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

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

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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

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SPE London Section Evening Meeting

Fractured Horizontal Well Decline

Branimir Cvetkovic, Ph.D.

Bayerngas Norge AS, Oslo, Norway The Geological Society, Piccadilly London September 28th 2010

SPE London Section Meeting

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Overview of Presentation

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

Motivation

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Exponential Hyperbolic Harmonic

q t

b Rate - Time Type Curves

Motivation

  • Empirical Arps’ rate-time curves (1945)
  • Fetkovich’s composite transient-depletion rate-time curves (1973, 1980)

rD

T D

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Surface Model Wellbore Model Well Model

}

Reservoir Model

Horizontal Well Vertical Well Motivation

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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

  • Validation (case studies with model

comparisons)

  • Risk Analysis Workflow

Objectives

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Main Challanges

Horizontal well with fractures

  • Modelling features

– Design-integration – Validation

  • Model

– Changing IBC

  • From constant rate to constant pressure
  • Fracture responses
  • Late time approximations

– Equivalent well radius – Equivalent fracture half-length

Main Challanges

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Late-Time Approximations for Rates

(Horizontal Well with N Fractures)

N r rwv Approximations

f

L L

2

f

L L

1

1 1 cot 2 4 2

(1 )

r r f

L r e e

 

f

L e 

2 1 2 3 2 4 1 2 2

1 2 cot log(1 ) 2 exp 2 1 (1 ) 2 cot log 1 3 2 1 4

f

r r r L r r e r r r

 

                          

2 4 2 9 3 3

2

f

L e r e

Main Challanges

1 1 2 2 f

L e r e

rwv1 3 2 rwv3 rwv2 1

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Reservoir, Well and Fracture Input

(Horizontal Well with N Fractures)

  • Reservoir

– Isotropic – Non-isotropic

  • Horizontal well

– No flow to the wellbore – Direct flow to the wellbore – Wellbore friction

  • Model Boundary Conditions

– Inner BC – Outer BC

Implementation

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Stepwise Constant Pressure IBC

(3 intervals)

Implementation

5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 4 5 0 0 5 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 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0

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

Cumulative production Q (bbl) Individual Fracture Rate q (bbl/d) Rate q (bbl/d)

Infinite Conductivity Fracture Finite Conductivity Fracture

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IBC Changing from Constant Rate to Constant Pressure

500 1000 1500 2000 2500 3000 3500 4000 100 200 300 400 500 600 700 1000 2000 3000 4000 5000 6000 7000 8000

IBC of Constant: Rate Pressure Variable Wellbore Rate Wellbore Pressure

Implementation

Time t (d) Rate q (bbl/d) Pressure difference Δp (psi)

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Field A - North Sea

  • Horizontal well with

fractures

– 9 injection wells – 11 production wells

  • Provided data for:

– 2-oil production wells

  • 14 fractures

– A water injection well

  • 16 fractures

Model Validation

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The Model vs. Observed Cumulative Production Match

2 0 0 0 0 0 0 4 0 0 0 0 0 0 6 0 0 0 0 0 0 8 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 1 4 0 0 0 0 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

Cumulative production Q (bbl) 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 ) 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 )

Model Validation Lf PP 36 50 34 40 20 40

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IBC Changing from Constant Rate to Constant Pressure

0.1 1 10 100 1000 10000 100000 500 1000 1500 2000 2500 3000 3500 1 10 100 1000 10000 100000

Constant Rate, IBC Constant Pressure, IBC Pressure-difference varies Rate varies for the constant Pressure-difference IBC

Time t (d) Pressure difference [Pi-Pwf] (psi) Rate q (bbl)/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

Model Validation

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Stepwise Constant Rate IBC

(1 and 3 intervals)

500 1000 1500 2000 2500 3000 3500 4000 500

Match

Implementation

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500

Match

Time t (d) Pressure difference Δp(psi) Rate q (bbl/d)

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 500

Match

Time t (d) Pressure difference Δp(psi)

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Water Injection Case

5000 10000 15000 20000 25000 30000 500 1000 1500 2000 2500 Ti t (D ) 5000000 10000000 15000000 20000000 25000000 30000000 35000000 40000000

Time t (d) Injection rate q (bbl/d) Qumulative injection Q (bbl)

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

Model Validation

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Field V - North Sea

1 2 3 4 5 6 7 100 200 300 400 500 600 700 PI, Productivity index PI, Productivity index PI, Productivity index

Fracture Permeability, kf (Fracture width w=0.008 ft) 50 D 15 D 2.5 D

WELL DATA

MFHOW-MODEL DATA

Model Validation Productivity Index PI [bbl/(d Psi)] Time t (d)

1 2 3 4 5 6 7 100 200 300 400 500 600 700 PI, Productivity index PI, Productivity index PI, Productivity index

Fracture Permeability, kf (Fracture width w=0.008 ft) 50 D 15 D 2.5 D

WELL DATA

MFHOW-MODEL DATA

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Late-Time Approximations for Rates

Rate vs. time match for:

  • A fractured horizontal well (2 transversal

fractures) vs. vertical well with calculated effective radius

  • A fractured horizontal well (3-

transversal fractures) vs. a single transversal fractured horizontal well with calculated effective half-length

  • A fractured horizontal well (3-

longitudinal fractures) vs. a single longitudinal fractured horizontal well with calculated effective half-length

1000 2000 3000 4000 5000 6000 7000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A transient rate calculated data for the vertical well with a derived effective well radius A horizontal well with two transversal fractures

1000 2000 3000 4000 5000 6000 7000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A transient rate calculated data for the vertical well with a derived effective well radius A horizontal well with two transversal fractures

2000 4000 6000 8000 10000 12000 14000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A transient rate calculated data for the horizontal well with a derived equivalent fracture half-length A horizontal well with three transversal fractures

2000 4000 6000 8000 10000 12000 14000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

A transient rate calculated data for the horizontal well with a derived equivalent fracture half-length A horizontal well with three transversal fractures

2000 4000 6000 8000 10000 12000 14000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 q ( )

A transient rate calculated data for the horizontal well with a derived equivalent fracture half-length A horizontal well with three longitudinal fractures A transient rate calculated data for the horizontal well with a derived equivalent fracture half-length A horizontal well with three longitudinal fractures

Model Validation

ref Lef

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The Horizontal Fractured Well Model- Concluding Remarks

Model Summary

  • A fast and robust algorithm is developed

– transient (SLAB model) – basic depletion (BOX model)

  • The bringing together of

– rate-time and – pressure-time analyses

  • The semi-analytical tool aids in

– optimizing the well production – screening analysis – the late-time approximations were verified

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Define the Model

Gathering Data Semi-Analytical Simulations Of the Provided Input Using the Model Reusults Match Observed Well with Fractures Data

2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 180000

Risk Analysis - Workflow

Phase A: Matching production profiles for the Fixed Number of Fractures

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Phase B: Screning Analysis and Optimizing Number of Transversal Fractures Positioned Along a Horizontal Well

PREDICTION SCENARIO UNCERTAINTY QUANTIFICATION PROJECT OPTIMIZATION UNCERTAINTY PARAMETERS RESPONSE PARAMETERS SENSITIVITY ANALYSIS PROBABILISTIC FOREACASTING

  • Define ‘Base

Case Model’- pre-screening process

high mean lo w

Reservoir data Fracture data Well data Risk Analysis - Workflow

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Phase C: History Match of Observed Well Data with the Model Obtained Data

PREDICTION SCENARIO UNCERTAINTY QUANTIFICATION PROJECT OPTIMIZATION UNCERTAINTY PARAMETERS RESPONSE PARAMETERS SENSITIVITY ANALYSIS PROBABILISTIC FOREACASTING

high mean lo w

Fracture

Half-length Height Spacing Conductivity hf Lf Δ L

Finite Conductivity

  • Kf fracture

permeability

  • W width

Risk Analysis - Workflow

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Fracture Diagnosis Analyses

  • Study is based on the screening analysis of a horizontal well

with fractures production data.

  • Prognosis profiles were generated manually and compared to

the real observed data.

  • Study provides workflow for optimising number of fractures

along a horizontal well.

  • Matching procedure should be further improved with risking

tool features for the fracture closure diagnosis.

  • The semi-analytical model for a multiple-fractured-horizontal

well, was applied providing fast and robust features and were used as screening tools for diagnostic and forecasting purposes.

Concluding Remarks

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Recommendations

Fractured horizontal well model limitations

  • Reservoir

– Heterogeneous features

  • Fracture

– orientation

  • Well

– Undulating well

  • Gas extension

– including non-Darcy flow

  • Further modelling features

– multiple well approach – Multilateral

  • Combaining the risk analysis with the network simulation

– Linking the semy-analytical model to the risk analysis software (commercial SW tool as MEPPO SPT-Group Kjeller Norway) – Linking the semy-analytical model to a network model (METTE – Yggdrasil A/S, Oslo Norway) Concluding Remarks

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FRACTURES

high mean low

Semi-analytical Input Reservoir, Fracture, Well Data Semi-analytical

  • utput

FRACTURE POSITIONING OPTIMIZATION

Thank you for your attentions!

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bc@bayerngas.com