Pipeline capacity and economics
Gas pipeline construction: calculating the pipe diameter, the pressure required for the transportation of natural gas compressors. The definition of capital costs for construction and operation of the pipeline. Financial management of the project.
Рубрика  Экономика и экономическая теория 
Вид  статья 
Язык  английский 
Дата добавления  05.12.2012 
Размер файла  774,7 K 
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PIPELINE CAPACITY AND ECONOMICS
INTRODUCTION
In the construction of natural gas transmission pipelines a lot of things should be considered. For example pipe sizes, the pressure required to transport natural gas from one location to another and the pressure drop that will proceed. To accurate this, compressors are required which need to be sized for the compression requirements. In addition Pipe loops will be designed that increase the capacity of the pipeline by adding theoretical diameter.
Pipelines are planned to integrate into existing networks and are constructed to transport a company's own natural gas, to transport natural gas through an owned section of pipeline for another company, or to transfer the ownership of natural gas to another and into their assets (pipeline). For these 3 permutations in operation investment in the infrastructure and assets will be made to a varying degree while meeting all of the regulation requirements to ensure that the safe operation and environment considerations have been made.
To meet the capital requirement (CAPEX) for developing pipelines, companies have to provide strong business cases in how the financing and remuneration through operation will be managed. The budget for pipeline development will be determined by the capital costs of the planned length of pipeline and operational term in service. Some of the elements of the capital costs are as follows:
1. Pipeline
2. Compressor stations
3. Mainline valve stations
4. Meter stations
5. Pressure regulator stations
6. SCADA and telecommunication
7. Environmental and permitting
8. Right of way acquisitions
9. Engineering and construction management
PIPELINE CAPACITY AND ECONOMICS
In the design and planning of the physical pipeline systems several variables are to be considered. The majority of these variables come from the general flow equation which is determines the daily capacity of a gas pipeline:
Using this equation produce derivative equations to illustrate the relationship with some of the variables and how impact on the overall capacity of the pipeline on a daily basis. This is shown as a capacity factor or as volumetric capacity for daily deliverables. In conditions of overall economical potential the pipeline capacity as earlier mentioned is a important factor in determining the transportation price and hence the capital recovery for investment in projects of this nature.
One of the capacity functions are:
1. Inlet pipe pressure
2. Pressure drop
3. Pipeline diameter
4. Pipeline Length
INLET PRESSURE
Use the derivative equation below the illustration of variation of inlet pressure in stages of 10 bar for a standard pipe diameter with a constant pressure drop ?P of 20 bar can be seen.
For this arrangement we can use the formula:
Q ?
This allows us to determine the capacity factor CF which is a function of the inlet pressure.
Table 1
Effect of Inlet pressure on pipeline capacity
Q 
?P 
P? 
?P(2P? ?P) 
CF 

20 
0 
400 

0 
20 
10 
0 
0 

20 
20 
20 
400 
1 

28.28427 
20 
30 
800 
1.06066 

34.64102 
20 
40 
1200 
1.154701 

40 
20 
50 
1600 
1.25 

44.72136 
20 
60 
2000 
1.341641 

48.98979 
20 
70 
2400 
1.428869 

52.91503 
20 
80 
2800 
1.511858 

56.56854 
20 
90 
3200 
1.59099 

63.08724 
20 
100 
3980 
1.585107 

Figure 1. Pipeline capacity increases with increased inlet pressure
From figure 1 any increase in inlet pressure for a standard pressure drop of 20 (bar) will increase the capacity of the pipeline. There is a rapid increase in capacity between 1020 (bar) and then a uniform or linear increase between 3090 (bar) for inlet pressure. Standard systems will use the linear increase in capacity as they will require a pressure drop in the system to be able to transmit efficiently. In terms of transmission pressures the majority of pipelines in the UK will transmit around 65 (bar) which is in the range of linear capacity building in pipelines.
Also using an example for a pipeline of fixed dimensions we can explore further the original equation by producing the derivative equation.
Where:
P1 (inlet pressure) is varied in stages of 10 bar
P2 (outlet pressure) is a function of the pressure drop known to be 20 bar for the system.
D is the diameter of the pipeline (30'' or equivalent to 750mm DN)
L is length of a standard section of pipeline taken to be 48km
EXAMPLE CALCULATION
Q ? x = 217.855 capacity (mill m^{3}/ day)
Table 2
Inlet pressure varied in stages of 10 bar
p1 
?P 
p2 
d 
L 
Q ? 

10 
20 
10 
750 
48 
0 

20 
20 
0 
750 
48 
44469530 

30 
20 
10 
750 
48 
62889412 

40 
20 
20 
750 
48 
77023485 

50 
20 
30 
750 
48 
88939059 

60 
20 
40 
750 
48 
99436891 

70 
20 
50 
750 
48 
1.09E+08 

80 
20 
60 
750 
48 
1.18E+08 

90 
20 
70 
750 
48 
1.26E+08 

100 
20 
80 
750 
48 
1.33E+08 

110 
20 
90 
750 
48 
1.41E+08 

120 
20 
100 
750 
48 
1.47E+08 

130 
20 
110 
750 
48 
1.54E+08 

140 
20 
120 
750 
48 
1.6E+08 

150 
20 
130 
750 
48 
1.66E+08 

160 
20 
140 
750 
48 
1.72E+08 

170 
20 
150 
750 
48 
1.78E+08 

180 
20 
160 
750 
48 
1.83E+08 

190 
20 
170 
750 
48 
1.89E+08 

200 
20 
180 
750 
48 
1.94E+08 

210 
20 
190 
750 
48 
1.99E+08 

220 
20 
200 
750 
48 
2.04E+08 

230 
20 
210 
750 
48 
2.09E+08 

240 
20 
220 
750 
48 
2.13E+08 

250 
20 
230 
750 
48 
2.18E+08 

Figure 2. Potential capacity increase for inlet pressure increase
PRESSURE DROP
The effect of pressure drop on pipeline capacity for a fixed inlet pressure can also be calculated from the derivative of the General Flow Equation.
Where, Q ? v (P_{1}^{2}P_{2}^{2}) with a fixed inlet pressure and variation of pressure drop.
SAMPLE CALCULATION
v (70^{2}50^{2}) = 48.99
Table 3
Uniform pressure drop in stages of 5 bar
Q 
p1 
p2 
?P 
CF 

0 
70 
70 
0 
0 

25.98076 
70 
65 
5 
0.53033 

36.05551 
70 
60 
10 
0.73598 

43.30127 
70 
55 
15 
0.883883 

48.98979 
70 
50 
20 
1 

53.61903 
70 
45 
25 
1.094494 

57.44563 
70 
40 
30 
1.172604 

60.62178 
70 
35 
35 
1.237437 

63.24555 
70 
30 
40 
1.290994 

65.38348 
70 
25 
45 
1.334635 

67.08204 
70 
20 
50 
1.369306 

68.37397 
70 
15 
55 
1.395678 

69.28203 
70 
10 
60 
1.414214 

69.8212 
70 
5 
65 
1.425219 

70 
70 
0 
70 
1.428869 

Figure 4. Capacity reduction after 20 bar
For gas, we can see by increasing the pressure drop there is a gradual decrease in capacity. We base this prediction by looking at how the capacity behaves before and after the standard pressure drop of 20 bar.
While before the standard pressure drop of 20 bar, in the early region on the graph between 0  10 bar there is an uniform increase in capacity. This steadily declines towards the pressure drop of 20 bar and beyond it. As the pressure drop increases the capacity steadily decreases to the point whereby at pressure drop of 70 bar there is no apparent increase in capacity at all.
DIAMETER
The affect the diameter has on the pipeline is quite apparent. As the pipelines diameter increases so does the capacity of that pipeline to hold potentially higher volume of gas or other hydrocarbons. This is because the dynamic viscosity of the gas increases due to greater width of pipeline boundary layers.
As gas is a compressible fluid it tends to be able to be `packed into' pipelines of higher theoretical diameter in methods such as reenforcement for line packing technique.
This relationship is proven through the derivative of the general flow equation:
Where Q ? d ^{2.5}
For the Midcontinential pipeline example which is comprised of 3 sections:
1. 48km of 30 inch pipe (750mm)
2. 317km of 36 inch pipe (900mm)
3. 442km of 42 inch pipe (1050mm)
This is evident that the planning is to allow an increase in capacity along the run of the pipeline. Calculations show how the capacity gained quite considerably along the run of the pipeline.
Table 4
Diameter driven capacity increase
CF(capacity factor) 
Q(volume) 
d (DN mm) 

1 
15404697 
750 

1.577441 
24300000 
900 

2.319103 
35725083 
1050 

Figure 5. Diameter driven capacity increase
From the graph of Midcontinential gas pipeline we can say that will increase in capacity factor from pipeline section to section. This corresponds to an increase of 1.5 from the 750mm section to 900mm section and an increase in capacity of 2.3 times from the 750mm to 1050mm section. This increase in capacity is used over ranges of 317km and 442km respectively and highlights how the capacity of 48km would most probably be for a feed in for the major transmission line and their potential to increase capacity.
Therefore the higher the diameter the more suitably cost effective it is to transport the gas from region to region. This would generally be used for the interstate (zone) relaying of gas on a national network. The pipelines would be designed to be used in rural locations due to the design factor for safety involved. However the increased costs of laying large diameter pipelines are generally offset by the increased capacity of these lines in years to come. This returns to the premise that most gas pipeline operators will design the network to efficiently yield the maximum capacity possible over the lifetime of the pipeline with planned increase designed in which will allow them to optimize the capacity of the pipeline and gain the maximum transportation tariff for the network within prescribed remuneration limits.
LENGTH
The capacity of the pipeline can be also fluctuate when the length of the pipeline is varied. For example in the 3 section pipeline which connects the Midcontinential pipeline with the Transcontinental pipeline in the USA, the variation in length needs to be determined for each section for optimization of capacity in operation.
For the total pipeline, which is planned, there is a current span of pipeline which is accumulated from;
Section 1 (442km), section 2 (317km), and section 3 (48km)
This gives an overall span of 807km of pipeline of diameters varying from 30''(750mm DN) to 42'' (1040mm DN).
To look at the varying economic trade off from this we can take one section of the pipeline e.g. Section 3 (48km) and vary the length of this pipeline to illustrate.
Table 5
Length as an inhibitor to capacity
Length (km) 
CF 

20 
0.223607 

24 
0.204124 

28 
0.188982 

32 
0.176777 

36 
0.166667 

40 
0.158114 

48 
0.144338 

52 
0.138675 

56 
0.133631 

60 
0.129099 

64 
0.125 

68 
0.121268 

72 
0.117851 

76 
0.114708 

80 
0.111803 

Figure 6.The effect of pipeline length on capacity
From this graph we can see that as with the drop in capacity the curve provided has the appearance of a declining semi parabolic. The red line indicates the minimum losses in capacity for an achievable span of 20km. However in planning if this length of pipeline were to be undertaken additional costs may be incur in permits and choice of pipeline to meet with design factor needed by the location, if in proximity to population and planning of the pipeline. There will always be an economic and capacity trade off.
If we take the midpoint of this curve (as a point of reference to where the optimum distance should occur knowing that pipeline cost increases and capacity factor decreases less steadily beyond this point) we should find the optimum length of pipeline length to capacity factor. gas pipeline financial capital cost
From the graph this comes to a value of 44 km whereas the actual section under investigation is the 48 km pipeline. The differences in actual planning a pipeline of this length may be down to a number of factors such as costs in negotiating terrain, environmental permits, location of pipeline to dwellings, suburban limits etc. However effectively the most economical length of pipeline would be achieved post the 44 km length as this is when the rate of decline in capacity begins to tailor away. Additional to these factors, as with the other variables, there is an amount of tolerance to the planned length.
COMPRESSOR STATIONS
Compressor stations and compressors generally added to a pipeline to increase capacity. By adding these units at strategically placed intervals in the pipeline the pressure drop in the pipeline is rectified in order to maintain a responsible pressure for further transmission. Pressure drop occurs naturally through the frictional forces in the pipeline which are ever occurring even though some major pipelines are fitted with an epoxy coating to minimize friction. An additional, the major contributor to pressure loss is when terrain inflicts a gradient in the pipelines design. In designing a compressor station along a pipeline consideration must be given to achieve efficiency in the design.
Usually a compression ratio of around 1.5 is acceptable. Thus design factors are considered to try to reduce power input to maintain this level of compression ratio. Effectively today, equipment such as centrifugal compressors are seen as the most efficient in compressing gas however the cost of running this sort of plant has high fuel costs. Therefore there is always a trade off between the economic implications of designing compressor, which are of a high capacity, to maintaining a high capacity in the pipeline. These points will be investigated further.
Compression stations work as a function of the pressure drop and as so will be designed and positioned as a corrective measure as shown in the diagram below.
In the diagram above the intermediate compression station is placed at the half way point between the source location and the end location. However the pressure drop in pipelines is generally nonlinear so this is only a theoretical positioning. Further adjustments on the compression stations position will be made by adjusting the compressor ratio in accordance with the end location. Also to ensure that the compressor works efficiently and any costs that are used up in compressing the gas back to a satisfactory transmission pressure will be justified. If the compression station is placed too close to the end location then two things will happen.
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Figure7. Incremental compressor arrangement
In addition, adjust the discharge pressure of the compression station so that the gas reaches the required pressure at the end location. Or we will have to move the compression station further upstream so that the pressure drop is able to decline the discharge pressure suitably to the end pressure.
Calculations to acquire a suitable location for compressor station are made on a trial and error basis using the general flow equation.
So the taking a standard value for source pressure P1 and receiving pressure P2 we can assume that the compressor in use will be operating within its capacity:
Initial/Discharge Pressure P1 = 70 bar
Receiving/Suction pressure P2 = 50 bar
?P = 20 bar (standard Optimum)
Compression ratio = P1/P2 = 1.4: 1
Compressor sizing 1.5 (centrifugal compressor)
EXAPLE CALCULATIONS
For the general gas flow equation we can overview a system such as the 48km pipeline in USA and how it could potentially use compressors to enhance flow rate to a location. For this example we estimate that the flow rate to be maintained beyond the end of the pipeline and hence the compression station will be at the 48km point.
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Figure 11. Practical example of compressor planning
Where, Ts = 288,
Ps= 1.013025,
70,
d = 750mm,
S = 0.7,
L= 48km
T = 288
and Z = 0.85
Q = 0.000575 x x= 163.4 x x
= 1.36 mill m^{3}/day
The daily capacity along the pipeline would be 1.36 mm^{3}/day. To maintain this capacity into the section of 327km pipeline a compression unit could be placed at the end to rectify the pressure drop across the pipeline.
The yearly capacity would therefore be 496.4 million m^{3}/year.
ADIABATIC COMPRESSION
In compression through a closed system, the compression can be considered as adiabatic when it doesn't give any heat off to the surroundings. If the compression is heat efficient, which generally they are, then the size of the compression unit can be calculated from the gas flow (capacity) and the suction pressure and discharge pressure( pressure differential) for the unit.
And the work done is calculated from the equation:
Wa = x T_{1}_{ }_{[}_{ 1]}
We can therefore use the 48km pipeline flow rate and the optimum pressure differential to calculate the number of compressors needed to maintain the flow rate prescribed for the next stage of the transmission line I.e. 1.35 mill m^{3}/day into the 327km section.
A simplified version of the equation for work done discounts any heat lost due to adiabatic process.
Wa = x (288) Log_{e}_{ }=_{ }39,162 J/Kg
The volume of gas processed per second can be found by:
1.36 x 10 ^{6} / (24 x 3600) = 15.74 cubic metres of gas/second.
And the weight of the gas is given by 15.74/0.714 = 22.05 kg
Wt, the total work done
22.05 x 39,162 = 863,336.4 J
The total work required to transfer 21.07 kg would be 863.33 KJ.
Further more, we can size the compressor power unit that we need.
Power = 4.0639 x 1.36 ((288) ( =
621.23 kW
The compressor driver may have mechanical efficiency of 98% so
Driver power = = 633.91kW
Sizing the compressor units for Horse Power we can use the equation
HP = 0.0857 x 48.85 ((288) ( = 470.66
HP.
With the mechanical efficiency of the driver taken into consideration as 0.98 we can calculate the break horse power of the unit.
BHP = = = 480.26 BHP
The BHP required to drive the compression operation could be effectively one 500 BHP unit.
Compression units vary in size from 50 BHP up to around 20,000 BHP. This is of the smaller capacity however in further planning it would be recommended to oversize the unit.
CONCLUSION
From the results obtained it shows that due economic analysis must be carried out before pipeline development:
1. Detailed market survey to ascertain peak loads, average and minimum demand of consumers in order to adequately size a pipeline
2. Detailed route survey to ascertain the nearest distance for gas supply to a customer
3. Detailed energy audit of consumer equipment in order for pressure distribution
4. Detailed engineering design to properly cost a pipeline network
With the knowledge of how the above four parameters discussed affects capacity one can properly cost and size adequately a pipeline for either transmission or distribution purpose.
REFERENCE
1. Kadir A., University of Salford, Distribution and Transmission Lecture Notes 2011/12.
2. E. Shashi Menon, Pipeline Hydraulics, Taylor & Francis 2005.
3. Roberts, John.,1996. Caspian Pipelines. The Royal Institute of International Affairs.
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