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PETE 324 (07A) — PTA Objectives; Petrophysics Review; PVT Review Slide — 1

Petroleum Engineering 324Reservoir Performance

Thomas A. Blasingame, Ph.D., P.E.Department of Petroleum Engineering — Texas A&M University

College Station, TX 77843-3116 (USA)+1.979.845.2292

[email protected]

Objectives of Well Tests —Review of Petrophysics —Review of Fluid Properties

29 January 2007


Objectives of PTA/PA: BasicsThe reservoir does not care how it is being produced.Better data = better analysis = better estimates.PTA: pressure history good. PA: rate history good.

Objectives of Well Test/Production Data AnalysisParameters to be Estimated


Objectives of Pressure Transient Testing:Evaluate reservoir pressure (initial or average pressure).Evaluate reservoir fluid (fluid samples collected for lab study).Estimate reservoir properties: k, S, xf, λ, ω, etc.Estimate reservoir volumetrics: fluid-in-place, drainage area.

Input Data:BOTTOMHOLE pressure data (accurate to < 1 part in 10,000).SURFACE flowrate data (often poorly measured/recorded).Fluid properties: FVF, viscosity, compressibility, ...Reservoir properties: h, φ, rw, cf, ...

Results of PTA Interpretation:Productive capacity of the WELL (damage/stimulation).Productive capacity of the RESERVOIR (transmissibility).Current average reservoir pressure.Reservoir limits (for production to pseudosteady-state).Well interference effects.Well/Reservoir specific parameters: Cs, xf, λ, ω, Lfault, rcomp, kv/kh, ...

Pressure Transient Analysis: Philosophy/ObjectivesQ. Issues with pressure transient analysis (PTA)?A. Design → implementation → interpretation → analysis → review.

Discussion: Pressure Transient Analysis — Philosophy/ObjectivesDesign/implementation issues? (prepare well for testing, model test)Interpretation/analysis issues? (model uniqueness)


Pressure Transient Analysis: Summary of DiagnosticsQ. Key elements of PTA diagnostics?A. Utilize "regime-specific" data functions, use multiple data functions.

Discussion: Pressure Transient Analysis — Summary of DiagnosticsΔp function (pressure drop)? (traditional diagnostic)Δpd function (Bourdet derivative)? (primary diagnostic — IARF)Δpβd function (β-derivative)? (new diagnostic — VF, NF, Hz, Faults, etc.)


Pressure Transient Analysis: Summary of Diagnostics


Diagnostic Plot: Infinite Acting Radial Flow

10-3

10-2

10-1

100

101

102

103

p D, p

Dd

and

p Db d

10-2 10-1 100 101 102 103 104 105 106

tD/CD

CDe2s=1×10-3

3×10-3

1×10-2 3×10-2 10-1

1 101

102 103

104106

108

1010

1020 1030

1015

1040

10100

1060

1080 1050

10100

1080

1060 1050

1040

1030

1020 1015

1010

108106

104 103

102 101

3×10-2 1×10-2

CDe2s=1×10-3

Type Curve for an Unfractured Well in an Infinite-Acting Homogeneous Reservoir with Wellbore Storage and Skin Effects.

3

3

10100

CDe2s=1×10-3

Legend: Radial Flow Type Curves pD Solution pDd Solution pDβd Solution

Radial Flow Region

Wellbore StorageDomination Region

Wellbore StorageDistortion Region

Discussion: Diagnostic Plot — Infinite Acting Radial FlowΔp function? ("hockey stick" behavior — WBS → IARF)Δpd function? (IARF — pDd = 1/2)Δpβd function? (WBS Domination — pDβd = 1)


Diagnostic Plot: Fractured Well (no WBS)

Discussion: Diagnostic Plot — Fractured Well (no WBS)Δp function? (BLF: pD = 1/4 slope, FLF: pD = 1/2 slope)Δpd function? (BLF: pDd = 1/4 slope, FLF: pDd = 1/2 slope, IARF: pDd = 1/2)Δpβd function? (BLF: pDβd = 1/4, FLF: pDβd = 1/2)

10-3

10-2

10-1

100

101

p D, p

Dd

and

p Dβ d

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

tDxf

CfD=0.250.5

1

CfD=1×104

Type Curve for a Well with a Finite Conductivity VerticalFractured in an Infinite-Acting Homogeneous Reservoir

(CfD = (wkf)/(kxf) = 0.25, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 10000)

Legend: pD Solution pDd Solution pDβd Solution

Radial Flow Region

CfD=0.25

CfD=1×104

1

5

2

0.51

21×103

500


Review of Petrophysics:Must understand the small-scale in order to understand the large scale.Porosity and permeability vary significantly — there is no "universal" concept (at least at present), all relations are defined by data.

Review of PetrophysicsObjectives


Review of Petrophysics: Scaling


Review of Petrophysics: k-φ Correlation.


Clean sandstone = power law model

Shaly sandstone = exponential model

pbpp ak φ=

)exp( φeee bak =

Permeability Models: HypothesisQ. Conceptual models for k and φ?A. "Perfect packings" → power-law basis. Shaly sands → exp. basis?

Discussion: Hypothesis modelsPower law model? (prove from perfect packings and using Archie's law)Exponential model? (large body of empirical evidence)Combined model? (model which represents "less perfect" packings)


pbpak φ=

)exp( φee bak =log(k)

log(φ)

pbpak φ=

)exp( φee bak =log(k)

φ

Permeability Models: k-φ RelationsQ. Is there a rigorous basis for the exponential and power law models?A. Power law ~ can infer from Archie's law. Exponential ~ ?

Discussion: k-φ Relationslog(k) vs. log(φ) plot? (clean, well-sorted, intergranular sands)log(k) vs. φ plot? (multiple depositional sequences(?), shaly sands(?))Is there a generic model(s)? (use power law as basis, with adjustment)


Review of Phase Behavior: Correlations — (p, T, composition)Gas: Correlations perform very well.Oil: Correlations perform reasonably well.Water: Correlations are simplistic, but sufficient.

Review of Phase Behavior (PVT)Objectives


Self-Evaluation: PVT Concepts1. Reservoir Fluids:

"Black Oil" (p>pb): Bo, μo, co are ASSUMED constant"Solution-Gas Drive" (all p): Bo, μo, co = f(p)"Dry Gas" (p>pd): Bg, μg, cg = f(p)

2. Diffusivity Equations:"Black Oil" case."Solution-Gas Drive" case."Dry Gas" case.

Reservoir Fluids: PVT Concepts


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: Fun

dam

enta

ls o

f Res

ervo

ir En

gine

erin

g—

Cal

houn

(195

3).

Schematic p-T Diagram: Multi-Component (Hydrocarbon) SystemNote the "Bubble Point" and "Dew Point" lines. Location of critical point determines fluid type.

Reservoir Fluids: Generic Schematic (Multi-Comp.)


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ls o

f Res

ervo

ir En

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—C

alho

un (1

953)

. (m

odifi

ed to

refle

ct

vario

us re

serv

oir f

luid

cas

es)

Schematic p-T Diagram: Hydrocarbon Reservoir FluidsNames represent conventional nomenclature. Locations of names represent relative locations of these fluid types.

Reservoir Fluids: Generic Schematic (Hydrocarbon)


Bo,g,w = Fluid volume at standard conditions

Fluid volume at reservoir conditions

Formation Volume Factor: Bo,g,w

The Formation Volume Factor "converts" surfacevolumes to downhole conditions.

Typical values: Oil: 1.2 to 2.4 RB/STBGas: 0.003 to 0.01 rcf/scf

Bo,g,w is defined as a volume conversion for oil, gas, or water — and is defined on a mass (or density) basis.

Reservoir Fluids: Summary (Formation Volume Fac.)


Viscosity: μo,g,w

Is a measure of a fluid's internal resistance to flow... the proportionality of shear rate to shear stress, a sort of internal friction.

Fluid viscosity depends on pressure, temperature,and fluid composition.

Typical values: Oil: 0.2 to 30 cpGas: 0.01 to 0.05 cpWater: 0.5 to 1.05 cp

Reservoir Fluids: Summary (Fluid Viscosity)


Fluid Compressibility: co,g,w

Typical values:Oil: 5 to 20 x10-6 psi-1 (p>pb)

30 to 200 x10-6 psi-1 (p<pb)Gas: 50 to 1000x10-6 psi-1Water: 3 to 5 x10-6 psi-1

Formation Compressibility: cf

Typical values:Normal: 2 to 10 x10-6 psi-1Abnormal: 10 to 100 x10-6 psi-1

dpdR

BB

dpdB

Bc so

o

go

oo +−=

1dpdR

BB

dpdB

Bc sw

w

gw

ww +−=

1dpdB

Bc g

gg

1−=

dpdc fφ

φ1

=

Reservoir Fluids: Summary (Fluid Compressibility)

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