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Weekly UpdatesAmong the regulatory aspects in the economic study of the pipeline industry, an important one is concerned both with the pricing policies recommended by the regulatory institutions and with the empirical and theoretical research that suggests more efficient ways of applying pricing policies in the face of practical problems. Below I will show with an engineering production function some facts related to the returns to scale of the gas transmission industry; after that a cost function is derived and the increasing returns to scale associated to that industry are shown in that cost function.
Research on the natural gas industry, particularly that focused on its economic aspects, shows that pipeline transportation of gas is characterized by economies of scale and large "sunk" costs. The fact that natural gas is largely restricted to pipeline delivery imposes significant economic constraints on the ability to create competition among suppliers. Since pipeline capacity increases much more rapidly with increasing pipe diameter than does investment, there are substantial economies of scale in gas pipelining.
Kahn (1988) emphasizes these particular characteristics of pipelines:
Increasing the diameter of a pipeline allows important economies of scale. As Kahn observes, the carrying capacity of a gas pipeline is proportional to its interior cross-sectional area, whereas the amount of pipeline material used is in proportion to the circumference of the pipe. Hence, if the input of material used in the pipe is doubled, the carrying capacity of the pipe is more than doubled. However, there are limits to the scale economies that can be achieved by increasing the diameter of the pipe, determined by pressure differentials between the inlet and outlet of the pipeline and the length of the line itself, among other factors.
In determining the cost of a pipeline, it is important to think in terms of the capital and operating and maintenance cost of the pipe and of the compressor stations. It is necessary to account for the costs of construction of the line and the compressor stations, as well as the cost of installing all the equipment they require. Furthermore, the operation and maintenance costs of both elements must be considered. In working with this kind of information, models have been proposed (e.g., Lehn, 1943; Chenery, 1949), whose analyses have been built around certain engineering concepts, as described below.
GAS TRANSMISSION PRODUCTION FUNCTION
In Chenery's (1949) formulation for the process of gas transmission, attention is centered on the two basic capital inputs to the process, pipe and compressors. Compressors are employed to raise the pressure of the gas, which decreases gradually due to frictional losses of energy when gas is moved along the pipe.
Chenery uses a system of equations to describe the engineering relations governing the flow of gas in a pipe. In the pipeline problem, compressors are required to transport the gas. Since there is energy loss in the pipe due to friction in transmission, and this loss is a decreasing function of pipe size, it follows that the greater the pipe diameter, the smaller the required compressor capacity to pump any given amount of gas a specific distance. Hence, the mechanism of substitution between pipes and compressors is based on calculations of energy loss in engineering processes and the effect of equipment's capacity size in reducing this loss. Hence, Chenery arrives at all engineering production function that he uses to get the pipeline capacity and power requirements. In order to get the natural gas transmission cost analysis shown below, Chenery's approach is considered together with some important technological changes that affect the substitutability between pipe diameters and compressor horsepower. Moreover, since Chenery's paper was written, some important empirical results have been obtained in the study of the gas transmission and compression process: therefore, some of these changes are considered in the study in order to get a more accurate gas transmission production function. (1)
Technical relations establish that the amount of gas transmitted by a pipe depends on the initial and terminal pressures of the pipe, its diameter, and its length. Considering a steady flow of natural gas, and according to engineering relationships, Chenery shows that the flow of natural gas through a pipeline may be expressed by the general flow equation: (2)
Q = 38.77 x [10.sup.-6] [T.sub.b]/[P.sub.b][[1/f].sup.1/2] [[P.sup.2.sub.1] - [[[P.sup.2.sub.2]/GTLZ].sup.1/2][D.sup.5/2] (1)
where Q is pipeline flow in MMcfd (millions of cubic feet per day); [T.sub.b] is base temperature in R: (3) T is mean flowing temperature in R; [P.sub.b] is base pressure in psia (pounds per square inch absolute): (4) PI is initial pressure in the pipe in psia: [P.sub.2] is terminal pressure in the pipe in psia: G is gas specific gravity; (5) L is pipeline length between compressor stations in miles; D is inside diameter of the pipe in inches; f is friction coefficient (dimensionless); and Z is compressibility factor at average conditions (dimensionless). (6)
The formula was derived from thermodynamic reasoning except for the introduction of the empirical flow coefficient. A standard approximation for the friction coefficient is the one that assumes that f varies as a function of the diameter in inches. (7) Considering additional changes in the elevation of the pipeline, it may be derived:
Q = 4.33.5 x [10.sup.-6][T.sub.b]/[P.sub.b][[[P.sup.2.sub.1] - [e.sup.s][P.sup.2.sub.2/GTZLe].sup.1/2] [D.sup.8/3] (2)
where
s = 0.0375 Gh/T (3)
and h is the outlet minus inlet pipeline elevation in feet.
Considering the former equation, and assuming a uniform slope along the pipeline and after some simplifications, the general flow equation becomes: (8)
Q = [C.sub.0][[[R.sup.2] - [alpha]/L].sup.1/2] [D.sup.8/3] (4)
where
[C.sub.0] = 433.5 x [10.sup.-6][T.sub.b]/[P.sub.b][[1/GTZ].sup.1/2] [P.sub.2][[s/[alpha] - 1].sup.1/2] (5)
and
[alpha] [e.sup.s]; R = [P.sub.1]/P.sub.2] (6)
In the case of compressors, the empirical characterization for computing the power needed to compress natural gas for common use is given by the following expression derived by Katz et al. (1959):
H = 3.0325E [P.sub.b]TZ/[T.sub.b] [k/k - 1] ([f.sup.(k-1)/k] - 1)Q (7)
where [T.sub.b] is base temperature in [degrees]R; T is suction temperature in [degrees]R; H is compressor horsepower per million of cubic feet of gas; Q is flow in MMcfd; [P.sub.b] is pressure of the gas in psia; Z is compressibility factor (dimensionless); r is compression ratio [P.sub.1]/[P.sub.0]; [P.sub.0] is compressor suction pressure in psia; [P.sub.1] is compressor discharge pressure in psia; E is mechanical efficiency (actual horsepower/theoretical horsepower); and k is ratio of specific heats. (9)
The previous equation can be rewritten as:
H = [C.sub.1]([r.sub.[beta]] - 1)Q (8)
where
[C.sub.1] = 3.0325E [P.sub.b]TZ/[T.sub.b][1/[beta]] (9)
and
[beta] = k - 1/k (10)
Assuming that the inlet pressure at the point of compression is equal to the outlet pressure of the pipe, then [P.sub.0] = [P.sub.2] and R = 1 = PI/Po. Thus, we are able to reformulate (4) and (8):
Q = [C.sub.0][[[r.sup.2] - [alpha]/L].sup.1/2][D.sup.8/3] (11)
and
H = [C.sub.l]([r.sup.[beta]] - 1)Q (12)
If we eliminate r in both (11) and (12), then the engineering production function can be written as:
F(Q, D, L, H) = [LQ.sup.2]/[C.sup.2.sub.0][D.sup.16/3] + [alpha] - [[H/[C.sub.1]Q + 1].sup.2/[beta]] = 0 (13)
[FIGURE 1 OMITTED]
A production function relating capital, labor, and other inputs to the level of output is defined implicitly by the function we have considered but cannot be written explicitly for this case. However, as long as the technical relationship between capital and labor is roughly fixed, we can consider a Leontief-like technology between capital, labor, and other inputs. The nature of the natural gas transmission process is such that the only possibility of substitution among factors is between compressors and pipe, because the quantities of labor and maintenance material are, to a general extent, determined by the size of the two types of capital goods installed. (10)
Figure 1 presents the engineering production function for different levels of capacity when the pipe length between compressor stations remains constant. From the graph we can appreciate the substitutability between the two capital factors, pipeline diameter and compressor horsepower: the larger the pipeline diameter available, the lower the horsepower required in the compressor station to move a given amount of gas.
COST FUNCTIONS
When comparing alternatives in providing natural gas transmission service, it is important to consider the overall costs of transmission, including capital and maintenance and operating costs. The choice between the different production factors, if an optimal level of efficiency is to be attained, must be selected considering their relative prices and marginal productivity. To reach that choice, two facts must be taken into account regarding the cost function of this industry. First, the cost structure of this industry can be characterized as one with large fixed costs; second, it is important to notice that the elements of cost in the long-run cost function may be divided into two categories: annual charges dependent on the cost of installed transmission equipment (return and depreciation of investment), and annual operating and maintenance costs dependent on the quantities of capital goods installed. (11)
The derivation of the cost of a pipeline should be performed considering the combination of capital, operating, and maintenance costs that minimize the total cost of the project over its lifetime. Furthermore, two fundamental elements must be considered in the cost analysis of a natural gas transportation system: the line cost, depending on its diameter, and the compressor station cost, depending on the horsepower capacity required. Hence, the estimating process described below considers the capital and the operating and maintenance costs for both pipe and compressor stations.
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