Monte Carlo Simulation – A Key for a Feasible Gas Pipeline Design
Sidney P. Santos
 2009
Copyright 2008, Pipeline Simulation Interest Group
This paper was prepared for presentation at the PSIG Annual Meeting held in Galveston, Texas, May 12 – May 15 2009.
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Abstract
Gas pipeline projects are capital intensive and are exposed to many risks related to uncertainties of their main components such as capital investment (material and services) – Capex, operation and maintenance costs – Opex, construction and assembly – C&A schedule, C&A Costs and others. Such items need to be properly addressed to mitigate project risk otherwise they may impact negatively the project sustainability normally measured by the project net present value – NPV.
The availability of the compression system, if not properly addressed, may expose a gas pipeline project to undesirable risks. This paper will present a case study demonstrating how useful is Monte Carlo Simulation in association with Thermohydraulic simulation and economic evaluation in identifying and quantifying risks and in helping defining the optimum level of availability for the gas pipeline compression system. The installation of standby compressor station units helps achieving the necessary availability level to face contractual obligations related to transmission capacity.
Technical and economical evaluation are of fundamental importance to support the decision making process in the design phase of a pipeline project. Monte Carlo Simulation is also used in the economical evaluation to provide accurate and reliable results.
The aforementioned approach impacts project positively while supporting transportation rate design and also defining pipeline capacity that Transporter will negotiate with the Local Distribution Companies (LDC’s) on a firm contractual basis.
This paper presents a case study that uses all the above mentioned technology.
Introduction
Credit for inventing the Monte Carlo method often goes to Stanislaw Ulam, a Polish born mathematician who worked for John von Neumann on the United States’ Manhattan Project during World War II. The Monte Carlo method, as it is understood today, encompasses any technique of statistical sampling employed to approximate solutions to quantitative problems. http://www.riskglossary.com/link/monte_carlo_method.htm Accessed in: May 28, 2008.
According to Evans and Olson (1998) Simulation is the process of building a mathematical or logical model of a system or a decision problem, and experimenting with the model to obtain insight into the system’s behavior or to assist in solving the decision problem. The authors define Monte Carlo simulation, basically, as a sampling experiment whose purpose is to estimate the distribution of an outcome variable that depends on several probabilistic input variables. Monte Carlo simulation is often used to evaluate the expected impact of policy changes and risk involved in decision making. Risk is often defined as the probability of occurrence of an undesirable outcome.
As a reference for applying Monte Carlo simulation in compressor station project selection Santos (2003) has evaluated the impact of Capex, Opex, and Construction and Assembly schedule on the economic sustainability of a project while comparing two different alternatives for implementing compressor stations in Petrobras gas pipeline network as described below:
 (a) Compressor station as a Transporter asset: in this alternative Capex, Opex are Transporter responsibility. Transporter will keep the ownership of the compressor station asset.
 (b) Compression service contract: in this alternative Capex and Opex are the responsibilities of a Service Provider Company that will be responsible for the installation, operation and maintenance of the compressor station and will be the owner of the asset. Transporter will pay for the compression service under a contractual relationship.
Monte Carlo simulation was of fundamental importance in supporting Petrobras final decision on contracting compression service in 2002 from a third party company instead of holding the ownership of the stations and being responsible for operation and maintenance thereof. The selected alternative was more economic and less risky. Since 2002 more than 18 compressor stations have been installed under compression service contracts.
The case study presented in this paper uses Monte Carlo simulation to help defining the optimum availability level for a gas pipeline project and also the project risk related to some important input variables (e.g. Capex, Opex and C&A Schedule).
Methodology
The methodology adopted for this case study considers the following steps:

A pipeline design from point A to point B for different diameters (four alternatives):
 Thermohydraulic simulations;
 Compressor stations quantity definitions based on predefined compressor ratio;
 Compressor units selection based on overall thermodynamic efficiency and market availability;
 Selection of the best pipeline alternative by comparing riskfree transportation rate (Jcurves) with nominal pipeline capacities;
 Availability study for the pipeline compression system using Monte Carlo simulation and different levels of compressor units redundancy for the pipeline compressor stations;

Rate design for the best alternative from item 2 incorporating risk analysis:
 Availability study with Monte Carlo simulation;
 Independent variables (e.g. Capex, Opex and C&A Schedule) with statistical distribution;
 Feasibility study
 Project’s final decision.
Thermohydraulic Simulation
Three configurations for unavailable compressor units were simulated as explained below:
 Failure of one compressor unit at one station
 Failure of two compressor units at one station
 Failure of one compressor unit at one station and failure of another one at a contiguous station (upstream or downstream)
Simulation Results Analysis
Compressor stations were modeled with two compressor units operating in parallel arrangement with standard flow of around 529.5 MMCFD each.
Unavailability of one compressor unit at one compressor station causes the remaining unit to shut down or stay in idle speed because one single unit does not have power enough to sustain the operation. As an example the unavailability of station #2 causes pipeline capacity to drop to 915.7 that is 72.9% higher than one compressor unit design capacity of 529.5 MMCFD. Same situation happens with the unavailability of 2 (1+1) compressor units at contiguous stations. As an example the unavailability of stations #2 and 3 causes pipeline capacity to drop to 792.8 MMCFD that is 49.7% higher than one compressor unit design capacity of 529.5 MMCFD.
Five different compressor station alternatives have been evaluated:
 (a) Without standby compressor units;
 (b) With 2 standby units (1 at station #3 and #6)
 (c) With 3 standby units (1 at #2, #4 and #6)
 (d) With 4 standby units (1 at # 1, #3, #5 and #7)
 (e) With 7 standby units (1 at #1 to #7).
Thermohydraulic simulations capacity results due to unavailability of compressor units are summarized on Tables 3, 4, 5, 6 and 7.
Monte Carlo Simulation
Monte Carlo simulation is based on a spreadsheet model where the uncertainties variables are modeled according to their statistical distribution and random number generation. While running the model all the uncertain (independent) variables will change randomically and in most of the cases independently as would happen in real life. When we have correlated variables they are modeled accordingly. The software @Risk 4.5 with Microsoft Excel was used to run this case study models.
 Availability Study: In the availability study all gas pipeline compressor stations are modeled with their two compressor units in parallel arrangement and availability value and statistical distribution are addressed to each compressor units. The model run more than 5000 iterations and then we evaluate the frequency of compressor units’ failures that will be simulated Thermohydraulically to support the availability level evaluation and consequently the decision making on standby units to be installed.
 Economic Study: In the economic study all uncertain independent variables (e.g. Capex, Opex, pipeline capacity, C&A schedule) are addressed a statistical distribution with their expected values (e.g. in the case of triangle distribution: minimum, best guess and maximum values) as part of a spreadsheet used to evaluate the impact of those independant variables on the dependant variables such as NPV or IRR. Statistical distributions are then generated for the dependant variables that will support risk quantification and mitigation.
Case Study
This case study is based on a pipeline project that goes from a gas supply receipt point to targeted market 1,000 miles distant delivering 1,059.4 MMSCFD (30 MMm3/d) of natural gas on firm contractual basis. Four pipeline alternatives have been considered as shown in Figure 1 and as described below:
Alternative I:  

Pipeline diameter:  30”  
Compressor stations quantity:  19  
Alternative II:  
Pipeline diameter:  32”  
Compressor stations quantity:  13  
Alternative III:  
Pipeline diameter:  34”  
Compressor stations quantity:  9  
Alternative IV:  
Pipeline diameter:  36”  
Compressor stations quantity:  7  
Technical Assumptions  
Pipeline  
Diameter:  (alt. I, II, III, IV)  
Length:  1000 miles  
Design code:  ANSI B31.8  
Max. Allowed Working Pres. – MAOP:  1440 PSIG  
Pipe material:  API 5L X80  
Pipe internal roughness (epoxy painted):  350 microinches  
Pipeline Inlet Pressure:  1420 psig  
Minimum Pipeline Delivery Pressure:  498 psig  
Pipeline overall heat transfer:  0.39 Btu/h.ft2.F  
Soil temperature:  61 to 86 F  
Depth of cover:  3 feet  
Compressor Station  
Maximum Compression ratio:  1.4  
Suction and Discharge Header pressure drop:  7 psi  
After cooler pressure drop:  14 psi  
After cooler outside temperature:  122 F  
Site elevation  0 feet  
Site Temperature  82.4 F  
Flow Equation:  Colebrook 
Economic Evaluation
To support the economic evaluation the following assumptions were considered:
Technical Assumptions

Three sizes of compressor sets selected according to the power requirement of each gas pipeline alternative:
 15000 ISO hp
 10300 ISO hp
 7800 ISO hp
 Fuel consumption for all four alternatives based on 80% efficiency on the compressor side and 32% on turbine side.
 Without standby compressor unit at the compressor stations.
 Jcurves developed based on the selection of the best available compressor set for each pipeline diameter versus compressor station quantity and at the maximum (nominal) capacity, as shown on Table 1.
Economic Assumptions
Construction schedule:  2 years  
Pipeline material cost:  2000 US$/ton  
Pipeline C&A cost:  
30”:  25,100 US$/mileinch  
32”:  24,473  
34”:  23,652  
36”:  22,864  
Compressor Station Capex  
(2) x 15000 ISO hp:  41.65 MMUS$  
(3) x 15000 ISO hp :  55.62  
(1) x 10300 ISO hp:  19.43  
(2) x 10300 ISO hp:  31.85  
(3) x 10300 ISO hp :  42.54  
(1) x 7800 ISO hp:  15.93  
(2) x 7800 ISO hp:  26.12  
(3) x 7800 ISO hp :  34.88  
O&M C. Sta. (without Fuel):  5% of C.Sta. Capex  
O&M Pipeline:  0.8% of Ppl. Capex  
Depreciation:  20 years  
Taxes:  40%  
Fuel price:  1.5 US$/MMBTU  
Discount rate:  12% a year  
Economic life:  20 years 
First Economic Analysis
This first economic analysis for each pipeline alternative – without standby compressor units – and their respective capacity build up, as Table 1 and Jcurves show in Figure 2 has the objective to help selecting the alternative that presents the lowest transportation rate. By adopting this criterion, Alternative III is the best. Considering that Alternative IV is the secondbest and very close to Alternative III and having the advantage of future expansion capability it was selected as the best one and it is evaluated in more detail with regard to firm capacity, reliability level and risk exposure.
The alternatives’ transportation rates are as follow:
 Alternative I, ND 30” : 1.5105 US$/MMBTU
 Alternative II, ND 32” : 1.4190
 Alternative III, ND 34” : 1.3857
 Alternative IV, ND 36” : 1.3887
The alternative IV allows future capacity expansion at lower Capex and Opex by increasing compressor ratio (from 1.3389 up to 1.40) increasing capacity from 1059 to 1112 MMSCFD. Also allows pipeline capacity expansion from 1059 to 1497 MMSCFD by doubling the compressor station quantity (from 7 to 14).
Availability Analysis
The purpose of the availability analysis is to define the level of redundancy to be adopted for the gas pipeline compression system. It takes into account the following information:
 Compressor unit availability (as shown on Table 2);
 Capex required for standby compressor units;
 Revenues from incremental pipeline firm capacity as a result of enhancing the overall compressor system availability.
Santos (2006) has presented the methodology adopted for the BoliviaBrazil gas pipeline to define the availability level to be adopted for that pipeline compression system and Monte Carlo simulation proved to be of fundamental importance to achieve the goals. Santos (2008) also presents the impact of compression system availability level and risk effects on gas pipeline transportation rate (tariff).
A comprehensive and accurate survey on compressor station reliability and availability was carried out by EPRI (1998) and their findings, as presented on Table 2, provide input for the evaluation of this case study that uses gas turbine drivers and centrifugal compressors.
The availability value of 97.1% or 0.971 is taken into the Monte Carlo simulation model used for the gas pipeline alternative IV with 7 compressor stations with two running compressor units per station without standby compressor units. Four different compressor station configurations are evaluated as defined in the Thermohydraulic Simulation paragraph.
Monte Carlo and Thermohydraulic simulations for configurations (a), (b), (c), (d) and (e) were performed and the frequency of unavailable compressor units was quantified as well as pipeline capacity as shown on Tables 3, 4, 5, 6 and 7 and in Figure 3.
The table first column shows the unavailability configurations of 1 and 2 units per station and also 2 (1+1) units unavailable in contiguous stations. Second column shows the total frequency of occurrence of such unavailability measured in days per operating year. Third column shows resulting pipeline capacity at downstream end of the pipeline that can be maintained under the defined unavailability of compressor units. The wider fourth column shows the unavailability frequency of compressor units (1, 2 or (1+1)) at each compressor station as identified on the header (#1 to #7).
Gas pipeline overall availability is evaluated by dividing the average capacity by the nominal (firm contractual) capacity and then we get the following results for each alternative of standby compressor units installation.
 (a) Without standby compressor units : 0.9456
 (b) With 2 standby units (1 at station #3 and #6) : 0.9594
 (c) With 3 standby units (1 at #2, #4 and #6) : 0.9661
 (d) With 4 standby units (1 at #1, #3, #5 and #7) : 0.9764
 (e) With 7 standby units (1 at #1 to #7) : 0.9994
Economic Evaluation
Second Economic Analysis
The purpose of this second economic analysis is to quantify the benefit of increasing the availability level of the compression system by installing standby units at the compressor stations. This evaluation takes into account the firm contractual pipeline capacity that can be committed and potential losses of revenue and penalties from nondelivered firm contractual capacity.
Two distinct situations may happen that requires economic analysis to define the availability level to be adopted:
 New gas pipeline project: transportation rate of each configuration incorporates all Capex and Opex associated with the pipeline and standby compressor units and represents gas pipeline total cost of the transportation service on energy basis. Transportation rates are calculated for average capacities;
 Existing gas pipeline: transportation rate does not incorporate Capex and Opex associated with standby units. The approach is to invest in standby compressor units to mitigate risk exposure to losses of revenue and contractual penalties as reflected by the NPV of each alternative. Transportation rate is constant and calculated for nominal (maximum) capacity.
New Gas Pipeline Projects
 Configuration (a)  Without Standby Units
 System availability : 0.9456
 Nominal capacity : 1059 MMCFD
 Average potential capacity shortfall : 57.7 MMSCFD
 Average capacity : 1001.8 MMCFD
 Transportation rate : 1.4668
 Average PV of Potential losses : (411.6) MMUS$
 Configuration (b) – With 2 Stand by Units
 System availability : 0.9594
 Nominal capacity : 1059 MMCFD
 Average potential capacity shortfall : 43.4 MMSCFD
 Average capacity : 1015.6 MMCFD
 Transportation rate : 1.4614
 Average PV of Potential losses : (309.1) MMUS$
 Configuration (c) – With 3 Stand by Units
 System availability : 0.9661
 Nominal capacity : 1059 MMCFD
 Average potential capacity shortfall : 36.4 MMSCFD
 Average capacity : 1022.7 MMCFD
 Transportation rate : 1.4587
 Average PV of Potential losses : (258.5) MMUS$
 Configuration (d) – With 4 Stand by Units
 System availability : 0.9764
 Nominal capacity : 1059 MMCFD
 Average potential capacity shortfall : 25.4 MMSCFD
 Average capacity : 1034.1 MMCFD
 Transportation rate : 1.4508
 Average PV of Potential losses : (179.3) MMUS$
 Configuration (e) – With 7 Stand by Units
 System availability : 0.9994
 Nominal capacity : 1059 MMCFD
 Average potential capacity shortfall : 1.0 MMSCFD
 Average capacity : 1058 MMCFD
 Transportation rate : 1.4391
 Average PV of Potential losses : (7.4) MMUS$
The economic results above allow us to come to the following conclusions: Configuration (e) is the best one; Presents the lowest risk related to potential losses; Presents the lowest transportation rate; Is the most competitive alternative configuration.
Existing Gas Pipeline
For an existing pipeline and assuming the nominal pipeline capacity has been contracted as firm capacity without standby compressor units all the associated costs (Capex and Opex) for the installation of standby compressor units are considered as new investments that are not included in the transportation rate.
 Configuration (a)  Without Standby Units
 System availability : 0.9456
 Nominal capacity : 1059 MMCFD
 Average capacity : 1001.8 MMCFD
 Transportation rate at nominal capacity : 1.3888 US$/MMBTU
 Average PV of Potential losses : (389.7) MMUS$
 Configuration (b) – With 2 Stand by Units
 System availability : 0.9594
 Nominal capacity : 1059 MMCFD
 Potential capacity shortfall : 43.4 MMSCFD
 Average capacity : 1015.6 MMCFD
 Transportation rate at nominal capacity : 1.3888 US$/MMBTU
 Average PV of Potential losses : (293.7) MMUS$
 Average PV of avoided losses : 96.0 MMUS$
 Capex PV for stand by units : 20.2 MMUS$
 NPV : 75.8 MMUS$
 Configuration (c) – With 3 Stand by Units
 System availability : 0.9661
 Nominal capacity : 1059 MMCFD
 Potential capacity shortfall : 36.4 MMSCFD
 Average capacity : 1022.7 MMCFD
 Transportation rate at nominal capacity : 1.3888 US$/MMBTU
 Average PV of Potential losses : (246.1) MMUS$
 Average PV of avoided losses : 143.6 MMUS$
 Capex PV for stand by units : 30.3 MMUS$
 NPV : 113.3 MMUS$
 Configuration (d) – With 4 Stand by Units
 System availability : 0.9764
 Nominal capacity : 1059 MMCFD
 Potential capacity shortfall : 25.4 MMSCFD
 Average capacity : 1034.1 MMCFD
 Transportation rate at nominal capacity : 1.3888 US$/MMBTU
 Average PV of Potential losses : (171.6) MMUS$
 Average PV of avoided losses : 218.1 MMUS$
 Capex PV for stand by units : 40.5 MMUS$
 NPV : 177.6 MMUS$
 Configuration (e) – With 7 Stand by Units
 System availability : 0.9994
 Nominal capacity : 1059 MMCFD
 Potential capacity shortfall : 1.0 MMSCFD
 Average capacity : 1058 MMCFD
 Transportation rate at nominal capacity : 1.3888 US$/MMBTU
 Average PV of Potential losses : (7.1) MMUS$
 Average PV of avoided losses : 382.6 MMUS$
 Capex PV for stand by units : 70.8 MMUS$
 NPV : 311.8 MMUS$
The economic results above allow us to come to the following conclusions:
 Configuration (e) is the best one;
 Mitigates risk related to potential losses;
 Presents the highest NPV.
Conclusions from Second Economic Analysis
Installation of standby units for existing or new pipeline projects presents significant economic benefits to Transporter. The Tables 8 and 9 show Monte Carlo simulation results for new and existing pipeline projects with 90% confidence interval for the variables. Monte Carlo simulation – in association with thermohydraulic simulation and economic analysis – is very powerful in providing information to support the decision making process.
Risk Evaluation
For a new gas pipeline project and once selected the best gas pipeline alternative and also defined the compression system availability level, as previously described in this paper, the next step is to perform the risk evaluation. The risk evaluation is performed by using a spreadsheet model and a risk simulator. For this case study it was used Microsoft Excel and @Risk 4.5. The economic model follows the traditional approach and the assumptions as defined previously in this paper. The only additional thing is to define the statistical distribution to be adopted for the selected independent variables (Pipeline capacity, Capex, Opex and C&A Schedule) and their volatility (variance, standard deviation or even minimum, maximum and best guess values over the average). The independent uncertainty variables and their statistical distributions for the purpose of this paper (see Figures 4, 5, 6 and 7) were assumed as follows.
 Pipeline Capacity: [Discrete from MC availability study]
 Capex: [Lognormal (1258, 126, 1,195)]
 Opex: [Lognormal (32.63, 3.26, 29.37)]
 C&A Schedule: [Pert (95%, 100%, 125%)]
Risk Evaluation Results
The simulation result shows the NPV – the dependant variable – behavior as shown in Figure 8. As seen from Figure 8 the NPV distribution has a probability of 0.8328 of being between 0 and a negative value of 328.72 MMUS$. An easy approach to protect against this risk would be to increase the transportation rate from 1.4391 to 1.6518 that gives a positive NPV of 328.72 MMUS$ without incorporating the independent variables uncertainties as previously described but the drawback of doing this is that it turns the project less competitive. A better approach comes from the NPV tornado diagram analysis. Figure 9 presents a Tornado Diagram that comes from the risk evaluation simulation. It presents a sensitive regression that shows the independent variables that are most responsible for the NPV volatility. This diagram shows how a change of one standard deviation of one independent variable affects the project dependant variable (NPV) under analysis. This helps to identify which independent variable (or variables) will be subject to special care to narrow down its (or their) volatility and therefore allowing risk mitigation.
Conclusions
By applying the methodology presented in this paper and getting at the stage of quantifying project risk as measured by the dependant variable as consequence of the volatility of the selected independent variables we can then have a more accurate view of the project sustainability and take actions to mitigate then.
References
 Monte Carlo simulation history. Available at http://www.riskglossary.com/link/monte_carlo_method.htm. (Visited in May 28, 2008).
 SANTOS, S. P., Availability and Risk Analysis Effects on Gas Pipeline Tariff Making. In: INTERNATIONAL PIPELINE CONFERENCE, 2008, Calgary, CA.
 SANTOS, S. P.; BITTENCOURT, M. A. S.; VASCONCELLOS, L. D., Compressor Station Availability – Managing its Effects on Gas Pipeline Operation. In: INTERNATIONAL PIPELINE CONFERENCE, 2006, Calgary, CA.
 SANTOS, S. P., “Compression Service Contracts – When is it Worth it?” In: Pipeline Simulation Interest Group, 2003, Bern, Switzerland.
About the Author
Sidney Pereira dos Santos, the author, is a Senior Consultant at PETROBRAS, holds a BS in Mechanical Engineering, a MBA in Corporate Finance and a Master’s in Logistics. He has 21 years in the oil and gas pipeline design at PETROBRAS. He has been deeply involved in most of the gas pipeline projects such as the BoliviaBrazil project and the ongoing gas pipeline expansion in Brazil and has been conducting technical and economic studies and conceptual design for the upcoming projects. Phone: +55 21 32294419 email: sidney.ps@petrobras.com.br
Tables
Table 1 – Pipeline Alternatives I, II, III and IV – Thermohydraulic Results
Table 2 – Compressor Station Units Reliability and Availability
Compressor Station Unit  Reliability  Availability  

Electric motor + Centrifugal compressor  99.4  98.9  
Gas turbine + Centrifugal compressor  98.2  97.1  
Gas motor + Reciprocating compressor  97.1  94.3 