Misan University

Engineering college Petroleum Department

Waterflooding Performance

Prediction

A project report submitted to the Department of Petroleum Engineering collage of

Engineering / Misan University in partial fulfillment of the requirement for the award of the degree of Bachelor of Petroleum Engineering

Prepared By :

Radhya Haneen Khalf

Hajar Tahir Hussain

Supervised By :

Dr. Munqith Aldhaheri

Dr. Haider Hasaan

May 2019

I

Dedication To those who taught us tender without waiting and ,To whom we carry their names

with all pride to

our dear fathers.

To our angel in life, To the meaning of love, To the smile of life and to whom was the secret of our

success to

our beloved mothers.

II

Acknowledgments First, thanks to Allah (God) for giving us the many blessings, opportunity, and strength to

complete this research journey. Second, we would like to exp ress our sincere gratitude to our

supervisors

Dr. Munqith Aldhaheri

Thanks are also extended to Dr. Ahmed ALSharaa College Dean of Engineering ,

Dr. Hanoon Hasan, the head of Petroleum engineering department

Special thanks to Dr. Mohammed Abd Alameer, Dr. Haider Hasaan,

Mr. Ali Noor ALdeen and for misan oil company for help us.

Many thanks to our dear colleagues friends in Petroleum Engineering Department for their helps

and encouragement to complete this work.

Finally, we would like to thank our parents, without them support, encouragement, and love this

accomplishment would have been impossible.

By:

Radhya Haneen Khalf

Hajar Tahir Hussain

III

Table of Content

Content Page

Dedication Ӏ

Acknowledgments ӀӀ

Table Of Content III

List of table Ӏѵ

List of figure ѵ

Symbols and abbreviations ѵӀ

Executive Summary ѵӀӀ

CHAPTER ONE – Introduction

1.1. Introduction 1

1.2. Factors effect on waterflooding 2

1.3. Location and History 3

1.4. Purpose of study 4

CHAPTER TWO – Literature Review

2.1. Introduction 5

2.2. Factors Affecting Waterflooding Performance 5

2.3. Practical Use of Waterflooding Prediction Methods 6

2.4. Prediction Methods Primarily Concerned with Reservoir Heterogeneity

6

2.4.1. Yuster-Suder-Calhoun method 6

2.4.2. Prats-Matthews-Jewett-Baker Method 9

2.4.3. Stiles method 8

2.4.4. Dykstra-Parsons method 01

2.5. Prediction Methods Concerned Primarily with Displacement Mechanism

00

2.5.1. Buckley and Leverett Method 12

2.5.2. Craig Geffen-Morse Method 01

2.5.3. Rapoport-Carpenter-Leas Method 13

2.5.4. Higgins-Leighton Method 02

2.6. Prediction Methods Based on Numerical Model 03

2.6.1. Douglas Blair-Wagner Method 15

2.6.2. Hiatt Method 15

2.6.3. Doglas-Peaceman-Rachford Method 04

2.6.4. Warren and Cosgrove Method 04

2.6.5. Morel-Seytoux Method 16

2.7. Prediction Methods Based on Empirical Models 05

IV

CHAPTER THREE – Theoretical Background

3.1. Introduction 17

3.2. Water flooding effectiveness 17

3.3. Oil recovery efficiency 18

3.4. Microscopic displacement efficiency 19

3.5. Fractional Flow Equation 19

3.5.1. Effect of Water and Oil Viscosities 21

3.5.2. Effect of Dip Angle and Injection Rate 22

3.5.3. Effect of Wettablity of Rock 23

3.5.4. Effect of Fluids Interfacial Tension 23

3.6. Classic Waterflooding Predictive Models 23

3.6.1. Buckley-Leverett-Welge Method 23

3.7. Oil Recovery Calculations 24

3.8.Areal sweep efficiency estimation 29

3.9. Areal sweep prediction method 30

3.6. Vertical sweep efficiency 34

3.11. Calculation of vertical sweep efficiency 34

3.12. Stiles’ Method 35

3.12.1 Procedure for Stiles Method 36

CHAPTER FOUR – Results and Discussions

4.1. Buckley-Leveret-Welge Method 37

4.2. Discussion of Buckley - Leveret –Welge results 31

4.2.Craig-Geffen-Morse Method 32

4.4. Discussion of results of CGM Method 47

4.5. Stiles Method for Stratified Reservoirs 48

4.6. Discussion of results Stiles Method 49

4.7. Comparison of Waterflooding Performance Predictions 50

4.8. Overall Discussion 53

CHAPTER FIVE – Conclusions and Recommendations

5.1. Conclusions 56

5.2. Recommendations 57

REFERENCES 58

List of table page

Tables Page

Table (4-1)values of saturation and water cut and its derivatives for EL

Tordillo oil field

38

Table (4-2)performance of EL Tordillo field for BLW before 40

V

breakthrough

Table (4-3) performance of EL Tordillo field for BLW after breakthrough

41

Table (4-4) Performance of EL Tordillo field by CGM Method before

Breakthrough

43

Table (4-5) performance of EL Tordillo field for Craig After breakthrough.

45

Table (4-6) performance of EL Tordillo field for CGM After and before breakthrough

46

Table (4-7) performance of EL Tordillo field for Stiles Method. 48

List of Figure

Figure Page

Figure (1.1 ) waterflooding 2

Figure (3-1 ) Oil recovery methods sequence in a typical oil field. 18

Figure (3-2 ) Fractional flow curves a function of saturations. 21

Figure (3-3 ) Effect of oil viscosity on fractional flow. 22

Figure (3-4) Effect of dip angle on fractional flow. 23

Figure (3-5) Idealized Layered System 35

Figure (4-1) Fractional flow curve 39

Figure (4-2) Water oil ratio (WOR) versus cumulative oil production

EL Tordillo field for BLW.

41

Figure (4-3) Reservoir performance graph of EL Tordillo field for BLW

42

Figure (4-4) Reservoir performance graph of EL Tordillo field for Craig et al

47

Figure (4-5) Reservoir performance graph of EL Tordillo field for

Stiles Method

49

Figure (4-6) oil production rate versus time, reservoir performance graph of EL Tordillo field for Simulation, BLW, CGM, and Stiles

50

Figure (4-7) Water Oil ratio versus time, reservoir performance graph

of EL Tordillo field for Simulation, BLW, CGM, and Stiles Method.

51

Figure (4-8) Cumulative water injected versus time, reservoir

performance graph of EL Tordillo field for Simulation, BLW, CGM,

and Stiles Method

52

VI

Symbols and abbreviations

Symbols Nomenclature

RF Overall Recovery Efficiency

ED Displacement Efficiency

EA Areal sweep Efficiency

EV Vertical sweep Efficiency

Fw Fraction of water in the flowing stream passing any point in

the rock, water cut ,bbl/bbl

K Absolute permeability, md

Kro Relative permeability to oil ,

Krw Relative permeability to water

A Cross sectional area,ft2

μₒ Oil viscosity ,cp

μw Water viscosity ,cp

iw Water injection rate, bbl/bbl

ρw Water density,g/cm3

ρₒ oil density,g/cm3

α Dip angle

EABT Areal sweep Efficiency at breakthrough

EvBT vertical sweep Efficiency at breakthrough

Np Cumulative oil production ,STB

Qo Oil production rate

Qw Water production rate

WORs Surface water oil ratio

Wp Cumulative water production

Winj Cumulative water injection

Ns Initial oil in place at start of flooding ,STB

M Mobility oil ratio

Bo Oil formation volume factor

Bw Water formation volume factor

(NP)BT Cumulative oil production at breakthrough ,STB

VII

Executive Summary

For decades, waterflooding has been the most applied secondary oil recovery

process around the world. Designing a waterflooding project involves deciding of

many operational variables and linking them to the economic assessments. This

design requires comparing the performances of waterflooding for different

suggested scenarios. The utilization of best waterflooding performance prediction

methods is also very important issue here.

In this study, three waterflooding performance predictions techniques were used to

estimate the water injection efficiency for the El Tordillo oil field, Argentina. The

methods included Buckley-Leverett-Welge, Craig-Geffen-Morse, and Stiles that

were coded in ready-to-use three excel spreadsheets. Then, the prediction results

were compared with the reservoir simulation to identify which method gives the

closest results to the simulated performance. We have prediction waterflooding in

every method. In Buckley-Leverett-Welge, we calculated the amount of oil

produced, the amount of water injected, the amount of water produced, before

breakthrough as well as after breakthrough and we calculated the Displacement

Efficiency. Finally, we found a prediction curve and compared the results with

simulation.in Craig et al method it was the same behavior as Buckley-Leverett-

Welge. We calculated areal sweep efficiency. finally, we found a prediction curve

and compared the results with simulation.in the Stiles Method. We calculated the

50 different layers of permeability to predict waterflooding performance and we

calculated the amount of oil produced, the amount of water injected, the amount of

water produced and water-oil ratio. finally, we calculated the prediction curve and

compare results with simulation.

Results indicated that the three methods are good in prediction of waterflooding

performance, but the nearest method to real results and value is Stiles Method.

Buckley-Leveret-Welge and Craig-Geffen-Morse methods almost have the same

behavior and results; the worst method is Buckley-Leverett-Welge method. The

results indicate that the method of Buckley-Leverett-Welge is the most method in

which the water is produced. At the moment of Breakthrough, the water will be

produced with oil water cut reaches 83%. We get 7% oil recovery factor when

injecting 10001491 barrel water.

1

Chapter one

Introduction

1.1. Introduction

Waterflooding is the method of secondary recovery that is used when making sure

that the natural methods of recovery are insufficient. It is the method of injecting

water into the oil zone and displace almost all of the oil except the residual oil

saturation from the portions of the reservoir contacted or swept by water. Extensive

waterflooding, which began in the 1940s, within a few decades became the

established method for secondary oil recovery, usually recovering about another 15

% of OOIP On average , about one - third of OOIP is recovered, leaving two-

thirds, or twice as much oil as is produced, in the ground after secondary recovery

Waterflooding considerations of Unit displacement efficiency is how water

displaces oil from a porous and permeable reservoir rock on a microscopic scale.

Calculations for determining how well waterflooding will work on a reservoir

scale must include the effects of geology, gravity, and geometry (vertical, areal,

and well-spacing/pattern arrangement).

2

figure 1.1 waterflooding

1.2. Factors effect on waterflooding

Many factors influence the success of waterflooding operations and immiscible

displacement processes. These factors can be separated into two categories, one

that refer to characteristics of the reservoir fluids and one that referred to the

formation. Reservoir characteristics that influence the efficiency of waterfloods

may include depth, porosity, fluid saturation distribution, rock structure and type,

and the degree of formation heterogeneity. This last reservoir characteristic, the

degree of formation heterogeneity, is a primary focus of this study. The

heterogeneity effect on immiscible displacement and waterflooding processes

depends on horizontal and vertical no uniformities that allow fluids to move

preferentially through the high permeability porous medium. This flow allows for

part of the oil in place to be bypassed in lower permeability areas Many prediction

methods have been created for this type of process, where fluid flow, well patterns,

3

and vertical heterogeneity are considered. Most of these methods assume

formations with homogeneous areal rock properties and include heterogeneities

only in the vertical direction. These techniques originate from Buckley and

Leverett’s work, and consist of prediction methods for waterfloods in stratified

formations. The earliest group of prediction methods in which heterogeneity of the

formation was considered includes works by Dykstra and Parsons, Stiles , and

Yuster-Suder-Calhoun. These methods have been modified and have become the

basis of other methods, such as, Higgins and Leighto, Craig-Geffen-Morse, and

Prats-Matthews-Jewett-Baker. These methods are among the most accepted

although the use of reservoir simulation has diminished the use of these prediction

techniques

1.3. Location and History

El Tordillo Field is located in Chubut Province, Argentina, approximately 50

kilometers from Comodoro Rivadavia and it is situated on the north flank San

Jorge Basin

In 1907 the San Jorge Basin yielded the first oil discovery. The El Tordillo Field,

located on the north flank of the Basin, was discovered in 1932 and was operated

by YPF from 1932 until 1991, when the UTE El Tordillo assumed operations.

Roughly 1000 wells have been drilled in the field and production is spread over

approximately 29,000 acres (117 square kilometers)

4

Since the water injection project in the field of El Tordillo has been preferred to

many options, we list below the main reasons for the selection of water injection as

follows:

Easy to provide sources of water in sufficient quantities

Cheap (low economic cost)

Variety of sources of water (superficial and juicy - tortoise and salty)

Water is considered better when compared to other fluids

Chemical homogeneous with reservoir water

less dangerous

1.4. Purpose of study

The project of waterflooding is one of the prevailing projects to maintain the

reservoir pressure and increase the extraction factor, and the importance of this

subject, it is necessary to refer to the positive results of this project and its capital

from a prominent role which is one of the most appropriate projects to support the

driving force of reservoir fluids and ways to extract them. The field of El Tordillo

is considered one of the productive fields that need to apply such a project by

reviewing the history of the production field and controlling the reservoir pressure,

noting the obvious decline at the beginning of the production, but because the field

stopped for a long period of production, Resumption of production The return of

reservoir pressure was observed again and gradually, so it is necessary to consider

the issue of water injection for planning, preparation and implementation of this

project

5

Chapter Two

Literature Review

2.1. Introduction

Secondary recovery and pressure maintenance by waterflooding is a significant

recovery process in the life of an oil field. This is a critical reservoir management

practice for optimum recovery from under saturated oil reservoirs. Varying reservoir

characteristics and limited water injection capacities make it critical to have a good

understanding of the reservoir and managing the waterflooding design and operations

to maximize the efficiency.

Predicting the performance of waterflooding can be done by methods of prediction

depends on each way and what measure. Some methods depend on the heterogeneity

of reservoirs and some on the measurement of displacement efficiency and some of

them on the numerical and mathematical models

Predicting future performance of a reservoir under existing operate conditions and/or

some alternative development plan such as infill drilling, waterflood after primary, etc.

is the final phase of a reservoir simulation study. The main objective is to determine

the optimum operating condition in order to maximize economic recovery of

hydrocarbon from the reservoir.

2.2. Factors Affecting Waterflooding Performance

Factors that affect the performance of oil recovery and which must be taken into

account and the engineer pays attention to it and we can explain factors. Is the

reservoir likely to perform as a series of dependent layers, or as zones of differing

permeability with fluid crossflow? Know there zones of high gas saturation or high

water saturation that could serve as channels for bypassing water. And does the

reservoir contain long natural fractures or directional permeability that could cause

6

preferential areal movement in some direction. And are there areas of high and of low

permeability that might cause unbalanced flood performance. And ensure of exist

crossbedding present to the degree that fluid communication between injection and

producing wells might be impaired. Is the reservoir likely to contain planes of

weakness or closed natural fractures that would open at bottom-hole injection

pressures?

Each of these questions represents factors that could cause the reservoir performance

to be drastically different from that predicted. The answers of these questions can in

many cases be determined by geological and petro physical studies, which are

important and which should be considered as prerequisite to waterflooding operations .

Even the absences of these factors that cause unfavorable performance waterflooding

frequently recover significantly less than predicted.

2.3. Practical Use of Waterflooding Prediction Methods

The practical use of waterflooding prediction methods is to forecast future oil

production performance. To use a prediction method for a reservoir about to be

waterflooded, one must be able to specify the water-oil flow properties, the initial fluid

saturations, and most importantly a description of the reservoir and its permeability

variation, both laterally and vertically. Some of this information is obtained by

measurement, some by analogy or extrapolation and the rest by guess.

Often the actual waterflood performs even in its early stages in a way quite different

from that predicted. The water injectivities do not agree with those predicted, an oil

production response obtained either earlier or later than predicted, and initial water

breakthrough occurs perhaps at different wells from those expected. Sometimes

differences in predicted and actual performance can be traced to operating problems:

casing leaks, plugged perforations, wellbore plugging by solids or bacteria. More

often, however, the difference is due to an inadequate reservoir description. Injection

surveys can be run to make certain that the injected water is confined to the desired

7

zones. Fluid level surveys will show whether the producers are pumped off. At this

point the wise reservoir engineer will turn again to his prediction method. He will

carefully examine the data he used to make his original waterflood performance

predictions, and concentrate on those reservoir characteristics that could be of doubtful

validity.

By prudently adjusting these reservoir characteristics, he can come closer and closer to

matching actual injection and production performance. When the important facets of

the actual waterflood behavior are matched, the experienced reservoir engineer will be

much more confident show whether the producers are pumped off. At this point the

wise reservoir engineer will turn again to his prediction method. He will carefully

examine the accuracy of his future performance predictions. This feedback of

information from the actual water- flood is an important part of the practical use of

waterflood prediction methods. It is precisely this incorporation of actual performance

i that makes it possible to forecast with increasing confidence the effects of future

changes in injection well location, distribution of injected water between injectors, into

the prediction technique and water and oil rates.

Prediction Methods Primarily Concerned With Reservoir Heterogeneity

Yuster-Suder-Calhoun method

Prats-Matthews-Jewett-Baker method

The Stiles method

Dykstra-Parsons method

Prediction Methods Concerned Primarily with Displacement Mechanism

Buckley and Leverett method

Craig Geffen-Morse method

Rapoport-Carpenter-Leas method

Higgins-Leighton method

8

Prediction Methods Based on Numerical Model

Douglas Blair. Wagner method

Hiatt method

Doglas Peaceman. Rachford method

Warren and Cogrove method

Morel. Seytoux method

Prediction Methods Based on Empirical Models

Guthrie Grreenberger method

Schauer method

Guerrero Earlougher method

2.4. Prediction Methods Primarily Concerned with Reservoir

Heterogeneity

2.4.1. Yuster-Suder-Calhoun method

In 1949, Yuster and Calhoun based on the developed of equations approximating the

variation in injectivity in five spot waterflooding pattern .this method was enlarged to

heterogeneity of the reservoirs could be simulated a number of layers, each layers has a

different permeability , insulated from each other .this method was assumed that the

water and oil had equal mobilities that cause the portion of the injected water entering

each layer was directly proportional to the fraction of the total flow capacity (kh) it

represents and assumed Piston-like displacement of the oil by water ,that mean there is

no flowing oil behind the flood front. , Yuster and Calhoun considered that the

waterflood through three stages:

Radial outward movement of water from the injection well with a declining

injectivity as the gas space becomes filled up, an intervening period of water injectivity

decline after interference from adjacent water injection wells until complete fill up, and

9

a final period of constant water injectivity. Muskat (1946) extended the applicability of

this method by considering the more general condition in which the water-oil mobility

ratio can range from 0.1 to 10. He also discussed the effects of both linear and

exponential permeability distributions

2.4.2. Prats-Matthews-Jewett-Baker Method

In 1959, this method based on the correlation of combined initial water injectivity is

controlled by the mobilities effects of mobility ratio and areal sweep efficiency. Using

basically the same approach of Yuster-Suder-Calhoun method, Prats et al. proposed a

more comprehensive method of predicting five- Spot waterflood performance After

water breakthrough a correlation is used that relates the injectivity with the radial

portion of the producing well invaded by water . is assumed Piston-like displacement

of oil by water. From any layer the production is either gas only during the period of

fill up, oil during the period between fillup and water breakthrough, then water and oil,

, the proportion depending upon a laboratory-developed correlation of areal sweep and

water cut. There are some assumptions of the Prats et al. method are:

Layer-cake model

the flow Steady state ,

Requires experimentally developed correlations

assume Piston-like displacement in swept area

Five-spot pattern (subject to availability of after-breakthrough sweep

correlations)

2.4.3. Stiles method

This method is commonly method of predicting waterflood behavior in stratified

reservoirs. In 1949, this method was used to measure of the vertical displacement (Ev).

Stiles proposed an approach that takes into accounting for the different flood front

positions in liquid-filled, linear layers have permeability variations each layer insulated

10

from the others, in predicting the performance of waterflood. Stiles assumes that the

volume of water injected into each layer depends only upon the kh of that layer ,This is

equivalent to assuming a mobility ratio of unity and assumes that there is piston-like

displacement of oil, so that after water breakthrough in a layer, only water is produced

from this layer. The Stiles method, therefore, contains an ambiguous condition

regarding the oil and water mobilities, it assumes a unit mobility ratio in the vertical

sweep calculations and takes into account in the calculation of producing WOR the

mobility ratio that exists. The method is subject to the following assumptions and

limitations:

1. No cross-flow between layers

2. Linear and steady-state flow

3. Equal rock and fluid properties, with the exception of absolute permeability, in all

layers

4. Piston-like displacement

5. The distance of flood front penetration into each layer is proportional to the

capacity (kh) of the layer. This is equivalent to assuming the mobility ratio is unity.

6. Fill up occurs in all layers prior to flood response

2.4.4. Dykstra-Parsons method

Dykstra-Parsons method presented a correlation between waterflood recovery and both

mobility ratio and permeability distribution. This correlation was based on calculations

applied to a layered linear model with no crossflow .In 1950 are traditionally used in

calculating the vertical sweep efficiency EV. Dykstra-Parsons developed a method of

predicting waterflood behavior in stratified systems which is particularly useful if a

rapid approximation of waterflood recovery is needed. This method requires

knowledge of the vertical permeability variation, V, the mobility ratio, M, the initial

water saturation, sw, and fractional oil recovery at a specified water - oil ratio.

11

Understand this method when Describe linear flow model consists of a series of

equal thickness layers arranged in order of decreasing permeability which depicts the

reservoir at the time of water breakthrough in the most permeable bed. In order to

describe water -oil flow behavior in this stratified system, consider it first at the time

when water has advanced a distance in the most permeable layer.

Dykstra-Parsons conducted linear waterflood tests on a large number of cores from

California sands. These cores were saturated with oil, water and gas in varying

amounts and flooded to determine fractional recovery. The method is subject to the

following assumptions and limitations:

1- layer-cake model with no crossflow between layers

2. Piston-like displacement with no oil production from behind the front

3. Linear flow

4. Steady-state flow

5. Except for absolute permeability, rock and fluid properties are the same for all

layers

6. Gas fill up occurs prior to flood response

2.5. Prediction Methods Concerned Primarily with Displacement

Mechanism

The methods considered thus far have assumed piston-like displacement behind the

water front. However, it is generally recognized that a saturation gradient does exist

behind the front and that oil production can be expected after water breakthrough from

the swept area. The following methods account for the mechanism of displacement in

predicting waterflood behavior

12

2.5.1. Buckley and Leverett Method

One of the simplest and most widely used methods of estimating advance of a fluid

displacement front in an immiscible displacement process ED in a waterflooding is the

Buckley-Leverett method. The Buckley-Leverett theory (1942) estimates the rate at

which an injected water bank moves through a porous medium then In 1952, Welge

published an approach that is widely used to perform the Buckley-Leverett frontal

advance calculation. As well as the modifications of Welge's a linear, homogeneous

reservoir. It has been shown that this method can be extended to describe the saturation

behavior in radial systems and in five-spot systems in other extensions to be described;

the method can also be applied to multilayered systems.

2.5.2. Craig Geffen-Morse Method

This prediction method is based upon the results of a series of five-spot model gas and

water drives. Craig et al. (1955) proposed performing the calculations for only one

selected layer in the multilayered system. The selected layer, identified as the base

layer, is considered to have a 100% vertical sweep efficiency. The approach is the use

of a modified Welge equation and two experimentally derived correlations .The first

correlation is that of areal sweep efficiency at breakthrough with mobility ratio. The

second relates the areal sweep efficiency after breakthrough with the logarithm of the

ratio Wi/Wibt, where W is the cumulative injected water and Wibt is that volume at

water breakthrough. The second correlation was expressed by the equation The method

considers that the average water saturation in the water-contacted portion of the pattern

is related to the cumulative injected water by a Welge-type equation modified to

consider the "displacement efficiency" caused by the increase in areal sweep.

13

2.5.3. Rapoport-Carpenter-Leas Method

Rapoport and et al. (1958) proposed as a waterflood prediction method a laboratory-

developed relationship between linear and five-spot flooding behavior. Roberts

suggested that the performance of each layer in a layered system could be computed

using Buckley-Leverett theory, with the injection into each layer being proportional to

the capacity of the layer. To predict the performance of a five-spot waterflood, a linear

laboratory waterflood is performed on the sample of the reservoir in question (or its

performance is calculated from water-oil relative permeability characteristics). The

correlation relates the linear and five-spot recoveries at the same pore volumes of

water injected through the oil-water viscosity ratio. There is no attempt to include areal

sweep except as its effect is accounted for by the oil-water viscosity ratio. The authors

established the correlation from flow tests on oil-wet glass beads, and implied that this

same correlation would apply regardless of the wettability or of the porous medium.

Assumptions and limitations are:

1. All assumptions involved in the Buckley-Leverett method apply to each layer.

2. Layer-cake model with no crossflow.

3. Injection into each layer is proportional to the fractional capacity of the layer.

4. Constant injection rate.

2.5.4. Higgins-Leighton Method

Between 1960 and 1964 This method basically applies the displacement theory of

Buckley and Leverett to any flooding pattern for which the isopotential and flow

streamlines are available. It is more complicated to use than previously discussed

methods and requires the use of a computer. To apply the method, the reservoir is

divided into flow channels based on flow streamlines as determined from

potentiometric model studies, or other methods. Each stream channel is subdivided

into equal volume cells and assuming unidirectional flow, a Buckley-Levetett type

material balance on each cell yields the rate of water accumulation and oil

14

displacement from which saturation gradients can be determined. From individually

calculated flow resistances for each cell, and the total pressure drop between wells,

instantaneous oil and water flow rates can be computed. Higgins and Leightons have

described a technique for approximating the waterflood recovery of oil using

streamlines generated by single-fluid how models (such as the method described by

Collins). Their technique uses these streamlines to divide the total flow area into

"stream channels", which flow in parallel between injection and production wells.

Each stream channel is divided into a number of recovery rectilinear flow cells, in

series, which closely approximate the shape of the stream channel. Through the use of

shape factors determined for each flow cell, a Buckley and Leverett type of frontal

displacement in each stream channel is computed. Combining the results from all

stream channels gives the waterflood production history by this method. Once the

stream channels, the flow cells, and the shape factors have been determined, a single

computer program is used to obtain the production history.

2.6. Prediction Methods Based on Numerical Model

A complete solution to the multiphase, multidimensional partial differential equations

which govern fluid flow porous and permeable media is probably the best prediction

model that we can use. Such a model can account for directional variation in fluid and

rock properties, layering effects, crossflow, gravity, capillary pressure, irregular

boundaries, individual well behavior, etc. The effects of varying injection patterns,

well locations, injection and producing rates, plus many other factors, can be studied

which were not possible using previously discussed models In general, mathematical

models are very expensive to develop and run. Furthermore, extensive amounts of data

are generally required to take advantage of the flexibility and accuracy afforded by

these models many studies simply do not justify the use of such a model.

15

2.6.1. Douglas Blair-Wagner Method

This Method one of the first papers dealing with a numerical analysis technique for

both capillary and viscous effects was that of Douglas et al (1958). The reservoir

system they simulated was linear, but it was the predecessor of a number of more

complex mathematical models.

2.6.2. Hiatt Method

Hiatt (1958) presented a detailed prediction method concerned with the vertical

coverage or vertical sweep efficiency attained by a waterflood in a stratified reservoir.

Using a Buckley-Leverett type of displacement, he considered, for the first time,

crossflow between layers. The method is applicable to any mobility ratio, but is

efficiency attained by a waterflood in a stratified reservoir difficult to apply

2.6.3. Doglas-Peaceman-Rachford Method

Douglas et al(1959) Extending the work of Douglas, Blair and Wagner in 1958.this

method presented the results of a two-dimensional mathematical model that included

the effects of relative permeability , fluid viscosities and densities, gravity, and

capillary pressure. Thus, it included all the necessary fluid flow effects and also

considered two-dimensional well pattern effects. For practical use, however, this

approach, with its completeness, requires a high-capacity, high-speed computer.

2.6.4. Warren and Cosgrove Method

Warren and Cosgrove (1964)presented an extension of Hiatt's original work. They

considered both mobility ratio and crossflow effects in a reservoir whose

permeability’s were log-normally distributed. No saturation oil by water was assumed

.The displacement process in initial gas saturation was allowed, and piston-like

displacement of each layer is represented by a sharp "pseudo interface" as in the

Dykstra-Parsons model

16

2.6.5. Morel-Seytoux Method

In (1965)This method is primarily concerned with predicting the effect of pattern

geometry and mobility ratio waterflooding recovery. Gravity and capillary effects are

neglected and displacement is assumed to be piston-like and occur at a unit mobility

ratio. However, the results can be refined to account for two-phase flow and for

mobility ratios other than unity. There are two steps to the approach: a numerical

solution to obtain the pressure distribution at a unit mobility ratio, then an analytical

technique to calculate injectivity, areal sweep at breakthrough, and subsequent

producing WOR performance.

2.7. Prediction Methods Based on Empirical Models

Several models are available which attempt to relate waterflood recovery to pertinent

project variables based on the past performance of waterfloodings. Although these

models can generally give answers that are reasonably correct, they should only be

used to make a cursory analysis of a project. They should certainly not be used as the

basis for the final design of a waterflooding.

2.7.1. Guthrie Grreenberger Method(1955)

2.7.2. Schauer method(1957)

2.7.3. Guerrero Earlougher method(1961)

71

Chapter Three

Theoretical Background

3.1. Introduction

Secondary oil Recovery essentially defined as the oil recovery by injection of water

or waterflooding. Waterflooding increase the amount of oil recovered from a

reservoir by pressure maintenance (maintain high well productivity) and

displacement of oil with water.

Usually 12 to 15% of original oil in place is produced by primary recovery

methods. Additional 15 to 20 % of oil in place is produced by secondary methods

such as water flooding. Tertiary recovery methods, such as CO2 flooding, have

been practiced with incremental oil recovery of 4 to 11 % of the original oil in place

(See figure 3.1). All the above mentioned numbers depend on the properties of oil

and the characteristics of reservoir rocks. The success of waterflooding can be

attributed to its operational simplicity, low cost and favorable displacement

characteristics. At most locations water is available or can be made available at low

cost.

Before being injected, water is usually treated to prevent plugging of the reservoir

rock and to inhibit corrosion of injection wells. Recovery efficiency of

waterfloodings can be as high as 70% of the initial-oil-in-place. Even when

conditions are optimal, waterflooding can never recover all the oil-in-place;

waterflooded rock still contains oil that is trapped in pores of the rock by capillary

forces. This so-called 'residual oil' may occupy as much as 40% of the total pore

volume of the rock.

3.2. Waterflooding Effectiveness

The efficiency of a waterflooding operation primarily depends on the following:

- Injected water is expected to provide wide coverage in contacting in-situ oil

within the injector/producer pattern.

71

- Once in-situ oil is contacted, the injected water should efficiently displace oil as

much as possible toward the producers aerially and vertically across all flow units

that may exist in the targeted formation leaving minimum oil saturation in the

reservoir.

Figure 3-1 Oil recovery methods sequence in a typical oil field.

In light of the above requirements, ultimate oil recovery from a reservoir

undergoing water injection is determined by the following: The displacement

efficiency of water displacing oil, a function of rock and fluid characteristics,

including relative permeability and viscosity of the fluid phases The areal sweep

efficiency, i.e., the fraction of the reservoir area contacted by injected water,

dependent on reservoir heterogeneity in the horizontal direction, relative location of

wells, and distance between the wells, among other factors The vertical sweep

efficiency, primarily controlled by flow units having different characteristics,

including vertical permeability across the flow units.

3.3. Oil Recovery Efficiency

The oil recovery efficiency is a measure of the fraction of the in-situ oil at the start

of waterflooding that would be recovered from the reservoir. In this context, the

71

amount of oil recovered during primary production is not considered. The equation

for overall waterflooding recovery efficiency (RF) is given by the following:

……………………………………………………. (3-1)

Where RF = overall recovery efficiency

ED=displacement efficiency

EA=areal sweep efficiency

3.4. Microscopic Displacement Efficiency

This represents the fraction of oil which water will displace in that portion of the

reservoir invaded by water:

………………………………………………….…. (3-2)

Where = average water saturation in the swept area

Sgi = initial gas saturation at the start of the flood

Swi = initial water saturation at the start of the flood

If no initial gas is present at the start of the flood, Equation 3-2 is reduced to:

3.5. Fractional Flow Equation

In 1941, leveret in his pioneering paper presented the concept of fractional flow.

Starting with the well-known Darcy's law for water and for oil, he obtained:

( ( ) )

[ ( ) ]

...…………………………….….. (3-3)

Where:

Fw = fraction of water in the flowing stream passing any point in the rock, i.e.,

water cut, bbl/bbl.

k = absolute permeability, md

02

kro = relative permeability to oil

krw = relative permeability to water

k = absolute permeability, md

A = cross-sectional area, ft2

µₒ= oil viscosity, cp

µw= water viscosity, cp

iw = water injection rate, bbl/day

ρw= water density g/cm3

ρₒ=oil density g/cm3

α=dip angle

sin(α)=positive for up dip flow and negative for down dip flow. For the further

simplification where displacement occurs in a horizontal system .when the dip angle

α is zero,

Equation (3-3) is reduced to the following simplified form:

(

)

where Kro and Krw are the relative permeabilities to oil and water, respectively.

The term fw is a function of water saturation. At increasing water saturations, the

value of kro declines, whereas that of kro rises, with the result that the value of fw

increases.

From the definition of water cut, i.e.,

( ) , Tarak Ahmed see that the

limits of the water cut are 0 and 100%. The shape of the water cut versus water

saturation curve is characteristically S-shaped, as shown in Figure (1-1). The limits

of the fw curve (0 and 1) are defined by the end points of the relative permeability

curves.

fo+fw=1 or fo=1-fw

07

The above expression indicates that during the displacement of oil by

waterflooding, an increase in fw at any point in the reservoir will cause a

proportional decrease in fo and oil mobility.

Figure 3-2 fractional flow curves a function of saturations.

The displacement efficiency is influenced by rock and fluid properties, as

detailed in the following discussion.

3.5.1. Effect of Water and Oil Viscosities

The general effect of oil viscosity on the fractional flow curve shows in figure (3-3)

for both oil –wet and water-wet .This illustration reveals that regardless of the

system wettability, a higher oil viscosity results in an upward shift (an increase) in

the fractional flow curve. The apparent effect of the water viscosity on the water

fractional flow. Higher injected water viscosities will result in an increase an overall

reduction in fw.

00

3.5.2. Effect of Dip Angle and Injection Rate

When a waterflooding is conducted in a reservoir with significant dip, the

magnitude of dip and the direction of water injection relative to the dip angle can

have considerable influence upon oil recovery. The effect of formation dip is

dictated by the gravity term, (ρᴡ-ρₒ) sinα in Eq. 1.1. When the sign of this term is

positive, the effect of gravity will be to minimize fw; this can only occur when

water displaces oil up-dip so that 0< α < 180. Conversely, when 180 < a < 360, i.e.,

when water displaces oil downdip, the effect of gravity is to decrease the

displacement efficiency. Figure 3.3 shows the effect of formation dip on the

fractional flow curve. The obvious conclusion from these observations is that water

should be injected down -dip-to obtain maximum oil recovery

Figure 3-3effect of oil viscosity on fractional flow.

02

Figure 3-4 effect of dip angle on fractional flow.

3.5.3. Effect of Wettablity of Rock

The effects of rock wettability on waterflooding , in general , water –wet rocks

perform better during the displacement of oil by injected water . in oil – wet rocks ,

however , there is atendency of in- situ oil to adhere to the pore surface , and the

resuiting displacement efficiency is poor .

3.5.4. Effect of Fluids Interfacial Tension

When interfacial tension is relatively low, displacement efficiency is generally

found to be higher . advance

3.6. Classic Waterflooding Predictive Models

3.6.1. Buckley-Leverett-Welge Method

Buckley and Leverett (1942) developed a mathematical approach to describe two-

phase, immiscible displacement in a linear system. In a differential element of

porous media, the frontal advance theory maintains that mass is conserved:

Volume of fluid entering – Volume of fluid leaving = Change in fluid volume

The buckley –leverett theory includes important assumptions :

1- Single layer homogenous reservoir

02

2- Capillary pressure effects are negligible

3- No free gas saturation in the reservoir at any time

4- Incompressible fluids

5- Steady-state flow conditions

6- Two immiscible fluids

7- Tilted-linear prous media

8- Piston like displacement

3.7. Oil Recovery Calculations:

The main objective of performing oil recovery calculations is to generate a set of

performance curves under a specific water-injection scenario. A set of performance

curves is defined as the graphical presentation of the time-related oil recovery

calculations in terms of:

1. Oil production rate, Qo

2. Water production rate, Qw

3. Surface water–oil ratio, WORs

4. Cumulative oil production, Np

5. Cumulative water production, Wp

6. Cumulative water injected, Winj

7. Water-injection rate, iw

In general, oil recovery calculations are divided into two parts: (1) before

breakthrough calculations and (2) after breakthrough calculations. Regardless of the

stage of the waterflooding, i.e., before or after breakthrough, the cumulative oil

production is given previously by Equation (3-4):

Np=Ns * ED * EA* Ev …………………………………………………. (3-4)

Where

Np = cumulative oil production, STB

NS = initial oil in place at start of the flood, STB

ED = displacement efficiency

02

EA = areal sweep efficiency

EV = vertical sweep efficiency

The displacement efficiency when Sgi = 0 is given by:

……………………………………………………………. (3-5)

At breakthrough, the ED can be calculated by determining the average water

saturation at breakthrough:

……………………………………………………..…. (3-6)

Where EDBT = displacement efficiency at breakthrough

= average water saturation at breakthrough

The cumulative oil production at breakthrough is then given by:

( ) …………………………...….. (3-7)

where (Np)BT = cumulative oil production at breakthrough, STB

EABT and EVBT = areal and vertical sweep efficiencies at breakthrough

Assuming EA and EV are 100%, Equation 3-7 is reduced to:

( ) ……………………………………………….… (3-8)

Before breakthrough occurs, the oil recovery calculations are simple when

assuming that no free gas exists at the start of the flood, i.e., Sgi = 0. The

cumulative oil production is simply equal to the volume of water injected with no

water production during this phase (Wp = 0 and Qw = 0). Oil recovery calculations

after breakthrough are based on determining ED at various assumed values of water

saturations at the producing well. The specific steps of performing complete oil

recovery calculations are composed of three stages:

1. Data preparation

2. Recovery performance to breakthrough

3. Recovery performance after breakthrough Stage

02

Stage 1: Data Preparation

1- Plot the ratio of relative permeability kro/krw versus water saturations on a semi-

log scale.

2- Assuming that the resulting plot of relative permeability ratio, kro/krw vs. Sw,

forms a straight-line relationship, determine values of the coefficients a and b of

the straight line. Express the straight-line relationship in the form given by

Equation:

………………………………………………………….. (3-9)

3- Calculate and plot the fractional flow curve ( fw,vs. sw), but neglecting the

capillary pressure gradient.

4- Select several values of water saturations between Swf and (1 – Sor) and

determine the slope (dfw/dSw) at each saturation.

(

)

(

)

[ (

) ]

……………………………………………... (3-10)

5- Prepare a plot of the calculated values of the slope (dfw/dSw) versus Sw on a

Cartesian scale and draw a smooth curve through the points.

Stage 2: Recovery Performance to Breakthrough (Sgi = 0, EA, EV = 100%)

1- Draw a tangent to the fractional flow curve as originated from Swi and

determine:

- Point of tangency with the coordinate (Swf, fwf)

- Average water saturation at breakthrough by extending the tangent line to fw =

1.0

- Slope of the tangent line (

)

2- Calculate pore volumes of water injected at breakthrough

(

)

( ) …………………………………. (3-11)

3- Calculate cumulative water injected at breakthrough

( ) …………………………………...….. (3-12)

01

4- Calculate the displacement efficiency at breakthrough

………………………………………………...….. (3-13)

5- Calculate cumulative oil production at breakthrough

( ) ) ……………………..…………………….….. (3-14)

6- Assuming a constant water-injection rate, calculate time to breakthrough

……………………………………………………….…… (3-15)

7- Select several values of injection time less than the breakthrough time, i.e., t <

tBT, and set:

Winj = iw * t

Qo = iw/Bo

WOR = 0

Wp = 0

…………………………………………………….. (3-16)

8- Calculate the surface water–oil ratio WORs exactly at breakthrough

(

)

……………………………………………….… (3-17)

where fwBT = fwf is the water cut at breakthrough

Stage 3: Recovery Performance After Breakthrough (Sgi = 0, EA, EV = 100%)

1- Select six to eight different values of Sw2 (i.e., Sw at the producing well)

between SwBT and (1 – Sor) and determine (dfw/dSw) values corresponding to

these Sw2 points.

2- For each selected value of Sw2, calculate the corresponding reservoir water cut

and average water saturation

(

)

…………………………………………...……. (3-18)

01

(

)

………………………………………………... (3-19)

3- Calculate the displacement efficiency ED for each selected value of Sw2:

………………………………………………………….. (3-20)

4- Calculate cumulative oil production Np for each selected value of Sw2 or: NP =

Ns ED EA EV

Assuming EA and EV are equal to 100%, then:

Np = Ns * ED

5- Determine pore volumes of water injected, Qi, for each selected value of Sw2

(

)

………………………………………………………….. (3-21)

6- Calculate cumulative water injected for each selected value of Sw2

……………………………………………………… (3-22)

( ) ………………………………………….. (3-23)

7- Assuming a constant water-injection rate iw, calculate the time t to inject Winj

barrels of

……………………………………………………………...… (3-24)

8- Calculate cumulative water production WP at any time t

……………………………………………………… (3-25)

9- Calculate the surface water–oil ratio WORs that corresponds to each value of

fw2:

(

)

……………………………………………………. (3-26)

10- Calculate the oil and water flow rates

…………………………………………………….. (3-27)

and

01

…………………………………………………… (3-28)

Where

Qo=oil flowrate STB/day

Qw=waterflow rate STB/day

iw=water injection rate bb/day

3.8. Areal Sweep Efficiency Estimation

EA is the horizontal portion of the reservoir that is contacted by water and is

primarily a function of the following variables:

1. Mobility Ratio

2. Reservoir heterogeneity (anisotrophy)

3. Cumulative volume of water injected

4. Waterflooding pattern configuration

1. Water mobility (krw/µw) increases after water breakthrough due to the increase in

the average reservoir water saturation and its continuity from the injection wells to

the offset producing wells.

2. Lower mobility ratios will increase areal sweep efficiency while higher mobility

ratios will decrease it.

3. Studies have shown that continued water injection can, over time, significantly

increase areal sweep efficiency, particularly in reservoirs with an adverse mobility

ratio.

4. In a tilted reservoir, areal efficiency is improved when the injection well is

located downdip (displacing oil updip).

5. Examples of reservoir heterogeneities that are always present to some degree

include:

a. Permeability anisotrophy (directional permeability);

b. Fractures

22

c. Flow barriers

d. Uneven permeability/porosity distribution.

EA typically increases from zero at the time of initial water injection until water

breakthrough. After water breakthrough, EA continues to increase, although at a

slower rate.

3.9. Areal Sweep Prediction Methods

Methods of predicting the areal sweep efficiency are essentially divided into the

following three phases of the flood:

• Before breakthrough

( ) …………………………………. (3-29)

where Winj = cumulative water injected, bbl (PV) = flood pattern pore volume, bbl

• At breakthrough

….. (3-30)

• After breakthrough

(

)……………………………………..… (3-31)

To include the areal sweep efficiency in waterflooding calculations, the

proposed methodology is divided into the following three phases:

1. Initial calculations

2. Recovery performance calculations to breakthrough

3. Recovery performance calculations after breakthrough the specific steps of each

of the above three phases are summarized below.

Initial Calculations (Sgi = 0, EV = 100%)

27

1- Express the relative permeability data as relative permeability ratios and plot

them versus their corresponding water saturations on a semi-log scale.

Describe the resulting straight line by the following relationship:

………………………………… (3-32)

2- Calculate and plot fw versus Sw.

3- Draw a tangent to the fractional flow curve as originated from Swi and

determine:

• Point of tangency (Swf, fwf), i.e., (SwBT, fwBT)

• Average water saturation at breakthrough

• Slope of the tangent (

)

4- Using Swi and determine the corresponding values of kro and krw.

Designate these values kro@SwBT and kro@ , respectively.

5- Calculate the mobility ratio as defined by Equation (3-33):

6- Select several water saturations Sw2 between Swf and (1 – Sor) and

determine the slope(

) at each saturation.

7- Plot (

) sus Sw2 on a Cartesian scale.

Phase 2: Recovery Performance to Breakthrough Assuming that the vertical

sweep efficiency EV and initial gas saturation Sgi are 100 and 0%, respectively

1- Calculate the areal sweep efficiency at breakthrough EABT

2- Calculate pore volumes of water injected at breakthrough

(

)

( )……………………………….. (3-34)

3- Calculate cumulative water injected at breakthrough WiBT

…………………………………….……. (3-35)

20

4- Assuming a constant water-injection rate iw, calculate time to breakthrough tBT:

………………………………………………………………. (3-36)

5- Calculate the displacement efficiency at breakthrough EDBT from

( )

…………………………………………………… (3-37)

6- Compute the cumulative oil production at breakthrough

( ) …………………………………. (3-38)

Notice that when Sgi = 0, the cumulative oil produced at breakthrough is equal to

cumulative water injected at breakthrough, or:

( )

……………………………………………… (3-39)

Recovery Performance After Breakthrough (Sgi = 0, EV = 100%)

1- Select several values of Winj > WiBT.

2- Assuming constant injection rate iw, calculate the time t required to inject Winj

barrels of water.

3- Calculate the ratio Winj/WiBT for each selected Winj.

4- Calculate the areal sweep efficiency EA at each selected Winj.

5- Calculate the ratio Winj/WiBT for each selected Winj.

6- Determine the total pore volumes of water injected

(

) …………………………………………………….. (3-40)

7- determine the slope (

) for each value of Qi by:

(

) ……………………………………………………………... (3-41)

8- Read the value of Sw2, i.e., water saturation at the producing well, that

corresponds to each slope from the plot of (dfw/dSw)Sw2 vs. Sw2.

9- Calculate the reservoir water cut at the producing well fw2 for each Sw2 by

equation (3-42) or equation (3-43)

22

(

)

or

(

)

10- Determine the average water saturation in the swept area

(

)

11- Calculate the displacement efficiency ED for each :

12- Calculate cumulative oil production

…………………………………………… (3-44)

For 100% vertical sweep efficiency:

Np=Ns * ED * EA ………………………………………………….…. (3-45)

13- Calculate cumulative water production

14- Calculate the surface water–oil ratio WORs that corresponds to each value of

fw2.

( ( ) )

[ ( ( ) )](

) …………………………………... (3-46)

15- Calculate the oil and water flow rates from Equations 3-47 and 3-48,

respectively:

and

22

3.10. VERTICAL SWEEP EFFICIENCY

The vertical sweep efficiency, EV, is defined as the fraction of the vertical section

of the pay zone that is the injection fluid. This particular sweep efficiency depends

primarily on (1) the mobility ratio and (2) total volume injected.

3.11. Calculation of Vertical Sweep Efficiency

Basically two methods are traditionally used in calculating the vertical sweep

efficiency EV: (1) Stiles’ method and (2) the Dykstra–Parsons method. These two

methods assume that the reservoir is composed of an idealized layered system, as

shown schematically in Figure 14-50. The layered system is selected based on the

permeability ordering approach with layers arranged in order of descending

permeability. The common assumptions of both methods are:

22

Figure 3-5 Idealized Layered System.

3.12. Stiles’ Method

Stiles (1949) proposed an approach that takes into account the effect of permeability

variations in predicting the performance of waterfloodings. Stiles assumes:

1- The layers are of constant thickness and are continuous between the injection

well and offset producing wells.

2- Linear system with no crossflow or segregation of fluids in the layers.

3- Piston-like displacement with no oil produced behind the flood front.

4- Constant porosity and fluid saturations.

5- In all layers, the same relative permeability to oil ahead of the flood front and

relative permeability to water behind the flood front.

22

6- Except for absolute permeability, the reservoir rock and fluid characteristics are

the same in all layers.

7- The position of the flood front in a layer is directly proportional the absolute

permeability of the layer

3.12.1 Procedure for Stiles Method

1- We divide a total thickness Assuming h = 1 ft for each layer.

2- Divide the permeability profile into layer of equal thicknesses and select a

representative permeability for each layer.

3- Calculate the cumulative thickness, h, and fractional thickness, ht, for the

layer.

4- Determine the dimensionless permeability ,ki, for each layer and sum of all

dimensionless permeability, ks:

…………………………………………………………...… (3-49)

∑ ………………………………………………………….… (3-50)

Where

Ki = permeability to water for a layer, md, and Kavg = average water permeability

of all layer, md.

5- Determine the incremental permeability or capacity, Fpi of each layer:

………………………………………………………………. (3-51)

6- calculate the coverage ,Ce:

………………………………………...………….…… (3-52)

7- Calculate the water/oil ratio, WOR:

( ) ……………..……………………………...… (3-53)

Where

M = mobility ratio ,and Bo=Oil formation volume factor ,bbl/STB

21

8- Estimate the product of ki*∑hi for layer.

9- Estimate the product of ∑ki*hi for layer.

10- Estimate the product of ht*ki for layer.

11- Calculate Ev:

∑

∑ ( )

………………………………………...… (3-53)

83

Chapter Four

Results and Discussions

In this chapter, the results of the current study are presented and discussed.

We made calculations on EL Tordillo field located in Chubut province, Argentina.

The following assumptions:

1- The viscosity of oil 2cp and the viscosity of water 1cp.

2- The gas saturation (Sg) = 0.

3- The water formation volume factor = 1(RB/STB).

4.1. Buckley-Leveret-Welge Method

Table (4-1) values of saturation and water cut and its derivatives for EL

Tordillo oil field.

Sw Fw dfw/dSw

0.2 0 0

0.25 0.043 0.77

0.30 0.103 1.74

0.35 0.228 3.31

0.40 0.430 4.62

0.45 0.660 4.23

0.50 0.833 2.63

0.55 0.927 1.27

0.60 0.970 0.54

0.65 0.988 0.22

0.70 0.995 0.09

0.80 0.999 0.01

83

Figure (4-1) Fractional flow curve.

From s-shap curve, we get the following information:

dfw/dSw at swf 2.78

fwf 0.83

Swf 0.5

- Summary of reservoir performance to the point of water breakthrough:

We need first to assume that EA = EV = 100% and gas saturation = 0 in order to use

the BLW method.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

wa

ter

cu

t,fw

,fra

cti

on

water saturation ,sw, fraction

04

Table (4-2) performance of EL Tordillo field for BLW before breakthrough.

t, days Winj, bbl Np Qo WORs Qw Wp

0 0 0 1389 0 0 0

100 150000 138889 1389 0 0 0

200 300000 277778 1389 0 0 0

300 450000 416667 1389 0 0 0

400 600000 555556 1389 0 0 0

500 750000 694444 1389 0 0 0

600 900000 833333 1389 0 0 0

700 1050000 972222 1389 0 0 0

800 1200000 1111111 1389 0 0 0

860.5 1290677 1,195,071 1389 5.3 7324 0

Now, we can construct a table for reservoir performance after water breakthrough:

Sw2 fw2 dfw/dSw Qi Sw2 avg Ed

0.50 0.833 2.63 0.38 0.564 0.455

0.55 0.927 1.27 0.79 0.607 0.509

0.60 0.970 0.54 1.84 0.655 0.568

0.65 0.988 0.22 4.56 0.704 0.630

0.70 0.995 0.09 11.52 0.753 0.692

0.80 0.999 0.01 75.18 0.853 0.816

04

Table (4-3) performance of EL Tordillo field for BLW after breakthrough.

Np, STB Winj, bbl Time, Days Wp, bbl WORs Qo, bpd Qw, bpd

1207590 1,365,028 910 60831 5.37 233 1248.76

1351940 2,821,861 1,881 1361765 13.77 101 1390.886

1509487 6,608,849 4,406 4978603 35.31 41 1455.478

1672180 16,340,745 10,894 14534790 90.55 16 1482.319

1836880 41,306,827 27,538 39322997 232.21 6 1493.056

2168149 269,552,011 179,701 267210410 1527.31 1 1498.94

Figure (4-2) Water oil ratio (WOR) versus cumulative oil production EL

Tordillo field for BLW.

-20

0

20

40

60

80

100

0 500000 1000000 1500000 2000000

Np

WOR

WOR-NP

04

Figure (4-3) reservoir performance graph of EL Tordillo field for BLW.

4.2. Discussion of Buckley - Leveret –Welge results

1- Before breakthrough there is no water produces at the surface from the producer

well.

2- At the moment of Breakthrough the water will be produced with oil becomes

water cut=83%.

3- A part of the water we produce is processed and re-injected and another section

is not treated.

4- We need to extract oil as much as we can before breakthrough because after

breakthrough a big problem will occur.

0

50000000

100000000

150000000

200000000

250000000

300000000

0

1000

2000

3000

4000

5000

6000

7000

8000

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

Qo

,Qw

,WO

R,N

p,W

p,W

inj

t(days)

Performance Curves of EL Tordilo field

Qo

Qw

WO

RNp

Wp

08

5- We started the water injection and we arrived moment of breakthrough injectors

Winj = 1290677bbl water and we produced Np = 1,195,071 STB there is no

water production.

6- After breakthrough the amount of water injected will be large Winj=

41,306,827bbl compare to the amount of oil produced Np= 1,836,880 STB.

4.3. Craig-Geffen-Morse Method

Table (4-4) Performance of EL Tordillo field by CGM Method before

Breakthrough.

Winj, bbl Time, days Np, STB Qo, bpd WORs Qw, bpd Wp, bbl

0 0 0 0 0 0 0

20000 13.33333 18518.52 1388.889 0 0 0

80000 53.33333 74074.07 1388.889 0 0 0

103020 68.68 95388.89 1388.889 0 0 0

203480 135.6533 188407.4 1388.889 0 0 0

648410 432.2733 600379.6 1388.889 0.89 1236.111 0

00

Winj, bbl T, days Winj/WiBt EA Qi/QiBt (Qi/QiBT)QiBT

648410 432.27 1 0.502 1.0 0.36

969020 646.01 1.494456 0.613 1.4410 0.518774

975146 650.10 1.503903 0.615 1.4484 0.521419

987990 658.66 1.523712 0.618 1.4638 0.526954

998817 665.88 1.54041 0.621 1.4767 0.531609

1030200 686.80 1.58881 0.630 1.5140 0.545049

1545300 1030.20 2.383214 0.741 2.1001 0.756033

2030200 1353.47 3.131044 0.816 2.6175 0.942305

3050200 2033.47 4.704122 0.928 3.6354 1.308761

3959876 2639.92 6.107056 1.000 4.4878 1.61561

3960000 2640.00 6.107247 1.000 4.4879 1.615651

3957300 2638.20 6.103083 1.000 4.4854 1.614762

3964796 2643.20 6.114644 1.000 4.4913 1.616853

3959999 2640.00 6.107245 1.000 4.4879 1.615651

dfw/dsw sw2 fw2 sw2

average ED NP

2.777778 0.5 0.832507 0.560298 0.450372 600876.09

1.927622 0.592 0.965657 0.609816 0.51227 833717.47

1.917844 0.607 0.973889 0.620615 0.525768 858104.4

1.897698 0.624 0.980907 0.634061 0.542576 890720.17

1.88108 0.634 0.984133 0.642435 0.553044 912304.68

1.834699 0.643 0.986574 0.650318 0.562897 941272.76

1.322693 0.662 0.990575 0.669126 0.586407 1154174.3

1.061228 0.675 0.992607 0.681966 0.602458 1305806.3

0.764081 0.697 0.995103 0.703409 0.629262 1550915.2

0.618961 0.711 0.996234 0.717085 0.646356 1716213.4

0.618946 0.722 0.996936 0.72695 0.658687 1748970.2

0.619286 0.737 0.997689 0.740732 0.675915 1794378.2

0.618486 0.75 0.99819 0.752927 0.691159 1835800.2

0.618946 0.777 0.998911 0.77876 0.72345 1920930.8

04

Table (4-5) performance of EL Tordillo field for Craig After breakthrough.

Wp, bbl (NP)NEWLY ƛ WORs Qo, bpd Qw, bps RF

0 0.455977 0.2749 0.894057 759.8566 679.3548 0.226258

68605.1 0.305112 0.183947 2.202907 456.9121 1006.535 0.313933

48393.22 0.303195 0.182791 2.280408 446.3743 1017.916 0.323116

26012.19 0.299254 0.180415 2.374529 434.2126 1031.05 0.335398

13527.92 0.29601 0.178459 2.435852 426.6391 1039.23 0.343525

13625.39 0.286993 0.173023 2.561692 411.8965 1055.152 0.354433

298791.7 0.191328 0.115348 4.348498 276.3195 1201.575 0.4346

619929.1 0.145631 0.087798 6.02773 211.0378 1272.079 0.491697

1375212 0.096931 0.058438 9.575747 140.7691 1347.969 0.583992

2106366 0.074664 0.045014 5.368027 232.6293 1248.76 0.646234

2071112 0.074662 0.045012 30.36748 47.69857 1448.486 0.658569

2019371 0.074713 0.045043 40.28231 36.2649 1460.834 0.675667

1982132 0.074571 0.044958 55.48565 26.51786 1471.361 0.691264

1885394 0.074662 0.045012 66.98605 22.03742 1476.2 0.72332

04

- Summary of reservoir performance of EL Tordillo field for Craig (before

and after breakthrough) Assume EV=100% and gas saturation=0.

Table (4-6) performance of EL Tordillo field for CGM After and before

breakthrough.

Winj, bbl Time, days Np, STB Qo, bpd WORs Qw, bpd Wp, bbl

0 0 0 0 0 0 0

20000 13.33333 18518.52 1388.889 0 0 0

80000 53.33333 74074.07 1388.889 0 0 0

103020 68.68 95388.89 1388.889 0 0 0

203480 135.6533 188407.4 1388.889 0 0 0

648410 432.2733 600379.6 1388.889 0.89 1236.111 0

648410 432.2733 600876.1 759.8566 0.894057 679.3548 0

969020 646.0133 833717.5 456.9121 2.202907 1006.535 68605.1

975146 650.0973 858104.4 446.3743 2.280408 1017.916 48393.22

987990 658.66 890720.2 434.2126 2.374529 1031.05 26012.19

998817 665.878 912304.7 426.6391 2.435852 1039.23 13527.92

1030200 686.8 941272.8 411.8965 2.561692 1055.152 13625.39

1545300 1030.2 1154174 276.3195 4.348498 1201.575 298791.7

2030200 1353.467 1305806 211.0378 6.02773 1272.079 619929.1

3050200 2033.467 1550915 140.7691 9.575747 1347.969 1375212

3959876 2639.917 1716213 232.6293 15.36803 1248.76 2106366

3960000 2640 1748970 47.69857 30.36748 1448.486 2071112

3957300 2638.2 1794378 36.2649 40.28231 1460.834 2019371

3964796 2643.197 1835800 26.51786 55.48565 1471.361 1982132

04

3959999 2639.999 1920931 22.03742 66.98605 1476.2 1885394

Figure (4-4) reservoir performance graph of EL Tordillo field for Craig et al.

4.4. Discussion of results of CGM Method

1- The method of Craig is the same of behavior and assumption of Buckley -

Leveret –Welge method.

2- The primary objective of this method to calculate areal sweep efficiency.

3- We started the water injection and we arrived moment of breakthrough injectors

Winj = 648410 bbl water and we produced Np = 600876 STB there is no water

production wp = 0.

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

0

100

200

300

400

500

600

700

0 500 1000 1500 2000 2500 3000 3500

Qo

,Qw

,WO

R'N

p,W

p,W

inj

t(day)

Performance Curves For El Trodillo Oil Field by CGM Method Qo

Qw

WOR

Np

03

4- After breakthrough the amount of water injected will be large Winj= 3959999

bbl. compare to the amount of oil produced Np= 1920931STB, Wp=1885394

bbl.

4.5. Stiles Method for Stratified Reservoirs

Table (4-7) performance of EL Tordillo field for Stiles Method.

hi(ft) ki(md) ∑ki∆hi hi*ki R NP ∆NP Fw qo t wi fw′

1 3541 3541 3541 0.140503 261194.5 261194.5 0.276 1005.556 307.7514 461627.136 0.623531

2 2858 6399 5716 0.1693 314729.1 53534.6 0.605301 548.1931 405.4079 608111.829 0.775585

3 2240 8639 6720 0.204973 381045.2 66316.12 0.761906 330.6863 605.9487 908923.122 0.841509

4 1833 10472 7332 0.237163 440886.2 59841.04 0.830973 234.7602 860.8515 1291277.26 0.878862

5 1491 11963 7455 0.273213 507902.2 67016 0.870427 179.9623 1233.241 1849861.02 0.902392

6 1273 13236 7638 0.302875 563044.8 55142.57 0.8954 145.2779 1612.807 2419210.1 0.919012

7 1085 14321 7595 0.334562 621951.2 58906.34 0.913096 120.7002 2100.845 3151267.64 0.931223

8 955 15276 7640 0.361047 671186.6 49235.44 0.926127 102.6009 2580.719 3871077.82 0.940756

9 847 16123 7623 0.386682 718842.6 47656 0.936319 88.44651 3119.53 4679295.09 0.948405

10 750 16873 7500 0.413413 768535.4 49692.79 0.944506 77.07463 3764.266 5646399.1 0.954627

11 673 17546 7403 0.437831 813927.1 45391.72 0.951174 67.8135 4433.627 6650440.73 0.959819

12 607 18153 7284 0.461516 857957.6 44030.49 0.956744 60.07821 5166.513 7749770.05 0.964216

13 555 18708 7215 0.48227 896540.4 38582.84 0.961463 53.5233 5887.374 8831060.86 0.968018

14 509 19217 7126 0.502358 933882.7 37342.28 0.965548 47.85047 6667.769 10001653.6 0.971337

15 464 19681 6960 0.523922 973971.8 40089.06 0.969114 42.89678 7602.316 11403474.2 0.974231

16 425 20106 6800 0.544471 1012171 38199.06 0.972226 38.57459 8592.581 12888871.4 0.976778

17 390 20496 6630 0.564615 1049620 37449.18 0.974967 34.76788 9669.701 14504551.3 0.979034

18 367 20863 6606 0.578692 1075789 26168.61 0.977395 31.39574 10503.21 15754814 0.981089

19 335 21198 6365 0.599582 1114623 38834.49 0.979607 28.32305 11874.34 17811504.3 0.98291

20 308 21506 6160 0.618831 1150407 35784.04 0.981568 25.59958 13272.17 19908259.5 0.98454

21 290 21796 6090 0.632414 1175657 25250.1 0.983324 23.16127 14362.36 21543538.8 0.986037

22 264 22060 5808 0.653333 1214547 38889.43 0.984937 20.92078 16221.25 24331873.3 0.98737

23 243 22303 5589 0.67177 1248820 34272.92 0.986373 18.92622 18032.12 27048178 0.988572

24 230 22533 5520 0.683739 1271071 22251.46 0.987669 17.12708 19331.32 28996974.2 0.989688

25 210 22743 5250 0.703143 1307143 36071.53 0.988872 15.45571 21665.18 32497771.5 0.990689

26 197 22940 5122 0.716548 1332063 24920.58 0.989952 13.95574 23450.87 35176302.1 0.991614

27 182 23122 4914 0.732747 1362177 30114 0.990949 12.57068 25846.44 38769662.9 0.992456

28 169 23291 4732 0.747574 1389740 27562.86 0.991857 11.30964 28283.55 42425330.3 0.993227

29 158 23449 4582 0.760633 1414017 24276.58 0.992689 10.1543 30674.32 46011484.6 0.993939

30 145 23594 4350 0.776828 1444122 30105.9 0.993457 9.087496 33987.22 50980823.6 0.994585

31 133 23727 4123 0.792782 1473782 29659.17 0.994154 8.119618 37639.99 56459992.4 0.995171

32 125 23852 4000 0.80384 1494339 20556.91 0.994786 7.241067 40478.93 60718392.1 0.995716

33 114 23966 3762 0.819649 1523728 29389.16 0.995375 6.42329 45054.33 67581501.3 0.996209

34 106 24072 3604 0.831698 1546127 22399.07 0.995907 5.684082 48995 73492501.1 0.996664

35 97 24169 3395 0.845773 1572292 26165.58 0.996398 5.002331 54225.68 81338517.5 0.997077

36 90 24259 3240 0.857111 1593370 21077.18 0.996844 4.383122 59034.39 88551590.5 0.997458

37 83 24342 3071 0.868675 1614866 21496.71 0.997255 3.812537 64672.82 97009231.2 0.997807

38 75 24417 2850 0.8824 1640382 25515.33 0.997631 3.289657 72429.05 108643410 0.99812

39 69 24486 2691 0.893043 1660168 19786.23 0.99797 2.819897 79445.7 119168382 0.998406

40 63 24549 2520 0.90381 1680182 20014.08 0.998279 2.38998 87819.86 131729623 0.998667

41 57 24606 2337 0.914737 1700496 20313.88 0.99856 1.999327 97980.22 146970164 0.998902

42 51 24657 2142 0.925882 1721215 20719.5 0.998814 1.647414 110557.2 165835641 0.999111

43 45 24702 1935 0.937333 1742503 21287.37 0.99904 1.333774 126517.5 189776027 0.999295

44 39 24741 1716 0.949231 1764620 22117.33 0.999238 1.05799 147422.5 221133756 0.999454

45 34 24775 1530 0.959412 1783546 18926.47 0.99941 0.819701 170512 255767962 0.999592

46 29 24804 1334 0.969655 1802589 19042.49 0.999559 0.612508 201601.4 302402044 0.999709

47 24 24828 1128 0.98 1821820 19231.03 0.999686 0.436184 245690.6 368535925 0.999806

48 20 24848 960 0.988 1836692 14872 0.999791 0.290539 296878.3 445317402 0.999887

49 16 24864 784 0.995 1849705 13013 0.999878 0.169359 373714.9 560572336 0.999952

50 12 24876 600 1 1859000 9295 0.999948 0.072541 501849.5 7.5277E+08 1

03

Figure (4-5) reservoir performance graph of EL Tordillo field for Stiles

Method.

4.6. Discussion of results Stiles Method:

1- This method assumes that there is piston-like displacement of oil, so that after

water breakthrough in a layer only water is produced from this layer.

2- The results in Stiles Method are expected and more trusted to reality in a multi -

layer reservoir up to mobility ratio of about 10.

3- The cumulative water injected Winj large compared cumulative oil production

Np, when the Winj=1849698bbl the Np=507902 STB.

4- We get 7% oil recovery when winj=10001491bbl.

0

100

200

300

400

500

600

0.01

0.1

1

10

100

1000

10000

100000

1000000

10000000

0 100 200 300 400

Wi, m

illion

s of b

arre

ls

Qo

,WO

R,N

p

Time, thousands of days

Performance Curve For El Tordillo Oil Field by Stiles Method

Qo

WORs

Np

Wi

44

5- At the beginning of production the oil flow rate Qo=1006.9 STB/day and

continues to decrease through production.

4.7. Comparison of Waterflooding Performance Predictions

In this section, we compared the results from the three waterflooding performance

prediction methods (BLW, CGM, Stiles)with the reservoir simulation results as

shown in figure below.

10

100

1000

10000

1 10 100 1000

Qil

Pro

du

cti

on

Ra

te, b

pd

Time from Waterflooding Initiation, months

Simulation

BLW

CGM

Stiles

44

Figure (4-6) oil production rate versus time, reservoir performance graph of EL

Tordillo field for Simulation, BLW, CGM, and Stiles.

Figure (4-7) Water Oil ratio versus time, reservoir performance graph of EL

Tordillo field for Simulation, BLW, CGM, and Stiles Method.

0

10

20

30

40

50

60

0 0.5 1 1.5 2

Wa

ter-

Oil

Ra

tio

Cumulative Oil Production, millions of STB

Simulation BLW CGM Stiles

44

Figure (4-8) Cumulative water injected versus time, reservoir performance graph of

EL Tordillo field for Simulation, BLW, CGM, and Stiles Method.

0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350 400

Cu

mu

lati

ve

Wa

ter

Inje

cte

d, m

illi

on

s o

f b

arr

els

ن ييالم

Time from Waterflooding Initiation, months

Simulation

BLW

CGM

Stiles

48

4.8. Overall Discussion

1- We conducted accounts on the EL Tordillo field in three methods, we found that

the three methods are good in prediction of waterflooding performance, but the

Stiles method is the best perdition technique.

2- All methods give high guess of of real results before breakthrough and guess less

than the real results after breakthrough.

3- The nearest method to real results and value is Stiles Method. Buckley - Leveret

–Welge and Craig et al. them almost the same behavior and results, the worst

method is Buckley-leveret.

4- In figure (4-6) oil production rate versus time, the results indicate that the

method of Stiles is closer to the real in behavior and value.

5- In figure (4-6) oil production rate versus time, the results indicate oil flow rate

1000 bbl can be produced 1n 10 month in stiles method is the closest actually,

but the method of Buckley - Leveret –Welge far from the real results.

6- Figure (4-6) oil production rate versus time, the intersection point between

simulation and three methods (Buckley - Leveret –Welge, Craig et al, Stiles

Method) is breakthrough time BT=860 days, 28.66667 month.

7- The results indicate that the method of Buckley - Leveret –Welge is the most

method in which the water is produced.

8- In Figure (4-8) Cumulative water injected versus time, the results indicate in

terms of water injection, the behavior same for all methods but different

quantities are different.

9- All method of the beginning flow rate has given the highest of the real results

and after a certain point given flow rate less than of the real results.

10- Through the results of Buckley - Leveret –Welge we get one million barrels

of oil and no production water. These results are far from the reality while in

stiles method we get one million barrels of oil and 30%barrels of water.

40

Technique Np/Winj Winj/Np

Buckley - Leveret –

Welge Method 0.008044 124.3235

Craig-Geffen-Mores

Method 0.485084 2.0615

Stiles Method 0.0033 303.0604

44

56

Chapter Five

Conclusions and Recommendations

5.1. Conclusions

1. Based on our calculations done using three prediction methods, Stiles,

Buckley-Leverett and Craig et al., that were coded using the Excel sheet in oil

field located in Argentine called El Tordllio oil field and comparing the results

of these methods with the results of the simulation we obtained conclusions for

each method .

2. The method of Stiles through its results is the best way because the same real

behavior and results are the same as simulation results. This can be observed

through the correlation of oil production rate with time, as well as water oil

ratio with cumulative oil production stiles, which was the closest between the

residual retention and simulation.

3. Buckley-Leverett-Welge and Craig-Geffen-Morse methods are very far away

from real and unreasonable behavior thought correlation of oil production rate

with time, as well as water oil ratio with cumulative oil production. For

example, the method (Buckley-Leverett-Welge) gives a large result of the

cumulative oil produced without injecting any water barrel, which means that

it does not behave real when applied to reality. Through these relations we

conclude that (Buckley-Levertt) method is the worst method.

4. The three methods for the cumulative water injected relation with time are

close to the simulation results but in different quantities.

5. In general, the best and close method to reality is Stiles and the Craig method

needs a longer time but it is far from real behavior either Buckley-Leverett-

57

Welge method calculations were easy but the worst of the three methods

compared to the reality.

5.2. Recommendations

1. This research is recommended to be done in subsequent years and the

development Craig method close to simulation results.

2. Its recommended to use the methods of a numerical analytics for Buckley-

Levertt so that may be will close the method from simulation, for example, we

can use a correction factor.

3. When applying waterflooding on the Iraqi oil fields, the cost must be reduce by

reduce water injection and increase oil production before Breakthrough.

4. Its recommended to injected polymer to avoid channeling problems to get

larger amounts of oil product before Breakthrough.

5. We tried to get data from the Amara field or the Buzurgan field or any field in

Misan, but we could not access the data of these fields because of his difficulty

getting it and because it was a secret and these reasons to be presented by this

project on the Tordllio field in Argentina so its recommended to use this

project on field data from Misan oil fields.

58

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