating pressure. The total amount of high-pressure linepack, which is defined as the volume of gas stored in the whole network, is automatically calculated by the program with every run.

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10 REM network program 20 DIM N%(2,99),Q(99),L(99),D(99) 30 DIM P(99),VOL(99) 40 PRINT "enter pressures in psis, load in mcf, len in mls, dia in in" 50 INPUT "run name";N$ 60 INPUT "enter max compr ratio";CR 70 INPUT "enter mol wt";MW 80 INPUT "enter flow margin";FM 90 INPUT "enter mean temp in pipe";TM

100 TM=TM+460 110 INPUT "enter mean temp in compressor";TC 120 TC = TC + 460 130 INPUT "enter press loss in comp inlet/outlet";PC 140 INPUT "enter comp eff (< than 1)";UC 150 INPUT "enter mean pipe eff";EF 160 INPUT "enter supercompressibility factor";ZF 170 INPUT "max press";MP 180 PRINT "enter 1 bse node, 2 network, 3 1st data, 4 calc, 5 end" 190 INPUT K 200 ON K GOTO 210,240,450,520,1260 210 INPUT "enter base node and press";BN,BP 230 GOTO 180 240 PRINT "enter node a, node b, dia/outlet pre preceded by ne sign, len/hp" 245 PRINT "load, and end with 0,0,0,0,0" 250 INPUT NANBDXLX,QX 260 IF ABS(DX) > MP THEN 265 262 GOTO 270 265 PRINT "warning, outlet press higher than max press, lowered to max press" 266 DX= -MP 270 IF NA = 0 THEN 370 290 N = N + 1 300 N%(1,N)=NA 310 N%(2,N)=NB 320 D(N) =DX 330 L(N) =LX 340 Q(N) = QX 350 PRINT "new pipe";NA;NB 360 GOTO 250 370 FOR J = N TO 1 STEP -1 380 FOR I = N TO 1 STEP -1 390 IF N%(1,J)< >N%(2,I) THEN NEXT I 400 IF N%(1,J) = N%(2,I) THEN 420 410 IF N%(1,I) = N%(2,I) THEN 420 420 Q(I) = Q(I) + Q(J) 430 NEXT J 440 GOTO 180 450 PRINT N$ 460 PRINT "na nb dia/outlet len/hp flow" 470 FOR I= 1 TO N 480 PRINT N%(l,I),N%(2,I),D(I),L(I),Q(I) 490 NEXT I 500 GOTO 180 510 REM start calc 520 N%(1,1) =BN

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530 A=BP 540 P(0) = BP 550 FOR I= 1 TO N 560 IF I = 1 THEN 580 570 GOTO 610 580 S = Q(I)*FM 590 S=S*41.667 600 GOTO 690 610 J= 1 620 IF N%(2,J) = N%(1,I) THEN 650 630 J = J +.1 640 GOTO 620 650 A = P(J) 660 S = Q(I)*FM 670 S=S*41.667 680 IF D(I) < = 0 THEN 770 690 IF S < 0 THEN 720 700 B = A*A - ((.07394*TM*L(I)*S A 1.8539*MW A .854)/(EF*EF*(ZF A .854)*D(I) A 4.8539)) 710 GOTO 730 720 B = A*A + (((- 1*S) A 1.854*.07394*TM*L(I)*MW A .854)/(EF*EF*ZF A .854*D(I) A

4.8539) 730 LE = L(I) 740 IF B > 0 THEN 940 750 PRINT "negative press" 760 GOTO 180 770 DA = ABS(D(I)) 780 IF A > DS THEN 980 790 IF L(I) > 0 THEN 870 800 IF (DA + PC)/(A - PC) < = CR THEN 840 810 P(I) = (A-PC)*CR-PC 820 LE = (.34806*TC*(S/41.667)*(((P(I) + PC)/(A - PC)) A .2308 - 1))/UC 830 GOTO 950 840 P(I) = DA 850 LE = (.34806*TC*(S/41.667)*(((DA + PC)/(A - PC)) A .2308 - 1))/UC 860 GOTO 950 870 P(I) = (L(I)*UC/((S/41.667)*.34806*TC) + 1) A 4.333*(A - PC) - PC 880 LE = L(I) 890 IF (P(I) + PC)/(A - PC) < = CR THEN 910 900 P(I) = (A - PC)*CR - PC 910 IF P(I) > DA THEN 1070 920 LE = (.34806*TC*(S/41.667)*(((P(I) + PC)/(A - PC)) A .2308 - 1))/UC 930 GOTO 950 940 P(I)=BA.5 950 P(I) = P(I) 960 L(I) = LE 970 GOTO 1110 980 L(I) = 0 990 P(I) = A

1000 GOTO 1110 1010 IF I< N THEN 1020 1020 NEXT I 1030 P(I) = P(I) 1040 GOTO 1050 1050 ZZ-0 1060 GOTO 180

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1070 .P(I) = DA 1080 LE = (.34806*TC*(S/41.667)*(((DA + PC)/(A - PC) A .2308 - 1))/UC 1090 L(I) = LE 1100 GOTO 1110 1110 ZZ=ZZ+1 1120 IF ZZ > I THEN 1140 1130 PRINT "na nb len/hp press flow, pack" 1140 IF L(I) > 100 THEN 1180 1150 WE = 28.7979*D(I)*D(I)*L(I) 1160 PM = (P(I) + (I - 1) - (P(I)*P(I - 1))/(P(I) + P(I - 1)))*.667 1170 GOTO 1190 1180 WE=0 1190 VOL(I) = WE*((PM + 14.7)/14.7)/1000000! 1200 PRINT N%(l ,I),N%(2,I),L(I),P(I),Q(I);" ";VOL(I) 1210 VOL(I) = VOL(I) + VOL(I - 1) 1220 IF I = N THEN 1240 1230 GOTO 1010 1240 PRINT "line pack storage in mcf is: ";VOL(N) 1250 GOTO 180 1260 PRINT "end of run" 1270 END

Acknowledgements-I am grateful to Professor W. Murgatroyd for his advice and encouragement, and I thank British Gas for supporting this research.

REFERENCES

1. BRITISH GAS ANNUAL REPORT (1986). 2. F. J. MONKHOUSE (1968) Principles of Physical Geography. University of London Press. 3. W. E. BERRY (1983) How carbon dioxide affects corrosion of line pipe. Oil Gas J. 21 March, 160-166. 4. R. F. FESSLER (1982) Status report given on prevention of stress corrosion cracking in buried pipelines. Oil Gas J. 17

May, 68-70. 5. A. J. FINDLAY and G. W. SPICER (1982) The Isle of Grain LNG installation. Gas Engng Mgmt February, 47-57. 6. G. E. REAVES and M. D. FELT (1982) New gas storage facility exceeds design capacity. Oil Gas J. 15 November, 97-102. 7. D. J. CLARKE, G. S. CRIBB and W. J. WALTERS (1971) The philosophy of gas storage. IGasE. Communication 845. 8. M. H. GOLDWATER, K. ROGERS and D. K. TURNBULL (1976) The Pan network analysis program. I.GasE.

Communication 1009. 9. E. HOLMBERG (1983) Programmable calculator finds gas pipeline pressure with Colebrook-White equation. Oil Gas J.

13 June, 117-122. 10. J. H. STANNARD (1985) Routine for computer or calculator solves gas flow problems. Oil Gas J. 15 April, 63-69. 11. W. G. JAMES (1984) Use steady state methods for seasonal modelling. Pipeline Industry May, 23-28. 12. R. N. MADDOX and P. ZHOU (1984) Using steady state equations for transient flow calculations in natural gas pipelines.

Oil Gas J. 2 April, 114-120. 13. AMERICAN GAS ASSOCIATION (1965) Steady state flow computation for natural gas transmission lines. 14. T. R. MEYER (1985) Model changes improve compressor station piping pressure-loss prediction. Oil Gas J. 29 April,

96-102. 15. M. CLARK (1985) The development of a simulation model for the operation of the national transmission system.

J. Opl Res. Soc. 36, 275-281.

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