School of Science and Engineering Department of Petroleum Engineering A Decision Support Model for Differential Sticking Avoidance by Affonso Marcelo Fernandes Lourenço This thesis is presented for the Degree of Doctor of Philosophy of Curtin University January 2012 Declaration To the best of my knowledge and belief this thesis contains no material previously published by any other person except where due acknowledgment has been made. This thesis contains no material which has been accepted for the award of any other degree or diploma in any university. Signature: . Date: . ... ii Contents 1 Introduction 1 2 Statement of the Problem 4 3 Literature Review 8 3.1 Works on Analytical Predictive Models . .8 3.1.1 Works on Drilling Fluid Filtercakes (Mudcake) . 11 3.1.1.1 Filtration and Growth . 11 3.1.1.2 Mechanical Behavior . 14 3.2 Works on Statistical and Knowledge-based Models . 18 4 The Risk Model 30 5 Experimental Assessment of Mechanical Properties of Mudcakes 33 5.1 High Pressure and High Temperature Mudcake Characterization Equipment . 33 5.2 Investigated Effects . 34 5.3 Major Parts . 35 5.4 Simplified Experimental Procedure . 37 5.4.1 General Steps . 37 5.5 Relevance and Use of Data . 39 5.6 Mechanical Behavior of Mudcakes under Compressive Loads. 42 5.7 Resistive Torque and Adhesion and Cohesion of Mudcakes . 44 5.8 Final Comments . 45 5.8.1 Hardness . 45 5.8.2 Torque and Adhesion and Cohesion . 45 5.8.2.1 General Tendencies . 45 5.8.3 Additional Capabilities of the HPHT MCCE . 46 6 Case-based Reasoning Model: Likelihood from Similarity Score 48 6.1 Theory of Fuzzy Sets . 49 6.2 Fuzzy Logic . 54 iii 6.3 Optimization of Weights in the Similarity Metric: Classification through History Match. 57 6.4 Analysis of Results . 57 6.4.1 Testing the Model . 58 6.4.2 Proposed Analog Method for Field Applications . 60 6.4.2.1 Further Comments . 62 7 Consequence Analysis: Approximate Unidimensional Mechanistic Model 64 7.1 Calculating Wall Contact, h ..................... 65 7.1.1 Contact Between BHA and Borehole Wall. 66 7.1.1.1 In Between Stabilizers . 66 7.1.1.2 Point of Tangency . 68 7.1.1.3 Tool Shape Effect . 68 7.1.1.4 Summarized Computation Procedure . 69 7.2 Calculating d ............................. 69 7.2.1 Geometrical Relation between Mudcake Embedment Depth and Parameter d ....................... 70 7.2.2 Algorithm for Calculating Parameter d ........... 71 7.3 Validation Method . 72 8 Combined Results of Risk Analysis 75 9 Conclusions, Observations and Recommendations 79 10 Nomenclature 84 Bibliography 87 A HPHT MCCE 93 A.1 General Experimental Stages . 93 A.1.1 Hardness . 94 A.1.2 Torque . 95 A.1.3 Adhesion-Cohesion . 96 A.2 Experimental Matrix and Results . 100 B Tables of Results - Raw Drilling Input Data 106 B.1 Input Data . 106 C Tables of Results - Raw Drilling Input Data (cont.) 125 C.1 Input Data . 125 iv D Tables of Results - Processed Input Data 132 D.1 Input Data . 132 E Risk Analysis Results 149 E.1 Testing the Model: Success Rate Analysis . 149 E.1.1 Proposed Method for Field Applications: Bi-dimensional Analysis based on Similarity Scores. 159 F Overpull Reference Data 160 F.1 CASE I . 160 F.1.1 Input Data . 160 F.1.2 Output Data . 160 F.2 CASE II . 163 F.2.1 Input Data . 163 F.2.2 Output Data . 163 F.3 CASE III . 165 F.3.1 Input Data . 165 F.3.2 Output Data . 167 G Fuzzy Sets and Fuzzy Logic 168 G.1 Introduction . 168 G.1.1 Logic Truth Tables . 168 G.1.2 Fuzzy Logic Controller Example: Dinner Tip Calculator from Matlab . 168 G.1.2.1 Fuzzy Sets (Fuzzification Step) . 168 G.1.2.2 Logical Operators and Related Fuzzy Methods . 168 G.1.2.3 Run Controller: Apply Fuzzy Methods to If-Then Rules . 168 G.2 Differential Sticking Fuzzy Sets . 173 G.3 Differential Sticking Fuzzy Controller Properties . 173 G.3.1 Overall Configuration . 173 G.3.2 If-Then Rules . 176 G.3.3 Relationship between Input and Output Variables . 178 v List of Tables 3.1 Review on Devices used for Mudcake Mechanical Assessment. 15 3.2 Most Common Hybrid Systems . 22 4.1 Risk Table . 31 5.1 Range of Relevant Variables. 38 6.1 Notation for Fuzzy Set H in Figure6.1 . 50 6.2 Input Variables for Calculating the Similarity Score . 53 6.4 Variables Composing the Case Structure . 56 6.5 Bi-dimensional Risk Analysis via Similarity Score - Arbitrary Rank 62 A.1 Mudcake Experiments . 100 B.1 Raw Input Data . 107 D.1 Cases - Processed Input Data . 133 E.1 Weights Optimization Statistics . 150 E.2 Average Similarity Scores Between Each Target Case and All Training Cases . 153 E.3 Average Similarity Scores Between Each Target Case and All Training Cases . 154 E.4 Example Computation of Average Similarity Score with Similar and Dissimilar Cases . 155 E.5 Dummy Cases Input Data . 156 E.6 Dummy Cases Weights Optimization Statistics . 158 E.7 Detailed Bi-dimensional Analysis . 159 F.1 BHA Data . 161 F.2 Summary of Operational Data for Occurrence . 161 F.3 Summary of Results . 162 F.4 BHA Data . 163 F.5 Summary of Operational Data for Occurrence . 164 vi F.6 Summary of Results . 165 F.7 BHA Data . 165 F.8 Summary of Operational Data for Occurrence . 166 F.9 Summary of Results . 167 G.1 Logic Truth Tables and Logical Operators . 169 G.2 Logical Operators . 171 G.3 Logical Operators . 176 vii List of Figures 2.1 Differential Sticking . .5 3.1 Flow of Information in the ANN . 21 3.2 Different Swarm Communication Networks. After Lins [27]. 28 4.1 Hypothetical Well. 32 5.1 HPHT MCCE . 35 5.2 Pressure Vessel and Internal Parts. 36 5.3 Typical Results . 40 5.4 Hardness Profile - Bentonite . 42 5.5 Hardness Profile - Carbonate . 43 6.1 Variable "Height" as Linguistic Variable of Three Fuzzy Sets . 49 6.2 Tool Shape Factor . 55 6.3 Objective of Weight’s Optimization in the Similarity Metric . 58 6.4 Risk from Average Similarity Scores . 61 7.1 BHA Deflection Curve . 66 7.2 Drillpipe Point of Tangency. 68 7.3 Geometry of Embedment . 71 7.4 Algorithm to Calculate Parameter d................. 73 8.1 3D Risk Analysis . 76 8.2 3D Risk Analysis - Well AL . 78 F.1 Well Data CASE I . 162 F.2 Well Data CASE II . 164 F.3 Well Data, CASE III . 166 G.1 Two-valued Logic and Multivalued Logic. After Matlabő Fuzzy Logic Toolbox User Manual. 169 G.2 Fuzzy Tip Calculator . 170 G.3 Inputs . 170 viii G.4 Output . 170 G.5 Tip Controller . 172 G.6 Fuzzy Sets Representing Input Linguistic Variables. 173 G.7 Fuzzy Sets Representing Input Linguistic Variables. 174 G.8 Fuzzy Sets Representing Output Linguistic Variables. 175 G.9 Controller’s Configuration . 175 G.10 Examples of the Relationship Between Inputs and Outputs. 179 ix Abstract An innovative theoretical model to quantify the risk of differential sticking is presented. The proposed risk assessment is based on the concept of like- lihood versus consequence. The likelihood of the problem’s occurrence in a given wellbore segment (case) is evaluated from a knowledge-based model and translated by a similarity measure of relevant operational conditions be- tween the target case and historical cases with known outcomes. The stand alone module performed satisfactorily and predicts the likelihood of occurrence by more than a chance probability, demonstrated by a.