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Copyright 2010 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.

Risk Analysis of Tubing Design- Integrating DOE andStochastic Study Into Design Optimization

Guijun Deng, Goang-Ding Shyu

Baker Hughes Incorporated

Girish Kamthe

Altair Engineering, Inc

2

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Slide 1

j2 Dr Curicuta is not listed as an author, but he is presenting?joreloua, 4/5/2010

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Agenda

Introduction to current tubing design program

Comparison between Safety Factor Method and Risk Analysis Method

An Example of Using Risk Analysis Method

1). Design of Experiments

2). Stochastic Study

Summary

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Breadth and Depth / TechnologyLeading Completion Systems

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`

Anim1.h3d

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Safety factor Method vs. Risk Analysis Method.

Safety Factor Method

1). It uses conservative elasticity-based theories and minimum yieldstrength in design

2). It gives the engineer no insight intodegree of risk, thus it is impossible to

assess the risk-cost balance

3). It is based on failure criterion, noton the uncertainties inherent in loads,geometry, and material.

4). It makes the design engineerchange loading or accept small safetyfactors to fit design specificationwithout knowing the risk he is taking

Risk Analysis Method

1). It is based on both mechanicalelasticity-based theories andcomputation of probability andstatistics

2). It presents a target of probability of

failure of design, thus it enableengineer to assess the risk.

3). All uncertainties inherent in loads,geometry, and material are addressedin calculation.

4). It leads to more rational, better andrisk-consistent designs

3

4

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Slide 5

j3 Factorjoreloua, 4/5/2010

j4 enables thejoreloua, 4/5/2010

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Design of Experiments (DOE)

What is DOE?

Design of Experiment (DOE) can be defined as a series of tests in whichpurposeful changes are made to the input variables of a process or systemso that the reasons for change in the output responses can be identified andobserved.

Objectives of DOE study

1). To determine which factors are most influential on the responses.

2). To determine where to set the influential controlled input variables so that:

The response is close to the designed nominal value.

Variability in output response is small.

The effects of the uncontrolled variable are minimized

3). To construct an approximate model that can be used as a surrogate modelfor the actual computationally intensive solver.

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Tbg/csg WT T/C WPE MIN MAX MIN NOMINAL MAX drift

size LB/FT LB/FT OD OD ID ID ID DIA

7.00 26.00 25.66 6.965 7.070 6.187 6.276 6.381 6.151

7.00 29.00 28.72 6.965 7.070 6.088 6.184 6.293 6.059

7.00 32.00 31.67 6.965 7.070 5.990 6.094 6.208 5.969

7.00 35.00 35.48 6.965 7.070 5.892 6.004 6.123 5.879

7.00 38.00 37.26 6.965 7.070 5.801 5.920 6.043 5.795

7.00 42.70 42.55 6.965 7.070 5.616 5.750 5.883 5.625

7.00 46.40 46.32 6.965 7.070 5.481 5.625 5.766 5.500

7.00 50.10 50.06 6.965 7.070 5.343 5.500 5.647 5.375

7.00 53.60 53.66 6.965 7.070 5.207 5.376 5.531 5.2517.00 57.10 57.24 6.965 7.070 5.068 5.250 5.413 5.125

Variables Nominal Variation

Thickness 0.362" ID=6.276" ID=5.25"

Size 7" 7" 9"

Ovality a=3.5" b=3.5" B=3.4825" A=3.535"

Eccentricity delta=0 (0.362 thick) 0 0.07"

Young's Modulus 30,000,000psi 27000,000psi 31,000,000psi

Loads

Collapse 10,000psi 9500 10500

Burst 10,000psi 9500 10500

Tension 100,000 lbf 95000 105000

Table1. Sample Data of API Tubing/CASING

Table2. Variation of Geometry, Material and Loads

SAMPLE DATA OF TUBING

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CAE Software Tools

Radioss/Optistruct

HyperMesh

HyperMorph

Hyperstudy

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Geometrical Parameters (Variables)

a). Size b). Thickness

c). Eccentricity d). Ovality

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Load Parameters (variables)

Burst

Collapse

Tension

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Material Parameters (variables)

Youngs Modulus: Nominal Values 30,000 ksi, and varies from 27,000 ksito 31,000 ksi

Poisson Ratio: Nominal values 0.3, and varies from 0.27 to 0.33

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DOE Process1. Assign design variables

2. Perform nominal run to create response for DOE study

3. Select DOE type for controlled and/or uncontrolled factors (full or fractional factorial)

4. Export the solver input files for the specified runs

5. Solved the above exported files with Radioss6. Extract the responses for the above solved files

7. Study the main effects, interactions, etc.

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Stress (psi)

Main Effects (all variables)

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Main Effects (Eccentricity, Ovality, E, and Nu)

Stress (psi)

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Main Effects (collapse and burst)

Stress (psi)

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Approximations/Regression

Regression is the polynomial expression that relates the response ofinterest to the factors that were varied.

Linear Regression Model

F(x) =a0+a1*x1+a2*x2+error

Interaction Regression Model

F(x)=a0+ a1*x1+a2*x2+a3*x1*x2+error

Quadratic Regression Model (2nd order)

F(x)=a0+a1*x1+a2*x2+a3*x1*x2+a4*x1^2+a5*x2^2

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3-D Regression Model

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The Plot of Analysis of Variance

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Stochastic Studies

Stochastic Methods (also called statistical or probabilistic methods) areused to measure uncertainty in any system

Steps for Stochastic Studies:

1). Define PDF (Probability Distribution Function) for random variables.

2). Sample the random variable values based on the PDF.

3). Perform simulation/experiments at each of these sampled values ofthe random variable.

4). The desired result is derived from analysis of the response data from

the simulations performed in the above step.

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Uncertainties in Tubing Design

Geometry

Size, thickness, eccentricity, ovality

Material

Youngs Modulus, Poisson Ratio

Load

Burst, collapse

Table 3. Randomization of Geometrical, Material and Loads

Thickness Normal distribution

Ovality Normal distribution

Eccentticity Normal distribution

Young's Modulus Normal distribution

Poission Ratio Normal distribution

collapse Normal distribution

Burst Normal distribution

0.015

250

250

0.02625

0.0175

0.035

15000

0.3

10,000psi

10,000psi

a=3.5", b=0.35

Variables Mean

0.362" (ID)

0

30,000,000psi

RandomizationStandard deviation

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Stochastic Studies

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Stochastic Studies

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Stochastic Studies

PDF (Probability Distribution Function) and CDF (Cumulative Distribution Function)

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Risk Analysis

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Result Comparison Between Two Methods

Risk Analysis of 7 26# Tubing to Stand Both 10ksi Burst and Collapse Pressure (BMS N201)

Stress Prediction of 7 26# Tubing to Stand Both10 ksi Burst and Collapse Pressure (BMS N201)

Pass Design Specification

with safety factor 1.1

Pass Design Specificationwith safety factor 1.25

Probability of Failure vs. Temperature

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350 400 450

Teperature (F)

ProbabilityofFailure(%)

BMS N201

Temp(F) Probability of Failure Reliability

70 7 93200 33 67

250 44 56

300 60 40

350 86.5 13.5

400 91 9

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Summary

Risk Analysis Method enables engineers or manager to do riskassessment.

Risk Analysis Method takes variation of all design variables intoconsideration, therefore it is more rational.

Risk Analysis method is an iterative process.

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Questions?

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