Structural Analysis Of Reliability Petroleum Equipment For Different Modes Of Action On Drilling Rigs

Structural Analysis Of Reliability Petroleum Equipment For Different Modes Of Action On Drilling Rigs

Structural Analysis Of Reliability Petroleum Equipment For Different Modes Of Action On Drilling Rigs

Avram Lazar Stan Marius

Universitatea Petrol-Gaze din Ploiesti Universitatea Petrol-Gaze din Ploiesti

Sorinel Alexandru Lazar

Romgaz S.A.

The latter can be of various types (according to its complexity and performance features). In order to identify some models destined to the simulation of various working conditions there are used the methods of analysing system structure and plant compunds. Due to these methods there can be carried out the logistic analysis of a relevant number of situations encountered in practice.

1. The core problem of the reliability models analysis is to determine the extent to which the characteristic parameters can remain within the limits set for the systems working condition

   From this point of view, the structural analysis is aimed at identifying the way a plant works.

   This shows the way in which main and auxiliary operating systems are grouped. Oil plants for drilling and drawing destined to ground and off-shore oil recovery are structured according to the appropriate technological processes.

2. The core problem of the reliability models analysis is to determine the extent to which the characteristic parameters can remain within the limits set for the systems working condition

   From this point of view, the structural analysis is aimed at identifying the way a plant works. This shows the way in which main and auxiliary operating systems are grouped. Oil plants for drilling and drawing destined to ground and off-shore oil recovery are

   structured according to the appropriate technological processes.

   A main operating system performs the functions necessary for the drilling technological process and consists of the driving system and the producer. The driving system consists of the engine or engine group

   (M) and gearing.The driving system, the structure is presented in (tabela.1), where the producer is the draw works (TF), and the actuator is the swivel hook (C).

   A main operating system (SM) carries out the functions necessary for the technological drilling process and consists of the driving system (SA) and the producer. SA consists of the engine (M), the gearing

   (T) and the gear box (CV). The latter can be of various types (with power take off from draw works or from

   gearing (T T1 T2 T3 T4), according to its

   complexity and performance features.

   Determining reliability parameter of broad interest is very important especially in the designing phase because the designer must solve not only the problems related to the systems functions but also those related to its safe operation. In the calculation of every system, the systems structure is shown by the structural model (MS), which may not differ from the block diagram of the systems functioning.

   Starting from these aspects, the structural analysis only presents the drilling plant as a complex system consisting of interconnected subsystems in order to identify some networks whose analysis can become operational.

   The reliability functions of the comprising subsystems are:

   Rm for engine; Rt for gearing; Rtf for draw works; Rc for assembly crown-block cable hook crane, Rgf for drill column and Rs for drill rod.

   The systems are equipped with the same gearing, and the table with a mechanical power take off and a gear box (CV) for MR. Below we will note the structural schemes for the rotating system (SR) and for the circulation system (SC), respectively.

   For the centralised or group operating mode the main operating systems (SM, SR and SC) are operated by the same engine or group of engines. Another operating mode would be the one for which SM and SR receive the energy flux from a

   common group of engines by means of common gearing, and SC works independently.

   This operating mode is called mixed1 (M1) because it refers to the logistic configuration 1 of subsystem connecting.

   We notice that M1 differs from G1 and G2 by the complete separation of SC (Figure 1), [3], [1] which has major implications on the whole IF project. These are to be found in the analysis of the whole systems reliability and in that of its technical security due to the physical separation.

   C

   Rc

   C

   Rc

   Engines Gearing(s) Machines Execution Swivel Structure work elements

   M1

   Rm1

   M5

   R

   Rr

   R

   Rr

   Rm2

   TF

   T1

   Rt1

   T1

   Rt1

   Rtf

   CV

   M2

   Rm2

   M2

   Rm2

   T2

   Rt2

   T2

   Rt2

   MR

   Rmr

   MR

   Rmr

   RCV

   Drive

   CH

   Rch

   CH

   Rch

   Sistem

   Rotary System Pump

   System

   M3

   Rm3

   M3

   Rm3

   T3

   Rt3

   T3

   Rt3

   PF1

   Rpf1

   PF1

   Rpf1

   P1

   Rp1

   P1

   Rp1

   M4

   Rm4

   M4

   Rm4

   T4

   Rt4

   T4

   Rt4

   PF2

   Rpf2

   PF2

   Rpf2

   P2

   Rp2

   P2

   Rp2

   Figure .1 Structural tabele modes

   The total reliability function for this operating mode is calculated using the features of structural analysis methods, as follows:

   RG1 =

   Rm · Rt · [1 (1 Rtf-c-r)(1 Rpf- p)]·Rch (1)

   where:

   Rtf-c-r =Rtf · [ 1 (1 Rc)(1 Rcv·Rmr·Rr)] Rpf-p = [1 (1 Rpf1 · Rp1)(1-Rpf2 · Rp2)] Rm

   n

   n

   = 1 1 Rmi

   i1

   the reliability function of the group of n engines

   Rch the reliability function of swivel casing

   There is also a second variant for the group operating mode, G2, where one of the pumps has its own group of engines and gearing, and for MR the power take off is connected either to TF or directly to T1, as shown in the chart below:

   The total reliability function in this case is:

   RG2 = [1 (1 RI) ·(1 RII)] · Rch (2)

   where:

   RI =

   Rm1,2 · Rt · [1 (1 Rtf- c r) · (1 Rpf1 ·Rp1)]

   RII = Rm3 · Rt2 · Rpf2 · Rp2

   the values of variables are known.

   Another operating mode would be the one for which SM and SR receive the energy flux from a common group of engines by means of common gearing, and SC works independently.

   This operating mode is called mixed1 (M1) because it refers to the logistic configuration 1 of subsystem connecting.

   We notice that M1 differs from G1 and G2 by the complete separation of SC (tabela 1), [3], [1] which has major implications on the whole IF project.

   These are to be found in the analysis of the whole systems reliability and in that of its technical security due to the physical separation of working areas.

   Thus, there appears mechanical gearing T2 (only for SC), given the fact that T has been replaced by T1 whose complexity decreased due to the removal of chain PF1-P from G2 and its transfer to M1.

   Similarly, from the logistic perspective of plant exploitation there can be organised an IF and an operating mode by means of which driving and rotating systems work together and circulation works independently.

   The total reliability function RM1 is calculated considering RI and RII shunted together, and the result concatenated with Rch is:

   RM1 = [1 (1 RI)(1 RII)] · Rch (3)

   where:

   RI = Rm12 · Rt · Rtf-c-r RII =

   Rm3 · Rt2 · [1 (1 Rpf1·Rp1)(1 Rpf2 ·

   Rp2)]

   the variables values are already kown.

   We notice that M1 differs from G1 and G2 by the complete separation of SC, which has major implications on the whole IF project.

   These are to be found in the analysis of the whole systems reliability and in that of its technical security due to the physical separation of working areas.

   Thus, there appears mechanical gearing T2 (only for SC), given the fact that T has been replaced by T1 whose complexity decreased due to the removal of chain PF1-P from G2 and its transfer to M1.

   Similarly there can be analyzed an alternative structure for the mixed operating mode, configuration 2, called mixed 2 (M2). Within this

   structure SR is completely separated from SM and SC, which operate on high power.

   As regards the physical charateristics of the main operating systems, complete separation can be distinguished as a design variant, so that each main operating system should work autonomously.

   That leads to a general approach to each operating system in such a way that every systems module is analysed. (tabela 1), [3], [1].

   The total reliability function RIND is calculated considering RI and RII shunted together, and the result concatenated with Rch is:

   RIND =

   [1 (1 RI)·(1 RII)·(1 RIII)·(1 RIV)]·Rch

   (4)

   where:

   RI = (1 (1 Rm1)·(1

   Rm2))·Rt1·Rtf·Rc

   RII = Rm3·Rt2·Rm·Rr RIII = Rm4·Rt3·Rpf1·Rp1 RIV = Rm5·Rt4·Rpf2·Rp2

   the variables values are already known.

3. Simulations by models

The system functions (R) contained by the models described above can be continuous or discrete or signal functions (known reliability functions or chance number generating functions following various distributions simulated by means of the programming mode (MathCad)) and will replace block functions (R) within computer-assisted simulation.

The structural models thus obtained can allow us to carry out simulations useful to the design of safe and efficient systems, enhancing their performances.

This software package provides the user with a complete series of probability distributions with continuous or discrete variation and the chance number generators distributed according to the corresponding partition law.

The partition law WEIBULL adapts to the reliability study of technological plants during their running, when failures occur mainly because of the plants runout and/or ageing.

The NORMAL partition law adapts to the various technical systems whose failures occur because of a great number of factors, which generally lead to materials wear and breakage.

Table 1. Reliability results modes

100	0.860	0.960	0.959	0.984
1000	0.852	0.963	0.958	0.983
10000	0.846	0.962	0.956	0.982
100000	0.846	0.960	0.955	0.982
1000000	0.846	0.960	0.955	0.982

100	0.860	0.960	0.959	0.984
1000	0.852	0.963	0.958	0.983
10000	0.846	0.962	0.956	0.982
100000	0.846	0.960	0.955	0.982
1000000	0.846	0.960	0.955	0.982

Number simulations Reliability total values Group1 Group2 Mixt1 Individual

For the estimation of the probability of failure by frequency of into occurrence the sufficiently large number of computer simulations should be performed as Gauss and Weibull trials. Each trial consists of the generations of the random realizations all input quantities, performing the deterministic analysis of the values R as the functions of these realizations. Analysis of accuracy must be performed using the

asymptotic distribution of the obtained estimate not the quantity of gives probability.

Then the average of these values from all trial is calculated with MathCad Program Modeling. The average this method its similarity and higher effectiveness it comparison which the estimation of the random probability frequency ( rnorm and rweibull).

0 .9

RG1J

RG2J

RM1 J

RINDJ

0 .8

0 .7

0 .6

0 5 10 15 20

J

Figure 2. Types of probability distributions and the corresponding chance number generators.

dates

N 100

PROGRAMMODELING

J 0 N 1

random distribution

RM rweibull( N 110) RT rnorm( N 0.85 0.1)

RMR rnorm( N 0.85 0.1) RP rweibull( N 110)

expresion solving

RCV rweibull( N 110) RTF rweibull( N 110) RR rnorm( N 0.85 0.1)

RPF rweibull( N 110) RC rnorm( N 0.85 0.1) RCH rweibull( N 110)

J

J

J

J

J

J

J

J

J

J

RPFP 1 1 RPF RP 1 RPF RP

J

J

J

J

J

J

J

J

J

J

J

J

RTFCR RTF 1 1 RC 1 RCV RMR RR

J

J

J

J

J

J

J

J

J

J

RG1 RM RT 1 1 RTFCR 1 RPFP

RIJ RMJRTJ1 1 RTFCR 1 RPF RPJ

J J

RII RM RT RPF RP

J J J J J

J

J

J

J

J

J

J

J

RG2 1 1 RI 1 RII RCH

J

J

R1J RMJRTJRTFCR

R2J RMJRTJ1 1 RPF RPJ1 RPF RPJ

J J

J

J

J

J

J

J

J

J

RM 1 1 1 R1 1 R2 RCH

J

J

RAJ 1RMJ1 RMJRTJRTF RCJ

RBJ RMJRTJRMJRRJ

RCJ RMJRTJRPF RPJ

RDJ RMJRTJRPF RPJ

J

J

J

J

RIND 1 1 RA 1 RB 1 RC 1 RD RCH

J J

RG1

J J

RG2

J J

RM 1

RIND

FRG1

N

FRG2

N

FRM1

N

FRIND

N

total reliability

FRG1 0.86

FRG2 0.965

FRM1 0.959

FRIND 0.984

The author proposes that the method should be also applied for the other operating modes of drilling plants which were mentioned taking into account their characteristics. In are presented three structural models (G1, G2, IND and M1, whose graphs are displayed in descending order of reliability analysis and numerical simulation for a drilling plant.

The procedure of calculations is as fallows: at which realisation of variable R is generated in accordance with its probability density function( this function MathCad is supposed to be know) and the value of the probability distribution function of quantity R corresponding is determined(this distribution is generated at MathCad system).

The average this method its similarity and higher effectiveness it comparison which the estimation of the probability frequency. Analysis of accuracy must be performed using the asymptotic distribution of the obtained estimate not the quantity of gives probability.

The main contribution this article makes is the introduction of structural models in the calculation of complex systems reliability (drilling plants or production installations).

In order to carry out some purely reliability comparatie analyses of finding the optimal operating mode, the designer may choose his own values for simulation so that he could decide which of the operating modes leads to a convenient value of reliability according to the number of elements taken into account and their grouping mode.

1. Stan, M. Metode avansate de proiectare a utilajului petrolier, Editura Universitii Petrol Gaze Ploieti, Ploieti, 2006.

2. Stan, M. Estimarea fiabilitii instalaiilor de foraj utiliznd modele mataematice de structur, Buletinul Universitii Petrol Gaze Ploieti LVII 2/2005.

3. Stan, M. Logistic plants in oil reliability, IMT ORADEA 2007, ISSN 1583-0691, 2007. 2.

4. Stan, M. Metode avansate de proiectare a utilajului petrolier, Editura Universitii Petrol Gaze Ploieti, Ploieti, (2006).

5. Stan, M. Fiabilitatea sistemelor si aplicatii, Editura Universitii Petrol Gaze din Ploieti, (2008).

6. Stan, M. , Avram, L., Dynamic System Composed of Top drive and Drill Pipe, Buletinul Universitii Petrol Gaze din Ploieti, volLXII No.1/2010, (2010)

7. Fraser, C., Hitec Products Drilling; G. White, SPE, Rowan Drilling; and E. DePeuter, LeTourneau Technologies SPE, IADC Drilling Conference and Exhibition, 17-19 March Amsterdam, The Netherlands, (2009) [8]Abrahamsen, E., SPE, Weatherford International Ltd, IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition, 25-27 August, Jakarta, Indonesia, (2008)

1. Egill Abrahamsen and Doug Reid, Weatherford Intl. Inc, SPE/IADC Drilling Conference, Amsterdam, Netherlands, (2007)

2. Miguel Belarde, Shell Canada and Ola Vestavik, Reel well, Offshore Europe, 6-8 September, Aberdeen, UK, (2011)

[11]. Martin Hofschröer, Bentec GmbH Drilling & Oilfield Systems, SPE/IADC Middle East Drilling Technology Conference and Exhibition, 20-22 October, Abu Dhabi, United Arab Emirates, (2003)