Fig. 9 Probability analysis for unpiggable pipelines subject to internal corrosion. The distributions of the size of localized corrosion features and the actual wall thickness are compared to estimate the PF for leak. The PF for burst is calculated by multi- plying the PF for leak times a multiplication factor from pipeline failure data in Alberta, Canada [9].

for leak into the PF for burst. The database of pipeline failures in Alberta, Canada is used to achieve this [9]. Pipelines are series systems because the failure of any section generates the failure of the entire system. Therefore, if the pipeline sections are​​​

considered independent, the system failure for the pipeline is equal to the failure of the weakest section for each time period [51].

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3.6 Consequence Analysis. The objective of the consequence analysis is the estimation of the consequence of failure CFfor leak and burst as a function of time and space. Figure 10 presents an overview of the consequence analysis, which includes two mechanistic models (fluid discharge and fluid dispersion model) and one mathematical model (monetary consequence model). The input for the consequence analysis includes characteristics of the fluids (e.g., fluid type, viscosity, flammability, toxicity, molecular weight, among others), pipe (e.g., diameter, actual wall thickness, pressure, temperature, leak detection system, emergency response system, number and location of main line valves, etc.), environment (e.g., topography, geography, soil type, weather, hydrology, etc.), and receptors (e.g., proximity, sensitivity to fire, explosion, toxicity, and contamination) [18].

The fluid discharge model is used to identify the discharge

type—leak or burst. The discharge model also facilitates the calculation of the amount of fluid discharged and the discharge rate for each discharge type. The elevation profile, the influence of leak detection systems, and the response time of valves are considered in this model. In the framework, the discharge model is utilized for each section and time. The dispersion model depends on the geographical location of the pipeline and enables the extent and mixing of fluids with the environment to be quantified. The mixing of fluids with the environment creates toxic areas, and areas that can be affected by immediate or delayed ignition depend on the characteristics of the discharged fluid and the environmental conditions [18].

The monetary consequence model is utilized to combine the output of the fluid discharge and dispersion models to estimate the consequence of failure (CF) to humans, environment, and economy. Human consequences include fatalities and injuries, and also require information about the population density, which is obtained following guidelines of Annex O of the CSA Z662 standard [17]. Environmental consequences include the contamination effects to land, water, and air. The economic consequences con- sider all of the direct costs of a pipeline failure including regulatory (penalties and fines), repair, clean up, and insurance. The average values for the economic consequences are obtained based on past failure data from an operator in Ecuador. Indirect costs such as loss of public reputation, share values, operational time,

and increased insurance costs are not included in the framework [18].

3.7 Risk Estimation and Evaluation. The purpose of the risk analysis is to estimate as a function of time and space the risk of failure RF for a leak or burst. The input for the risk estimation are the probabilities and consequences of failure obtained with the probability and consequence analysis. Figure 11 presents an over- view of the risk analysis which includes two mathematical models (risk estimation and evaluation models). The second part of the risk analysis is the risk evaluation that has the objective of evaluating the risk significance. The RAC that was defined during the objective definition is used in the risk evaluation to define risk control or monitoring for each section and time. If the RF (s, t) for leak or burst are smaller than the RAC (significant risk), the pipeline is considered safe and risk-based monitoring is implemented at the locations suggested by the framework to verify changes in the conditions that can increase the risk. On the other hand, if the RF (s, t) for leak or burst is greater than the RAC, the pipeline is considered unsafe and risk control strategies are implemented in the framework by RBI and RBM planning to optimize the inspection and maintenance plans.

3.8 Risk Control. The objective of the risk control is to develop inspection and maintenance plans as a function of time and space. Figure 12 presents the risk control, which includes RBI and RBM planning as well as the risk-based optimization model. The RBI planning in the framework allows for identification of the number, location, and time of inspections. The results of the inspections are used to update the flow and corrosion analysis as well as the maintenance plans in the RBM planning. RBM planning allows for the selection of maintenance plans, which include the location, type, and time. After the maintenance plan is executed, the system state (risk) is used to update the probability analysis and to verify if the risk for the system is below the RAC

Fig. 12 Risk control is implemented using RBI and RBM planning. The results of the inspections are used to update the fluid and corrosion analysis and the system state after the repair is used to update the probability analysis. The risk-based optimization allows to modify the RAC [51].

The last part of the risk control is the risk-based optimization, which, in the framework, is used to select the optimum inspection and maintenance plans that minimize the total costs, which are the sum of the inspection, maintenance, and failure costs. The results of the risk-based optimization are also used to update the RAC in the objective definition.

Fig. 11 Risk estimation is performed in the framework for leak and burst failure modes. In the risk evaluation, the safety of the pipeline is verified by comparison with the RAC [17].

RBI and RBM planning facilitate decision-making for risk control. Figure 13 presents an overview of the preposterior and posterior decision analysis, which are used to optimize inspection and maintenance plans. The first decision is the number, location, and time for the inspections. The outcomes of the first decision are the inspection results that are used for the next decision about the maintenance of the pipeline. The maintenance decision is used to select the number, type, location, and time for the maintenance actions. The outcome of the maintenance decision is the system state for the pipeline. In the final part of the analysis, the system state of the pipeline is the risk and it is used to select the optimum inspection and maintenance plans that minimize total costs (inspection, maintenance, and failure).

3.9 Risk Monitoring and Risk Mitigation. The purpose of the risk monitoring is to select as a function of time and space the risk monitoring plan. Figure 14 presents the risk monitoring and mitigation analysis, which includes risk-based monitoring and a probability and consequence analysis. Risk estimation and risk evaluation are used as input for the risk-based monitoring analysis to select optimal locations for the risk monitoring devices. Given that internal corrosion is the main risk driver in the framework, the monitoring devices used are for internal corrosion. Internal corrosion monitoring may include nonintrusive (e.g., hydrogen probes, ultrasonic testing sensors, or magnetic flux sensors) and intrusive techniques (e.g., corrosion coupons, linear polarization resistance probes, or electrochemical noise) [61]. The results of the risk monitoring efforts allow to update flow and corrosion analysis in order to inform risk assessment and mitigation. Risk mitigation is used in addition to risk control to reduce the risk of sections above the RAC. The output of the inspection, maintenance, and monitoring plans are the input for the probability and consequence analysis. Inspections that are feasible for

Fig. 14 Risk monitoring allows the selection of the best locations and devices for internal corrosion monitoring. Risk is reduced in addition to risk control using risk mitigation that facilitates the improvement of internal corrosion mitigation plans as well as leak detection systems, and emergency response plans.

operating in one of the fields of Petroamazonas EP in Ecuador. The pipeline transports multiphase fluids, which consist of a com- bination of oil, gas, and water. The spatiotemporal corrosion growth process is discretized into s 58 pipeline sections and t 10 production scenarios to achieve approximately homogeneous deterioration for each section and scenario. In this simplified example, it is assumed the sections are of equal length. However, this assumption may not apply in practice where additional factors such as the locations of welds and crossings points are considered. The general corrosion rates for each section and production scenario are estimated using proprietary flow and corrosion analysis (software) [36,37]. Table 1 summarizes the data used as input for the flow and corrosion analysis. The temperature is presented as a range because it varies for each of the production scenarios identified for the analysis. The pipeline fluids have no H2S and therefore only the partial pressure of CO2 is considered for the estimation of the general corrosion rates using the proprietary corrosion analysis [36,37]. The water flow rate increases between the first and last production scenarios, which is normal behavior for an oil production field.

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Table 2 summarizes the results obtained from the flow and corrosion analysis. To simplify the case study, the localized and MIC factors were not estimated. The results were calculated for each of the 58 sections and ten production scenarios, but Table 2 only presents a summary in terms of minimum and maximum values. There is a significant variation of the partial pressure of CO2, which directly affects the shear stress on the wall. The pH is stable

according to the results. The uninhibited general corrosion rates are also similar, which may be generated by the short length of pipeline that reduces the changes in the conditions that affect the corrosion process. The uninhibited corrosion rates are transformed into inhibited corrosion rates using a corrosion inhibitor efficiency of 0.95 and a corrosion inhibitor availability of 0.90, which is recommended based on other investigations [63].

5 Conclusions

The proposed framework is a step toward risk-based optimiza- tion of inspections and maintenance of unpiggable pipelines. The spatiotemporal uncertainties of the corrosion growth process are the main driver for the risk-based integrity management. The advantages of the proposed approach are as follows: (1) The framework can be easily scaled to large pipeline systems due to the applied spatial and temporal discretization in the flow and cor- rosion growth analysis. (2) Expert opinion and information from pipelines with similar operating conditions that the one considered can be incorporated in the analysis. (3) The cost-benefit analysis ensures that the operator minimizes the lifecycle costs while maintaining the integrity and safety of the system.

The consequence analysis in the framework only considers direct costs. Indirect costs of pipeline failures in many cases are greater than direct costs. Pipeline failure data are a source to obtain a relation between direct and indirect costs based on previ- ous failure incidents. The use of indirect costs for the consequence analysis of pipeline failures is an improvement of the framework that can be evaluated by other researchers in the future.

The RBI and RBM planning need to consider dependency between the pipeline sections, i.e., during inspection and mainte- nance, the optimization of resources is increased when adjacent sections are intervened at the same time. This consideration is another field for future research of the proposed framework.

The monitoring techniques considered by the framework are intrusive due to the corrosivity of the fluids; however, on-line monitoring techniques for the direct inspection of the structure are also applicable. An optimum result will require a combination of monitoring of the fluids and the structure. The data collected by these monitoring devices can provide valuable information to update the corrosion analysis between inspections and confirm that the re-assessment intervals are still safe. It is also important to note that monitoring devices with the ability to measure local- ized corrosion rates and MIC influences will be of great value.

The optimization of internal corrosion mitigation by corrosion inhibitors, mechanical cleaning, and biocides is also part of the framework. These actions are also part of the risk mitigation actions currently implemented by most operators of unpiggable pipelines. The use of the information provided by the internal cor- rosion monitoring devices and the flow and corrosion analysis will also support decisions about changes in these internal corrosion mitigation plans.

Acknowledgment

The first author gratefully acknowledges the financial support provided by the Secretariat of Higher Education, Science, Tech- nology, and Innovation from the National Government of the Republic of Ecuador. The authors are thankful to the Maintenance Department of Petroamazonas EP and Broadsword Corrosion

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Engineering for providing the required data and for their guidance on this project, respectively.

Nomenclature

AER ¼ Alberta Energy Regulator

API ¼ American Petroleum Institute

ASME ¼ American Society of Mechanical Engineers

CF ¼ consequence of failure

CSA ¼ Canadian Standards Association DA ¼ direct assessment

DOT ¼ Department of Transportation ICDA ¼ internal corrosion direct assessment

ILI ¼ in-line inspection LSF ¼ limit state function

MAOP ¼ maximum allowable operating pressure MIC ¼ microbiologically influenced corrosion

NACE ¼ International Association of Corrosion Engineers NDI ¼ nondestructive inspection

NEB ¼ National Energy board

PF ¼ probability of failure

PHMSA ¼ pipeline hazardous materials safety administration PIP ¼ pipeline integrity program

PRA ¼ probabilistic risk analysis PT ¼ pressure testing

QRA ¼ quantitative risk analysis

RF ¼ risk of failure

RBI ¼ risk-based inspection RBM ¼ risk-based maintenance

SP ¼ stochastic process

SRA ¼ structural reliability analysis

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