Inflow Performance Relationship

Introduction

Subsurface production of hydrocarbon has to do with the movement of fluid from the

reservoir through the wellbore to the wellhead. This fluid movement is divided into

two as depicted in Fig. 9.1.

The flow of fluids (hydrocarbons) from the reservoir rock to the wellbore is

termed the inflow. The inflow performance represents fluid production behavior of

a well’s flowing pressure and production rate. This differs from one well to another

especially in heterogeneous reservoirs. The Inflow Performance Relationship (IPR)

for a well is the relationship between the flow rate of the well (q), average reservoir

pressure (Pe) and the flowing pressure of the well (Pwf). In single phase flow, this

relationship is a straight line but when gas is moving in the reservoir, at a pressure

below the bubble point, this is not a linear relationship.

A well starts flowing if the flowing pressure exceeds the backpressure that the

producing fluid exerts on the formation as it moves through the production system.

When this condition holds, the well attains its absolute flow potential.

The backpressure or bottomhole pressure has the following components:

• Hydrostatic pressure of the producing fluid column

• Friction pressure caused by fluid movement through the tubing, wellhead and

surface equipment

• Kinetic or potential losses due to diameter restrictions, pipe bends or elevation

changes.

The IPR is often required for estimating well capacity, designing well comple￾tion, designing tubing string, optimizing well production, nodal analysis calcula￾tions, and designing artificial lift.

Factors Affecting IPR

Factors influencing the shape of the IPR are the pressure drop, viscosity, formation

volume factor, skin and relative permeability across the reservoir.

There are several existing empirical correlations developed for IPR. This are:

9.3 Straight Line IPR Model

When the flow rate is plotted against the pressure drop, it gives a straight line from

the origin with slope as the productivity index as shown in the figure below.

Steps for Construction of Straight Line IPR

Step 1: Obtain a stabilize flow test data

Step 2: Determine the well productivity

Step 3: Assume different pressure value to zero in a tabular form

Step 4: Calculate the rate corresponding to the assume pressure

Step 5: Make a plot of rate versus pressure

9.4 Wiggins’s Method IPR Model

Wiggins (1993) developed the following generalized empirical three phase IPR

similar to Vogel’s correlation based on his developed analytical model in 1991:

For Oil

Klins and Majcher IPR Model

Based on Vogel’s work, Klins and Majcher (1992) developed the following IPR that

takes into account the change in bubble-point pressure and reservoir pressure.

Standing’s Method

The model developed by Standing (1970) to predict future inflow performance

relationship of a well as a function of reservoir pressure was an extension of Vogel’s

model (1968).

Vogel’s Method

Undersaturated Oil Reservoir

An undersaturated reservoir is a system whose pressure is greater than the bubble

point pressure of the reservoir fluid. For the fact that the pressure of the reservoir is

greater than the bubble point pressure does not mean that as production increases for

a period of time, the pressure will not go below the bubble point pressure. Hence,

careful evaluation will lead to a right decision and vice versa.

Since the reservoirs are tested regularly, it means that the stabilized test can be

conducted below or above the bubble point pressure. Thus, for:

Case: pressure above bubble point

From stabilized test data point, the productivity index is:

Vogel IPR Model for Saturated Oil Reservoirs

This is a reservoir whose pressure is below the bubble point pressure of the fluid. In

this case, we calculate the maximum oil flow rate from the stabilized test and then

generate the IPR model. Mathematically

Fetkovich’s Model

According to Tarek (2010), the model developed by Fetkovich in 1973 for under￾saturated and saturated region, was an expansion of Muskat and Evinger (1942)

model derived from pseudosteady-state flow equation to observe the IPR nonlinear

flow behavior.

9.8.1 Undersaturated Fetkovich IPR Model

Saturated Fetkovich IPR Model

Cheng Horizontal IPR Model

Cheng (1990) presented a form of Vogel’s equation for horizontal wells that is based

on the results of a numerical simulator. The proposed expression has the following

form

 

Pressure Regimes and Fluid Contacts

Introduction

The main source of energy during primary hydrocarbon recovery is the pressure of

the reservoir. At any given time in the reservoir, the average reservoir pressure is an

indication of how much gas, oil or water is remaining in the porous rock media. This

represents the amount of the driving force available to push the remaining hydro￾carbon out of the reservoir during a production sequence. Most reservoir systems are

identified to be heterogeneous and it is worthy to note that the magnitude and

variation of pressure across the reservoir is a paramount aspect in understanding

the reservoir both in exploration and development (production) phases (Fig. 8.1).

Hydrocarbon reservoirs are discovered at some depths beneath the earth crust as a

result of depositional process and thus, the pore pressure of a fluid is developed

within a rock pore space due to physical, chemical and geologic processes through

time over an area of sediments. There are three identified pressure regimes:

• Normal (relative to sea level and water table level, i.e. hydrostatic)

• Abnormal or overpressure (i.e. higher than hydrostatic)

• Subnormal or underpressure (i.e. lower than hydrostatic)

Fluid pressure regimes in hydrocarbon columns are dictated by the prevailing

water pressure in the vicinity of the reservoir (Bradley 1987). In a perfectly normal

pressure zone, the water pressure at any depth can be calculated as:

Pressure Regime of Different Fluids

Some Causes of Abnormal Pressure

• Incomplete compaction of sediments

Fluids in sediments have not escaped and are still helping to support the overburden.

• Aquifers in Mountainous Regions

Aquifer recharge is at higher elevation than drilling rig location.

• Charged shallow reservoirs due to nearby underground blowout.

• Large structures

• Tectonic movements

Abnormally high pore pressures may result from local and regional tectonics. The

movement of the earth’s crustal plates, faulting, folding, lateral sliding and slipping,

squeezing caused by down dropped of fault blocks, diapiric salt and/or shale

movements, earthquakes, etc. can affect formation pore pressures.

Due to the movement of sedimentary rocks after lithification, changes can occur

in the skeletal rock structure and interstitial fluids. A fault may vertically displace a

fluid bearing layer and either create new conduits for migration of fluids giving rise

to pressure changes or create up-dip barriers giving rise to isolation of fluids and

preservation of the original pressure at the time of tectonic movement.

When crossing faults, it is possible to go from normal pressure to abnormally high

pressure in a short interval. Also, thick, impermeable layers of shale (or salt) restrict

the movement of water. Below such layers abnormal pressure may be found. High

pressure occurs at the upper end of the reservoir and the hydrostatic pressure gradient

is lower in gas or oil than in water.

8.4 Fluid Contacts

In the volumetric estimation of a field’s reserve, the initial location of the fluid

contacts and also for the field development, the current fluid contacts are very critical

factor for adequate evaluation of the hydrocarbon prospect. Typically, the position of

fluid contacts are first determined within control wells and then extrapolated to other

parts of the field. Once initial fluid contact elevations in control wells are determined,

the contacts in other parts of the reservoir can be estimated. Initial fluid contacts

within most reservoirs having a high degree of continuity are almost horizontal, so

the reservoir fluid contact elevations are those of the control wells.

Estimation of the depths of the fluid contacts, gas/water contact (GWC), oil/water

contact (OWC), and gas/oil contact (GOC) can be made by equating the pressures of

the fluids at the said contact. Such that at GOC, the pressure of the gas is equal to the

pressure of the oil and the same concept holds for OWC.

Methods of Determining Initial Fluid Contacts

8.4.1.1 Fluid Sampling Methods

This is a direct measurement of fluid contact such as: Production tests, drill stem

tests, repeat formation tester (RFT) tests (Schlumberger, 1989). These methods have

some limitation which are:

• Rarely closely spaced, so contacts must be interpolated

• Problems with filtrate recovery on DST and RFT

• Coring, degassing, etc. may lead to anomalous recoveries

8.4.1.2 Saturation Estimation from Wireline Logs

It is the estimation of fluid contacts from the changes in fluid saturations or mobility

with depth, it is low cost and accurate in simple lithologies and rapid high resolution

but have limitations as:

• Unreliable in complex lithologies or low resistivity sands

• Saturation must be calibrated to production

8.4.1.3 Estimation from Conventional and Sidewall Cores

Estimates fluid contacts from the changes in fluid saturation with depth which can be

related to petrophysical properties. It can estimates saturation for complex litholo￾gies (Core Laboratories, 2002). The limitations are:

• Usually not continuously cored, so saturation profile is not as complete

• Saturation measurements may not be accuratPressure Methods

There are basically two types of pressure methods: the pressure profiles from repeat

formation tester and pressure profiles from reservoir tests, production tests and drill

stem tests.

8.4.1.5 Pressure Profiles from Repeat Formation Tester

It estimates free water surface from inflections in pressure versus depth curve.

8.4.1.6 Pressure Profiles from Reservoir Tests, Production Tests

and Drill Stem Tests

It estimates free water surface from pressures and fluid density measurements which

makes use of widely available pressure data.

Both pressure techniques are pose with limitations such as:

• Data usually require correction

• Only useful for thick hydrocarbon columns

• Most reliable for gas contacts, Requires many pressure measurements for profile,

Requires accurate pressurese

Estimate the Average Pressure from Several Wells

in a Reservoir

When dealing with oil, the average reservoir pressure is only calculated with material

balance when the reservoir is undersaturated (i.e when the reservoir pressure is

above the bubble point pressure). Average reservoir pressure can be estimated in

two different ways but are not covered in this book (see well test analysis textbooks

for details).

• By measuring the long-term buildup pressure in a bounded reservoir. The buildup

pressure eventually builds up to the average reservoir pressure over a long enough

period of time. Note that this time depends on the reservoir size and permeability

(k) (i.e. hydraulic diffusivity).

• Calculating it from the material balance equation (MBE) is given below

For a gas well

   

Decline Curve Analysis

 Introduction

Globally, the oil and gas production profiles differ considerably. When a field starts

production, it builds up to a plateau state, and every operator will want to remain in

this stage for a very long period of time if possible. But in reality, it is practically not

possible, because, at a point in the life of the field, the production rate will eventually

decline to a point at which it no longer produces profitable amounts of hydrocarbon

as shown in Fig. 7.1. In some fields, the production build-up rate starts in the first few

years, most fields’ profiles have flat top and the length of the flat top depends on

reservoir productivity.

Some fields have long producing lives depending upon the development plan of

the field and reservoir characteristics such as the reservoir, drive mechanism. Wells

in water-drive and gas-cap drive reservoirs often produce at a near constant rate until

the encroaching water or expanding gas cap reaches the well, thereby causing a

sudden decline in oil production. Wells in gas solution drive and oil expansion drive

reservoirs have exponential or hyperbolic declines: rapid declines at first, then

leveling off.

Therefore, decline curve analysis can be defined as a graphical procedure used for

analyzing the rates of declining production and also a means of predicting future oil

well or gas well production based on past production history. Production decline

curve analysis is a traditional means of identifying well production problems and

predicting well performance and life based on measured oil or gas well production.

Today, several computer software have been built to perform this task and prior to

the availability of computers, decline curve analysis was performed by hand on

semi-log plot paper. Several authors (Rodriguez & Cinco-Ley (1993), Mikael

(2009), Duong (1989) have developed new models or approach for production

decline analysis. Agarwal et al. (1998) combined type curve and decline curve

analysis concepts to analyse production data. Doublet et al. (1994), applied the

material balance time for a field using decline curve analysis.

Furthermore, as stated by Thompson and Wright (1985), decline curve is one of

the oldest methods of predicting oil reserves with the following advantages:

• They use data which is easy to obtain

• They are easy to plot

• They yield results on a time basis, and

• They are easy to analyze.

7.2 Application of Decline Curves

• Production decline curve illustrates the amount of oil and gas produced per unit

of time.

• If the factors affecting the rate of production remaining constant, the curve will be

fairly regular, and, if projected, can give the future production of the well with an

assumption that the factors that controlled production in the past will continue to

do so in future.

• The above knowledge is used to ascertain the value of a property and proper

depletion and depreciation charges may be made on the books of the operating

company.

• The analysis of the production decline curve is employed to determine the value

in oil and gas wells economics.

• Identify well production problems

• Decline curves are used to forecast oil and gas production for the reservoir and on

per well basis and field life span.

• Decline curves are also used to predict oil and gas reserves; this can be used as a

control on the volumetric reserves calculated from log analysis results and

geological contouring of field boundaries.

• It is often used to estimate the recovery factor by comparing ultimate recovery

with original oil in place or gas in place calculations

Causes of Production Decline

• Changes in bottom hole pressure (BHP), gas-oil ratio (GOR), water-oil ratio

(WOR), Condition in drilling area

• Changes in Productivity Index (PI)

• Changes in efficiency of vertical & horizontal flow mechanism or changes in

equipment for lifting fluid.

• Loss of wells

7.4 Reservoir Factors that Affect the Decline Rate

• Pressure depletion

• Number of producing wells

• Reservoir drive mechanism

• Reservoir characteristics

• Saturation changes and

• Relative permeability.

7.5 Operating Conditions that Influence the Decline Rate

• Separator pressure

• Tubing size

• Choke setting

• Workovers

• Compression

• Operating hours, and

• Artificial lift.

As long as the above conditions do not change, the trend in decline can be analyzed

and extrapolated to forecast future well performance. If these conditions are altered,

for example; through a well workover, the decline rate determined during

pre-workover will not be applicable to the post-workover period.

7.6 Types of Decline Curves

Arps (1945) proposed that the “curvature” in the production-rate-versus-time curve

can be expressed mathematically by a member of the hyperbolic family of equations.

Arps recognized the following three types of rate-decline behavior:

Exponential decline

• Harmonic decline

• Hyperbolic decline

Arps introduces equations for each type and used the concept of loss-ratio and its

derivative to derive the equations. The three declines have b values ranging from 0 to

1. Where b ¼ 0 represents the exponential decline, 0 < b < 1 represents the

hyperbolic decline, and b ¼ 1 represents the harmonic decline (Fig. 7.2).

The plots of production data such as log(q) versus t; q versus Np; log(q) versus

log(t); Np versus log(q) are used to identify a representative decline model.

7.6.1 Identification of Exponential Decline

If the plot of log(q) versus t OR q versus Np shows a straight line (see figures below)

and in accordance with the respective equations, the decline data follow an expo￾nential decline model.

Mathematical Expressions for the Various Types of Decline

Curves

The three models are related through the following relative decline rate equation

(Arps 1945):

Relationship Between Nominal and Effective Decline Rate

The nominal decline rate (Di) is defined as the negative slope of the curvature

representing the natural logarithm of the production rate versus time

Cumulative Production for Exponential Decline

The Integration of the production rate over time gives an expression for the cumu￾lative oil production as:

Steps for Exponential Decline Curve Analysis

The following steps are taken for exponential decline analysis, for predicting future

flow rates and recoverable reserves (Tarek, 2010):

• Plot flow rate vs. time on a semi-log plot (y-axis is logarithmic) and flow

rate vs. cumulative production on a cartesian (arithmetic coordinate) scale.

• Allowing for the fact that the early time data may not be linear, fit a straight line

through the linear portion of the data, and determine the decline rate “D” from the

slope (b/2.303) of the semi-log plot, or directly from the slope (D) of the rate￾cumulative production plot.

• Extrapolate to q ¼ qt to obtain the recoverable hydrocarbons.

• Extrapolate to any specified time or abandonment rate to obtain a rate forecast and

the cumulative recoverable hydrocarbons to that point in time

7.7.2 Harmonic Decline Rate

Cumulative Production for Harmonic Decline

The expression for the cumulative production for a harmonic decline is obtained by

integration of the production rate. This is given by:

Hyperbolic Decline

The hyperbolic decline model is inferred when 0 < b < 1

Hence the integration of