This document provides an overview of water influx and well testing. It discusses various water influx models including the Pot aquifer model, Schilthuis' steady-state model, Hurst's modified steady-state model, Van Everdingen-Hurst unsteady-state model, Carter-Tracy model, and Fetkovich's method. It also covers causes of water influx, classification of aquifers, and recognition of natural water drive. The document concludes with an introduction to well testing, covering objectives, the diffusivity equation, data used, and types of well tests.

1. SEMINAR ON WATER
INFLUX AND WELL
TESTING

2. WATER
INFLUX

3. 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.

4. 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.

5. 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

6. 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.

7. CLASSIFICATION OF AQUIFERS
• Reservoir-aquifer systems are commonly classified on
the basis of:
 • Degree of pressure maintenance
 • Flow regimes
 • Outer boundary conditions
 • Flow geometries

8. 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

9. 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.

10. 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

11. 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

12. Figure : Flow geometries.

13. 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

14. CONSTANT
PRESSURE
CONSTANT
FLOW RATE
CONVINIENT
INNER
BOUNDARY
CONDITIONS
CONSTANT
PRESSURE
INFINITE
CLOSED
LINEAR RADIAL SPHERICAL
CONVINIENT
OUTER
BOUNDARY
CONDITIONS
GEOMETRIES
I8
DIFFERENT
SOLUTIONS

15. 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

16. 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

17. 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

18. 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:

19. 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.

20. 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]

21. Contd from previous slide…
The Hurst modified steady-state equation can be
written in a more simplified form as:

22. 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.

23. 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.

24. 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

25. 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

26. 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:

27. 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

28. 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:

29. Introduction to Well
Testing

30. 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

31. 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.

32. 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

33. 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

34. Types of Well Tests
q
Single-Well Multi-Well
How Is A Well Test Conducted?

35. 35
Types of Well Tests
Single-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. 36
Information from Well Tests
• Reservoir information
• Extents and structure
• Permeability and skin
• Pressure
• GOR
• Samples for PVT analysis
• Production estimation

37. 37
Well Test Applications
Exploration
• 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?)

44. REFERENCES
• SCHLUMBERGER OILFIELD GLOSSARY
• ANSWERS.COM
• RESERVOIR ENGINEERING BY TAREK
AHMED
• PRACTICAL ENHANCED RESERVOIR
ENGINEERING
• THE WORLD WIDE WEB

45. Factors affecting well test
• Afterflow effect
• Wellbore storage
• Skin effect
• Boundary effect

46. THANK YOU