The methodology of application of the system analysis and the relevant mathematical models for optimization of gas flows in complex gas transportation systems (GTS) are considered taking into account the gas pipelines emissions’ environmental impact. The proposed approach allows the researcher to estimate the level of geoecological risks at separate sections of pipelines and rank the GTS subsystems by this index. In turn, it permits to single out the pipeline sections sets, where the management solutions and measure have to be undertaken in order to decrease the level of geoecological risks. The stage of the system synthesis envisages the possibility of the geoecological risk assessment during operation of the whole system.
In the gas industry of the Russian Federation the gas transportation system (GTS) exerts the main impact on the environmental condition, which is caused by its large length - to the tune of 155 thou km, and by its capacity - over 44 mln kW. The most significant emissions of pollutants in the process of gas pipelines operation occur due to the so-called gas consumption for own needs. On the gas mains the main share of gas consumption for own needs includes the fuel gas used for compressor stations (CS), technological losses, including leakages on the linear part and during CS operation, emergency situations and other technological needs, including losses during repair of gas pipelines.
On the average, in the structure of gas consumption for own needs the fuel gas accounts for 80 percent, other technological needs - 8 percent and technological losses of gas - 12 percent. Furthermore it should be noted that in the total consumption of fuel-energy resources the share of natural gas is about 92 percent . Figure 1 presents the dynamics of the fuel gas consumption in GTS, in percentage, by 1999. If this tendency keeps on, then with the planned gas production by 2020 amounting up to 590 bcm this index can exceed 50 bcm. Therefore the problems of reduction of the GTS energy intensity and, as a result, the decrease of negative impact on the environment, become of first priority.
Among the most promising technological solutions, which allow the gas industry to improve the indices of the energy intensity of gas pipelines, are the increase of the working pressure, the use of internal smooth coating of pipes, application of high-efficiency gas producing units (GPU). For example, the use of pipes with internal smooth coating and high-efficiency GPU allows increasing the gas pipeline capacity up to 10 percent .
The optimization of the of gas pipeline parameters seems the most effective direction of energy saving on the basis of system approach. It implies the consideration of the gas pipeline as an element of GTS taking account of its technological, and technical and economic interrelations with other UGSS (unified gas supply system) objects. In fact, this implies the consideration of the gas transportation complex as a unified system and the formation of general scenarios of development and reconstruction.
Moreover an optimum distribution of gas flows in GTS allows a wider use of new technologies with the increased pressure and corresponding reduction of the overall power inputs .
The mathematical models, which allow the researcher to minimize the costs of gas transportation through complex gas transportation networks are very well studied . However, in practical realizations the functionals, which, together with the technical and economic indices, take account of geoecological components, are very seldom considered. Of course, in terms of economy, expenditures for reduction of the geoecological risks are much less than overall power inputs. Nevertheless, the optimization of gas flows in the gas transport networks, subject to the economic assessment of the GTS environmental impact, will allow somebody to work out decisions on the geoecological risks management. This will enable to decrease the costs of direct gas losses occurring due to gas leakage during its transportation, storage and conducting repair works. In addition to the obvious economic damage from these losses, this approach allows the company to consider the reduction of indirect losses, connected with the possible trade in greenhouse gas emission quotas [5,6].
Let us examine the methodical approaches and mathematical models allowing to realize the above stated principles. Figure 2 shows the schematic aggregated diagram of the gas transportation system of the unified gas supply system.
The degree of the system’ aggregation is selected, on the basis of existing zones with different selling prices for natural gas, so that for the GTS sections this index at the entrance and at the exit would be different. With the currently existing approaches the planned gas flows are calculated by the maximization of the functional:
where Qi - flow along the i arc, vi - weight of the i arc.
The optimization of the functional is carried out with limitations:
Qi <= Mi, (2)
where Mi - the maximum output of the gas pipeline section.
Actually the issue in question is the calculation of annual gas flows at all sections of the gas transportation system subject to minimization of transportation costs and the fulfillment of commitments regarding gas supplies to users. Value Ti, in turn, is function of gas flow Qi, therefore, the optimization of functional (1) is carried out iteratively. The methods of construction and optimization of gas flows in complex gas transportation systems and gas-distribution networks are well studied for different classes of tasks [2, 7, 8]. Therefore, we won’t dwell on them and come to the formation of the functional for optimization of gas flows taking account of ecological component.
For each section the economic component of the estimation of geo-ecological consequences includes:
- determination of the volumes of probable gas emissions in accidents and leakage on the basis of statistical models;
- determination of the volumes gas release during the planned repair works on the basis of optimization of schedules of their conducting;
- determination of the volumes of gas consumed for the fuel needs on the basis of minimization power inputs at compressor stations.
The mathematical models, which allow evaluation of specific economic losses from environmental impact for all enumerated tasks are represented in the paper . Thus, the weight of arcs in minimized functional (1) is determined from the ratio:
vi = Ti + Ei , (5)
where Ei - the economic component of environmental impact during the year in the i-section of the gas transportation system.
Let us explain the above said on a simple numerical example (Fig.3). Let us assume that the annual production in node S amounts to 400 bcm. Accordingly, the annual consumption in node W will be equal to 400 bcm. (gas consumption for its own needs is tied to node W).
The additional data, necessary for conducting the calculation are represented in Table 1.
Let variant 1 be understood as the calculation of the gas flow without taking account of the ecological component, and variant 2, accordingly, as the calculation with ecological component. Then for variant 1 we have:
weight of the 1-st arc vi = 2*200/100 = 4.00 $/thou m3
weight of the 2-nd arc vi = 2*210/100 = 4.20 $/thou m3
Conducting the optimization with account of limitations for the maximum capacity of the arc (section of gas pipeline) we receive the gas flows (Table 1).
For variant 2 we have:
weight of the 1-st arc vi = 2*200/100 +0.25*200/100 = 4.50 $/ thou m3
weight of the 2-nd arc vi = 2*210/100 +0.10*210/100 = 4.41 $/ thou m3
The results of optimization with account of limitations for the maximum capacity of the arc (section of gas pipeline), subject to the ecological component, are shown in Table 1.
Thus, from the obtained results of the calculation it is obvious that in variant 1 completely loaded was the first section of the system, and in variant 2 - the second. The presented simple example shows that consideration of the ecological component can to a significant degree influence the redistribution of gas flows.
As applied to the considered system (Fig. 2) practical calculations have been carried out, their results are shown in Table 2.
The value of the geoecological risk level in Table 2 is determined in the range: "low" (L), "medium" (M) and "high" (H). The estimation of risk levels is conducted on the basis of the change in the gas flow value for each section. In case of significant increase of gas flow, as a result of optimization taking account of the ecological component, relative to the analogous value, calculated without its account, it is assumed, that in this section the level of the geoecological risk is "low". In this case the consequences from environmental impact of operating gas pipeline, as compared with other sections, will be lower. These consequences are estimated in value terms per volume unit of gas transmitted through the GTS section.
Similarly, in case of significant decrease of gas flow of gas (column 4, Table 2) as compared with its value without taking account of the ecological component (column 3, Table 2), the level of the geoecological risk is evaluated as "high". For the remaining sections the level of risks is defined as "medium". In the given calculations the range of the "medium" level of geoecological risks in the section is accepted as 1.5% of the gas flow value, calculated without taking account of the geoecological component.
The obtained results allow us to distinguish sections, where geoecological risks are relatively small. Risk levels for such sections in Table 2 are highlighted with green color. At the same time, the carried out calculations allow to reveal sections with increased (compared with the average value for the whole system) level of environmental impact of trunk gas pipelines emissions (in Table 2 these sections are highlighted with red color).
Thus, for each unfavorable GTS section from the cited list it is expedient to envisage measures allowing to decrease the geoecological risks. Furthermore, the proposed approach allows us to estimate the total geoecological risks both for the entire GTS system and individual subsystems (corridors, gas pipelines belonging to separate companies, etc.). Table 2 contains the obtained weighted average estimation of geoecological risk for the entire gas transportation system, which shows that the environmental impact of the GTS system’s emissions thus far are at the average admissible level (functional F).