# (425e) Prediction of Pipeline Erosion Uncertainty for Scale-up

#### AIChE Annual Meeting

#### 2015

#### 2015 AIChE Annual Meeting Proceedings

#### Upstream Engineering and Flow Assurance Forum

#### Poster Session: Upstream Engineering and Flow Assurance

#### Tuesday, November 10, 2015 - 3:15pm to 5:45pm

**Prediction
of pipeline erosion uncertainty for scale-up**

Wei Dai, Ravi Nukala, Selen Cremaschi

^{a}Russell School of Chemical

Engineering, The University of Tulsa, 800 S Tucker Drive, Tulsa,OK, USA selen-cremaschi@utulsa.edu Abstract

In this study, a dimensional analysis is used for quantification

of erosion-rate prediction uncertainty within pipelines that transport

particles in multiphase gas-liquid flows. The transport of solids in multiphase

flows is common practice in energy industries because of the unavoidable

extraction of solids from oil and gas bearing reservoirs either onshore or

offshore sites. The safe and efficient operation of these pipelines requires

reliable estimates of erosion rates, and production rates are generally limited

to keep the effects of erosion at acceptable levels. Erosion in pipelines is

defined as the material removal from the solid surface due to solid particle

impingement. The phenomena that leads to this type of erosion, especially in multiphase

flow systems, is very complex and depends on many factors including fluid and

solid characteristics, the pipeline material properties and the geometry of the

flow lines.

Given this complexity, most of the modeling work in this

area focuses on developing empirical or semi-mechanistic models. For example, Oka

et al. (2005) developed their erosion model using particle impingement in air

with empirical constants based on particle properties and hardness of the

target materials. Their model is one of the most commonly cited in the literature.

Another semi-mechanistic model called 1-D SPPS (Zhang, 2007), which is widely

used for predicting erosion rates by the oil and gas industry, was developed

with several empirically estimated parameters, like the sharpness factor of

particles, Brinell hardness and the empirical constants in the impact angle

function. These empirical parameters are calculated using experimental

observations. However, the experimental data used in these calculations and also

for model validation and uncertainty quantification are, for the most part,

collected in small pipe diameters (from 2 to 4 inches). These small pipe sizes

do not coincide with the field conditions, where the pipe diameters generally

exceed 8 inches. Hence, the predictions of erosion models are routinely

extrapolated to conditions where experimental data or even operating experience

is not available, and the estimation of erosion-rate prediction uncertainty

becomes crucial especially for systems too-costly to fail. The goal of this study

is to develop a systematic approach to estimate erosion-rate prediction

uncertainty for extrapolations. To achieve this goal, the erosion-rate model

discrepancy, which is defined as the difference between experimental erosion

rates and the corresponding erosion rate predictions, is modeled using Gaussian

Process Modeling (GPM, Rasmussen, 2006).

We used functions of dimensionless numbers that are relevant to erosion

phenomena as the inputs to the GPM. Use of dimensionless numbers as inputs

enables the scale-up of uncertainty estimates.

The GPM models erosion-rate model discrepancy as a Gaussian

random process, which is defined by mean and covariance functions assuming a

multivariate normal distribution (Zhen, 2013). The most likely values of mean

and covariance function parameters are determined by Maximum Likelihood

Estimation (MLE) using experimental data. The GPM model not only provides prediction in locations where

experimental data is not available but also constructs the prediction

confidence using the covariance functions through conditional probability

distribution.

The approach developed to determine dimensionless groups and

the functions as inputs to GPM has four main steps: (1) Identify all possible

dimensionless groups that are relevant to erosion phenomena using Buckingham ¦Ð

theorem. Here, we considered pipe diameter, particle size, density of particle

and flow, viscosity of flow, flow rates, gravitation constant and surface tension

as the dimensional variables. Time, length and mass are the three basic units.

Therefore, we obtain 67 sets of 8 dimensionless numbers. Because some

dimensionless numbers are repeated in different sets, the Buckingham ¦Ð theorem

yields 200 distinct dimensionless numbers. Including pipe geometry, particle

hardness and sharpness, which are already dimensionless, results in 203

distinct dimensionless numbers. (2) Calculate the correlation between each

dimensionless number and model discrepancy, and find the sum of the correlation

coefficient values that are greater than 0.5 (these refer to strong

correlations) for each set. (3) Select the dimensionless group sets with the

five highest correlation sums, and flag their corresponding dimensionless

numbers as candidate inputs to GPM. (4) Formulate and solve the optimization

problem to select the best function of candidate dimensionless numbers. Here,

the best is defined as the function that minimizes the selected performance

metric, i.e., area metric.

The performance of different input sets and functions as

inputs to GPM is assessed using a modified area metric (Ferson, 2008). Area

metric is defined as the integral of disagreement area between the estimated

erosion rate and experimental data. A smaller area metric represents a better

prediction of the model discrepancy. It can also be used to locate

under-prediction regions of the erosion model.

For estimating erosion-rate-prediction uncertainty, we compiled

an experimental database of erosion rate measurements from literature. It

contains 544 data points in single or multiphase carrier flows. Eighty percent

of the data in the database are collected for gas dominated flows (i.e., gas

only, annular, mist and churn flow). The experimental database covers a wide

range of input conditions resulting in significantly different erosion rates.

We selected the 1-D SPPS model as our case study, quantified

its erosion-rate discrepancy using our developed approach. The 1-D SPPS model calculates

the maximum erosion by defining how a hypothetical representative particle will

impinge the target material. The abrasion caused by this particle is defined by

length loss in the target material, and is calculated using the momentum of

impingement. The maximum erosion rate model in 1-D SPPS calculates the target

material length loss per unit time, and uses a power law correlation of the

characteristic impact velocity. The 1-D SPPS model accounts for pipe geometry,

size and material, fluid properties (density and viscosity) and rate, and particle

sharpness, density and rate. The 1-D SPPS model discrepancy is calculated for

544 experimental data points. The model discrepancies and the corresponding

values of the candidate dimensionless numbers are used as inputs to our uncertainty

estimation framework. Then, the overall analysis is performed for each flow

regime and the corresponding average area metric is calculated. For mist flow, gas

velocity, density and pipe diameter are the repeating variables that yielded

the dimensionless groups with the smallest averaged area metric value, which

was equal to 0.047. For churn flow, particle size, gas density and surface

tension are the repeating variables that yielded the dimensionless groups with

the smallest averaged area metric value, which was equal to 9.2x10^{-4}.

For slug flow, pipe diameter, gas viscosity and surface tension are the

repeating variables that yielded the dimensionless groups with the smallest

averaged area metric value, which was equal to 8.1x10^{-4}. While for

annular flow, gas velocity, gas density and surface tension are the repeating

variables that yielded the dimensionless groups with smallest averaged area

metric value, which was equal to 0.0074. Those dimensionless groups identified

in each flow regime provided most influential variables in the quantification

of erosion-rate model discrepancy and also suggested possible modeling and

experimental improvements involving those variables. Besides, extrapolation of erosion

discrepancy prediction is possible based on the identified dimensionless groups

in each flow regime.

Our analysis indicate that the use functions of

dimensionless numbers as inputs to GPM improves the erosion rate prediction

discrepancy and reduces the confidence intervals of uncertainties compared to

using dimensional inputs to GPM as evidenced by smaller area metrics. More

specifically, compared to GPM results with dimensional inputs, our approach

yields a 60% decrease of area metric value in mist flow, 23% decrease in churn,

78% decrease in slug and 12% increase in annular flow with respective best

dimensionless groups.

**Acknowledgement**

This work is supported by the Chevron Energy Technology

Company. Discussions and comments from the Haijing Gao, Gene Kouba and

Janakiram Hariprasad of Chevron and Brenton McLaury, Siamack Shirazi of E/CRC

at the University of Tulsa were highly acknowledged.

Reference

Ferson, S., Oberkampf, W. L., and

Ginzburg, L., 2008, Model Validation and Predictive Capability for the Thermal

Challenge Problem, Computer Methods in Applied Mechanics and Engineering, Vol.

197, No. 29-32, pp 2408-2430.

Jiang, Z., Chen, W., Fu, Y., and Yang,

R., 2013, Reliability-Based Design Optimization with Model Bias and Data Uncertainty,

SAE International.

Oka, Y. I., Okamura, K., and Yoshida,

T., 2005, Practical estimation of erosion damage caused by solid particle impact:

Part 1: Effects of impact parameters on a predictive equation, Wear, 259(1-6),

page 95-101.

Rasmussen, C.E. and Williams, C.K. I.,

2006, Gaussian Processes for Machine Learning, The MIT Press.

Zhang, Y., Reuterfors, E.P., McLaury,

B.S., Shirazi, S.A., and Rybicki, E.F., 2007, Comparison of Computed and

Measured Particle Velocities and Erosion in Water and Air Flows, Wear, 263.