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Monte Carlo-based assessment of system availability.

A case study for cogeneration plants

Adolfo Crespo Marqueza,*, Antonio Sanchez Heguedasb, Benoit Iungc

aDepartment of Industrial Management, School of Engineering, University of Seville, Camino de los Descubrimientos s/n. 41092 Sevilla, SpainbQualmaint, S.L. Maintenance Engineering, Av. San Francisco Javier, 2. 41018 Sevilla, Spain

cFaculte des Sciences, Nancy Research Centre for Automatic Control, University Henri Poincare, BP 239, 54506 Vandoeuvre les Nancy Cedex, France

Received 21 May 2004; accepted 30 July 2004

Available online 22 October 2004

Abstract

The complexity of the modern engineering systems besides the need for realistic considerations when modeling their availability and

reliability render analytic methods very difficult to be used. Simulation methods, such as the Monte Carlo technique, which allow modeling

the behavior of complex systems under realistic time-dependent operational conditions, are suitable tools to approach this problem.

The scope of this paper is, in the first place, to show the opportunity for using Monte Carlo simulation as an approach to carry out complex

systems’ availability/reliability assessment. In the second place, the paper proposes a general approach to complex systems

availability/reliability assessment, which integrates the use of continuous time Monte Carlo simulation. Finally, this approach is exemplified

and somehow validated by presenting the resolution of a case study consisting of an availability assessment for two alternative configurations

of a cogeneration plant.

In the case study, a certain random and discrete event will be generated in a computer model in order to create a realistic lifetime scenario

of the plant, and results of the simulation of the plant’s life cycle will be produced. After that, there is an estimation of the main performance

measures by treating results as a series of real experiments and by using statistical inference to reach reasonable confidence intervals.

The benefits of the different plant configurations are compared and discussed using the model, according to their fulfillment of the initial

availability requirements for the plant.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Availability assessment; System simulation; Operational evaluation; Simulation results

1. Introduction

Availability and/or reliability studies of industrial

systems such as the large scale-ones, have now to take

into account a lot of constraints [1]: the system structure

may be very complex (different abstraction levels; vast

array of units, components, etc.); the components have a

range of potential failure modes and follow various failure

distributions which have sometimes to integrate the initial

state of the system at the failure time, the operating mode,

the environmental context, etc. the components may

0951-8320/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ress.2004.07.018

* Corresponding author. Tel.: C34 954 487215; fax: C34 954 486112.

E-mail addresses: [email protected] (A. Crespo Marquez),

[email protected] (A. Sanchez Heguedas), [email protected]

(B. Iung).

conform to arbitrary failure and repair distributions for

maintained systems; these studies should be coupled with

economic analyses to manage for the system the compro-

mise between safe operation and economic service; The

failure modeling may be complicated because based on

various (functional, technical) dependencies between the

components [2] and requires a lot of data about component

failure which are sometimes no sufficient and/or not

available, etc.

Taking into account these considerations, the opportunity

to carry out system availability assessments through

analytical models, will be many times very restrictive. Let

us discuss some of the reasons for this: Some analytical

models like replacement after failure and/or periodic

testing/replacement assume system components indepen-

dence, i.e. that if one component fails and it is repaired,

Reliability Engineering and System Safety 88 (2005) 273–289

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A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289274

all the other components in the system will function as

normal without regard to the repair going on, which is very

unrealistic for many systems as the ones referred above

[3, p. 181]. An alternative approach could be based on

Markov models. These models can take into account a wide

range of dependencies, however, they are rather restrictive

in terms of components’ life, preventive maintenance and

repair time distributions. Furthermore it is not possible to

take into account any trends or seasonal effects. This is the

case of items with variable profiles for which the MTBF

varies with some process output or when there is any

seasonal effect in the system [4]. Another alternative could

be the use of semi-Markov models. Semi-Markov models

[16] generalize the Markov models by: (a) allowing, or

requiring, the decision maker to choose actions whenever

the system state changes; (b) modeling the system

evolution in continuous time; (c) allowing the time spent

in a particular state to follow an arbitrary probability

distribution. The scalability in terms of number of possible

states of the system, and number of maintenance actions, is

an important advantage of this models, however they are

also complex and therefore very difficult to handle when

the number of the system possible states increases (see a

trade-off study in [5]).

After highlighting the complexity and relevance of the

problem in this short introduction, we have organized the

rest of the paper as follows: We first explain the interest of

using Monte Carlo modeling for availability/reliability

assessment in Section 2, where we discuss the pros

and cons of this approach. Section 3 is devoted to present

a generic approach for the assessment of a system

availability/reliability, based on continuous time Monte

Carlo modeling of the system’s operation and maintenance.

The case study is presented in Section 4, this section

includes the presentation and discussion of the results of the

study. Finally, Section 5 concludes the paper with a

summary of our findings and some useful directions for

future research.

1 The reader is referred to [17] for a discussion regarding both simulation

practices.

2. Monte Carlo simulation in availability/reliability

assessments

A more general approach to our problem than previously

mentioned analytical models can be based in Monte Carlo

(stochastic) simulation [6]. The idea of this method is the

generation of certain random and discrete events in a

computer model in order to create a realistic lifetime

scenario of the system. Therefore the simulation of the

system’s life process will be carried out in the computer,

and estimates will be made for the desired measures

of performance [3]. The simulation will be then treated as

a series of real experiments, and statistical inference will

then be used to estimate confidence intervals for the

performance metrics. The events can be simulated either

with variable time increments (discrete event simulation)

or with fix time increments, at equidistant points of time

(continuous time simulation).1

The Monte Carlo simulation method allows us to

consider various relevant aspects of systems operation

which cannot be easily captured by analytical models such

as K-out-of-N, redundancies, stand-by nodes, aging,

preventive maintenance, deteriorating repairs, repair teams

or component repair priorities. By doing so, we can avoid

restrictive modeling assumptions that had to be introduced

to fit the models to the numerical methods available for their

solution, at the cost of drifting away from the actual system

operation and at the risk of obtaining sometimes dangerous

misleading results [7]. Lately the utilization of this method

is growing for the assessment of overall plants availability

[8] and the monetary value of plant operation [9].

In this paper, we will use the continuous time simulation

technique. This simulation will evaluate the system state

every constant time interval (Dt), the new system state will

be recorded and statistics collected. We will consider

chronological issues by simulating the up and down cycles

of all the components, and then the system operating

cycle will be obtained by combining all the components

cycles and their dependencies (as explained by Billington

and Tang [10], for their Monte Carlo sequential approach).

Then the time is incremented another Dt, and so on. As a

simulation tool we will use VENSIM (Ventana Systemsw),

which has special features to easy Monte Carlo type of

simulation experiments, and to provide confidence

interval estimations.

The weak point of the Monte Carlo method is the

computing time [9] specially when we deal with the problem

of finding suitable maintenance control policies, and the

search space for the control variables of the problem to test

increases. In our case, however, testing values of a set of

control variables is not the problem; we will not be trying to

find an optimal maintenance policy. The scope of our case

study will be assessing the availability of two alternatives of

plant configuration and for a certain predetermined main-

tenance strategy. In our case, randomness is constrained to

the failure generation process and maintenance policy is set

by the plant manufacturer. Pseudo random numbers will be

generated every time interval, and therefore when consider-

ing the entire simulation horizon, the requirements in terms

of number of simulation is expected not be very exigent, as

we will have time to test later in the paper.

3. A general approach to system availability/reliability

assessment

The procedure that we propose in this paper, in order to

develop the availability/reliability study using continuous

Table 1

Steps in the availability/reliability assessment

Step name Description Result

1. System’s configuration definition Determination of the basic functional blocks for the

plant configuration and for every function to

analyze

List of functional blocks: function, input, output, etc.

Determination of the dependencies among func-

tional blocks for the fulfillment of every function

Functional chart of the system that contains the

relations among blocks and their reliability features

2. Data collection Compilation of the necessary reliability and

maintenance data (and information) for each one

of the considered blocks

Reliability and maintenance data for each block:

MTTR, MTBF, MTTM, preventive schedule, times,

etc.

3. Model building Continuous time stochastic simulation model

building

VENSIM simulation models

4. Simulation Simulation scenarios and experiments design Scenario listings, required simulation replications,

confidence intervals for the results, etc.

5. Results and analysis Simulation results calculation Result of the parameters of availability and reliability of

the functions of our interest in the different configur-

ations

Simulation results discussion Interpretation of results and their discussion

A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 275

time stochastic simulation, is described in Table 1, where

we distinguished a total of five steps.

Step 1: System’s configuration definition. The first step of

the study is the definition of the configuration of the system,

that means the selection/determination of the system’s

functional blocks, and how they relate to each other. A

functional block provides the output of a system as the

outcome of a joint event defined by the inputs to the system

and its various states. Functional blocks corresponding to

different subsystems are combined together to form a

functional block diagram representing the functional

characteristics of the combined system [11]. Conversely, a

complex system represented by a single functional block is

decomposed to constituent components with a correspond-

ing functional block diagram.

As a result of this step, we will obtain a functional chart of

the system that contains the relations among its blocks and

their reliability features. It is important to know how this

functional chart will have to be obtained for each function

provided by the system. For instance, if our system produces

electric power and steam, we will need two separate charts

indicating the dependencies of the different functional blocks

to provide each one of these two functions.

Step 2: Data collection. Before starting to build the

simulation model in step 3, we need to know the design, the

complete taxonomy of components of the plant, and we will

try to find out full reliability and maintainability information

of each item [8]. Once the functional blocks and their

interactions are identified, it is required to define for

each block two categories of data: failure rates, and repair/

restoration and preventive maintenance times and

dependencies.

In terms of components failure rate and repair date

data information, there are several sources to find this

information [3]: (1) public data books and databanks,

(2) performance data from the actual plant, (3) ‘expert’

judgments, and (4) laboratory testing. An introduction to

reliability data collection and management is given in [12].

Once the data for each functional block component is

gathered, MTBF and MTTR can be calculated for each

functional block of the system attending to their configuration

and probability rules.

In terms of block’s preventive maintenance, we will have

to gather complete information about the system’s main-

tenance plan. At the same time, we will have to find out the

elements conditioning the final preventive maintenance

program. The preventive maintenance program of the

system might be conditioned by any of the components

(many times, one of the block most relevant component

conditions opportunistic maintenance of the rest of the

components), but can also be conditioned by the dependen-

cies among system elements, or even between blocks.

For instance, in some occasions, although scheduled

hours for maintenance may arrive, it is possible that

elements/blocks will remain operating until the repair or

the preventive maintenance of another element/block is

finished (maintenance is therefore backlogged). All these

types of dependencies will have to be clarified before

advancing to the next step.

Step 3: Building the simulation model. A generic

system’s maintenance model, which will be applied to the

maintenance of each functional block in our model, will

now be built following some of the basic principles as

explained in [13]. The notation will be as follows

(notice that this variable list will be later subscripted by

functional block of the model in our case study).

System status information related variables

CAt
decrease in system’s age due to corrective
maintenance action in t

LCt
time when the last corrective maintenance, for a
system in t, started

LPt
time when the last preventive maintenance, for a
system in t, started


PAt
decrease in system’s age due to preventive
maintenance action in t

RNt
random number within the interval (0,1), generated
in t

Tt
system’s age in t
TI
increase of system’s age in period t
TOt
decrease of system’s age in period t
l(Tt)
failure rate of the system in t
At
system availability (1 available, 0 unavailable) at t
AAt
all sub-systems available (1 yes, 0 no) at t
SMt
sheduled maintenance (1 yes, 0 no) in period t
MBt
maintenance backlogged (1 yes, 0 no) at t
RMt
maintenance released (1 yes, 0 no) in period t
Model parameters

CT
average time of a corrective maintenance action
n
minimum age of the system to do preventive
maintenance actions

PT
average time of a preventive maintenance action
T1
maximum time the system operates without a failure
3.1. Modeling system’s age

The process requires first to model the age of the

system (Tt):

Tt Z Tt CTIt KTOt (1)

We will consider that age will increase when the system

is available. That means that we assume that available

means ‘running’, no idling nor standing-by, therefore

TIt Z At (2)

and age will decrease when the system is maintained

TOt ZPAt; if PAt !O0 and CAt !O0

PAt CCAt; Otherwise

((3)

CAt ZTt; if lðTtÞRRNt

0; Otherwise

((4)

where RNt is a random number generated for every t within

the range (0,1), l(Tt) is the failure rate of the system, and

CAt and PAt are decreases in the system’s age as a

consequence of the corrective and preventive maintenance

actions, respectively.

3.2. Modeling age based preventive maintenance

In the age based maintenance policy, the only one

considered in our case study, if the system does not fail until

a given time n, then it is preventively maintained.

Otherwise, it is correctively maintained at the failure time

PAt ZTt; if Tt Rn

0; Otherwise

((5)

Here, we also assume that a failed system will be maintained

correctively at failure.

3.3. Modeling system’s availability

The conditions of the system that will make it

unavailable will be the corrective or preventive maintenance

that is being carried out

At Z

1 K ðPulseðLCt;CT; tÞ

CPulseðLPt; PT; tÞÞ; if LCt O0 or LPt O0

1; Otherwise

8><>:

(6)

Notice that when tZ0, LCtZLPtZ0 (LCt and LPt, are

the times when the last corrective [or preventive,

respectively] maintenance, for a system in t, started).

The function Pulse, previously introduced to calculate

STMt is defined as follows:

Pulseða; b; tÞ Z1; a! t!a Cb

0; Otherwise

((7)

3.4. Modeling maintenance backlog

In some occasions, although scheduled hours for the

preventive maintenance of an equipment may arrive,

it could be suitable that this equipment would remain

functioning until the repair or the preventive maintenance of

another equipment is finished. In this way, we will be able to

consider in the model functional and operational dependen-

cies of the functional blocks. This will be the case, for

instance, of the scheduled maintenance of each of the

turbines of the plant of our case study, and in order to avoid

losing back-up of the power supply provided by

the cogeneration. Therefore, it is necessary to model the

possible backlog of maintenance activities, i.e. activities

which are due and waiting to be carried out by the

maintenance department. Let then imagine for instance

that we have a system with two units (iZ1, 2), and both of

them need to be in operating conditions in order to

preventively maintain one of them, i.e. AAtZ1, where

AAt is defined in Eq. (8) as follows:

AAt ZYiZ2

iZ1

At;i; with i Z1;2 (8)

SMt;i Z1; ti=n Z Intðti=nÞ and tiO0

0; Otherwise

((9)


MBt;i ZMBtK1;i CSMt;i KRMt;i (10)

RMt;i Z1; ðSMt;i Z1 or MBt;i Z1Þ and AAt Z1

0; Otherwise

((11)

Maintenance activities will be scheduled according to (9),

then could be backlogged according to (10), and finally

released as explained in (11). Notice that if both units are OK

(i.e. AAtZ1) a scheduled maintenance is immediately

released, just in time, without being backlogged. Then,

when a preventive activity is released, we will record this

time (in LPt) to allow downtime modeling as explained

previously in (6). Notice that, in this example, to make this

formulation simple, we suppose that a backlogged activity

will be released before a new preventive maintenance will be

scheduled, but of course, this could not be the case, and we

would need extra formulation to consider that case. The

model formulation as presented above, is in our case built

using the software named VENSIM.2 VENSIM is a entire

simulation environment package for continuous time simu-

lation, this software allows to represent the functional blocks

and easy their parameterization. At the same time, VENSIM

offers special features to deal with stochastic simulation

within the continuous time models. For instance, sensitivity

analysis is easily performed, as well as parameters

optimization, etc. When writing the simulation model code

we will have to specify simulation parameters like: initial and

final time of the simulation, and the time step.

Finally, and within this third step, we cannot forget the

importance of validating our model prior to start producing

any results for their discussion. We have to make sure that the

structure of the whole model is properly considered, that the

simulation of each block’s performance is consistent and

expected according to existing dependencies within

the entire system.

Step 4: Simulation. Once model validation is done,

Andijani and Duffuaa [14] have remarked how many

simulation studies on maintenance systems ignored proper

design of experiments and some way of output analysis.

Now we start to deal with this issues in our process.

For each one of the system configurations considered in

our simulation study, we will have to define the number of

replications that, using different seeds in the generation of

pseudorandom numbers for failure distributions of the

different functional blocks, will be carried out. This can be

many times an iterative process. Once a few simulation

results are obtained (n), the mean values and standard

deviation of the samples are calculated. With these values,

and once the size of the sample is known (n), the confidences

intervals of the results can be calculated. That is to say, we

estimate with a certain percentage of results confidence, that

the final values of the variables for the different configur-

ations of the system will fall within the interval that we

2 Trade Mark of Ventana Systems, Inc.

provide. In case we may require a higher accuracy, we will

need to increase the sample size.

Step 5: Results and analysis. This step will include the

presentation of result for the availability and reliability

parameters corresponding to the functions of our interest in

the different configurations. These results will later require

their discussion when compared with availability and

reliability requirements that may be established for the

functions provided by the system. This step implies

explaining the results obtained with the simulation, and the

factors that may lead to those results, but also providing

possible actions to improve system’s availability or

reliability to meet system’s functional requirements.

Another important aspect of the study that has to be

introduced at this time is the sensitivity analysis. Once input

parameters may not be very accurate sometimes, the influence

that parameters have on the final results, specially those more

important and uncertain for the study, must be explored.

4. COGEPLANT case study. Availability assessment

of a cogeneration plant

Electrical power generation systems represent examples

of processes where Monte Carlo techniques have traditionally

provide a practical approach to reliability analysis (Henley

and Kumamoto, 1991, p 480). Reasons for this are related to

feasible configurations of the systems (on-line and stand-by),

scheduled or un-scheduled shut-downs, repair and preventive

times distribution functions, etc. Clearly, an attempt to obtain

reliability parameters for this kind of problems by determi-

nistic methods is virtually impossible [15].

The cogeneration plant that we will describe in this paper

(that we will now refer as COGEPLANT) is currently being

designed in Seville, and will have equipment to produce

electrical power and to co-produce steam according to

certain very high availability requirements established by a

large refinery located near by, consuming 100% of

COGEPLANT’s output. At the moment of producing this

paper, the plant is in the design phase and the most suitable

configuration is being evaluated. The plant will supply

100% of the electrical power required by the refinery

by means of two independent systems, in automatic

stand-by, and with a transparent operation with regards to

the Refinery. It is accepted that one of these system is the

Local Electrical Transportation Network (LETN), providing

that the proposed configuration fulfils the reliability

demanded in the project. From the LETN the possible

supply will be constrained to a maximum of 25 MW of

power. The justification to build a cogeneration is mainly

the reach of a substantial improvement in the operational

stability of the refinery, through a dedicated electrical power

and steam generation system. Therefore, the steam and

electricity supply must guarantee maximum reliability and

availability ratios. In the technical conditions included in

the documentation that was provided in order to elaborate


the bidding of the project, we could find the following

availability requirements.

4.1. COGEPLANT availability requirements

The project that we will analyze is said to be articulated

in two phases: Phase 1 will last 2 years and will consider a

lower demand than the final one. Phase 2 will be for a total

of 15 years after Phase 1, at full level of plant designed

supply. For each of those phases, the availability

requirements for electrical power and steam production

will be the following.

Steam production availability:

†
Phase 1. Steam 600 psi: 70 Tn/h 350 days/yr, 35 Tn/h
15 days/yr.

†
Phase 2. Steam 600 psi: 70 Tn/h 350 days/yr, 35 Tn/h
15 days/yr. Steam 150 psi: 70 Tn/h 365 days/yr.

Electrical power production availability:

†
Phase 1. 20 MW with back-up for 350 days/yr, 20 MW
without back-up for 15 days/yr.

†
Phase 2. 40 MW with back-up for 335 days/yr, 20 MW
with back-upC20 MW without backup for 30 days/yr.

Let us now use our approach described above to validate

through simulation whether the previous user’s availability

requirements will be satisfied or not, and according to the

plant technical structure/configuration and the dependability

parameters of each of their components (Turbine,

Generator, Boiler, etc.)

Fig. 1. Description of an electrical pow

Step 1: COGEPLANT configurations definition. The

system used for the generation of the electrical power is

conformed by a dual turbine (where dual refers to the

possibility to of using gas or fuel as combustible, with

natural gas used under normal operating conditions), and

a turbine-coupled generator. Two configurations are

considered to be analyzed: The first one is three turbine–

generators that will provide energy of 30 MW each;

The second one is a two- turbine configuration with

45 MW output per unit. Output in both cases will be to a

nominal voltage of 12 kV. It is also foreseen the existence of

a transformer and a circuit-breaker per turbine–generator

subsystem. The generation of steam will be done using a

boiler that will benefit from the turbine exhaust gasses

temperature in order to generate the necessary steam flow

(see Fig. 1). The boiler, using a by-pass system, allows a set of

post-combustion burners to be used, providing back-up in

case of a turbine–generator set failure (obviously, it is

considered no post-combustion under normal operating

conditions). Clearly, this provides 100% back-up to

the solution adopted against potential failures in the turbine

system. Finally, the use of several economizers permits the

production of steam in low (150 psi) and high pressure

(600 psi). A demineralized water plant will produce equal

amount of water than the steam generation of the system.

This is required once the water produced by steam

condensation in the refinery facilities will not be directly

recycled to the cogeneration unit. Besides this, there will

exist a water tank to allow total supply of water during a

sufficiently wide period (this provides 100% water

supply back-up).

er and steam cogeneration unit.

Table 2

Functional blocks considered in the simulation study

Functional block Components Inputs Outputs Function

Power generation

system named:

[RgasTGasGen]

Gas network Natural gas (or fuel,

eventually)Cair

Electrical power

(30/45 MW) in

12 kVCwarm

exhaust gasses

The generation of the electrical power is done

by a dual turbine (where dual refers to the

possibility to of using gas or fuel as

combustible, with natural gas used under

normal operating conditions), and a turbine-

coupled generator. Exhaust gasses will be then

used to generate steam

Turbine

Generator

Transformer

Circuit switch

Steam generation

system named:

[RAguaCaldera]

Boiler Demineralized waterC

turbine exhaust gases

(Cnatural gasCair

eventually)

Steam 600 psiC

steam 150 psiC

water drain Cexhaust gases

The generation of steam will be done using a

boiler that will benefit from the turbine

exhaust gasses temperature to generate the

necessary steam flow. The boiler, using a

by-pass system, allows a set of post-combus-

tion burners to be used. The use of several

economizers permits the production of steam

in low (150 psi) and high pressure (600 psi).

The water produced by steam condensation in

the refinery facilities will not be directly

recycled to the cogeneration unit. Besides this,

there will exist a water tank to allows total

supply of water during a sufficiently wide

period

Steam extraction and

network system

Pump 1

(from degasifier to boiler)

Pump 2

(between economizers)

Valve 1

(after pump 1 before boiler)

Valve 2 (after pump 2, to

bypass second economizer)

10 joints and connections

(water network system)

Local electrical trans-

portation network

(LETN) named:

[RedElec]

LETN 25 MW in 12 kV 25 MW in 12 kV Supply constrained to a maximum of 25 MW

of power


To the effects of these paper calculations, we will

consider perfect water supply to the steam generation

system, therefore we will only include in our study those

elements that compose the water network, the boilers

and the steam network in the plant. Taking into account

previous considerations, the operating mode of the plant and

its environmental constraints, we have decided to model

the three different functional blocks that we describe in

Table 2, where also the components of the blocks are

described. Some of these blocks will be then replicated,

according to the specific physical system configuration

which is being analyzed.

As we mentioned above, there are two plant configur-

ations that will be the object of our analysis in this paper.

These two configurations will lead to the implementation of

interactions between the functional blocks in order to meet

project requirements. We will now express, for both

configurations, the possible interactions of their functional

blocks, and in the different phases, for the availability

requirements to be fulfilled:

Configuration 1:3 Three TGs of 30 MW in stand-by, with

one B each, for the production of 25.2 Tn/h of steam in high

and low pressure.

Steam availability (see, as an example of chart, Fig. 2).

Phase 1. The steam production at 600 psi with volumes

of 70 and 35 Tn/h will be obtained when the following

conditions are met:

3 Note: TG, turbine–generator set; B, boiler.

†
The 70 Tn/h flow requirements are met those days that all
three boilers work simultaneously.

†
The 35 Tn/h flow requirements are met those days that
two, out of three boilers work simultaneously (actually

50.4 Tn/h will be produced those days).

Phase 2. The conditions for the steam production at

600 psi with volumes of 70 and 35 Tn/h. are the same that

in the previous phase. Moreover, it will be necessary that

all three boilers work together to reach 70 tn/h. with

150 psi.

Availability of electrical power.

Phase 1: 20 MW of electrical power, with 20 MW

back-up in standby, will be available those days that two

out of the three TGs are available. In case that a contract with

LETN exist, for the supply of 25 MW during this phase, it

would be enough then with two out of four blocks

(RGasTGasGen1, RGasTGasGen2, RGasTGasGen3,

LETN) availability to obtain the required electrical power.

The production of 20 MW of electrical power without any

back-up will correspond with those days where only one TG

is available (or only one of above mentioned four blocks is

available in case that a contract with the LETN is in place).

Phase 2: The 40 MW of electrical power with 40 MW

back-up in standby will be available the days that all

four functional blocks offering electrical power to the

refinery are available (RGasTGasGen1, RGasTGasGen2,

RGasTGasGen3, LETN). Notice how it will be necessary

the contract with the LETN to fulfill this requirement

with this configuration of the plant. For the production of

Fig. 2. Steam production diagram with 3 Bs.


20 MW with standbyC20 MW without standby three of

the previous four blocks need to be available.

Configuration 2. Two TGs of 45 MW in stand-by, with

one B each, for the production of 35 Tn/h of steam in high

and low pressure.

Steam availability.

Phase 1. The steam production at 600 psi with volumes

of 70 and 35 Tn/h will be obtained when the following

conditions are met:

†
The 70 Tn/h flow requirements are met those days that all
two Bs work simultaneously.

†
The 35 Tn/h flow requirements are met those days only
one out of two Bs works.

Fig. 3. Electrical power product

Phase 2. The conditions for the steam production at

600 psi with volumes of 70 and 35 Tn/h. are the same that in

the previous phase. Besides this, it will be necessary the two

Bs to work to reach 70 tn/h with 150 psi.

Availability of electrical power (see, as an example of

chart, Fig. 3).

Phase 1. 45 MW of electrical power (not only 20 MW)

with 45 MW back-up in stand-by will be available the days

that the 2 TGs are available. No contract with LETN is

considered in thiscase.Theproductionof45 MW ofelectrical

power (not only 20 MW) withoutany back-up in stand-by will

correspond with those days where only one TG is available.

Phase 2: The 45 MW of electrical power (not only 40)

with 45 MW backup in stand-by will be available the days

ion diagrams with 2 TGs.

Table 3

Reliability data (in failures per running day)

Functional block Components Data bank Selected value

FARADIP IEEE Own value

TG [RgasTGasGen] Gas network 0.0000 0.00000000

Turbine 0.001320 0.00548 0.00547945

Generator 0.004800 0.00046300 0.00046300

Circuit Breaker 0.000036 0.00000821 0.00000821

Transformer 0.00002700 0.000024 0.00002700

B [RaguaCaldera] Boiler 0.0110 0.01100000

Steam extraction and network system 0.0001 0.00000000

Pump 1(from degasifier to boiler) 0.0110 0.00500000

Pump 2 (between economizers) 0.0110 0.00500000

Valve 1(after pump 1 before boiler) 0.000480 0.00048000

Valve 2(after pump 2, to bypass 2nd economizer) 0.000480 0.00048000

10 joints and connections (water network system) 0.000120 0.00012000

LETNl [RedElec] LETN 0.000480 0.03405088 0.03405088


that the 2 TGs are available. The production of 20 MW with

20 MW back-up in stand-byC20 MW without back-up does

not apply for this case. No contract with LETN is considered

in this case.

Step 2: COGEPLANT’s data collection. Step 1 has

provided a clear definition of the plant configuration

alternatives. At the same time, we had opportunity to

clarify functional dependencies among defined blocks in

order to produce a certain COGEPLANT service. Now we

have to gather data in order to have then the possibility to

model the plant properly.

In this occasion, we have searched and found data items

in two data banks (FARADIP and IEEE) and at the same

time we have retrieved some information from the company

designing the plant, according to their experience in similar

projects and sometimes according to their experts judg-

ments (we call this ‘own value’ in Table 3). In Table 3

failure rate data of the different components in the

considered functional blocks is presented. The criteria

followed in this paper, according to company designing the

plant, has been to select the final value has been by order of

preference: IEEE, Own value and FARADIP.

Table 4

Functional blocks MTTR (mean time to repair, in days)

Functional block Components Data source

IEEE

TG [RGasTGasGen] Gas network

Turbine

Generator 1.36250000

Circuit breaker 0.50000000

Transformer 3.54166667

B [RAguaCaldera] Boiler

Steam network

Pump 1

Pump 2

Valve 1

Valve 2

9>>>>>>>=>>>>>>>;

Water network

LETN [RedElec] LETN

In Table 4, mean time to repair of the different components

in the considered functional blocks are defined. In this

occasion, we have found data items in the IEEE data bank and

at the same time we have retrieved some information from the

company designing the plant, according to their experience in

similar projects and sometimes according to their experts

judgments (we call this again ‘own value’ in Table 4). The

criteria followed in this paper, according to company

designing the plant, has been to select the final value has

been by order of preference: IEEE and Own value.

From Table 4, mean time to repair is calculated for every

functional block and presented in Table 5.

To complete the blocks with preventive maintenance

data, Table 6 identifies the information about the mainten-

ance plan for the plant.

But the following consideration, operational dependen-

cies related to maintenance, have to be taken into account to

build the final maintenance schedule:

†
The preventive maintenance of the plant will be
conditioned by the preventive maintenance of the turbine

sets, so that in the subsequent simulation model we will

Selected value

Own value

2.54166667 2.54166667

1.36250000

0.50000000

1.000 3.54166667

1.000 1.000

1.000 1.000

1.000 1.000

Table 5

Basic functional blocks data

Functional block Failure rateP

li MTTRP

ðli=miÞ=P

li

TG [RGasTGasGen] 0.00597766 2.45204697

B [RAguaCaldera] 0.02208000 !1

LETN [RedElec] 0.03405088 !1

In failures per day (l) and repair days (MTTR).

Table 6

Maintenance steps and scheduled downtime for the whole turbo-generator

and boiler set

Maintenance step Scheduled down time hours

Monthly (off-line wash) 6

Each 4.000 operating hours 48



4


suppose that every set turbine–generator–boiler will stop

together for the accomplishment of the different steps of

maintenance. The maintenance of the boilers will be

therefore opportunistic and determined by that of the

turbo-generator sets.

†
An important aspect of the preventive maintenance is
that it will pursue that no more than one turbo-generator

set will be stopped for the accomplishment of a

preventive task (i.e. no simultaneous stop of TG sets

due to preventive maintenance). Therefore, in some

occasions, although scheduled hours for the maintenance

may arrive, it is possible that groups remain operating

until the repair or the preventive maintenance of another

group is finished (maintenance is backlogged).

Step 3: COGEPLANT simulation model. So far, we have

complete information about plant configurations, functional

and operational dependencies, and we have to gather

required reliability and maintainability data of the plant.

Our next step will be to introduce all this into a continuous

time Monte Carlo simulation model. The model is built with

VENSIM4 tool (for instance, Figs. 2 and 3 are produced by

VENSIM while modeling this problem) and simulates a

temporary horizon of 6205 days with a time step for the

simulation of one day. Every day, the failures that will take

place in the available functional blocks will be randomly

obtained, in the event that a failure takes place in a block, this

will turn to be unavailable. Then the time will be advanced

for those preventive or corrective maintenance operations

that are in process of accomplishment (and blocks will return

to the availability state in case these operations are finished).

The breakdowns of the turbo-generator sets will not affect the

steam production since there is a back-up system with natural

gas post-combustion. Similarly, breakdowns in the boiler

will not affect the production of electrical power (a bypass

system for the exhaust turbine gases exists at the entry of the

boiler). The preventive maintenance operations are modeled

taking into account the possible backlog of preventive

actions.

4.2. Simulation model output validation

In this section, we present graphical examples for

relevant variables in the simulation model and we test

Trade Mark of Ventana Systems, Inc.

their behavior patterns. This will help us to validate

model structure and to achieve the necessary confidence

in results that will be later presented. For instance, in

Fig. 4, we do present maintenance program scheduling

for Configuration 2, and we show assigned maintenance

for different frequencies and TGs. It can be appreciated

how our simulation model represents the maintenance

operations when they are scheduled using binary

variables (1 maintenance action scheduled, 0 no main-

tenance action scheduled). These variables will be later

used by the model to calculate availability of the

different services according to previously defined inter-

actions among building blocks and according to

reliability and maintainability data that we estimated

for the building blocks.

In Fig. 5, the corrective maintenance of both turbine

sets in Configuration 2 are presented. These are repairs

resulting from failures generated randomly. Our simu-

lation model represents the corrective maintenance actions

using again binary variables (1 corrective maintenance

action released, 0 no corrective maintenance action

released). Again, these variables will be later used by

the model to calculate availability of the different services

according to previously defined interactions among

building blocks, and according to reliability and

maintainability data that we have estimated for the

building blocks.

Fig. 6 captures backlog of maintenance programmed

activities, i.e. moments in time where a given scheduled

maintenance activity could not be carried out (and was

backlogged), because it would cause losing back-up or losing

functionality of the system.

Fig. 7 shows availability of the TGs functional blocks

over the simulation timeframe. Despite initial failures

and therefore different starting TGs performance, avail-

ability over time will tend to be very similar in both blocks.

In Fig. 8, we can see three graphs for the accumulated

days of electrical power supply provided at different

requirement levels (40 MW with back-up, 20 MW with

back-upC20 MW without back-up, and other less exigent

supply).

In Fig. 9, we can see three graphs for the accumulated

days of high pressure steam (600 psi) supply provided at

different flow requirement levels (70, 35 Tn/h, and other

less exigent supply).

Fig. 4. Example of the maintenance program for Configuration 2.


4.3. Sensitivity analysis

In this case study several univariate (changing one

parameter at a time) and multivariate (changing many

Fig. 5. Example of TGs correcti

parameters at a time) sensitivity analysis were carried out.

As an example, we present here results for the multi-

variate sensitivity analysis to variations in the corrective

time for both TG blocks of configuration 2 which was

ve maintenance (repairs).

Fig. 6. TGs backlog of maintenance activities for Configuration 2. These were activities carried out after the scheduled date.


found to be interesting to analyze the suitable level of

spare equipment to keep stored on site. We assume

variations for the parameters CT[RGasTGasGen1] and

CT[RGasTGasGen2], uniformly distributed in the interval

[2,10] days of MTTR of each block. Fig. 10 Shows the

results. Worse case shown in the graph, MTTR of 10 days

Fig. 7. TGs availabi

for both TGs, shows 4850 days of correct 45 MW

with Backup supply in F2. These results should be then

considered later, they add additional information when

doing analysis in step 5.

Step 4: COGEPLANT simulations. After presenting all

these figures in previous step 3, we can conclude that

lity over time.

Fig. 8. Days of electrical power production for different power requirements. Second phase of the project.


the outputs of the COGEPLANT model are the ones expected

for the inputs considered, and that we can now proceed to

compare the different configurations, defining the corre-

sponding scenarios. We will therefore present now a set of

simulations containing, for each one of the two plant

Fig. 9. Days of high pressure steam production for differe

configurations considered in the study, five replications

using different seeds in the generation of pseudorandom

numbers for failure distributions of the different functional

blocks. Once these simulation results are obtained, the mean

values and standard deviation of the samples are calculated.

nt flow requirements. Second phase of the project.

Fig. 10. Sensitivity analysis results for MTTR of the TGs [2,10] days.

Table 7

Results for the fulfillment of the power and steam supply requirements in

Configuration 1. Two phases. Assuming contract with LETN in the second

phase.

Supply (requirements) Repl. Values Statistics

Phase 1

20MW with back-up

(note: MINZ700 days)

1 723 Mean 726.20

2 725 Std. dev. 2.68

3 729 Conf(G95%) 2.35

4 725 Max 728.55

5 729 Min 723.85

20 MW without back-up

(note: MAXZ30 days)

1 8 Mean 4.80

2 6 Std. dev. 2.68

3 2 Conf(G95%) 2.35

4 6 Max 7.15

5 2 Min 2.45

75.6 Tn/h of 600 psi steam


1 678 Mean 669.00

2 664 Std. dev. 5.92

3 666 Conf(G95%) 5.19

4 665 Max 674.19

5 672 Min 663.81


(note: MAXZ30 days of

35 Tn/h)

1 19 Mean 33.40

2 36 Std. dev. 10.78

3 31 Conf(G95%) 9.45

4 49 Max 42.85

5 32 Min 23.95

Phase 2

50 MW with back-up

(note: MINZ5025 days

40 MW with back-up)

1 4792 Mean 4780.40

2 4783 Std. dev. 27.34

3 4781 Conf(G95%) 23.96

4 4810 Max 4804.36

5 4736 Min 4756.44

20 MW with BC20 MW

without B

(note MAXZ450 days)

1 647 Mean 655.80

2 665 Std. dev. 36.97

3 656 Conf(G95%) 32.40

4 604 Max 688.20

5 707 Min 623.40

75.6 Tn/h 600 psi steam


70 Tn/h)

1 4746 Mean 4796.40

2 4789 Std. dev. 37.75

3 4783 Conf(G95%) 33.09

4 4818 Max 4829.49

5 4846 Min 4763.31


(note: MAXZ225 days

35 Tn/h)

1 638 Mean 596.40

2 620 Std. dev. 40.17

3 617 Conf(G95%) 35.21

4 548 Max 631.61

5 559 Min 561.19


With these values, and once the size of the sample is known

(nZ5), the confidences intervals (for the 95% confidence) of

the results are obtained. That is to say, we estimate with a

95% o confidence, that the final values of the variables for the

different configurations of the plant will fall within the

interval that we provide (we do think that the selected number

of replications place the blocks reliability and availability

measures within reasonable intervals and with a reasonable

probability, therefore we have accepted this sample size).

Finally, we will mention that failure rates are not considered

constant in the model, although we use Table 5 values, we

have considered that exists infant mortality and wear out

effect, according to experience for similar plants and

equipment (a typical failure rate curve topology is presented

in Fig. 11).

COGEPLANT results and analysis. We will now present

and discuss the simulation results obtained for both plant

configurations.

4.4. Results for requirements fulfillments

in Configuration 1 (3 TGs)

In Table 7, we present results of the model for all the

different supply requirements fulfillments, and for configur-

ation 1, with three turbines. Requirements are presented in

the first column and in terms of service quality required over

Fig. 11. Curve topology for the failure rate of the block [RGasTGasGen1] in

the simulation study.



70 Tn/h)

1 4746 Mean 4796.40

2 4789 Std. dev. 37.75

3 4783 Conf(G95%) 33.09

4 4818 Max 4829.49

5 4846 Min 4763.31

a certain period of time during each phase. This time is

measured in minimum or maximum number of days per year

of supply of the specific service. Second column contains the

number of replication and third column are the values

obtained for each variable. The fourth column presents the

statistics for each variable: mean value, standard deviation

and the 95% confidence interval. Table 8 presents the same

results for configuration 2.

Table 8

Results for the fulfillment of the power and steam supply requirements in

Configuration 2. Two phases. Assuming no contract with LETN in the

second phase.

Supply (requirements) Repl. Values Statistics

Phase 1

45 MW with back-up

(note: MINZ700 days

20 MW with B)

1 703 Mean 698.00

2 695 Std. dev. 3.74

3 701 Conf(G95%) 3.28

4 696 Max 701.28

5 695 Min 694.72


(Note: MAXZ30 days)

1 28 Mean 30.40

2 32 Std. dev. 4.34

3 24 Conf(G95%) 3.80

4 34 Max 34.20

5 34 Min 26.60



1 680 Mean 685.60

2 691 Std. dev. 5.98

3 693 Conf(G95%) 5.24

4 681 Max 690.84

5 683 Min 680.36

35 Tn/h of 600 psi steam

(Note: MAXZ30 days of

35 Tn/h)

1 44 Mean 35.20

2 30 Std. dev. 7.29

3 26 Conf(G95%) 6.39

4 40 Max 41.59

5 36 Min 28.81

Phase 2

45 MW with back-up


40 MW with back-up)

1 5115 Mean 5118.80

2 5100 Std. dev. 15.32

3 5135 Conf(G95%) 13.43

4 5110 Max 5132.23

5 5134 Min 5105.37


(note MAXZ450 days

20 MW with B. C20 MW

without)

1 352 Mean 349.20

2 366 Std. dev. 11.71

3 338 Conf(G95%) 10.27

4 352 Max 359.47

5 338 Min 338.93

70 Tn/h 600 psi steam


70 Tn/h)

1 4980 Mean 5001.40

2 5006 Std. dev. 16.73

3 4996 Conf(G95%) 14.66

4 5026 Max 5016.06

5 4999 Min 4986.74


(note: MAXZ225 days

35 Tn/h)

1 425 Mean 409.60

2 409 Std. dev. 16.12

3 412 Conf(G95%) 14.13

4 383 Max 423.73

5 419 Min 395.47



70 Tn/h)

1 4980 Mean 5001.40

2 5006 Std. dev. 16.73

3 4996 Conf(G95%) 14.66

4 5026 Max 5016.06

5 4999 Min 4986.74

Table 9

Example of results for final reliability of some blocks and sub-blocks in

Configuration 1

Block or sub-block Repl. Values Statistics

[RgasTGasGen3], TG3,

BLOCK

1 0.9886 Mean 0.9877

2 0.989 Std. dev. 0.0027

3 0.9905 Conf(G95%) 0.0023

4 0.9869 Max 0.9900

5 0.9835 Min 0.9854

[RedElec], LETN, BLOCK 1 0.9697 Mean 0.9629

2 0.9592 Std. dev. 0.0056

3 0.9655 Conf(G95%) 0.0050

4 0.9553 Max 0.9678

5 0.9647 Min 0.9579

[RedAgua], Water network,

SUB-BLOCK

1 0.9885 Mean 0.9906

2 0.9922 Std. dev. 0.0034

3 0.9857 Conf(G95%) 0.0030

4 0.9929 Max 0.9936

5 0.9937 Min 0.9876

[Caldera1], Boiler 1,

SUB-BLOCK

1 0.9808 Mean 0.9824

2 0.9815 Std. dev. 0.0023

3 0.982 Conf(G95%) 0.0021

4 0.9865 Max 0.9844

5 0.9811 Min 0.9803

Table 10

Example of results for days of post-combustion needed in Configuration 1


4.5. Results for requirements fulfillments

in Configuration 2 (2 TGs)
Post-combustion
days

Repl. Values Statistics

Total days in

postcombustion

for three boilers

(Conf. 1)

1 240 Mean 194.0000

2 198 Std. dev. 32.7490

3 161 Conf(G

95%)

28.7053

4 207 Max 222.7053

5 164 Min 165.2947

4.5.1. Sample results for availability/reliability

of functional blocks

In Table 9, we present as an example, the simulation

results for the reliability variables of several functional

blocks and sub-blocks. Regardless of the level of fulfillment

of the different supply requirements of the plant as a complete

system, these result show high levels of the reliability of the

blocks over the total simulation time. We have check that

values in Table 9 are in accordance with data provided by

several original equipment manufacturers (we have check for

instance turbine–generator sets and boilers data for other case

studies provided by the OEM). Once this data is validated, we

have another clear argument to support the reliability of our

study for the entire plant (in case of course that all

interactions among blocks were well defined).

4.6. Post-combustion natural gas consumption

This feature is of main interest for the economic

evaluation of the project with each one of the configur-

ations. In both cases, steam production availability will

require a certain number of days of post-combustion in the

boilers once TGs will suffer failures and will be out of order

while they are repaired. The total number of days of post-

combustion in the entire project will be then very important,

and although we do not provide economic estimations for

the project, we have calculated that data. In order to do that

Table 11

Example of results for days of post-combustion needed in Configuration 2

Post-combustion

days

Repl. Values Statistics

Total days in post-

combustion for two

boilers (Conf. 2)

1 109 Mean 132.8000

2 146 Std. dev. 21.0404

3 122 Conf(G95%) 18.4424

4 162 Max 151.2424

5 125 Min 114.3576


we add the days the Boiler is available and the TG of the

same set is not. Results are presented in Tables 10 and 11.

4.7. Simulation results analysis and discussion

†

Tab

Sim

Con

1 (3

1 (3

2 (2

2 (2

Regarding the fulfillment of the power and steam supply

requirements. See Table 12.

†
Regarding availability and reliability of the blocks. A key
aspect of the study is the confirmation that every

functional block meets a few minimal requirements in

terms of reliability and availability, when compared to

other facilities of similar recent plants or to the OEM

information. In this respect, it is important to verify, for

example, that the information offered by the simulation

establishes values of availability of the TGs within

the range [96–97%] with 95% of confidence, and that

the values for the reliability of the same equipment, with

identical confidence, are within the interval [98–99%].

We have also checked that simulations for both

configurations offer similar results for these two metrics.

le 12

ulation results discussion

fig. Phase Production of electrical power

TG) F1 All requirements are fulfilled working with three turbines from

the start of Phase 1. A higher supply quality could even be offer

No contract with the LETN is considered

TG) F2 The minimum of 5025 days of 40 MW with back-up is not

reached in this phase. A reasonable estimation could be aroun

4756 days of 50 MW with back-up, assuming the existence o

contract with the LETN

The system runs over the maximum number of days supplyin

20 MW with B.C20 MW without B

TG) F1 The requirement of 700 days of 20 MW with back-up is not

reached by a short margin, an estimation of a supply of 45 M

with back-up during 694 days in this phase would be reasona

The system exceeds the requirement for maximum number of

days supplying 20 MW without back-up, but now even increas

this power to 45 MW

TG) F2 The system fulfills the requirement of 5025 days providing

40 MW with back-up

The requirement of 20 MW with B. C20 MW without B. is n

not applicable. However an availability of 45 MW without

back-up during 339 days can now be reached and offered

With regard to the rest of the blocks, the simulation results

are considered to be equally reasonable.

†
With respect to number of days of natural gas consump-
tion in post-combustion, to fulfill with the requirements in

Table 12. Table 12 of this report contains a series of

availabilities for the production of steam and of electrical

power that take into account the fact that a certain number

of days it will be necessary to produce steam through post-

combustion, once TGs could suffer failures and will be out

of order while they are being repaired. In Tables 10 and 11

of the results, we can find out interesting information. We

can know the days we will produce steam without TGs,

and therefore Boilers will be working using post-

combustion natural gas. This will have of course

important economical consequences and therefore it is a

fact very relevant and which needs to be assessed. We

have found for our specific case study that:

† In case of configuration 1 (3TG), we should consider

an incremental cost of gas consumption equivalent to

194 days of operation of a gas turbine of 30 MW.

† Configuration 2 (2TG): To consider an incremental

cost of consumption of gas equivalent to 133 days of

operation a of gas turbine of 45 MW.

ed.

d

f a

g

W

ble

ing

ow

5. Conclusions

This paper discusses the opportunity to use Monte Carlo

simulation techniques for reliability/availability assessment

Production of steam

The requirement of supplying 70 Tn/h of 600 psi steam a

minimum of 700 days/year is not fulfilled

A reasonable estimation, could be 664 days/year with a flow

of 75 Tn/h

The minimum of 5250 days of 70 Tn/h 600 psi steam is not

reached. A reasonable estimation could be 4763 days of 75.6 Tn/h

The system runs over the maximum number of days to supply

35 Tn/h of steam, even increasing to 50.4 Tn/h the amount

of this flow

The system does not reach the 5475 days of 70 Tn/h 150 psi steam

established as minimum value for this phase. A more reasonable

estimation would be 4763 days of 75.6 Tn/h

The requirement of 700 days of 70 Tn/h 600 psi steam is not met

in this phase. A reasonable estimation would be 680 days of

70 Tn/h

Supply of 35 Tn/h 600 psi of steam is over the maximum

for this phase

The requirement of a minimum of 5250 days of 70 Tn/h steam

600 psi supply is not obtained. A more reasonable estimation

would be 4987 days of 70 Tn/h

The system delivers more than 35 Tn/h flow of steam 600 psi.

in this phase

The minimum of 5475 days of 70 Tn/h 150 psi steam is not fulfill

either. A reasonable estimation is 4987 days of 70 Tn/h 150 psi


studies of complex systems, and presents a generic approach

for these type of studies using continuous time Monte Carlo

simulation modeling, that is exemplified and validated in the

paper for an availability study of a cogeneration plant

(COGEPLANT). For this case study, we have assessed

availability of a couple of configurations considered by the

plant design engineers. We have shown how meeting

requirements expressed in the technical conditions appearing

in the initial documentation for bidding of this engineering

project is not totally possible with no one of the plant

configurations. That means that availability expectations of

proposed configurations should be lower, or reliability and

maintainability of the functional blocks should be higher to

meet requirements. At the same time, we provide reasonable

estimations for the availability of the production of power

and steam that could be included in a realistic engineering

project proposal to the same final customer. These esti-

mations are based in validated reliability and availability

calculations of each functional blocks that has been

considered in the simulation model, but we also showed the

importance and opportunity of sensitivity analysis when data

is important und uncertain.

The case study was carried out at the same time than the

engineering project proposal, and it was decisive for the final

selection of the technical configuration of the plant. The

configuration selected was Number 2 of this study, which

offers higher availability of supply, meeting current elec-

trical power supply requirements for phase 2, for the entire

project horizon. At the same time this study served to adjust

initial availability requirements of the technical conditions of

the bid for the cogeneration plants, once data in the model

was considered to be adjusted to real equipment including in

the bid.

Extensions of this work could be related to design aspects

of the plants in order to increase the assessed reliability and

availability. For instance, a current project is considering the

assessment of steam production availability increase by

adding parallel/auxiliary boilers to the original configur-

ation. At the same time, some logistics aspects, like spare

parts to keep in stock, could be also studied.

Finally, we would like to mention that when comparing

several configurations using this assessment, not only

availability and reliability are important (in our case were a

requirement), but also cost estimations are a key factor.

Therefore, a clear point to extend this work will be to transfer

the information provided by these models to a comprehen-

sive life cycle cost analysis model (LCCAM) in order to

produce a global value assessment for the plant.

Acknowledgements

This research has been carried out by members of a

group (Project number DPI 2004-01843) founded by

the Spanish Ministry of Science and Education and the

European Union (through FEDER funds). This particular

work was possible thanks to the support of the company

ABENER ENERGIA S.A. and especially we do thank

Juan Hernandez, Francisco Perez and Emilıo Rodrıguez

for their knowledge sharing and more than generous

help. We also thank Jesus Ivars from INTERQUISA for

his thoughtful comments and interest in potential out-

comes from this research. Finally we are very grateful to

the reviewers for their valuable anonymous contribution

to the final quality of this paper.

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