flow concepts

8/10/2019 Flow Concepts

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Fluid Flow Conceptsin Oil and Gas Reservoirs

Nature of flow in porous media

Steady state flow-- Single-phase and two-phase -- Linear and radial-- Incompressible and compressible

Transient flow-- Continuity equation -- Diffusivity equation-- Pressure distribution

pplications-- Water influx from aquifers -- Well productivity-- Reservoir simulation equations -- Well test analysis-- Water and gas coning phenomena


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Nature of Fluid Flowin Oil and Gas Reservoirs

Coning near partially-penetrating wellsSpherical r , ,3-D

Large open areas in thick reservoirsCartesian x , y , z3-D

Well in a layered reservoirRadial r , z2-D

Cross-section of a layered reservoirCartesia x , z2-D

Large open areas in thin reservoirsCartesian x , y2-D

Well in thin reservoir, Peripheral influxRadial r1-D

Core sample, Thin linear aquiferCartesian x1-D

ExamplesCoordinatesDimensions


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Coordinate Systems

x

yz

r

z

r

Cartesian

x, y , z

Radial

r, , z

Spherical

r , ,


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Examples of Reservoir Flow Types

Flow

1-D Linear

Flow

1-D Linear

Producing well

Gas

Oil

Coning 2-D Radial

Homogeneous 1-D Radial rHeterogeneous 2-D Radial r , z

3-D Spherical r , ,


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Types of Reservoir Flow

One-phase, two-phase or three-phase

Incompressible liquid or compressible gas Isothermal or variable temperature

Steady state or transient (time variations) With or without gravity and capillary effects

Constant phase compositions (black oil) orvariable composition (miscible, chemical,combustion and steam distillation)


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Steady State Single-Phase Flow

Linear, incompressible liquid


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Steady State Single-Phase Flow

Linear, compressible gas

Differential form of Darcys law:q g = - (kA / B gg)(dP/dx)

Gas formation volume factor B g = 5.04 ZT / P

Integration yields:q g = (0.703 kA (P 12 P 22) / (ZT gL)

Aq g

P 2P 1

L


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Steady State Single-Phase Radial Flow


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Steady State Two-Phase Radial Flow


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Transient Flow Equations


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Pressure Distribution


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Pressure Distribution


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Transient Pressure SolutionsSingle-phase, infinite linear system

Interior boundaryx = 0 , P = P w

Exterior boundaryx = , P = P i

Reservoir Aquifer


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Single-Phase, Infinite Linear System

Example


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Transient Pressure SolutionsSingle-phase, radial system

r e

Reservoir

Wellr w

r e

ReservoirAquifer

r w


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Transient Pressure Solutions

Single-phase, radial system Solution is presented as:

P D = f (t D , r D) for constant flow rateQ D = f (t D , r D) for constant boundary pressureP D = f (t D) for constant flow rate, infinite systemQ D = f (t D) for constant boundary pressure, infinite system

Both graphical form and tables Some solutions include exterior boundary conditions and

geometry For large values of dimensionless time (t D), simple

expressions are also presented These solutions provide basis for transient well test

analysis and water influx from aquifers


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Additional Flow Equations

Capil lary pressureP c o-w = P o P w and P c g-o = P g P o

Gravity effectIf gravity effect is significant, a pressure gradient is added :(w - o)g sin or ( w - o)g sin

FluidSaturations

EQUATIONCASE

So = 1.0 S wOil and water twophase flow

So + S w + S g = 1.0Oil, water and gas three-phase flow

So + S g = 1.0 S wiOil and gas two-phase flow

Sg = 1.0 S wWater drive gas reservoirs

Sg = 1.0 S wiConstant volume gas reservoir

So = 1.0 - S wiUndersaturated reservoirs

Sw = 1.0Aquifers

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