SEMINAR ON WATER

INFLUX AND WELL

TESTING

WATER

INFLUX

ABSTRACT

• There is more overall more water

produced in reservoirs worldwide than oil

& gas production. Thus it is clear that an

understanding of reservoir/aquifer

interaction can be an important aspect of

reservoir management to optimize

recovery of hydrocarbons.

WHAT IS WATER INFLUX

• The incursion of water (natural or

injected) into oil- or gas-bearing

formations.

• The replacement of produced fluids

by formation water.

Occurrence of Water Influx

Most petroleum reservoirs are underlain by water, and

water influx into a reservoir almost always takes place

at some rate when gas or oil is produced. Whether

appreciable ,water is produced along with gas or oil &

depends on the proximity of the productive interval to

the oil-water contact or gas-water contact and whether

the well is coning (vertical well) or cresting (horizontal

well).

As explained in Schlumberger Oilfield Glossary

CAUSES OF WATER INFLUX

• As reservoir fluids are produced and reservoir pressure

declines, a pressure differential develops from the

surrounding aquifer into the reservoir.

• Following the basic law of fluid flow in porous media, the

aquifer reacts by encroaching across the original

hydrocarbon-water contact.

• In some cases, water encroachment occurs due to

hydrodynamic conditions and recharge of the formation

by surface waters at an outcrop.

CLASSIFICATION OF AQUIFERS

• Reservoir-aquifer systems are commonly classified on

the basis of:

• Degree of pressure maintenance

• Flow regimes

• Outer boundary conditions

• Flow geometries

Degree of Pressure Maintenance

• Active water drive

ew = Qo Bo + Qg Bg + Qw Bw• Where

ew = water influx rate, bbl/day

Qo = oil flow rate, STB/day

Bo = oil formation volume factor, bbl/STB

Qg = free gas flow rate, scf/day

Bg = gas formation volume factor, bbl/scf

Qw = water flow rate, STB/day

Bw = water formation volume factor, bbl/STB

• Partial water drive

• Limited water drive

Outer Boundary Conditions

• A). Infinite system indicates that the effect of the

pressure changes at the oil/aquifer boundary can never

be felt at the outer boundary. This boundary is for all

intents and purposes at a constant pressure equal to

initial reservoir pressure.

• B). Finite system indicates that the aquifer outer limit is

affected by the influx into the oil zone and that the

pressure at this outer limit changes with time.

Flow Regimes

• There are basically three flow regimes that influence the

rate of water influx into the reservoir.

a. Steady-state

b. Semi steady (Pseudo steady)-state

c. Unsteady-state

Flow Geometries

• Reservoir-aquifer systems can be classified on the basis

of flow geometry as:

a. Edge-water drive

b. Bottom-water drive

c. Linear-water drive

Figure : Flow geometries.

RECONOCIMIENTO DE LA AFLUENCIA

DEL AGUA NATURAL

• Natural water drive may be assumed by analogy with

nearby producing reservoirs, but early reservoir

performance trends can provide clues.

• A comparatively low, and decreasing, rate of reservoir

pressure decline with increasing cumulative withdrawals

is indicative of fluid influx

CONSTANT

PRESSURE

CONSTANT

FLOW RATE

CONVINIENT

INNER

BOUNDARY

CONDITIONS

CONSTANT

PRESSURE

INFINITE

CLOSED

LINEAR RADIAL SPHERICAL

CONVINIENT

OUTER

BOUNDARY

CONDITIONS

GEOMETRIES

I8

DIFFERENT

SOLUTIONS

RESERVOIR

ENGINEERING

CONSISTS OF

UNCERTAINITIES

WATER

INFLUX

MODELS

REQUIRES

HISTORICAL

RESERVOIR

PERFORMANCE DATA

HISTORICAL WATER

INFLUX PROVIDED BY

MBE EQUATION

PROVIDED OOIP IS

KNOWN FROM PORE

VOLUME ESTIMATES

WATER INFLUX MODELS

THE MATHEMATICAL WATER INFLUX

MODELS Pot aquifer

Schilthuis’ steady-state

Hurst’s modified steady-state

The Van Everdingen-Hurst unsteady-state

a) Edge-water drive

b) Bottom-water drive

The Carter-Tracy unsteady-state

Fetkovich’s method

a) Radial aquifer

b) Linear aquifer

POT AQUIFER MODEL

• El modelo más simple que puede utilizarse para estimar

la afluencia del agua en un tanque de gas o petróleo se

basa en la definición básica de compresibilidad (ΔV = c

V Δ p). Una caída en la presión del depósito, debido a la

producción de fluidos, causa el acuífero de agua ampliar

y desembocan en el embalse. Aplicando la anterior

definición de compresibilidad básico para el acuífero da:

afluencia del agua = (compresibilidad del acuífero)

(inicial de volumen de agua)(pressure drop) o nos = (cw

+ cf) Wi (pi − p)

Based on compressibility equation concept

Schilthuis’ Steady-State Model

• Schilthuis (1936) propuso que para un acuífero que está

fluyendo bajo el régimen de flujo de estado

estacionario, el comportamiento de flujo podría ser

descrito por la ecuación de Darcy. El gasto de flujo de

agua que EW entonces puede determinarse mediante la

aplicación de la ecuación de Darcy:

Contd from previous slide…

The above relationship can be more conveniently

expressed as:

where ,ew = rate of water influx, bbl/day

k = permeability of the aquifer, md

h = thickness of the aquifer, ft

ra = radius of the aquifer, ft

re = radius of the reservoir

t = time, days

El parámetro C se llama la constante afluencia de agua y se expresa

en bbl/día/psi.

Hurst’s Modified Steady-State Model

• One of the problems associated with the Schilthuis’ steady-state

model is that as the water is drained from the aquifer, the aquifer

drainage radius ra will increase as the time increases. Hurst (1943)

proposed that the “apparent” aquifer radius ra would increase with

time and, therefore the dimensionless radius ra/re may be replaced

with a time dependent function, as: ra/re = at

Schilthuis’ Steady-

State Model

Hurst’s Modified

Steady-State Model

We consider the log of ra/re

and consider the term as

constant.

We take ra/re as not as a

constant and take

[ra/re = at]

Contd from previous slide…

The Hurst modified steady-state equation can be

written in a more simplified form as:

The Van Everdingen-Hurst Unsteady-

State Model

• Las fórmulas matemáticas que describen el flujo del sistema

de petróleo crudo en el pozo son idénticas en forma a las

ecuaciones que describen el flujo de agua de un acuífero en

un depósito cilíndrico. Cuando un pozo de petróleo es traído

en producción con un caudal constante después de un

período cerrado, el comportamiento de presión esencialmente

es controlado por la condición que fluye (estado no

estacionario) transitoria. Esta condición de flujo se define

como el período de tiempo durante el cual el límite no tiene

ningún efecto sobre el comportamiento de la presión.

Need superposition theorem here.

Based on dimensionless diffusivity equation.

Contd from previous page….

• Van Everdingen and Hurst (1949) proposed solutions to

the dimensionless diffusivity equation

for the following two reservoir-aquifer boundary conditions:

• Constant terminal rate

• Constant terminal pressure

• For the constant-terminal-rate boundary condition, the

rate of water influx is assumed constant for a given

period; and the pressure drop at the reservoir-aquifer

boundary is calculated.

Contd from previous slide….

• Van Everdingen y Hurst resolvieron la ecuación de

difusividad para el sistema acuífero-yacimiento mediante

la aplicación de la transformación de Laplace a la

ecuación. Solución authors' puede utilizarse para

determinar la afluencia del agua en los siguientes

sistemas:

• • Edge-water-drive system (radial system)

• Bottom-water-drive system

• Linear-water-drive system

The Carter-Tracy Water Influx Model

• To reduce the complexity of water influx

calculations, Carter and Tracy (1960) proposed a

calculation technique that does not require superposition

and allows direct calculation of water influx.

Carter-Tracy Water

Influx Model

Van Everdingen-Hurst

Unsteady-State Model

Assumes constant water influx

rates over each finite time interval

Does not assume constant water

influx rates over each finite time

interval

Does not need superposition concept

Contd from previous slide…..

Using the Carter-Tracy technique, the cumulative water

influx at any time, tn, can be calculated directly from the

previous value obtained at tn − 1, or:

Fetkovich’s Method

• Fetkovich (1971) desarrolló un método para describir el

comportamiento de afluencia del agua de un acuífero

finito para geometrías lineales y radiales. In many

cases, the results of this model closely match those

determined using the Van Everdingen-Hurst approach.

• Fetkovich arrived at the following equation:

Based on productivity index concept

Contd from previous slide…

• The previous equation has no practical applications

since it was derived for a constant inner boundary

pressure. To use this solution in the case in which the

boundary pressure is varying continuously as a function

of time, the superposition technique must be applied.

Rather than using superposition, Fetkovich suggested

that, if the reservoir-aquifer boundary pressure history is

divided into a finite number of time intervals, the

incremental water influx during the nth interval is:

Introduction to Well

Testing

Well Testing

Objectives

• To evaluate well condition and reservoir

characterization.

• To obtain reservoir parameters for

reservoir description.

• To determine whether all the drilled length

of oil well is also a producing zone

Contd from previous slide…

•To estimate skin factor or drilling- and

completion-related damage to an oil

well. Based upon the magnitude of the

damage, a decision regarding well

stimulation can be made.

Introduction To Well Testing

Outline

• Applications and objectives of well

testing

• Development of the diffusivity equation

• Definitions and sources for data used

in well testing

What Is A Well Test?

• A tool for reservoir evaluation and

characterization

• Investigates a much larger volume of

the reservoir than cores or logs

• Provides estimate of permeability

under in-situ conditions

• Provides estimates of near-wellbore

condition

• Provides estimates of distances to

boundaries

Types of Well Tests

q

Single-Well Multi-Well

How Is A Well Test Conducted?

35

Types of Well TestsSingle-well tests

• Drawdown (producing a well at constant rate beginning at time zero and measuring the resulting pressure response)

• Buildup (shutting a well that has been producing and measuring the resulting pressure response)

• Injection (Similar to a drawdown test. Conducted by injecting fluid into a well at constant rate beginning at time zero and measuring the resulting pressure response)

• Injection-falloff (Similar to a buildup test. Conducted by shutting in an injection well and measuring the resulting pressure response)

Multi-rate Test

Multi-well tests

• Interference tests

(producing one well at

constant rate beginning

at time zero and

measuring the resulting

pressure response at

one or more offset wells)

• Pulse tests (alternately

producing and shutting

in (“pulsing”) one well

beginning at time zero

and measuring the

resulting pressure

response at one or more

offset wells)

36

Information from Well Tests

• Reservoir information

• Extents and structure

• Permeability and skin

• Pressure

• GOR

• Samples for PVT analysis

• Production estimation

37

Well Test ApplicationsExploration

• reservoir size, hydrocarbon volume, hydrocarbon type, productivity

• (is this zone economic?, how large is the reservoir?)

Reservoir Development

• pressure, permeability, connectivity, productivity, formation damage, drive mechanism

• (what is the reservoir pressure?, how can we estimate reserves?, forecast future performance, optimize production)

Reservoir Management

• pressure, permeability, drainage, sweep efficiency, formation damage

• (is the well damaged?, stimulation treatment efficiency, why is the well not performing as expected?)

REFERENCES

• SCHLUMBERGER OILFIELD GLOSSARY

• ANSWERS.COM

• RESERVOIR ENGINEERING BY TAREK

AHMED

• PRACTICAL ENHANCED RESERVOIR

ENGINEERING

• THE WORLD WIDE WEB

Factors affecting well test

• Afterflow effect

• Wellbore storage

• Skin effect

• Boundary effect

THANK YOU