Dr Bennion-Relative Permeability

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ENPE 617 ADVANCED

PRODUCTION

OPERATIONS

Measurement ofRelative

Permeability Data



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Common Determination Methods

Steady State

Unsteady State

Centrifuge

Field tuning

Ambient vs. Reservoir Condition Testing

Sample Selection

Rock typing and classification

Single plug vs. composite stacks

Plug vs. full diameter testing

Vertical vs. horizontal flooding methods



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Steady StateMethod

The Steady State DeterminationMethod for Relative Permeability (2

Phase)

R e l a t i v e

P e r m e a b i l i t y

Water Saturation

Sample at Initial Conditions of

Water (Irreducible) and Oil

(Maximum) Saturation



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The Steady State Determination

Method for Relative Permeability (2

Phase)

R e l a t i v e P e r m e a b i l i t y

Water Saturation

Commence Injection of 100%

Oil at Swi, Measure Ko atSwi


Phase)

R e l a t i v e


Water Saturation


Oil and 10% water, Measure Ko

And Kw at New Stabilized

Higher Sw



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Phase)


Water Saturation


Oil and 30% water, Measure KoAnd Kw at New Stabilized

Higher Sw


Phase)

R e l a t i v e


Water Saturation


Oil and 70% water, Measure Ko

And Kw at New Stabilized

Higher Sw



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Phase)


Water Saturation


Oil and 90% water, Measure KoAnd Kw at New Stabilized

Higher Sw


Phase)

R e l a t i v e


Water Saturation


Oil and 100% water, Measure

Kw at Sorw



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Phase)


Water Saturation

Advantages of the Steady StateMethod

Computationally very simple

Inherently stable (no viscous effects)

Test modifications can reduce or eliminate

impact of capillary end effects

‘Classic’ method of relative permeabilitydetermination



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Disadvantages of the Steady State

Method

Complex and expensive method, very timeconsuming

Difficult and expensive for full reservoirconditions

Large volumes of reservoir fluids required

In-situ saturation monitoring essential foraccuracy

More of a research method in many casesthan a viable commercial technique

Typical Steady State Apparatus

Capillary Contact Paper

Inlet Section Outlet Section



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Typical Steady State Apparatus

Pressure Taps

External Core SleeveFlow Head Flow Head

Steady State Apparatus

Water Inj Pump

Oil Inj Pump

Injection Pumps

Coreholder

In-Situ Saturation

Monitoring

Three Phase

Separator

BPR

PistonCylinders

Pressure Transducers

Core Sample

OVEN



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Common In-situ Saturation

Determination Methods

Gravimetric

Electrical resistivity

X-ray

MRI

Gamma ray

Microwave attenuation

Typical Steady State Lab Apparatus



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Displacement Pumps

Production Equipment



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UnsteadyState Method

The Unsteady State DeterminationMethod for Relative Permeability (2

Phase)

R e l a t i v e


Water Saturation

Sample at Initial Conditions of

Water (Irreducible) and Oil

(Maximum) Saturation



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Phase)


Water Saturation


Oil at Swi, Measure Ko atSwi


Phase)

R e l a t i v e


Water Saturation

Switch to Injection of 100%

Water at Swi, Measure Transient

Pressure and Production

History



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Transient Pressure and Production

History

D i f f e r e n t i a l P r e s s u r e

( C o n s t a n t R a t e T e s t )

Cumulative Run Time

Breakthrough

Point

Transient Pressure and ProductionHistory

P r o d u c t i o n R a t e

( C o n s t a n

t P r e s s u r e T e s t )

Cumulative Run Time

Breakthrough

Point



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Transient Pressure and Production

History

P r o d u c t i o n V o l u m e

( C o n s t a n t R a t e T e s t )

Cumulative Run Time

Breakthrough

Point

The Unsteady State DeterminationMethod for Relative Permeability (2

Phase)

R e l a t i v e


Water Saturation



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Advantages of the Unsteady State

Method

Rapid

Relatively inexpensive, even for full

reservoir condition HTHP tests

Limited reservoir fluid requirements

Easy to run at full reservoir conditions

Simplier equipment and procedures than

steady state

Disadvantages of the UnsteadyState Method

Unstable flow possible

Capillary end effects possible

More complex data reduction procedures

Data may be poorly conditioned

depending on computational method usedto regress transient lab results



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Typical Unsteady State Apparatus

Injection Pump

Coreholder

Three Phase

Separator

BPR

Piston

Cylinders

Pressure Transducers

Core Sample

OVEN

Typical Unsteady State Apparatus



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Centrifuge Methods

Use transient production vs. capillary

pressure history to generate psuedo rel

perm curve

Limited to very small samples and higher

perm media

Reservoir condition tests can not be easily

conducted Very limited commercial application

Field Methods

Estimate rel perm from material balance and

fractional flow in the reservoir

Takes into account overall bulk heterogenuity

Excellent and detailed field data required and

very well specific

Often the end result of adjusting rel perm curves

as the ‘easiest’ (but not most correct) adjustable

variable in field simulation



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What is the Best Method to Use?

What is the Best Method to Use

Many of the limitations of the unsteady

state method have been overcome in

recent years by experimental and

numerical modifications

95% plus of all commercial rel permmeasurements are conducted using

variants of the unsteady state method



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Reduction of Relative Permeability

Data From Lab Tests

Steady State – only simple (hand

calculator) data reduction is required to

directly reduce rel perm data once

saturations are known

Unsteady State – more complex

manipulation of transient

pressure/rate/production data is required

Unsteady State CalculationMethods – a History

Welge method (rel perm ratios only – circa

1949)

JBN Method (circa 1957)

Jones-Roselle Method (circa 1976)

Simulation methods (circa 1985 – 2001)



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Limitations of Classical Methods

(Welge, JBN, JR)

These methods assume no capillarypressure

These methods assume perfectlyhomogenoeus samples with dispersedmonotonic saturation increasing flow

These methods require two phase flow tocompute relative permeability as they are

based on variants of the Buckley – Leverett fractional flow equation

No Capillary Pressure

Dispersing effect of cap pressure on

frontal advance is neglected

Capillary end effects which may impact

breakthrough time and water cut are

neglected



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Typical Methods Used in the Past

to Negate This Effect

Very high displacement rates so that thetotal delta P across the sample is large incomparision to the capillary pressure

Problems – fines migration and highlyunstable flow

Viscous mineral/synthetic oils to increasedelta P to overcome cap effects

Problems – totally wrong IFT, viscosityratio and potential effects on wettability

Example – Typical High Rate RelPerm Test Showing Fines

Migration Induced Damage

Saturation

R e l a t i v e P e

r m e a b i l i t y

True Undamaged

Curve



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2

Homogeneous Samples and

Monotonic Fractional Flow

Fw

Average Sw

Homogeneous Samples andMonotonic Fractional Flow

Fw

Average Sw



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2

Heterogeneous Samples and Non-

Monotonic Fractional Flow

Fw

Average Sw

Heterogeneous Samples and Non-Monotonic Fractional Flow

Fw

Average Sw



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Relative Perm Configuration is

Based on Derivative Analysis of the

Fractional Flow Curve

Fw

Average Sw Water Saturation


Relative Perm Configuration is

Based on Derivative Analysis of the

Fractional Flow Curve

Fw

Average Sw Water Saturation

R e l a t i v

e P e r m e a b i l i t y



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Hetrogeneous Flow Effects May

Occur in

Fractured media

Vugular Media

High perm media

Extreme viscosity ratio

Unstable displacements

Capillary Induced Perm Reductions

Rate cc/hr Delta P – psi Perm - mD

10 1.2 2.5520 1.7 3.60

50 3.8 4.02

100 7.4 4.13

200 14.7 4.16



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Rate and Cap Pressure Effects

Perm vs. Rate

0 50 100 150 200 250Inj Rate - cc/hr

Permeability-mD

Capillary Induced Perm Reductions – Fines Migration Problems

Rate cc/hr Delta P – psi Perm - mD

10 1.2 2.5520 1.7 3.60

50 14.5 1.06

100 67.7 0.45

200 389 0.16



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Rate and Cap Pressure Effects

Perm vs. Rate

0 50 100 150 200 250Inj Rate - cc/hr

Permeability-mD

Requirement for Two Phase Flow

Fw

Average Sw

Water Saturation

R e l a t i v


Results in Highly

Compressed Saturation

Range



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2


Fw

Average Sw

Water Saturation



Fw

Average Sw

Water Saturation

R e l a t i v


Results in a More

Dispersed Saturation

Range



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3


Fw

Average Sw

Water Saturation


Common Techniques Used in thePast to Disperse Flow

Viscous refines oils used instead of

reservoir oil to ‘smear’ production profile

Problem – wrong viscosity, IFT and

possibly wettability

High rate displacements Problem – unstable flow



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Overcoming These

Deficiencies UsingModern Simulation

Methods

Simulation or ‘History Matching’Generation of Rel Perm Data

Most common current technique

Basically a numerical simulation study in

reverse



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History Matching Technique

In a normal simulation we know the relperm curves and we use this, along withother input data, to predict the reservoirpressure and production history

In the history matching method we knowthe pressure and production history fromthe lab tests, and we use this data in an

iterative fashion to generate the rel permcurves

Typical History Match ModelInput Physical Parameters (L, A, Kabs, Porosity, Pore Volume, # Blocks

Input Fluid Properties – Viscosity, Density, Rate, Initial Saturations

Input Test Properties – Endpoint Perms and Saturations, Pressure

History, Production History

Input Cap Pressure

File and Outlet

Boundary Cond-

ition to Model

Capillary Effects



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The HistoryMatching

Process

Time Time Saturation C u m u l a t i v e P r o d u c t i o n



Step 1 – Pick Functional Form

For Rel Perm Curve

Step 2 – Pick Initial ‘Guess’

For Rel Perm Curve Configuration



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D i f f e r e n t i a l P

r e s s u r e

R e l a t i v e P e r

m e a b i l i t y






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r e s s u r e


m e a b i l i t y






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r e s s u r e


m e a b i l i t y

History Matching Process

Continue the iterative process until theerror between the stimulated and actualproduction and pressure data is as smallas possible

The resulting set of rel perm curvesrepresent the best fit to the lab generateddata

Algorithms to avoid localized or non-physical solutions



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r e s s u r e


m e a b i l i t y

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Dr Bennion-Relative Permeability