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Low-Permeability Black Oil/Gas Condensate Reservoirs Using - - PowerPoint PPT Presentation

Analysis of Short-term (Flowback) and Long-term (Online) Production Data from Low-Permeability Black Oil/Gas Condensate Reservoirs Using Analytical/Semi-Analytical Methods C.R. Clarkson University of Calgary Outline Introduction A


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SLIDE 1

Analysis of Short-term (Flowback) and Long-term (Online) Production Data from Low-Permeability Black Oil/Gas Condensate Reservoirs Using Analytical/Semi-Analytical Methods

C.R. Clarkson University of Calgary

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SLIDE 2

Outline

Slide 2

 Introduction

  • A few facts
  • Problem statement and objectives

 Methods

  • Modification of pseudovariables
  • Iterative integral
  • Dynamic drainage area

 Special Application of RTA Methods:

  • Fracture Height Estimation

 Future Work  Conclusions

slide-3
SLIDE 3

Introduction

Slide 3

1000 m+ Horizontal Well Perforations Induced Hydraulic Fracture Network Extent of Contacted Reservoir Area

 Fact:

  • When producing from MFHWs completed in ultra-low permeability

reservoirs:

  • a complex series of processes occurring at multiple scales are

initiated that we don’t completely understand

From: Clarkson et al. (JNGSE, 2016)

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SLIDE 4

Introduction

Slide 4

 Fact:

  • When producing from MFHWs completed in ultra-low permeability

reservoirs:

  • a complex series of processes occurring at multiple scales are

initiated that we don’t completely understand

meters Reactivated Natural Fractures Induced Hydraulic Fracture centimeters Natural Fracture Matrix millimeters Matrix with fine-scale laminations and fractures

A

0.5 mm STYLIOLINA

micrometers Matrix with interspersed organic and inorganic matter nanometers Nanopore structure

  • f organic and

inorganic matter

From: Clarkson et al. (JNGSE, 2016)

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SLIDE 5

Introduction

Slide 5

 Fact:

  • Reservoir characterization methods that account for the appropriate

physics are in their infancy

  • Understanding how to advance characterization methods is

critical for sustainable development through primary and enhanced recovery processes

Multi-Phase Flow

Pressure Distance from hydraulic fracture Gas phase Condensate phase Hydraulic fracture pi pd pw Zone A B C?

Pore Confinement Effects

Free gas Adsorbed gas

Velocity ≠ 0

Complex Fracturing

etc.

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SLIDE 6

Introduction

Slide 6

 Reservoir and Hydraulic Fracture Characterization:

Reservoir Sample Analysis

km, kf, So, Sg, Sw, kro, krg, krw, ρm, ρb, øm, PSD, PTD, Pc, a, m, n, OM, IOM, Ro, Gc, Es, νs

Development Stage Pre-Drill Pre-Frac Frac Treatment Drill/Post-Drill Post-Frac Long-Term (Online) Production Analysis Type Properties Derived Seismic, 2D, 3D Analysis Category Reservoir and Hydraulic Fracture Characterization Log Analysis

km, kf, h, So, Sg, Sw, ρb, øm, øf, PSD, OM, IOM, ED, νD

Pre-Frac Welltest (DFIT)

khsys, Pclosure , Preservoir

Frac Monitoring (Microseismic) Flowback Analysis Frac Modeling Post-Frac Welltest (F/BU) Production Analysis

Frac geometry, SRV khf , khsys, Pbreakthrough, xf khsys, OGIP/OOIP , CGIP/COIP , xf, Ac, FcD khsys, xf, Ac, FcD xf, Ac, FcD

From: Clarkson et al. (JNGSE, 2016)

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SLIDE 7

Introduction

Slide 7

 RTA – Flowback/Online:

From SPE 166279

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SLIDE 8

Introduction

Slide 8

 RTA – Flowback/Online:

From: Clarkson et al. (TLE, 2014)

Flow Period Illustration of Flow Periods Flow-Regimes

X-Section View Plan View

Flowback: Depletion (Fracture) Before Breakthrough

  • f Formation Fluids

(single-phase flow in fracture) Flowback: Transitional After Breakthrough

  • f Formation Fluids

(multi-phase flow in fracture, single or multi-phase flow in formation) Long-Term Production: Linear Flow Formation Fluid Production Dominant (multi-phase flow in fracture, multi-phase flow in formation)

Flow-Period Illustration of Flow-Periods Flow-Regimes

X-Section View Plan View

Flowback: Depletion (Fracture) Before Breakthrough

  • f Formation Fluids

(single-phase flow in fracture) Flowback: Transitional After Breakthrough

  • f Formation Fluids

(multi-phase flow in fracture, single or multi-phase flow in formation) Long-Term Production: Linear Flow Formation Fluid Production Dominant (multi-phase flow in fracture, multi-phase flow in formation) ASSESS DATA VIABILITY

Review Production Data Review Well History Gather Reservoir, Completion and PVT Data

CHECK FOR DATA CORRELATION PRELIMINARY DIAGNOSIS

Filter Data for Clarity Review/Edit Data

IDENTIFY FLOW REGIMES PERFORM STRAIGHT- LINE ANALYSIS

Obtain Preliminary Estimate of Hydraulic Fracture Properties Obtain Preliminary Estimate of Reservoir Permeability Obtain Preliminary Estimate of Hydrocarbons-in-Place

PERFORM TYPE-CURVE ANALYSIS

Validate Hydraulic Fracture Property Estimates Validate Reservoir Permeability Estimate Validate Hydrocarbons- in-Place Estimate

PERFORM FORECAST WITH MODEL FIT EMPIRICAL MODEL TO FORECAST

STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: STEP 6: STEP 7: STEP 8:

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SLIDE 9

Introduction

Slide 9

 Problem Statement:

  • Analytical solutions used in RTA commonly assume:
  • Single-phase flow of liquids
  • Static reservoir and fracture properties
  • Darcy’s Law is valid
  • Constant rate or pressure production
  • …..
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SLIDE 10

Introduction

Slide 10

 Objectives:

  • Develop approaches that account for:
  • Multi-phase flow
  • Stress-dependent fracture and matrix properties
  • Pore confinement effects: non-Darcy flow
  • Pore confinement effects: fluid properties

2 4 6 8 10 12 14 10 20 30 40 50

Unpropped Fracture Gas (N2) Permeability (D) Effective Stress (MPa)

Mean Pore Pressure = 0.19 MPa Mean Pore Pressure = 0.53 MPa Mean Pore Pressure = 0.88 MPa Mean Pore Pressure = 1.23 MPa

Pore Confinement Effects

Free gas Adsorbed gas

Velocity ≠ 0

5 10 15 20 25 30 35 40 45 50

  • 150
  • 100
  • 50

50 100 150 200 250 300 350 400

Pressure (MPa) Temperature (oC)

Phase Envelope of a Gas-Condensate Fluid Under Confinement

pore width = 300 nm pore width = 10 nm pore width = 5 nm pore width = 2 nm

“Dewpoint Suppression”

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SLIDE 11

Methods

Slide 11

 Multiple Approaches to Account for Non-Linearities:

  • Modification of pseudovariables
  • Iterative integral method
  • Dynamic drainage area
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SLIDE 12

Methods: Modification of Pseudos

Slide 12

1.Linearization Technique

  • Linearization of governing PDE
  • Using Pseudovariables

2.Method of Calculation

  • Pseudovariables calculations
  • Saturation pressure relationship

3.Backward Modeling

  • Liquid solution
  • Validation

Image Courtesy of Hamid Behmanesh

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SLIDE 13

Methods: Modification of Pseudos

Slide 13

Images Courtesy of Hamid Behmanesh

Pseudopressure Pseudotime Liquid Solution Analogy!

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – JNGSE 2015, SPE 172928)

  • Linearization
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SLIDE 14

Methods: Modification of Pseudos

Slide 14

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – JNGSE 2015, SPE 172928)

  • Pseudovariable Calculations:

(1) (2) (3) p PVT So (4) (5) pp

Image Courtesy of Hamid Behmanesh

a

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SLIDE 15

Slide 15

Image Courtesy of Hamid Behmanesh

ta

t

(1) (2) (5) (6) (7)

p

(3) (4) p

Ginv. Material Balance Ginv. Np Gp

Methods: Modification of Pseudos

  • Pseudovariable Calculations:
  • Calculation procedure: model inversion - linear flow analysis

(2P flow – JNGSE 2015, SPE 172928)

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SLIDE 16

Methods: Modification of Pseudos

Slide 16

Images Courtesy of Hamid Behmanesh

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – JNGSE 2015, SPE 172928)

  • Inverse Modeling
  • Infinite-acting linear flow solution - CP
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SLIDE 17

Methods: Modification of Pseudos

Slide 17

  • Application: model inversion - linear flow analysis (2P flow –

JNGSE 2015, SPE 172928)

1200 2400 3600 4800 1 10 100 1000 10000 100 200 300 400 500 Flowing Bottomhole Pressure, psia

Gas Rate (Mscf/D), Oil, Water Rate (STBdD)

Time, days Oil Rate Gas Rate Water Rate pwf

10 20 30 40 50 60 100 200 300 400 500 CGR and WGR, STB/MMscf Time, days Condensate Gas Ratio Water Gas Ratio

Constant CGR

  • MFHW, tight (lean) gas condensate reservoir
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SLIDE 18

Methods: Modification of Pseudos

Slide 18

  • Application: model inversion - linear flow analysis (2P flow –

JNGSE 2015, SPE 172928)

1/qgas, 1/(qoil) versus √t

mCP

xf√k

Initial Properties

p

Distance of Investigation Material Balance

fCP

Cartesian coordinates

0.0 0.5 1.0 1.5 2.0 5 10 15 20

Inverse of Gas Rate, 1/(MMscf/D) Square Root of Time, days0.5

xf√k* = 21.5 ft.md0.5

  • MFHW, tight (lean) gas condensate reservoir
slide-19
SLIDE 19

Method: Iterative Integral

Slide 19

  • Calculation procedure: model inversion - linear flow

analysis (2P flow – JNGSE 2013; 2016 and SPE 167176)

Image Courtesy of Farhad Qanbari

  • Integrate non-linearities over the domain

t m q p f p m

CP

  • w

c w

  ) ( ) (

1 1

) ( ) ( 1 :

D D D D c

dm m m g f  

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1000 2000 3000 4000 fc pw(psi) Bubble point pressure dSo/dp = 2 10-4 psi-1 dSo/dp = 1.75 10-4 psi-1 dSo/dp = 1.5 10-4 psi-1 (c)

 

. ˆ )) ( ( 2 exp ˆ )) ( ( 2 exp 1

ˆ ˆ

   

                                 

  

d d erfc m d d erfc m g m

D D D D D

) ( : guess Initial  erfc mD 

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SLIDE 20

Method: Iterative Integral

Slide 20

  • Calculation procedure: model inversion - linear flow

analysis (2P flow – JNGSE 2013; 2016 and SPE 167176)

Image Courtesy of Farhad Qanbari

Pressure Distance from hydraulic fracture Gas phase Condensate phase Hydraulic fracture pi pd pw Zone A B C?

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SLIDE 21

Method: Iterative Integral

Slide 21

  • Application: model inversion - linear flow analysis (2P flow

– JNGSE 2013; 2016 and SPE 167176)

  • Example 1: MFHW, tight (rich) gas condensate reservoir

2000 4000 6000 8000 10000 12000 14000 5 10 15 20 25 30 (∆m)1P/qg/fc1P; (∆m)2P/qg/fc2P; (∆m)3P/qg/fc3P 106 psi2/cp/MMscf Gas linear superposition time (√day) Single-phase gas Two-phase gas+condensate Three-phase gas+condensate+water Three phase + stress-sensitivity (Ac√k)2P = 1.3 (Ac√k)1P (Ac√k)3P = 1.5 (Ac√k)1P Correction for condensate dropout Correction for water Correction for stress- sensitivity of permeability

Clarkson et al. (JNGSE, 2016)

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SLIDE 22

Method: Iterative Integral

Slide 22

  • Calculation procedure: model inversion - linear flow

analysis (2P flow – JNGSE 2013; 2016 and SPE 167176)

Image Courtesy of Farhad Qanbari

Pressure Distance from hydraulic fracture Oil phase Gas phase Hydraulic fracture pi pb pw Zone A B C

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SLIDE 23

Method: Iterative Integral

Slide 23

  • Application: model inversion - linear flow analysis (2P flow

– JNGSE 2013; 2016 and SPE 167176)

  • Example 2: MFHW, tight oil reservoir

10 20 30 40 50 60 70 5 10 15 20 25 30 35 40 45 50 Δp/qo, (Δmo)/qo/fc2P; (Δmo)/qo/fc3P Oil linear superposition time (√day) Single-phase oil Two-phase oil+gas Three-phase oil+gas+water (Ac√k)O+G = 0.97 (Ac√k)O (Ac√k)O+G+W = 2.67 (Ac√k)O

Image Courtesy of Farhad Qanbari

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SLIDE 24

Method: Iterative Integral

  • Calculation procedure: model inversion - linear flow analysis

(Pore confinement – SPE 171357 and 180264)

 

            

 

1

) ( ] )[ ( ) ( 1 ˆ ) ˆ ( ) ˆ ( ) ˆ ( ) ( ) ( ) (

D D d r g D D c p p g g CP g c w i

d k c c c f p d p B p p k p t m q f p p           

   

Bulk w i c ti gi ai i Confined w i c ti gi ai i Bulk f Confined f

p p f c k Z p p f c k Z x x                    ) ( ) ( ) ( ) (      

Stress sensitivity and adsorption layer Changes in gas critical properties Desorption

Square-root-time plot

Slide 24

Clarkson et al. (JNGSE, 2016)

500 1000 1500 2000 2500 3000

  • 200
  • 100

100 200 300 Pressure, psia Temperature, oF 2-Phase boundary 2-Phase boundary confined Reservoir pressure path Critical point Critical point 0.5 1 1.5 2 2.5 3 2000 4000 6000 8000 10000 z-factor Pressure, psia z bulk z confined 0.0025 0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095 2000 4000 6000 8000 10000 Bg, bbl/scf Pressure, psia Bg bulk Bg confined 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 2000 4000 6000 8000 10000 µ, cp Pressure, psia µ bulk µ confined

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SLIDE 25

Method: Dynamic Drainage Area

Slide 25

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – SPE 180230)

1 inv ,

  • S

1 inv

p

Hydraulic Fracture

yinv1

ye1

yinv2

2 inv ,

  • S

2 inv

p

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SLIDE 26

Method: Dynamic Drainage Area

Slide 26

Slide Courtesy of Farhad Qanbari

ti gi i i c inv D inv tD inv D inv gD g wf g inv g

c t k A T p k p c p p q p m p m     56 . 576 ) ( ) ( ) ( ) ( ) ( ) (  

            ) ( 615 . 5 ) ( ) ( ) ( ) ( 615 . 5 1000 4

, , inv

  • inv
  • inv

inv s inv gd inv g inv

  • i
  • i

i si gdi gi i inv ft p

p B S p p R p B S p B S R B S h y x G    

ti i i i inv

c t k y    

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – SPE 180230)

  • An approximate semi-analytical/empirical method
  • Uses boundary-dominated solution for transient flow
slide-27
SLIDE 27

Method: Dynamic Drainage Area

Slide 27

  • Calculation procedure: model inversion - linear flow analysis

(2P flow – SPE 180230)

Slide Courtesy of Farhad Qanbari

  • An iterative process
  • Time instead of superposition time
  • Average pressure instead of initial pressure
  • Coefficient of linear flow equation is different

A√k

t q p m p m

g wf g inv g

  ) ( ) (

f (A√k)

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SLIDE 28

Method: Dynamic Drainage Area

Slide 28

SPE 180230

  • Application: model inversion - linear flow analysis (2P flow –

SPE 180230)

  • Example 1: MFHW, wet gas reservoir (CGR=20 STB/MMscf)

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 200 400 600 800 1000 1200 pwf (psia) qg (Mscf/Day) Time (days) Gas Rate - Field Fata Flowing Bottomhole Pressure

(a)

slide-29
SLIDE 29

Method: Dynamic Drainage Area

Slide 29

  • Application: model inversion - linear flow analysis (2P flow –

SPE 180230)

  • Numerical history-match and DDA-corrected linear flow plot

1000 2000 3000 4000 5000 10 20 30 DDA-Corrected Gas RNP (psi2/cp/scD) √Time (√day) 500 1000 1500 2000 2500 3000 500 1000 Gas Rate (Mscf/Day) Time (days) Gas Rate - Field Fata Gas Rate - Numerical Simulation

Parameter RC1 Total Ac√ki – numerical simulation 8200 Total Ac√ki – DDA-corrected linear flow plot 7400 (10%)

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SLIDE 30

Method: Dynamic Drainage Area

Slide 30

SPE 180230

  • Application: model inversion - linear flow analysis (2P flow –

SPE 180230)

  • Example 2: MFHW, gas condensate reservoir (CGR = 100

STB/MMscf)

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 100 200 300 400 pwf (psia) Gas Rate (Mscf/Day) Time (days) Gas Rate - Field Fata Flowing Bottomhole Pressure

(a)

100 200 300 400 500 100 200 300 400 Condensate Rate (STB/Day) Time (days)

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SLIDE 31

Method: Dynamic Drainage Area

Slide 31

SPE 180230

  • Application: model inversion - linear flow analysis (2P flow –

SPE 180230)

  • Numerical history-match

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 100 200 300 400 Well Bottomhole Pressre (psia) Gas Rate (Mscf/Day) Time (days) Gas Rate - Field Fata Gas Rate - Numerical Simulation

(a)

100 200 300 400 500 100 200 300 400 Condensate Rate (STB/Day) Time (days) Condensate Rate - Field Fata Condensate Rate - Numerical Simulation

(a)

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SLIDE 32

Method: Dynamic Drainage Area

Slide 32

  • Application: model inversion - linear flow analysis (2P flow –

SPE 180230)

  • DDA-corrected gas linear flow plot

100 200 300 400 500 10 20 DDA-Corrected Gas RNP (psi2/cp/scfD) √Time (√day)

Parameter RC2 Total Ac√ki from numerical simulation 23500 Total Ac√ki from DDA-corrected linear flow plot 26200 (12%)

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SLIDE 33

Method: Dynamic Drainage Area

Slide 33

  • Calculation procedure: long-term forecasting (2P flow –

SPE 175929)

1 inv ,

  • S

1 inv

p

Hydraulic Fracture

yinv1

ye1

yinv2

2 inv ,

  • S

2 inv

p

slide-34
SLIDE 34

Method: Dynamic Drainage Area

Slide 34

  • Calculation procedure: long-term forecasting (2P flow –

SPE 175929)

   

                                   

ft inv wf g inv g i wf v ft inv

  • i
  • i

wf

  • inv
  • i
  • x

y T p m p m h k p R x y B p m p m h k q    2 1424 ) ( ) ( 1000 ) ( 2 2 . 141 ) ( ) (

              ) p ( B S ) p ( ) p ( R ) p ( B . S ) p ( B S R B . S h y x t q N

inv gd inv , g inv inv v inv

  • inv

,

  • inv

gdi gi i vi

  • i
  • i

i inv ft

  • p

6 6

10 615 5 10 615 5 4    

  • + analogous equations for gas…
  • Pseudopressure calculations require S-P relationships – used

empirical approach

slide-35
SLIDE 35

Method: Dynamic Drainage Area

Slide 35

  • Application: long-term forecasting (2P flow – SPE 175929)
  • MFHW, tight gas condensate reservoir

2000 4000 6000 8000 10000 12000 14000 16000 18000 200 400 600 800 1000 Gas Rate (Mscf/d), BHP (psia) Time (day) Gas Rate - Field Data BHP Gas Rate - DDA 500 1000 1500 2000 2500 3000 3500 4000 200 400 600 800 1000 Cumulative Gas (MMscf) Time (day) Gas Rate - Field Data Gas Rate - DDA 200 400 600 800 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 Condensate Rate (STB/d) Time (day) Condensate Rate - Field Data Condensate Rate - DDA 20 40 60 80 100 120 140 160 180 200 200 400 600 800 1000 Cumulative Condensate (MSTB/d) Time (day) Condensate Rate - Field Data Condensate Rate - DDA

Slide Courtesy of Farhad Qanbari

slide-36
SLIDE 36

Method: Dynamic Drainage Area

Slide 36

  • Calculation procedure: flowback forecasting (2P flow – URTeC

2460083)

Flow Period Illustration of Flow Periods Flow-Regimes

X-Section View Plan View

Flowback: Depletion (Fracture) Before Breakthrough

  • f Formation Fluids

(single-phase flow in fracture) Flowback: Transitional After Breakthrough

  • f Formation Fluids

(multi-phase flow in fracture, single or multi-phase flow in formation)

Flow-Period Illustration of Flow-Periods Flow-Regimes

X-Section View Plan View

Flowback: transient/depletion Before Breakthrough

  • f Formation Fluids

(single-phase flow in fracture) Flowback/Early Production: transitional/linear Breakthrough

  • f Formation Fluids

(multi-phase flow in fracture, single or multi-phase flow in formation)

Element of symmetry yinv1 wf ye xf Swi,m Soi,m pi,m Swi,f Soi,f pi,f (Sw,inv,f)1 (So,inv,f)1 (pav,inv,f)1 (Sw,inv,m)1 (So,inv,m)1 (pav,inv,m)1 (Sw,inv,f)2 (So,inv,f)2 (pav,inv,f)2 (Sw,inv,m)2 (So,inv,m)2 (pav,inv,m)2 yinv2 xinv1

Source: Clarkson et al. (URTeC 2016)

slide-37
SLIDE 37

Method: Dynamic Drainage Area

Slide 37

  • Application: flowback forecasting (2P flow – URTeC 2460083)
  • MFHW, tight oil reservoir

2000 4000 6000 8000 10000 0.1 1 10 100 1000 10000 2 4 6 8 10 12

Pwf (psia) and GOR (SCF/STB) Gas (Mscf/D), Water and Oil (STB/D) Rate

Time, days

Fluid Production Rates

Water Rate Oil Rate Gas Rate Pwf GOR

From Clarkson et al. (TLE, 2014)

slide-38
SLIDE 38

Method: Dynamic Drainage Area

Slide 38

  • Application: flowback forecasting (2P flow – URTeC 2460083)
  • MFHW, tight oil reservoir

100 200 300 400 500 600 2 4 6 8 10 qo (STB/day) Time (day) Oil rate - field data Oil rate - DDA

a)

0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 Np (MSTB) Time (day) Cumulative oil - field data Cumulative oil - DDA

b)

100 200 300 400 500 600 2 4 6 8 10 qg (Mscf/day) Time (day) Gas rate - field data Gas rate - DDA

a)

0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 Gp (MMscf) Time (day) Cumulative gas - field data Cumulative gas - DDA

b)

500 1000 1500 2000 2500 3000 2 4 6 8 10 qw (STB/day) Time (day) Water rate - field data Water rate - DDA

a)

1 2 3 4 5 6 7 8 2 4 6 8 10 Wp (MSTB) Time (day) Cumulative water - field data Cumulative water - DDA

b)

slide-39
SLIDE 39

Special Application: Fracture Height

Slide 39

 Concept

 With known initial compositions of two layers (target and bounding), it is possible to estimate penetration height ratio (h1/h2) based on the short-term flow rate and composition of the production stream

Impermeable Layer

Source: Ghaderi and Clarkson (JNGSE, in press)

slide-40
SLIDE 40

Special Application: Fracture Height

Slide 40 Source: Ghaderi and Clarkson (JNGSE, in press)

  • Calculation procedure:
  • Writing material balance for each individual component, it can be

concluded that:

It is important to find a proper average pressure to evaluate these properties for each layer with different composition

slide-41
SLIDE 41

Special Application: Fracture Height

Slide 41 Source: Ghaderi and Clarkson (JNGSE, in press)

  • Calculation procedure:

Behmanesh (2014) proposed the following relationship for average pressure: It is possible to show that the above equation is equivalent to: If we make the equation more general we can it use more efficiently:

slide-42
SLIDE 42

Special Application: Fracture Height

Slide 42 Source: Ghaderi and Clarkson (JNGSE, in press)

  • Comparison with numerical simulation:

82.00 82.20 82.40 82.60 82.80 83.00 83.20 83.40 83.60 83.80 84.00 5 10 15 20 25

η, mole percentage Time, day

  • Config. I
  • Config. II

82.00 82.20 82.40 82.60 82.80 83.00 83.20 83.40 83.60 83.80 84.00 5 10 15 20 25

η, mole percentage Time, day

  • Config. III
  • Config. IV

y = 1.0017x - 0.0008 R² = 0.9924 2 4 6 8 10 12 2 4 6 8 10 12 h2/h1 (Analytical) h2/h1 (Simulation)

τ = 0.80

slide-43
SLIDE 43

Future Work

Slide 43

 Continue development

  • f

multi-phase RTA analysis, including improvement of our previous work on boundary- dominated flow (FMB; SPE 169515)  Incorporation of fluid chemistry (e.g. salinity) into the analysis  Extension of methods to account for inter-well/stage communication  Application of fracture height-growth method to field data

slide-44
SLIDE 44

Conclusions

Slide 44

 Conventional RTA methods use simplified solutions that do not capture the physics of flow and storage in unconventional reservoirs  Our research group have applied 3 different approaches (pseudovariables, interative integral, dynamic drainage area) to account for unconventional reservoir complexities  These approaches have been successfully applied to extract reservoir and hydraulic fracture information from multi-fractured horizontal wells producing from tight

  • il/gas condensate reservoirs
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Acknowledgements

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 AITF, Encana, Shell  TOC sponsors  Students  NSERC CRD program  SPE