Figure 1. Pipeline capacity increases with increased inlet pressure

Inlet pressure varied in stages of 10 bar

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 (P₁²-P₂²) with a fixed inlet pressure and variation of pressure drop.

SAMPLE CALCULATION

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 re-enforcement 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

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

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 non-linear 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 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 m³/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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