SEMINAR ON WATER INFLUX AND WELL

TESTINGPRESENTED BY :

Rishiraj Phukan

Rupam Sarmah

Satyajit Chowdhury

ACKNOWLEDGEMENT

• We thank our faculty Mr. Prasenjit Talukdar, Asst. Professor of Reservoir Engineering, Petroleum Engineering Department, DUIET, for giving us this opportunity to present ourselves on select topics.

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.

RECOGNITION OF NATURAL WATER INFLUX

• 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

CONSTANTPRESSURE

CONSTANT FLOW RATE

CONVINIENTINNER

BOUNDARY CONDITIONS

CONSTANT PRESSURE

INFINITE

CLOSED

LINEAR RADIAL SPHERICAL

CONVINIENTOUTER

BOUNDARY CONDITIONS

GEOMETRIES

I8DIFFERENTSOLUTIONS

RESERVOIRENGINEERING

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

• The simplest model that can be used to estimate the water influx into a gas or oil reservoir is based on the basic definition of compressibility (ΔV = c V Δ p).

• A drop in the reservoir pressure, due to the production of fluids, causes the aquifer water to expand and flow into the reservoir.

• Applying the above basic compressibility definition to the aquifer gives: Water influx = (aquifer compressibility) (initial volume of water)(pressure drop) OR We = (cw + cf) Wi (pi − p)

Based on compressibility equation concept

Schilthuis’ Steady-State Model• Schilthuis (1936) proposed that for an aquifer that is

flowing under the steady-state flow regime, the flow behaviour could be described by Darcy’s equation. The rate of water influx ew can then be determined by applying Darcy’s equation:

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, daysThe parameter C is called the water influx constant and is expressed inbbl/day/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/reand 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

• The mathematical formulations that describe the flow of crude oil system into a wellbore are identical in form to those equations that describe the flow of water from an aquifer into a cylindrical reservoir. When an oil well is brought on production at a constant flow rate after a shut-in period, the pressure behaviour is essentially controlled by the transient (unsteady-state) flowing condition. This flowing condition is defined as the time period during which the boundary has no effect on the pressure behaviour.

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 and Hurst solved the diffusivity equation for the aquifer-reservoir system by applying the Laplace transformation to the equation. The authors’ solution can be used to determine the water influx in the following systems:

• 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) developed a method of describing the

approximate water influx behaviour of a finite aquifer for radial and linear geometries. 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 TestingOutline

• 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?

36

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)

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Information from Well Tests• Reservoir information

• Extents and structure• Permeability and skin• Pressure

• GOR • Samples for PVT analysis• Production estimation

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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