Statistical Characterization of Performance of Biopolymer Drill-in Fluid for Different Rheological Models.
ABSTRACT
Appropriate selection of rheological models is important for hydraulic calculations of pressure loss prediction and hole cleaning efficiency of drilling fluids. Power law, Bingham-Plastic HerschelBulkley models are the conventional fluid models used in the oilfield. However, there are other models that have been proposed in literature which are under / or not utilized in the petroleum industry.
The primary objective of this study is to recommend a rheological model that best-fits the rheological behaviour of xanthan gum-based biopolymer drill-in fluids for hydraulic evaluations. Ten rheological models were evaluated in this study. These rheological models have been posed deterministically. Obviously, this is unrealistic so these deterministic models are replaced by statistical models by adding an error (disturbance) term and making suitable assumptions about them.
Rheological model parameters were estimated by least-square regression method. Models like Sisko and modified Sisko which are not conventional models in oil industry gave a good fit. Modified Sisko model which is a four-parameter rheological model was selected as the best-fit model since it produced the least residual mean square. There is 95% certainty that the true best-fit curve lies within the confidence band of this function of interest.
TABLE OF CONTENT
Title Page ……………………………………………………………………………………………………………………………i
Signature Page……………………………………………………………………………………………………………………ii
ABSTRACT………………………………………………………………………………………………………………………iii
TABLE OF CONTENT ……………………………………………………………………………………………………..iv
LIST OF FIGURES ……………………………………………………………………………………………………….….vi
LIST OF TABLES……………………………………………………………………………………………………….. ….vii
ACKNOWLEDGEMENT…………………………………………………………………………………………… ….viii
CHAPTER ONE INTRODUCTION …………………………………………………………………………………..1
1.1 INTRODUCTION……………………………………………………………………………………………………..1
1.1 PROBLEM DEFINITION …………………………………………………………………………………………..2
1.2 OBJECTIVES ……………………………………………………………………………………………………………3
1.3 METHODOLOGY……………………………………………………………………………………………………..3
CHAPTER TWO LITERATURE REVIEW……………………………………………………………………….. 4
2.0 INTRODUCTION………………………………………………………………………………………………………4
2.1 DRILL-IN FLUIDS……………………………………………………………………………4
2.2 POLYMER STRUCTURE ………………………………………………………………………………………….5
2.3 APPLICATION OF POLYMERS ………………………………………………………………………………..6
2.3.1 Hydroxymethylcellulose (HEC)…………………………………………………………………………….6
2.3.2 Carboxymethylcellulose (CMC)…………………………………………………………………………….6
2.3.3 Starches ……………………………………………………………………………………………………………..6
2.3.4 Polyacrylamides ………………………………………………………………………………………………….7
2.3.5 Biopolymers………………………………………………………………………………………………………..7
2.3.5.1 Rheology…………………………………………………………………………………………………….7
2.3.5.2 Shear Stability …………………………………………………………………………………………….8
2.3.5.3 Temperature Stability……………………………………………………………………………………8
2.3.5.4 Salt Solubility ……………………………………………………………………………………………..9
2.3.5.5 Acid Stability ………………………………………………………………………………………………9
2.4 PROPERTIES OF XANTHAN GUM…………………………………………………………9
2.4.1 Shear Thinning……………………………………………………………………………10
2.4.1 Low Shear Rate Viscosity, LSRV………………………………………………………..11
2.4.3 Shear Degradation of Xanthan Gum……………………………………………………..11
2.5 THEORY OF THE RHEOLOGICAL MODELS…………………………………………………………. .12
2.5.1 Bingham Plastic Model……………………………………………………………………………………….13
2.5.2 Power Law Model………………………………………………………………………………………………14
2.5.3 Herschel-Bulkley Model……………………………………………………………………………………..14
2.5.4 Robertson-Stiff Model ……………………………………………………………………………………….15
2.5.5 Prandtl-Eyring Model …………………………………………………………………………………………15
2.5.6 Sisko Model………………………………………………………………………………………………………16
2.5.7 Modified-Sisko Model………………………………………………………………………………………..16
2.5.8 Casson Model ……………………………………………………………………………………………………17
2.6 REGRESSION ANALYSIS AND MODEL COMPARISON …………………………………………18
CHAPTER THREE DEVELOPMENT OF STATISTICAL MODEL ………………………………… 20
3.0 INTRODUCTION…………………………………………………………………………………………………….20
3.1 DATA COLLECTION ………………………………………………………………………………………………20
3.2 MODEL SPECIFICATION………………………………………………………………………………………..21
3.3 CHOICE OF FITTING METHOD AND MODEL FITTING …………………………………………22
3.4 STATISTICAL MEASURE ………………………………………………………………………………………23
3.4.1 Model Comparison ………………………………………………………………………………………….. 23
3.4.2 Confidence Interval ……………………………………………………………………………………………23
CHAPTER FOUR APPLICATION OF MODEL EQUATION ON DATA………………………….. 25
4.0 INTRODUCTION…………………………………………………………………………………………………….25
4.1 EVALUATION OF BINGHAM PLASTIC MODEL …………………………………………………….25
4.2 EVALUATION OF POWER LAW MODEL………………………………………………………………..26
4.3 EVALUATION OF HERSCHEL-BULKLEY MODEL…………………………………………………26
4.4 EVALUATION OF ROBERSTON-STIFF MODEL…………………………………………………….27
4.5 EVALUATION OF MODIFIED ROBERTSON-STIFF MODEL…………………………………..27
4.6 EVALUATION OF PRANDTL-EYRING MODEL………………………………………………………28
4.7 EVALUATION OF MODIFIED PRANDTL-EYRING MODEL ……………………………………29
4.8 EVALUATION OF SISKO MODEL…………………………………………………………………………..29
4.9 EVALUATION OF MODIFIED SISKO MODEL ………………………………………………………..30
4.10 EVALUATION OF CASSON MODEL……………………………………………………………………..30
CHAPTER FIVE ANALYSIS OF RESULT………………………………………………………………………. 32
5.0 INTRODUCTION…………………………………………………………………………………………………….32
5.1 DETERMINATION OF STATISTICAL CORRELATION…………………………………32
5.2 FITTED CURVES AND RESIDUAL ANALYSIS…………………………………………32
5.3 SUM-OF-SQUARES AND MEAN SQUARES…………………………………………….41
5.4 CONFIDENCE INTERVAL……………………………………………………………………………..43
CHAPTER SIX CONCLUSION(S) AND RECOMMENDATION(S)…………………………………. 44
REFERENCES………………………………………………………………………………………………………………… 45
NOMENCLATURE………………………………………………………………………………….50
APPENDIX A ………………………………………………………………………………………………………………….. 52
INTRODUCTION
The use of rheological models to approximate the behaviour of non-Newtonian fluids is very paramount in the oil and gas industry especially during drilling, well completion, workover and acidizing. In drilling operations, mathematically designed rheological models are used to describe the viscous forces to develop frictional pressure loss equations. Accurate prediction of pressure losses help in the determination of bit optimization hydraulics, estimation of equivalent circulating density (ECD) and drilling fluid compressibility.
The benefits of a more accurate estimation of ECD is adequate hole cleaning efficiency to enhance total drilling rate which in turn reduces total drilling cost. Prevention of circulation loss, maintenance of under-balanced drilling conditions and detection of potential kick are achieved if ECD is rightfully predicted (Bailey and Peden, 2000). Estimated model parameters help to perform other hydraulics calculations. Power Law and Bingham Plastic models are widely used for hydraulics evaluation.
They are assumed for standard API hydraulics calculations. Herschel-Bulkley, Roberston-Stiff and Casson models have been accepted to some extent in the petroleum industry. These models and the corresponding hydraulic calculations do provide a way for fair estimates of hydraulics for conventional wells using simple drilling fluids as asserted by Guo and Hong in 2010. Power Law model predicts shear stress well at low shear rate (in the annulus) and Bingham Plastic model describes the characteristics of drilling fluid at high shear rate (in the drill pipe).
Biopolymer drill-in fluid is a complex fluid formulated with several compositions to desired properties for optimum performance particularly in unconventional wells. It is a water soluble ‘rheology engineered’ drilling fluid designed to optimize the performance of rotary drilling. It is a complex high molecular weight (MW) polymer with a strong bond between the chains of its molecules which is efficiently used in unconventional wells like onshore and offshore horizontal wells, coiled tubing drilling and slim holes.
REFERENCES
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Makromolekulare Chemie, pp. 61-67, 1998.
Ash, S.G., Clarke-Sturman, A.J., Calvert, R., and Nisbet, T.M., “Chemical Stability of
Biopolymers Solutions”, SPE 12085, presented at the 58th Annual Technical Conference and
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StudentsandScholarship Team.
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