5 1 Reservoir Description EM

Reservoir Simulation – Reservoir Description

Data review

• Why run a flow simulation ? • Mathematical & Numerical considerations • ECLIPSE Reminder

Introduction

Etienne MOREAU







History matching

Space & Time Discretisation Reservoir description Fluid description Initialisation Aquifer & Well representation Flow description




Production Forecast

• • • • • •




Outline

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EP - Reservoir Simulation - Introduction - E.M.

NUMERICAL FLOW MODEL =

Flow model

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Data review


History matching • Production allocation per well • Production data (pressure, GOR, WOR, …)


Well description • Production constraints • Productivity index


Aquifer description • Geometry, Volume, Compress. • Permeability


Flows description • One phase: Permeability Tensor • Multiphase: Kr & Pc

Flow Simulator + Modelled Data

EP - Reservoir Simulation – Reservoir Description - E.M.


Reservoir geometry • Top Reservoir • Flow units
Rock description • Net to Gross • Porosity & permeability • Pore compressibility
Fluids description • In reservoir conditions (PVT) • In stock conditions
Initial State • Contact depths (WOC and GOC) • Pressure at a reference depth.

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EP - Reservoir Simulation – Reservoir Description - E.M.

Structural model

Flow Model

Upscaling

Stratigraphic Model

Petrophysical Model

Reservoir description

Sedimentological Model

Geostatics

Reservoir description

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Flow model

• Integration of seismic data, geology, petrophysics, fluid description, production data to : • Characterize the reservoir geometry and rock properties. • Define flow units. • Estimate the fluids initially in place.

Petrophysical model

EP - Reservoir Simulation – Reservoir Description - E.M.







• Grid definition. • Estimation per grid cell of the data related to reservoir description at initial state (geometry, porosity, single phase and multi phase flows, fluids, pressures, saturations). • Estimation of the fluids initially in place. • Simulation of the dynamic behaviour of the reservoir.

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EP - Reservoir Simulation – Reservoir Description - E.M.







Main issues

Reservoir description • Interpolate (or extrapolate) data in non recognised areas. • Give only one value for each parameter in each grid cell. • Take into account discretisation effects (cell dimensions, time step,…)

Data Upscaling • Rocks are heterogeneous at all scales. − Measurements are done at all scales.

• Data vary rapidly in each cell. − Data need to be averaged in each cell.

• Flows between cells must be correctly represented. − Variations of pressure & saturation must be fully captured.

• Hence the necessity for each parameter : − to describe how the parameter is distributed in the grid cell. − to precise how the complete distribution can be replaced by one value.

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EP - Reservoir Simulation – Reservoir Description - E.M.




Flows are calculated in the flow model (coarse grid).

Reservoir is described in the Geomodel (fine grid).

Data Upscaling: Flows between cells must be correct





It is important to precise how to go from the geological model to the flow model

EP - Reservoir Simulation – Reservoir Description - E.M.

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Data Upscaling: Rocks are heterogeneous Rocks are heterogeneous at all scales: • Pore • Core • Strata

EP - Reservoir Simulation – Reservoir Description - E.M.

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Well tests :

Reservoir simulation cell:

Reservoir geological cell:

Logs:

Cores:

Plug:

Data

104

500

100

20

10-1

10-1

10-2

Dx (m)

104

500

100

20

10-1

10-1

10-2

Dy (m)

102

40

10

2.5

10

10-1

3. 10-2

Dz (m)

1010 m3

107 m3

105 m3

103 m3

10-1 m3

10-3 m3

10-5 m3

Volume

Data Upscaling: Data are defined at different scales

Reservoir volume:

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EP - Reservoir Simulation – Reservoir Description - E.M.

1

e

2.5 3 2.5 3

10-5 m3 PLUGS

2.5

10-1 m3 LOGS

× 100

?

103 m3 3D/4D Seismic

Data Upscaling: Data are defined at different scales

× 108

× 104 105 m3 COARSE MODEL CELL

to a Coarse Grid Model

Up-scaling from a Fine Grid

103 m3 FINE MODEL CELL

mini-models or similar and apply lab rel perms provided model sufficiently fine (layers of 0.5-1.0 metres)

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EP - Reservoir Simulation – Reservoir Description - E.M.

Homogenization length or REV

Data Upscaling: Data need to be averaged

Average property (e.g., porosity)

EP - Reservoir Simulation – Reservoir Description - E.M.

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Data Upscaling: Flows between cells must be correct AVERAGE SHALINESS = 10%

EP - Reservoir Simulation – Reservoir Description - E.M.

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Q=

T × ∆P µ

∆x

Heterogeneous porous medium

Data Upscaling: Flows between cells must be correct Homogeneous porous medium

∆x

k A ∆P Q= × µ ∆x

Reservoir parameters controlling flows between two cells are Permeability, Section area & distance between grid centers (Homogeneous Porous Medium) Transmissivity (Heterogeneous Porous Medium)

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EP - Reservoir Simulation – Reservoir Description - E.M.










Plug Log Pressure transient test Seismic scale

Measurements at different scales • • • •

Data Upscaling

Impossible to consider all levels of heterogeneities in a flow model • Each cell is considered as homogeneous. − Flows inside each cell are not represented.

• Heterogeneity is only captured between cells − Flows between cells must be correctly represented

Need of methodology to include all scales of information:

MACRO

GIGA

CORE

Data Upscaling

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CELL

• Averaging data (that do not depend on flows) in each individual cell • Upscaling data (that depend on flows) between cells

MEGA

MICRO

EP - Reservoir Simulation – Reservoir Description - E.M.

PORE GRAIN

FIELD

EP - Reservoir Simulation – Reservoir Description - E.M.

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∆y

Reservoir description : Geometry

∆z

XZ section

Ztop

Depths are defined at the grid block centre. ∆x

XY view

Cell volume is Vt = ∆x . ∆y . ∆z

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EP - Reservoir Simulation – Reservoir Description - E.M.

Reservoir description : Geometry

Data kept in memory

Flow Simulator keeps in memory locations of grid block centres and porous volumes.

Grid

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EP - Reservoir Simulation – Reservoir Description - E.M.

+

+

+

+

+

+

+

+ +

+

Reservoir description : Grid

+

+

Grids I et II are equivalent

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Pf - ∆Pf

Vs+∆ ∆Vs

Vp - ∆Vp

Reservoir description : Pore compressibility

EP - Reservoir Simulation – Reservoir Description - E.M.

Vp

Vs

Pf

1 dVp Cp = Vp dP

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EP - Reservoir Simulation – Reservoir Description - E.M.

1 dVp Vp dP

1 dVs Vs dP

1 dVt Vt dP

Cs = −

Cp =

Reservoir description : Pore compressibility

Pores :

Solid :

Total :

Ct =

Pore compressibility and total compressibility are not identical : Ct = Φ . Cp - (1 - Φ) . Cs

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EP - Reservoir Simulation – Reservoir Description - E.M.

Identification of flow units

Reservoir description : Main issues


Population of the petrophysical model

Upscaling

− Interpolate (or extrapolate) data in non recognised areas. − Give an average for each parameter in each grid cell.

• Two main problems

• Definition per Grid Cell of Net to Gross, Porosity and Permeability







• Reservoir engineering data are often defined at a small scale (core data or even pore data). • These data are not constant in one grid cell. • Hence the necessity for each parameter : − to describe how the parameter is distributed in de the grid cell. − to precise how the complete distribution can be replaced by one average value.

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EP - Reservoir Simulation – Reservoir Description - E.M.

210/15a-6

T4

2800

2950

T5

3000

-240 psi

744 kg/m3

a6

-25 psi

2900

T3

1025 kg/m3

2850

3050

3100

Reservoir Description : Identification of flow Units 1960

1980

2000

210/15a-T5 Tarbert3 Tarbert2 Tarbert1

2080

2060

2040

2020

210/15a-T4

Ness4 Ness3 Ness2 Ness1 Etive Rannoch2 Rannoch1 Broom 2100

2120

2750

2140

Pressure (psia)

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3150

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Cell Volume : Vt = ∆x . ∆y . ∆z Net Volume : Vu = Vu1 + Vu2

Porosity : Φ = Vp / Vu

Net Thickness : Hu = Ht . Vu / Vt

Porous Volume : Vp = Φ1 . Vu1 + Φ2 . Vu2

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EP - Reservoir Simulation – Reservoir Description - E.M.

Non reservoir

Facies 2 (Φ Φ2, Vu2)

Facies 1 (Φ Φ1, Vu1)

Reservoir description : Net thickness and porosity

EP - Reservoir Simulation – Reservoir Description - E.M.

Depth (m TVDSS)

NTG

0.01

1

PermX (mD)

1

10,000

0.9

Initial Soil

0.33

Porosity

Reservoir Description : Example

0.1

0

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EP - Reservoir Simulation – Reservoir Description - E.M.