Fractured Horizontal Well Decline SPE London Section Meeting - PowerPoint PPT Presentation

SPE London Section Evening Meeting Fractured Horizontal Well Decline SPE London Section Meeting Branimir Cvetkovic, Ph.D. Bayerngas Norge AS, Oslo, Norway The Geological Society, Piccadilly London September 28 th 2010 1

Overview of Presentation • Motivation • Objectives • Main Challenges • Implementation - Type Curves • Model Validations - Case Studies Motivation • Model Summary • Risk Analysis Workflow • Concluding Remarks • Acknowledgments 2

Rate - Time Type Curves • Empirical Arps’ rate-time curves (1945) • Fetkovich’s composite transient-depletion rate-time curves (1973, 1980) Harmonic q Hyperbolic b Exponential t Motivation D T r D 3

Vertical Well Well Model Wellbore Model Surface Model } Reservoir Model Horizontal Well Motivation 4

Overall Objectives Fractured horizontal well model • Full-time scope screening analysis tool for modelling of flow from a reservoir to a fractured well • Selected pressure-rate wellbore conditions with late-time approximations Objectives • Validation (case studies with model comparisons) • Risk Analysis Workflow 5

Main Challanges Horizontal well with fractures • Modelling features – Design-integration – Validation • Model – Changing IBC Main Challanges • From constant rate to constant pressure • Fracture responses • Late time approximations – Equivalent well radius – Equivalent fracture half-length 6

Late-Time Approximations for Rates (Horizontal Well with N Fractures) N r r wv Approximations L  f 1 r wv1 e Main Challanges 1 1 L e r 1 1 cot L  1 L r r   2 f f (1 ) 2 2 4 2 r wv2 r e 2 e L e f   2 2 4 2  1  L L  1   2  2 cot log(1 )  r r r      2  L f 2 3 9 3 3  f exp   e r r wv3  2 3 2 4 2 1 (1 ) e  r r  L   1 2 cot log r   e   2 2 1 3 2 1 4 f  r r  7

Reservoir, Well and Fracture Input (Horizontal Well with N Fractures) • Reservoir – Isotropic – Non-isotropic • Horizontal well – No flow to the wellbore Implementation – Direct flow to the wellbore – Wellbore friction • Model Boundary Conditions – Inner BC – Outer BC 8

Stepwise Constant Pressure IBC (3 intervals) Individual Fracture Rate q (bbl/d) 5 0 0 0 1 8 0 0 0 4 5 0 0 1 6 0 0 0 Infinite Conductivity Fracture 4 0 0 0 1 4 0 0 0 Rate q (bbl/d) Finite Conductivity Fracture 3 5 0 0 1 2 0 0 0 3 0 0 0 1 0 0 0 0 2 5 0 0 8 0 0 0 2 0 0 0 6 0 0 0 Implementation 1 5 0 0 4 0 0 0 1 0 0 0 2 0 0 0 5 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 7 0 0 0 0 0 0 8 0 0 0 0 0 0 9 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Cumulative production Q (bbl) F ra c tu re q fr1 a n d q fr5 - in fin ite c o n d u c tiv ity flo w F ra c tu re q fr2 a n d q fr4 - in fin ite c o n d u c tiv ity flo w F ra c tu re q fr3 - in fin ite c o n d u c tiv ity flo w F ra c tu re q fr1 a n d q fr5 - fin ite c o n d u ctivity flo w F ra c tu re q fr2 a n d q fr4 - fin ite c o n d u ctivity flo w F ra c tu re q fr3 - fin ite c o n d u ctivity flo w R a te , q in fin ite c o n d u ctivity fra c tu re s R a te , q fin ite c o n d u c tiv ity fra c tu re s 9

IBC Changing from Constant Rate to Constant Pressure 4000 8000 Δ p (psi) IBC of Constant: Rate 3500 7000 Pressure 3000 6000 Rate q (bbl/d) Pressure difference 2500 5000 2000 4000 Implementation Variable Wellbore Rate 1500 3000 Wellbore Pressure 1000 2000 500 1000 0 0 0 100 200 300 400 500 600 700 Time t (d) 10

Field A - North Sea • Horizontal well with fractures – 9 injection wells – 11 production wells Model Validation • Provided data for: – 2-oil production wells • 14 fractures – A water injection well • 16 fractures 11

The Model vs. Observed Cumulative Production Match 1 4 0 0 0 0 0 0 1 2 0 0 0 0 0 0 Cumulative production Q (bbl) 1 0 0 0 0 0 0 0 8 0 0 0 0 0 0 6 0 0 0 0 0 0 Model Validation L f PP 4 0 0 0 0 0 0 36 50 34 40 2 0 0 0 0 0 0 20 40 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 Time t (d) M odel cu m ulative ra te (Lf= 20, P P = 40) M o del c um ulativ e rate (L f=3 4, P P =40 ) 12 W e ll c u m ula tiv e rate M o del c um ulativ e rate (L f=3 6, P P =50 )

IBC Changing from Constant Rate to Constant Pressure 100000 100000 Pressure difference [Pi-Pwf] (psi) 10000 10000 Rate q (bbl)/d 1000 1000 100 100 Constant Rate, IBC Model Validation 10 10 Constant Pressure, IBC Pressure-difference varies Rate varies for the 1 1 constant Pressure-difference IBC 0.1 0 0 500 1000 1500 2000 2500 3000 3500 Time t (d) Model - Variable Pressure Difference, Pi-Pwf Constant Rate, q IBC Well_Pressure_Difference Conatant Pressure, Pi-Pwf IBC Model - Variable Well with Fractures Rate, q Well_Rates 13

Stepwise Constant Rate IBC (1 and 3 intervals) 5000 5000 Match 4000 4500 4500 Δ p(psi) Δ p(psi) 3500 Match Match 4000 4000 3000 Rate q (bbl/d) 3500 3500 Pressure difference Pressure difference 2500 3000 3000 2500 2500 2000 Implementation 2000 2000 1500 1500 1500 1000 1000 1000 500 500 500 0 0 0 0 0 500 500 0 500 Time t (d) Time t (d) 14

Water Injection Case 30000 40000000 Qumulative injection Q (bbl) 35000000 25000 Injection rate q (bbl/d) 30000000 20000 25000000 15000 20000000 15000000 10000 10000000 Model Validation 5000 5000000 0 0 0 500 1000 1500 2000 2500 Ti t (D ) Time t (d) Model - Water injection rate, qw Water Injection Rate Model - Cumulative water injection, Qw Fracture injection rate (equal for fracture 1 and 14) Fracture injection rate (equal for fracture 7 and 8) Well cumulative water injection 15

Field V - North Sea 7 7 MFHOW-MODEL DATA MFHOW-MODEL DATA Productivity Index PI [bbl/(d Psi)] 6 6 Fracture Permeability, kf (Fracture width w=0.008 ft) Fracture Permeability, kf (Fracture width w=0.008 ft) 50 D 50 D PI, Productivity index PI, Productivity index 5 5 15 D 15 D PI, Productivity index PI, Productivity index 2.5 D 2.5 D PI, Productivity index PI, Productivity index 4 4 Model Validation 3 3 2 2 WELL DATA WELL DATA 1 1 0 0 0 0 100 100 200 200 300 300 400 400 500 500 600 600 700 700 Time t (d) 16

Late-Time Approximations for Rates Rate vs. time match for: 7000 7000 A transient rate calculated data A transient rate calculated data 6000 6000 for the vertical well with a for the vertical well with a 5000 5000 derived effective well radius derived effective well radius r ef 4000 4000 3000 3000 2000 2000 • A fractured horizontal well (2 transversal A horizontal well with two A horizontal well with two 1000 1000 fractures) vs. vertical well with transversal fractures transversal fractures 0 0 calculated effective radius 0 0 500 500 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 4500 4500 5000 5000 14000 14000 A transient rate calculated data for the A transient rate calculated data for the 12000 12000 horizontal well with a derived horizontal well with a derived equivalent fracture half-length equivalent fracture half-length 10000 10000 8000 8000 Model Validation 6000 6000 L ef 4000 4000 • A fractured horizontal well (3- 2000 2000 A horizontal well with three transversal fractures A horizontal well with three transversal fractures transversal fractures) vs. a single 0 0 0 0 500 500 1000 1000 1500 1500 2000 2000 2500 2500 3000 3000 3500 3500 4000 4000 4500 4500 5000 5000 transversal fractured horizontal well 14000 A transient rate calculated data for the A transient rate calculated data for the horizontal well with a derived horizontal well with a derived with calculated effective half-length 12000 equivalent fracture half-length equivalent fracture half-length 10000 • A fractured horizontal well (3- ) 8000 q ( longitudinal fractures) vs. a single 6000 longitudinal fractured horizontal well 4000 with calculated effective half-length 2000 A horizontal well with three longitudinal fractures A horizontal well with three longitudinal fractures 17 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

The Horizontal Fractured Well Model- Concluding Remarks • A fast and robust algorithm is developed – transient (SLAB model) – basic depletion (BOX model) • The bringing together of – rate-time and Model Summary – pressure-time analyses • The semi-analytical tool aids in – optimizing the well production – screening analysis – the late-time approximations were verified 18

Define the Model Gathering Data 0 0 Semi-Analytical 0 0 Simulations Risk Analysis - Workflow 0 Of the Provided Input 0 0 Using the Model Reusults 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 180000 Match Observed Well with Fractures Data Phase A: Matching production profiles for the Fixed Number of Fractures 19