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The University of Tulsa

Mcdougall School of Petroleum Engineering

Independent Study

Barite sag simulation via Particle-Elimination Method

Kai Zhong

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Summary:

For this independent study, a FORTRAN based program were developed to calculate the barite

particles settling tendency and mud properties data under Yield Power Law (YPL) fluid. The

program will determine the new mud density after the barite particles settling.

Since I have coded a FORTRAN program to simulate the barite sagging. My proposal for this

independent study was going to simulate barite sagging in PIPE. However, after the program

simulate the flow in PIPE there is no change in barite concentration and mud density after

calculation. So I assume there are two reasons which this happened:

1 The barite do not settle in the PIPE or it only has very minor settling in the PIPE.

2 The Particle Elimination Method can only be used for full barite flow loop, which is include

PIPE flow and ANNULAR flow.

Since I don't know how to solve my first assumption guess, I am adding ANNULAR flow in the

code. According to the Particle Elimination Method, the program will need to input profiles. One

is the PIPE and ANNULAR information data named drillingifo.dat, which include the input of

radius of pipe, radius of annular, mud density, barite density, inclination angle, and eccentricity.

The second input profile will be the lab data of barite sizes and concentrations.

Introduction:

In conventional drilling, the drilling mud used to control the formation fluids, subsurface

pressures and the formation stability. Sometimes the mud weight should be high enough to

control the formation fluids pressure, so some high gravity solids is added to the mud to increase

its weight to the desired value. Under certain drilling conditions, the weighting material particles

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can settle down and this phenomena is known as barite sagging. This phenomena can cause

many drilling problems including well control issues and stuck pipe. This phenomena can be

caused by different aspects such as mud rheology, well trajectory design and drilling practices.

The modeling for all these aspects is necessary in case if barite sagging problems is anticipated

or expected to be happening to avoid it or minimize its effects. In this project, modeling for

barite sagging determination was developed for YPL fluid.

Barite sag is the settling of barite particles (or other weighting materials), which results in the

undesirable fluctuations in drilling fluid density. A variety of major drilling problems including

lost circulation, well control difficulties, poor cement jobs and stuck pipe can result from

uncontrolled barite sag.

Problem Statement:

Barite sagging is a major problem and the variation in the mud weight caused by barite sagging

can cause a lot of drilling troubles such as:

• Lost circulation due to variation in mud weight.

• Well control due to reduction of mud weight.

• Stuck pipe due to mud weight variation and barite beds formed.

• Wellbore stability due to reduction and fluctuation of mud weight.

• Torque and drag due to the forming barite beds.

• Poor cement jobs due to the bad bonding between the cement and wellbore in barite beds

areas

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• Mud-weight variations (in and out) which will cost a lot of money due to continuous

addition of mud weighting materials.

These drilling problems that are caused by barite sagging can cost a lot of money, delay the time

for delivering wells, losing the wells if the drilling problems level is elevated or can cause

disastrous blow outs. So, a model to identify the barite sagging problems and methods to cure or

prevent these problems is needed to be done. In this project, a tool was developed by using

FORTRAN to identify if the barite sagging problem will occur for YPL fluid in specific well

trajectory data (inclined and eccentric annulus) and it will measure the effect of barite sagging in

the fluid density variation. Also, it will measure the barite sag bed forming and disassociation in

the fluid with time and circulation. The Particle Elimination technique (reference 1) is used for

this modeling.

Barite Sagging Modeling for YPL Fluid:

The narrow slot approximation were used to obtain the velocity profile and flow rate for YPL

fluid. The assumption in the approach that the annulus is equivalent to a rectangular slot that has

width w and height h. The width and height are described by the following equations:

ℎ =𝐷𝑜 − 𝐷𝑖2

𝑤 =𝜋(𝐷𝑜 + 𝐷𝑖)

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This approach is accurate when𝐷𝑜

𝐷𝑖> 0.25. The steady isothermal flow for YPL fluid in narrow

slot approach is given by:

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𝑄 =𝑤 ℎ2 (𝜏𝑤 − 𝜏𝑦)

𝑛+1𝑛

2 𝐾1𝑛 𝜏𝑤2

(𝑛

1 + 2𝑛) (𝜏𝑤 +

𝑛

1 + 𝑛𝜏𝑦)

In term for average velocity, the shear rate for laminar flow is given by:

12 𝑣

𝐷𝑜 − 𝐷𝑖=(𝜏𝑤 − 𝜏𝑦)

𝑛+1𝑛

𝐾1𝑛 𝜏𝑤2

(3𝑛

1 + 2𝑛) (𝜏𝑤 +

𝑛

1 + 𝑛𝜏𝑦)

Where, 12𝑣

𝐷𝑜−𝐷𝑖= 𝑆ℎ𝑒𝑎𝑟 𝑟𝑎𝑡𝑒

The YPL fluid Reynolds number is given by:

𝑅𝑒𝑌𝑃𝐿 =12 𝜌 𝑣2

𝜏𝑤

The friction factor for laminar flow in annulus is given by:

𝑓 =24

𝑅𝑒𝑌𝑃𝐿

The YPL fluid apparent viscosity is given by:

µ𝑎𝑝𝑝 =𝜏𝑦

ϔ+ 𝐾 ϔ𝑛−1

The particle elimination technique were used in this project to determine the mud density and the

particles settling. The lift force was incorporated in the calculated density and it is obtained by:

𝐹𝑙𝑖𝑓𝑡 =1

2𝐶𝐿𝑣

2𝜌𝐴 =1

2𝐶𝐿𝑣

2𝜌 𝜋 (𝐷𝐵2)2

Saffman’s Lift Force is given by:

𝐹𝐿𝑖𝑓𝑡 = 1.615𝑅𝑝2√𝜌𝜇𝛾 𝑣𝑠𝑙𝑖𝑝𝑠𝑔𝑛𝛾

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The resultant particle density after incorporating the lift force effect is given by:

𝜌𝑝,𝑛𝑒𝑤 =𝑊𝑝𝑎𝑟𝑖𝑐𝑙𝑒,𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 − 𝐹𝐿𝑖𝑓𝑡

43 𝜋 𝑅

3𝑔= 𝜌𝑝 −

𝐹𝐿𝑖𝑓𝑡43𝜋𝑅

3𝑔

The steps and equations that has been used to calculate the density and concentration in the flow

are shown below:

1- 𝐶𝐵,𝑖𝑛𝑖𝑡𝑙 =𝜌𝑡𝑜𝑡𝑎𝑙,𝑖𝑛𝑖𝑡𝑖𝑎𝑙−𝜌𝐿

𝜌𝐵−𝜌𝐿

2- 𝑉𝑡𝑜𝑡𝑎𝑙,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝑉𝑡𝑎𝑛𝑘 + 𝑉𝑎𝑛𝑛𝑢𝑙𝑢𝑠

3- 𝑉𝐵,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝐶𝐵,𝑖𝑛𝑖𝑡𝑖𝑎𝑙𝑉𝑡𝑜𝑡𝑎𝑙,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

4- 𝑉𝐿,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = (1 − 𝐶𝐵,𝑖𝑛𝑖𝑡𝑖𝑎𝑙)𝑉𝑡𝑜𝑡𝑎𝑙,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

5- { ∆ℎ =

𝑅𝑜−𝑅𝑖

𝑁 ; 𝐿 =

∆ℎ

𝑉𝑓𝑎𝑙𝑙 ∑ 𝑉𝑎𝑥𝑖𝑎𝑙,𝑗

𝑛𝑗=1 ; ℎ = 𝑛∆ℎ

𝑡 = 𝑡−1 + ∆𝑡 ; ∆𝑡 = 𝑛∆ℎ

𝑉𝑓𝑎𝑙𝑙

6- 𝑉𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 = 𝐿 [𝑅2𝑎𝑐𝑜𝑠 (

𝑅−ℎ

𝑅) − (𝑅 − ℎ)√2𝑅ℎ − ℎ2]

7- 𝑅𝑒𝑝𝑒𝑎𝑡𝑖𝑛𝑔 𝑙𝑜𝑜𝑝:

{

𝑉𝐵,𝑡 = 𝑉𝐵,𝑡−1 − 𝑉𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝐶𝐵,𝑡−1

𝜌𝑡𝑜𝑡𝑎𝑙,𝑡 =𝜌𝐵𝑉𝐵,𝑡+𝜌𝐿𝑉𝐿,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

𝑉𝐵,𝑡+𝑉𝐿,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

𝐶𝐵 = 𝜌𝑡𝑜𝑡−𝜌𝐿

𝜌𝐵−𝜌𝐿

The fluid density is calculated by the following equation:

𝜌𝑓𝑙𝑢𝑖𝑑 =𝑎 [𝑏 −

𝑒𝑎 − 𝑐

(∑ 𝜌𝑖−1 − 𝑛𝑐𝑛𝑖=1 )] + 𝑐𝑑

𝑏 −𝑒

𝑎 − 𝑐(∑ 𝜌𝑖−1 − 𝑛𝑐

𝑛𝑖=1 ) + 𝑑

𝑎 = 𝜌𝐵𝑎𝑟𝑖𝑡𝑒 ; 𝑏 = 𝑉𝑏𝑎𝑟𝑖𝑡𝑒,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 , 𝑐 = 𝜌𝑙𝑖𝑞𝑢𝑖𝑑 , 𝑑 = 𝑉𝑙𝑖𝑞𝑢𝑖𝑑,𝑖𝑛𝑖𝑡𝑖𝑎𝑙 , 𝑒 = 𝑉𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛 ,

𝑛 = 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 [𝑡

∆𝑡] , ∆𝑡 = 𝑡𝑖𝑚𝑒 𝑛𝑒𝑒𝑑𝑒𝑑 𝑓𝑜𝑟 𝑠𝑒𝑡𝑡𝑙𝑖𝑛𝑔 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 , 𝑡

= 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒

The total density of fluid will be:

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𝜌𝑡𝑜𝑡𝑎𝑙,𝑡 =(𝜌𝐵 ∑ 𝑉𝐵,𝑗,𝑡

𝑀𝑗=1 ) + 𝜌𝐿𝑉𝐿,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

(∑ 𝑉𝐵,𝑗,𝑡𝑀𝑗=1 ) + 𝑉𝐿,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

Volume of setteled Barite:

𝑉𝐵,𝑠𝑒𝑡𝑡𝑒𝑙𝑒𝑑 = |𝑉𝐵,𝑖𝑛𝑖𝑡𝑖𝑎𝑙,𝑡𝑜𝑡𝑎𝑙 − ∑𝑉𝐵,𝑗,𝑡

𝑀

𝑗=1

|

Average velocity for sliding bed is given by:

𝑣𝑎𝑣𝑔,𝑠𝑙𝑖𝑑𝑖𝑛𝑔𝑏𝑒𝑑=

𝜌 𝑔 𝛿2 𝐶𝑜𝑠𝛽3𝜇

−2 𝛿 𝜏𝑤3 𝜇

Modeling Tool:

A FORTRAN based tool was developed to identify if the barite sagging problem will occur for

YPL fluid in specific well trajectory data (inclined and eccentric annulus) and it will measure the

effect of barite sagging in the fluid density variation. Also, it will measure the barite sag bed

forming and disassociation in the fluid with time and circulation. The Particle Elimination

Technique (reference 1) is used for this modeling. The inputs are including particles size and

concentration, outer radius, radius ratio, eccentricity, fluid rheology parameters such as n, k and

τy, dP/dL, inclination angle, flow rate and liquid density. The output of the file includes new

density of mud after barite settling.

The FORTRAN PROGRAM

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Conclusion:

In this independent study a modeled FORTRAN based program was developed to identify if the

barite sagging problem will occur for YPL fluid in specific well trajectory data (inclined and

eccentric annulus) and it will measure the effect of barite sagging in the fluid density variation.

Also, it will measure the barite sag bed forming and disassociation in the fluid with time and

circulation. This tool was tested and verified working. Moreover, some preventive measures

were mentioned to eliminate or minimize the barite sagging problem.

However, there is something wrong in the code so the output of density by time of the mud

always gives a ridiculous number. Since this is my first time coding a long program by

FORTRAN, I have double checked my formulate compared to the Particle Elimination Method

paper by Dr. Yahya Hashemian Adariani and I still did not find the reason. I will keep working

on the problem until I have figured out where is going wrong and I will send a new program to

Dr. Yu.

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References:

1- Yahya Hashemian Adariani, “EXPERIMENTAL STUDY AND MODELING OF

BARITE SAG IN ANNULAR FLOW”, PhD dissertation in University of Tulsa,

November 2012.

2- Yahya Hashemian, “Prediction of Barite Sag in Horizontal Annular Flow”, SPE 160916-

STU.

3- T.C. Nguyen, S. Miska, M. Yu and Takash, “Predicting Dynamic Barite Sag in

Newtonian Oil Based Drilling Fluid”, SPE 124137.

4- P A Bern, M Zamora, K S Slater and P J Hearn, “The Influence of Drilling Variables on

Barite Sag”, SPE 36670.

5- William Dye, Terry Hemphill, William Gusler, and Gregory Mullen, “Correlation of

Ultralow-Shear-Rate Viscosity and Dynamic Barite Sag”, SPE 70128.

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