Design of Optimal Pipeline Systems Using Internal Corrosion Models

Jun 16, 2014 - Corrosion is among the principal causes of damage and failure in pipeline systems and is linked to various economic and environmental r...
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Design of Optimal Pipeline Systems Using Internal Corrosion Models and GIS Tools Eftychia C. Marcoulaki,*,† Angelos V. Tsoutsias,†,‡ and Ioannis A. Papazoglou† †

System Reliability and Industrial Safety Laboratory (SRISL), National Centre for Scientific Research “Demokritos”, Athens 15310, Greece ‡ Department of Physics, University of Patras, Patras 26504, Greece ABSTRACT: Corrosion is among the principal causes of damage and failure in pipeline systems and is linked to various economic and environmental risks. The consideration of corrosion phenomena at the early stages of pipeline system design can help quantify these risks and include risk reduction alternatives in the analysis. The present work builds upon previous research on the optimization of pipeline systems and to consider corrosion factors in making preliminary decisions on routing and equipment selection. The optimization tool is herein extended by including corrosion models and upgrading the equipment design and cost functions. The proposed developments are tested against a case study involving a crude oil pipeline system and a range of corrosion related properties for the transmitted fluid.

1. INTRODUCTION In their extensive study of incidents in hazardous liquid pipelines, PHMSA1 found internal corrosion responsible for 5.2% of the total incident costs and 32.7% of the costs related to corrosion. FHWA2 estimated the annual cost of internal corrosion related incidents in USA liquid and gas pipelines at $7.0 billion. Their analysis highlighted the need for more and better ways to encourage, support, and implement optimal corrosion control practices. This work presents a framework for coconsideration of corrosion phenomena at the early stages of pipeline design, suggesting that this could help in preventing the frequency and severity of corrosion related incidents. The pipeline design problem involves various criteria, such as the initial investment, the fuel consumption, maintenance costs, environmental impact, and system availability. Marcoulaki et al.3 described a general and systematic tool for the optimal pipeline routing and equipment design. The pipeline system design problem was formulated mathematically and treated with advanced optimization tools to derive optimal design configurations. The tool took into account given fluid supply/demand flow rate and location data, hydraulic equations, equipment cost, reliability, operation and maintenance features, and geographical information. The present work upgrades the pipeline optimization tool of Marcoulaki et al.3 to consider the trade-offs between initial design, operation, and maintenance costs in the presence of internal corrosion phenomena. The paper is organized as follows. Section 2 discusses the effect of corrosion phenomena on pipeline operation and the available pipeline corrosion models. Section 3 describes the pipeline optimization tool and the modifications made here to include corrosion phenomena. Section 4 presents an application to study the effect of different corrosion factors on the optimal designs. Section 5 concludes the work.

In the U.S., between 1991 and 2010, in 281 635 km of hazardous liquid pipelines, corrosion was responsible for the 23.6% of significant incidents and 5.3% of serious incidents. Among the significant incidents, internal corrosion was responsible for 9% of their total number, or 38% of significant incidents related to corrosion. In terms of serious incidents, internal corrosion was responsible for 1% of their total number, or 11.7% of serious incidents related to corrosion.1 For European pipelines there are data available for the period 1971 to 2011 on about 35 993 km pipelines. These include the vast majority of pipelines in Europe, transporting around 719 million m3 per year of crude oil and oil products. The collected data describe 485 spillage events. There have been 131 failures related to corrosion (27% of the total), giving an average of 3.2 spillages per year. Among the corrosion related failures, 19.1% are due to internal corrosion.7 The major effect of pipeline corrosion is the loss of metal cross section. If no countermeasures are taken, a corrosion defect is expected to grow with the exposure period.8 The results of corrosion vary from pipeline leakage to full bore rupture. The fluid escaping from the pipes is a vast economic loss to the pipeline operating company and poses threats to the environment and human health.9,10,6 Accurate corrosion prediction and management are key factors in meeting the design life requirement of an oil or gas pipeline or export line.11 Numerous mathematical models have been proposed for modeling the corrosion inside the pipelines. Nešić12 divides them into three main categories: (a) mechanistic models that describe the mechanisms of the underlying reactions and have a strong theoretical background, (b) semiempirical models that are partly based on firm theoretical hypotheses, and (c) empirical models that have very little or no

2. PIPELINE CORROSION Corrosion on the internal walls of a pipeline disintegrates the pipe and is among the main causes of damage and failure.4−6

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© 2014 American Chemical Society

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Figure 1. Pipeline system optimization framework.

The search procedure is inspired by design procedures followed in practice by pipeline engineers. Figure 1 illustrates the optimization algorithm. The algorithm starts with an initialization step to get an initial design guess. Then, it proceeds iteratively as new solutions are generated, evaluated, and compared to previously considered designs. The procedure terminates when convergence criteria are satisfied. The shaded boxes depend on the specific application. The dashed line encloses links to available information sources. Section 3.1 describes how the pipeline system is represented and how the performance of design instances is evaluated. Section 3.2 describes briefly how the algorithm generates new feasible instances of the system. Section 3.3 presents in more detail the optimizer of Figure 1 and discusses its propagation and termination rules. Section 3.4 comments on the convergence properties of SA stochastic optimizers. 3.1. Pipeline System Representation and Modeling. Every instance of the pipeline system can be mapped to a set of decision variables and dependent variables. The decision variables are derived through the optimal search, following the screening procedures described later. The values of dependent variables can be estimated when the decision entities are known. For instance, the elevations can be derived from the pairs of latitude and longitude coordinates if geographical information is available. The required pipe thickness at any given point of the pipeline depends on the pipe internal diameter, the roughness, and the transmitted fluid pressure. A pipeline design instance is uniquely defined when all its design variables are known. Evaluation of the design performance requires data and models to determine the dependent variables and calculate the design objectives. The data are engineering data and coefficients obtained from databases of physical properties, fuel prices, and process equipment. The latest may include design characteristics of pipes and pressure control devices (PCDs), reliability and maintenance features, and unit costs for procurement, deployment, construction, installation, operation, maintenance, repair, inspection, etc. Geographical information is obtained through links to Geographic Information System (GIS) tools to retrieve data on (a) elevation, slope, medium (soil/water), soil type, etc; (b) land use, population density, presence of other critical infrastructures, and real estate costs; (c) crossings with rivers, forests, natural heritage, etc; (d) factors affecting the construction, operation, and maintenance costs of the pipeline network and its components; (e) environmental condition and weather data; (g) probability for natural disasters (e.g., earthquakes), etc.

theoretical background. The recent advances in data mining technologies present opportunities for more intelligent corrosion prediction tools.13,14 In oil pipelines, corrosion phenomena generally depend on the presence of carbon dioxide (CO2), hydrogen sulfide (H2S), water, and/or other typical contaminants. The most widely known corrosion rate model in this case is the Norsok M-506,15 an empirical model developed by the Norwegian oil companies Statoil, Norsk Hydro, and Saga Petroleum.16 The model fits a large amount of laboratory data and takes better account of phenomena occurring at higher temperature and pH regions, compared to other corrosion rate models.13

3. PIPELINE OPTIMIZATION FRAMEWORK A typical pipeline system design problem involves the transmission of a given fluid, of known flow rate, from a known supply location to a known demand location. The scope is to obtain optimal solutions for the pipeline routing, the locations, and design attributes of the pipeline network components, the system construction, operation, and maintenance. Optimality is according to one or a set of design objectives. Likewise other engineering problems and objectives here may include initial investment costs, energy consumption for the system operation repair and maintenance costs, environmental impact, system availability, as well as combinations of the above. In practice, pipeline engineers try different configurations until a solution that can be considered satisfactory is obtained. Assessment of the solutions generated during this search requires a multitude of information to run cost and engineering models. The required information can roughly be divided into the following: • Geographical information on the terrain that the pipeline is traversing. This information is crucial in the design of main pipeline systems, as pipelines of the same length and capacity have completely different construction, operation, and maintenance costs in different geographical locations. • Data and coefficients used in engineering calculations. Similar information is required for other process design applications. The pipeline design problem can be formulated as a mixedinteger nonlinear programming (MINLP) problem, aiming to provide optimal locations of pipeline equipment and equipment sizes/types. The optimization framework adopted here is according to Marcoulaki et al.3 Their method launches a stochastic optimization search based on simulated annealing. 11756

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amount of improvement that the perturbation brings to the objective and on the value of a search control parameter, τ. Parameter τ is reduced periodically once a fixed number of iterations has been completed. When the new design is better (e.g., less expensive) than the current one, the modification is immediately accepted. When the new design is worse (e.g., more expensive), the modification is accepted with probability Pr = exp(−(E2 − E1)/τ), where E1 and E2 denote the values of the objective function to be minimized for the new and the current design, respectively. So the same modification can be accepted with high probability at the beginning of the search and rejected with high probability as the search reaches termination. Marcoulaki and co-workers19,20 provide details on the practical issues of using SA, including propagation and termination rules and models to control the parameter τ. The optimization framework presented here can, in principle, collaborate with any single and multiobjective method using transitions between the system solutions (see ref 21). It is also possible to consider hybridization of SA with deterministic optimizers to achieve improvement in the CPU time, as proposed in the work of Rodriguez et al.22 3.4. Convergence of SA Algorithms. Since SA is a stochastic method, every time we run the pipeline optimization algorithm3 we get a different final pipeline system design. Even though the specific design details of these designs (routing, equipment locations, and capacities) are different, their objective function values may be quite similar. The convergence quality of the optimal search depends on (a) how close to each other and (b) how low (if we do minimization, high otherwise) are the objective function values of these final designs. Better convergence, therefore, is associated with a distribution of objective function values that is narrower and located at lower values. SA has a very strong background on Markov processes, as the iterations performed at each constant τ interval constitute a homogeneous Markov chain. Clearly, longer Markov chain lengths (MCLs) lead to longer computational times. When an SA algorithm has asymptotic convergence, longer MCLs yield increased convergence quality. Marcoulaki and co-workers have tested the convergence properties of the SA algorithm used here3 as well as SA tools for other process engineering applications.19,20 Their analysis provided evidence for asymptotic convergence to the vicinity of the global optimum.

The models include process simulators for hydraulic calculations, models to estimate energy consumptions, cost functions, etc. The present work also employs models for the prediction of corrosion rates. The collection of models depends on the specific design application to meet the desired process simulation accuracy and evaluate the user-defined set of system objective(s). The employed optimizer poses no restrictions on the complexity the employed models or the types of their equations. Black-box models can also be accommodated. In the case study of section 4, the final objective is expressed as the total cost of building the pipeline and running it over a given lifetime. The latter involves the annual costs of maintaining the pipeline and its components and the annual operating costs for PCDs. 3.2. Modifications on Pipeline Configurations. The search for an optimal solution proceeds iteratively by generating a series of consecutive design instances. Each new design instance is the outcome of modifications applied on the decision variables of the current design in the series, according to a set of available modifications. The choice of performing a specific modification is random, according to given probabilities distribution functions (pdf’s). Modifications can be applied on (i) the characteristics of the current solution components or (ii) the solution topological features. Modifications of type i are applied to the decision variables of each piece of equipment. Modifications of type ii screen different options for the pipeline routing and the location of PCD’s. Let us consider a simplified illustration example. Starting from a current pipeline design, we identify which modifications can be applied, e.g., relocating a PCD or changing the routing of the pipeline to route A or B. Each one of these three modifications has been assigned a specific probability to occur. The new design depends on the probabilistic choice over the three modifications. Starting from a known pipeline and its PCDs, if the perturbations alter the length of the pipeline, the capacity of the PCDs needs to be adjusted so that the pumping power input exceeds the pressure drop and the head losses along the pipeline. If the perturbations alter the location, number, or type of PCD, then the capacities of the PCDs in the resulting design need to be properly adjusted. Likewise, when the PCD capacities change, the new design might have an excess or deficit of pumping power. The adjustment actions follow a set of good practice rules, and they are performed in collaboration with the process simulation models discussed in the previous subsection. This collaboration is illustrated in Figure 1, where the simulator models are called before the new design is finalised. 3.3. Optimizer. The optimizer guides a search among the space of all the possible pipeline system configurations. The search is according to the standard simulated annealing (SA), a well established heuristic method for global optimization.17 SA generates a biased random search of the solution space. The search proceeds by applying small modifications on each current state to generate a new state. In Figure 1, each modification is assessed according to the standard Metropolis criteria.18,19 These criteria (a) compare the objective function values of the new and the current designs and (b) return a verdict on accepting or rejecting the modification. “Accept” means that the new design replaces the current design. “Reject” means that the current design is maintained. Then another perturbation is applied, the perturbation is assessed, etc. The verdict of the Metropolis criteria depends stochastically on the

4. DESIGN APPLICATION EXAMPLE 4.1. Problem Description. The proposed methodology is illustrated using the design of a simple pipeline system for the transmission of 160 kBPD crude oil between two given transmission points on a given terrain. Objectives for this design problem are aggregated in a single cost function using a typical lifetime of 35 years, and they include the following: • initial investment costs for pipeline network components, • construction costs, including deployment and installation activities, • operating costs based on the pump operating fluid requirements, and • costs for scheduled maintenance, inspection and repairs. The main corrosion factors considered here are the pH and the partial pressure of CO2 in the vapor phase of the transmitted crude. Both of these depend on the crude composition and the exact pressure and temperature conditions, and their values are interdependent. The development of accurate phase equilibria 11757

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Table 1. Optimal Search Results for Different CO2 Partial Pressures for MCL = 20 and pH = 5 rCO2 no corrosion 3

investment and real estate (10 $) construction cost (103$) pipeline maintenance cost (103$) pump investment and construction (103$) operational cost (fuel = NG) (103$) pump maintenance cost (103$) total cost (103$) total pipeline length (km) number of simulations

1%

3%

6%

median

QV

median

QV

median

QV

median

QV

679 35902 541 1123 5542 6420 50196 41.590 17316

0.487% 0.141% 0.140% 0.289% 0.346% 0.289% 0.177% 0.142% 18.46%

18380 39957 608 1121 5533 6411 72038 41.612 19545

0.174% 0.191% 0.186% 0.135% 0.162% 0.135% 0.123% 0.219% 15.83%

37153 43863 673 1123 5543 6421 94756 41.648 16354

0.271% 0.123% 0.115% 0.160% 0.193% 0.160% 0.123% 0.170% 13.79%

59736 48093 745 1122 5533 6412 121671 41.649 17865

0.222% 0.144% 0.142% 0.109% 0.130% 0.109% 0.163% 0.084% 8.78%

4.2. Problem Data. The considered region for the pipeline route takes the form of a 35 km × 40 km orthogonal rectangle. Specific geographical information is available on this region and includes ground elevation, soil type, population density, real estate data, presence of other infrastructures, etc. The length of a pipeline with straight x−y projection between the start and destination points is 40 317 m. Ground elevations at the start and destination points are 292 and 70 m, respectively. There is a mountainous area between the given transmission points, and the minimum distance pipeline traverses near the peak of 482 m. The total pressure is calculated at each point along the pipeline by taking into account static and frictional pressure drops along the pipeline routes visited during the optimal search. The partial CO2 pressure is then calculated using the known rCO2 value. Pump locations are not considered in the present exercise, since the pipeline is quite short and the maximum head is below 300 m, so a single pump at the source point is enough. The pump head is adjusted to meet the static and frictional pressure drops along the route of each pipeline design generated. The operating fuel used here is natural gas. On the basis of past design experience, the nominal pipe diameter for the mass flow rate assumed here is 20 in. This is for standard pipes with thickness 0.75 in.; however, the pipe wall thickness should comply with safety regulations or other design requirements.24 Therefore, internal diameter 19.25 in. is used here for all the pipes in the network, regardless of their final thickness. The resulting oil flow resides in the turbulent region. The pipe wall thickness depends on the pressures along the pipe, the available geographical information on class location, and the estimated corrosion rate, at each pipeline point. The pipe material is commercial steel. Cost coefficients and design factors depend on the geographical characteristics of the location where the equipment is to be placed. Pressure drop is calculated from Darcy’s correlation.25 The models for equipment costing and the associated data can be found in ref 3. The corrosion rate is correlated according to the Norsok model (see Appendix). 4.3. Different Corrosion Factors: Results and Discussion. The first set of computational experiments studies the effect of different pH and rCO2 values on the optimal choices for pipeline routing and equipment design. Table 1 itemizes the moments (median and dispersion as QV) of the obtained final cost pdf’s for pH 5 (design cases DC{−,−}, DC{5,1%}, DC{5,3%}, and DC{5,6%}). The table also reports the statistics for the total pipeline lengths and the number of simulations performed. Values are presented with accuracy of at least three significant digits. Operating and maintenance (including repair)

models to calculate these entities for a specific crude is a difficult task,13 far from the scope of this work. The aim here is to study the sensitivity of the optimal pipeline designs on different ranges of pH and CO2 partial pressure values. We will, therefore, assume a set of fixed values for the pH and the fraction of the CO2 partial pressure over the total pressure. The latter is denoted by rCO2 and takes here the values 1%, 3%, and 6%. The former takes here the values pH = 4 and pH = 5. Note that the pH values and the resulting CO2 partial pressures are typical for crude oil, particularly for crudes transmitted from the extraction point to special treatment plants.15 Seven design cases and two sets of computational experiments are considered. Design cases are denoted as DC{pH,rCO2 }. Case DC{−,−} is the base design assuming that there is no corrosion. The first set of computational experiments is to investigate how the final designs and their costs are affected by the corrosion related factors. This set involves all design cases and uses MCL = 20. The second set tests the convergence of the design tool by manipulating the optimizer parameters that control the extent of the optimal search. This set involves only design cases DC{5,3%} and DC{4,3%}. The optimizer used here is stochastic and converges to a statistical distribution of solutions for each design case rather than a single optimal design. A number of 20 computational experiments is taken to sample the final pdf of total costs at each design case. Note that each computational experiment starts with a randomly selected initial design. Since the sample size is small and the pdf is not necessarily normal, the following statistical analysis is based on the sample median and quartiles. The quartile variation coefficient, QV, is also used as a measure of dispersion: QV = (Q 3 − Q 1 )/(Q 3 + Q 1 )

where Q1 and Q3 are the lower and upper quartiles, respectively.23 The main parameters controlling the optimal search have the following values: • The initial SA temperature is automatically set at 10 times the objective function value of a randomly generated design. • The cooling control parameter is always set at 0.05. • The MCL is 20 in the first set of computational experiments and ranges between 6 and 30 in the second set. For more details on the selection of these values, the employed annealing schedule, and specific search termination/propagation criteria, see refs 19 and 20. 11758

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Table 2. Optimal Search Results for Different CO2 Content for MCL = 20 and pH = 4 rCO2 no corrosion 3

investment and real estate (10 $) construction cost (103$) pipeline maintenance cost (103$) pump investment and construction (103$) operational cost (fuel = NG) (103$) pump maintenance cost (103$) total cost (103$$) total pipeline length (km) number of simulations

1%

3%

6%

median

QV

median

QV

median

QV

median

QV

679 35902 541 1123 5542 6420 50196 41.590 17316

0.487% 0.141% 0.140% 0.289% 0.346% 0.289% 0.177% 0.142% 18.46%

65199 49134 762 1121 5532 6411 128163 41.752 15918

0.366% 0.164% 0.165% 0.209% 0.250% 0.209% 0.237% 0.142% 11.13%

146001 65466 1036 1021 4941 5835 224081 45.401 18488

0.259% 3.264% 3.049% 5.381% 6.467% 5.381% 0.685% 4.656% 10.24%

256064 77780 1260 1066 5206 6093 347452 43.672 17628

0.356% 3.016% 2.742% 5.508% 6.620% 5.508% 0.234% 4.747% 10.69%

costs are considered over the 35-year lifetime of the project. Likewise, Table 2 presents the results obtained at pH = 4 (design cases DC{−,−}, DC{4,1%}, DC{4,3%}, and DC{4,6%}). Figure 2 shows the trends in the number of simulations, the total pipeline length, and the total pipeline system cost at increasing rCO2 . The error bars are according to the first and third quartiles, meaning that half of the sample values fall within the error bar range. The location of the median (closer to Q1 or Q3) indicates the skewness of the pdf and its departure from normality (where the median is placed in the middle). Number of Simulations. The main computational effort is spent here on simulations to calculate design costs. We can therefore assume that the computational times are proportional to the number of simulations. According to Tables 1 and 2 and Figure 2 (top plot), in at least half of the runs the number of simulations ranges between 15 × 103 and 22 × 103 simulations. We expect that the number of simulations for the same optimizer parameters depends mainly on the scale of the problem. The problem considered here has 10185 design options, and the scale is the same for all pH and rCO2 values. The results of Tables 1 and 2 and Figure 2 (top plot) show that the number of simulations (i.e., the computational time requirements) has no evident dependence on the value of corrosion factors. Final Pipeline Routes. According to Tables 1 and 2 and Figure 2 (middle plot), the median of the pipeline length at pH = 5 increases slightly by 0.053%, 0.140%, and 0.142% compared to the DC{−,−} when rCO2 is 1%, 3%, and 6%, respectively. Increase of rCO2 at increased acidity seems to bring more evident, though not monotonic, changes on the length medians. When rCO2 goes to 1%, 3%, and 6%, the length median increases by 0.39%, 9.2%, and then 5.0% compared to DC{−,−}. Therefore, the length median drops by 3.8% as the rCO2 doubles from 3% to 6%. The length quartile values provide insights on the variance of the pipeline length pdf. The DC{4,3%} and DC{4,6%} samples give {Q1, Q3} = {41.7, 45.8} and {41.8, 45.9}, respectively. The two pdf’s have significant overlapping, but the median of the DC{4,3%} lengths is located in longer pipelines (so the pdf is negatively skewed). Figures 3−5 illustrate the pipeline routes obtained for different pH and rCO2. The routes for the base design DC{−,−} indicate a very strong preference for a route around the mountain top (Figure 3). For the three design cases assuming pH = 5, the designs follow (more or less) the same route as in the base case (Figure 4). For the three design cases assuming pH = 4, two routing options are developed here (Figure 5).

Figure 2. Obtained results vs rCO2 at different pH levels.

The first one is similar to the base case route. The second route is longer and at lower altitudes. The two routes are very similar in terms of the total costs of the underlined designs. We can observe that as the rCO2 increases, the longer route takes over in the final designs. 11759

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Figure 3. Obtained pipeline routes for design case DC{−,−} and MCL = 20.

Final Pipeline Costs. Tables 1 and 2 give the moments for the total costs as well as the investment (including real estate) costs, the costs for pipeline construction, the pump investment and construction costs, pipeline operation costs (in terms of the energy required to transmit the oil), and the maintenance costs for the pipeline system. Note that the thicknesses at each pipe segment are properly adjusted to endure corrosion. The adjustments take into account the segment pressure and the safety standards where the segment is located. The result of these adjustments is the increase of the required steel mass, which in turn increases the pipeline investment costs. Figure 2 (bottom plot) shows the total cost medians and quartiles. The medians increase as the rCO2 increases and pH decreases. Compared to the base design DC{−,−}, the design cases with pH = 5 DC{5,1%}, DC{5,3%}, and DC{5,6%} have total cost medians increased by 44%, 89%, and 142%, respectively. The designs DC{4,1%}, DC{4,3%}, and DC{4,6%} at lower pH feature total cost medians increased by 1.5, 3.5, and 5.9 times the base design cost, respectively. From the itemized cost medians, pipeline investment costs are the ones most affected by the presence of corrosion factors and they go up by 2−3 orders of magnitude. This increase is mainly due to the steel mass required to build longer pipelines with thicker pipe walls. Pipeline construction and maintenance costs are affected at a lesser extent. Their increase compared to the values of DC{−,−} ranges from 11% to 34% for pH = 5 and from 37% to 117% for pH = 4, as rCO2 increases from 1% to 6%. Pump investment, construction, operation, and maintenance costs follow different trends compared to pipeline costs. Compared to DC{−,−}, there is a very small decrease of about 0.15% in the total pumping cost medians for designs DC{5,1%} and DC{5,6%}, while the pumping costs of DC{5,3%} are very similar to the base case. The pumping costs for DC{4,1%}, DC{4,3%}, and DC{4,6%} are decreased by 0.16%, 9.8%, and 5.5%, respectively, compared to the base design. This small reduction in pumping costs cannot alter the trends in total costs which are governed by the pipeline costs. The reduction can be attributed to the different routing (longer pipelines at lower altitudes) preferred as the corrosion factors increase. The variation in total cost values is on the order of 0.1%, and this is the reason why the quartile ranges are not visible in Figure 2, bottom plot. From at the costs in Tables 1 and 2, their quartile variation coefficients remain below 0.5% with the exception of the itemized costs for designs DC{4,3%} and DC{4,6%}. The deviations in these cases indicate that, although

Figure 4. Obtained pipeline routes for design cases DC{5,*} and MCL = 20.

the final designs are close in terms of their total costs, there are significant differences in the design parameters. Final Equipment Design Characteristics. Together with the cost figures and the routing, the final solutions provide detailed information on the design characteristics of every pump and pipe segment used in the system. Figures 6 and 7 show the elevation and corrosion rate profiles along the route of final pipeline designs for pH equal to 5 and 4, respectively. The right y-axis (blue lines) is for elevations, and the left y-axis (black lines) is for corrosion rates. Similar to the routes in Figures 3−5, each line corresponds to a different final design. From the elevation profiles at pH = 5 (Figure 6), it is evident that the final designs show a distinct preference to more-or-less the same route. At pH = 4 (Figure 7) and as the rCO2 increases, there is a gradual move toward two distinct design options, a longer pipeline at lower altitudes, and a shorter pipeline at higher altitudes. Note that the observations in terms of the elevation profiles coincide with the routes shown in Figures 4 and 5. The corrosion rate profiles follow the changes in 11760

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Figure 6. Obtained elevation and corrosion rate profiles for design cases DC{5,*} and MCL = 20. Figure 5. Obtained pipeline routes for design cases DC{4,*} and MCL = 20.

thicknesses participate in the calculation of investment, construction, operation, maintenance, and repair costs, which increase in turn. The optimization tool should then seek solutions featuring thinner pipe walls to reduce the costs. The wall thicknesses depend on the pressures developed within the pipeline. Since we use a single pump, the pressures depend on the maximum elevation and the pipeline length. So the tool should return different optimal routes according to the values of corrosion factors. The designs obtained for the same set of corrosion factors should have very similar total cost (since cost is the objective function) but not necessarily similar route or other design choices. All the results presented above prove that the pipeline optimizer behaves exactly as expected. The present work considers a range of conditions affecting the corrosion rate. This makes possible the investigation of how the optimal pipeline configuration depends on corrosive conditions. As the results indicate, the consideration of corrosion effects increases significantly the pipeline costs, especially at pH = 4 and rCO2 = 6%. In these cases the corrosion rates can go up to 12 mm/year, which is at severity level 5 for unmitigated corrosion, according to Nyborg.13 The required pipes are very

elevation, since the internal pressure decreases at higher altitudes. In the top plots of Figures 6 and 7 (i.e., where rCO2 = 1%) we observe a minimum corrosion rate plateau between 17−25 and 17−29 km, respectively. This is the part of the pipelines where the internal pressure in the fluid stream is minimal, and the CO2 partial pressure drops below the application range of the Norsok model (see Appendix), so we take the minimum corrosion rate equal to 0.585 and 1.90 mm for pH = 5 and pH = 4, respectively.16 As the results indicate, the consideration of corrosion effects increases significantly the pipeline costs compared to the nocorrosion case. The Norsok model employed here provides a very simple and deterministic prediction of the corrosion rates along the pipelines. In reality, corrosion is a complex stochastic phenomenon. Future work involves using a more advanced model to consider the uncertainties in the initiation and propagation stages of corrosion phenomena. In conclusion, when the corrosion factors increase, the required wall thicknesses along the pipe also increase. These 11761

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Figure 8. Obtained results for design cases DC{*,3%} at different MCLs.

Figure 7. Obtained elevation and corrosion rate profiles for design cases DC{4,*} and MCL = 20.

Figure 8 gives the results for MCLs ranging from 6 to 30 nodes assuming rCO2 = 3%. The number of iterations (Figure 8, top plot) increases exponentially with MCL, as expected based on the behavior of similar stochastic processes. The statistics are very similar for the two acidity values, since the characteristics of the transmitted fluid should not have any effect on the robustness of the optimal search. The statistics on the length of the pipeline (Figure 8, middle plot) show that the finals designs for pH = 5 converge to a narrow distribution around 41.6 km, when the MCLs are just 10. The situation is very different at pH = 4, where even at MCL = 30 the variations in the length of the pipeline are significant. Figure 8 (bottom plot) shows the final costs (left y-axis for pH = 5, right y-axis for pH = 4). Despite any variations in the routing choices, the costs appear to converge even at MCL = 10. The cost distributions for pH = 4 at MCLs of 20 and 30 have similar span, but the median moves down as the MCL increases. Tables 3 and 4 report the itemized cost statistics for pH = 5 and pH = 4, respectively. Again, despite the microtrends in different cost items, the overall trend at increasing MCL is that both the total cost median and the quartile deviation decrease. Therefore, as the MCL increases, the objective function values gather closer

thick, thus very expensive, and the resulting total cost is almost 7 times the cost of no corrosion (see Table 2). At pH = 5 and rCO2 = 1%, the maximum observed corrosion rate is about 1.3 mm/year. This is between severity levels 3 and 4,13 and the total cost is about 50% over the no-corrosion cost (see Table 1). In real case studies it is possible to apply mitigating measures to reduce the effect of acidity and CO2; thus, the costs can be reduced significantly. 4.4. Convergence Experiments: Results and Discussion. The second set of computational experiments is to test the effect of search control parameters on the convergence of the optimizer. Computational experiments are run for MCLs 6, 10, 20, and 30. According to theory, when the MCL increases, the search converges to the globally optimal objective function value with higher probability. In practice, this means that the probability distribution of the objective function values of the final solutions is narrower and moves closer to the global optimum. Similar studies can be found in refs 19 and 3. The latter tests the perturbation set of algorithm used here. The results are obtained with randomly chosen initial designs to keep the analysis independent of the initial guess. 11762

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Table 3. Optimal Search Results for Different Markov Chains and pH = 5 and rCO2 = 3% MCL 6 investment and real estate (103$) construction cost (103$) pipeline maintenance cost (103$) pump investment and construction (103$) operational cost (fuel = NG) (103$) pump maintenance cost (103$) total cost (103$) total pipeline length (km) number of simulations

10

20

30

median

QV

median

QV

median

QV

median

QV

41114 47117 724 1144 5665 6539 103205 44.002 1402

7.155% 5.032% 5.061% 5.633% 6.759% 5.633% 5.029% 4.962% 40.38%

37551 44017 676 1127 5566 6444 95448 41.756 4284

0.925% 0.273% 0.285% 0.426% 0.511% 0.426% 0.545% 0.311% 9.80%

37153 43863 673 1123 5543 6421 94756 41.648 16354

0.271% 0.123% 0.115% 0.160% 0.193% 0.160% 0.123% 0.170% 13.79%

36996 43765 672 1121 5528 6406 94502 41.580 40570

0.181% 0.128% 0.126% 0.051% 0.061% 0.051% 0.083% 0.133% 11.51%

Table 4. Optimal Search Results for Different Markov Chains and pH = 4 and rCO2 = 3% MCL 6 3

investment and real estate (10 $) construction cost (103$) pipeline maintenance cost (103$) pump investment and construction (103$) operational cost (fuel = NG) (103$) pump maintenance cost (103$) total cost (103$) total pipeline length (km) number of simulations

10

20

30

median

QV

median

QV

median

QV

median

QV

155626 64501 1026 1139 5639 6513 235068 42.770 1062

2.294% 2.872% 2.755% 1.049% 1.258% 1.049% 1.875% 3.139% 32.15%

147708 66133 1046 1074 5257 6142 225770 45.980 4218

1.074% 4.433% 4.202% 4.946% 5.942% 4.946% 1.529% 5.416% 15.34%

146001 65466 1036 1021 4941 5835 224081 45.401 18488

0.259% 3.264% 3.049% 5.381% 6.467% 5.381% 0.685% 4.656% 10.24%

145595 61616 979 1118 5510 6390 221605 41.777 41875

0.185% 3.313% 3.121% 5.598% 6.728% 5.598% 0.596% 4.708% 11.33%

Table 5. Correlations Used in the Corrosion Modela t

a

k

n

pH

f (pH), f(s), CR

a

b

5

0.420

0.36

15

1.590

0.36

20

4.762

0.62

40

8.927

0.62

60

10.695

0.62

80

9.949

0.62

90

6.250

0.62

120

7.770

0.62

5.203

0.62

eq 1, −, eq 4 eq 1, −, eq 4 eqs 1, 3, 4 eqw 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 2, 3, 4 eqs 1, 3, 4 eq 2, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eqs 1, 3, 4 eq 1, 3, 4 eq 1, 3, 4 eq 1, 3, 4 eqs 1, 3, 4

2.0676 4.342 2.0676 4.342 2.0676 4.986 2.0676 5.1885 1.836 15.444 2.6727 331.68 3.1355 21254 0.4014 1.5375 5.9757 0.546125 1 17.634 0.037

−0.2309 −1.051 −0.2309 −1.051 −0.2309 −1.191 −0.2309 −1.2353 −0.1818 −6.1291 −0.3636 −1.2618 −0.4673 −2.1811 −0.0538 −0.125 −1.157 −0.071225

150

3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.6 4.6 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.57 4.57 ≤ pH < 5.62 5.62 ≤ pH ≤ 6.5 3.5 ≤ pH < 4.3 4.3 ≤ pH < 5 5 ≤ pH ≤ 6.5 3.5 ≤ pH < 3.8 3.8 ≤ pH < 5 5 ≤ pH ≤ 6.5

−7.0945

c

d

0.0708 0.0708 0.0708 0.0708 0.8204

−0.0371

0.715

Temperatures, t, are in °C.

convergence and provide strong evidence on the robustness of the pipeline underlying optimization tool. Apart from supporting previous analyses, this work demonstrates that good results can be obtained even at lower MCLs. The performance of SA tools is not hindered by nonlinearities in the model equations or discontinuities in the

around a minimal (target) value. Figure 9 shows the evolution of the obtained pipeline routes as the MCL increases. The results of section 4.3 are taken for MCL = 20. Previous SA applications3,19 prove this to be a very reasonable value, and this choice also agrees with the convergence analysis. The convergence results confirm the expected trends for stochastic 11763

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upgrading the equipment design and cost functions. The proposed developments are tested against a case study involving a crude oil pipeline system. Seven design cases are assumed with varying acidity and CO2 content in the transmitted fluid. In the obtained results, the total pipeline cost increases significantly when the corrosion agents increase; i.e., the pH drops and the CO2 partial pressure increases. The optimal routings are also affected by the presence of corrosion enhancing agents. The corrosion rate model used here is deterministic and thus cannot capture the stochastic nature of corrosion mechanisms. Future plans involve the consideration of uncertainties in the initiation and propagation stages of corrosion.

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APPENDIX: NORSOK CORROSION RATE MODEL The Norsok is the most commonly used empirical model for corrosion rate.15 This section presents the Norsok Standard M-506, revision 2, June 2005, for carbon steel. The model input variables are the following: • The temperature that develops inside the pipeline (in °C). The model considers temperatures in the range between 5 and 150 °C. • The partial pressure of CO2 as a fraction of the pressure that develops inside the pipeline (in bar), pCO2, which can lay in the range between 0.1 and 10 bar. • The pH of the mixture, which can lay in the range between 3.5 and 6.5. Note that pure oil is not acidic but the oil extracted from oil wells contains some water. • The shear stress (in Pa) lays in the range between 1 and 150 Pa. The model can also consider the option of having special inhibitors and calculate their contribution to the reduction of the corrosion rate. These are included as additional factors in the following model, and their values range between 0 and 1 according to their inhibition effect. Corrosion rates at intermediate temperatures can be estimated using linear interpolation. The following equations are considered for the pH factor, f(pH), used in corrosion rate calculations:

Figure 9. Obtained pipeline routes for design cases DC{*,3%} at different MCLs.

design variables. In the case of pipeline system design, we may consider more detailed models for process simulations and cost evaluations without compromise on the quality of the final results. The tool can in principle consider problems of larger size resulting from longer pipelines and/or higher GIS grid resolution. The management of extremely large GIS files is expected to give rise to memory issues. These can be considered using vector representation of geographical information, minimizing the interaction between the optimizer and the geographic databases, etc. The distribution of final objective function values obtained at the same MCL indicates the quality of convergence, so the values appear very close at long MCL. As in section 4.3, however, the underlying structural and operational features could be quite different. This is very important in practical applications, like process systems engineering problems. Engineers can benefit from having a set of promising designs to apply nonquantifiable criteria in choosing the design to be finally implemented.

f (pH) = a + b·pH + c·pH2 + d ·pH3

(1)

f (pH) = a ·eb

(2)

where a, b, c, and d denote equation coefficient, and where values were determined through data fitting at different temperatures, t, and ranges of acidity. The choice between eq 1 and eq 2 depends on the acidity of the fluid (see Table 1). The following equation is considered for the equation giving the shear stress factor, f(s):

5. CONCLUSIONS This work demonstrates how internal corrosion phenomena can be considered at the early design stages of pipeline systems used for fluid transmission, as part of an integrated optimization task. Pipeline corrosion is one of the most common causes of damage and failure that leads to accidents and loss of transmitted fluid. Taking into account the corrosion processes during pipeline design could help in preventing the frequency and severity of such incidents. The work expands available optimization tools to address the corrosion phenomena by including suitable models and

f (s) = (s /19)0.146 + 0.0324log(pCO2 )

(3)

where s is the pipe wall shear stress (in Pa) and pCO2 is the partial pressure of CO2 in the pipe (in bar). The equation used for calculation of the corrosion rate is CR = k·pCO2 n ·f (s)·f (pH)

(4)

were CR is the corrosion rate (in mm/year), while k and n are coefficients based on fitting data at different temperatures. Table 5 gives the values of coefficients k, n, a, b, c, and d. 11764

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Paper 10371; http://www.ife.no/publications/2010/matkor/ publication.2010-08-20.5577493619 (accessed June 2014). (15) Marsh, J.; Teh, T. Conflicting Views: CO2 Corrosion Models, Corrosion Inhibitor Availability Philosophies, and the Effect on Subsea Systems and Pipeline Design, Offshore Europe Conference, Aberdeen, Scotland, U.K.; Society of Petroleum Engineers: Richardson, TX, 2007; DOI: 10.2118/109209-MS. (16) M-506 CO2 Corrosion Rate Calculation Model (Rev. 2, June 2005). http://www.standard.no/en/sectors/energi-og-klima/ petroleum/norsok-standard-categories/m-material/m-5061/ (accessed June 2014). (17) Kirkpatrick, S.; Gelatt, C. D., Jr; Vecchi, M. P. Optimization by Simulated Annealing. Science 1983, 220, 671. (18) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. Equation of State Calculations for Fast Computing Machines. J. Chem. Phys. 1953, 21, 1087. (19) Marcoulaki, E. C.; Kokossis, A. C. Screening and Scoping Complex Reaction Networks Using Stochastic Optimization Techniques. AIChE J. 1999, 45 (9), 1977. (20) Marcoulaki, E. C.; Kokossis, A. C. On the Development of Novel Chemicals Using a Systematic Synthesis Approach. Part I: Optimisation Framework. Chem. Eng. Sci. 2000, 55 (13), 2529 (DOI: 10.1016/S0009-2509(99)00522-9). (21) Marcoulaki, E. C.; Papazoglou, I. A. A Dynamic Screening Algorithm for Multiple Objective Simulated Annealing Optimization. Comput.-Aided Chem. Eng. 2010, 28, 349 (DOI: 10.1016/S15707946(10)28059-8). (22) Rodriguez, D. A.; Oteiza, P. P.; Brignole, N. B. SimulatedAnnealing Optimization for Hydrocarbon Pipeline Networks. Ind. Eng. Chem. Res. 2013, 52 (25), 8579−8588 (DOI: 10.1021/ie400022g). (23) Evans, M.; Hastings, N.; Peacock, B. Statistical Distributions, 3rd ed.; Wiley: New York, 2000. (24) Gas Transmission and Distribution Piping Systems, revision B31.82010; American Society Mechanical Engineers (ASME): New York, 2010. (25) Flow of Fluids through Valves, Fittings and Pipe. Technical Paper No. 410M; Crane Co.: Stamford, CT, 2009.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +302106503743. Fax: +302106545496. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Nathalie Pixopoulou (HSE Engineer at Fluor, The Netherlands) for her valuable input at the beginning of this project. A.V.T. gratefully acknowledges the financial support from the Greek National Strategic Reference Framework 2007−2013.

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REFERENCES

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