Reservoir Performance

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Semester January 2015, Credit hour 3Duration 14 weeks Lecture + 2 Weeks Study & Exam

Lecture 30 hours + Lab/Tutorial 24 hours

InstructorDr. Mohammed MahbuburRahman

1. Beggs H.(2003), Production Optimization Using NODAL Analysis, Second Edition, OGCI2. Economides M. et al. (1994), Petroleum Production Systems, Prentice-Hall Inc.3. Michael Golan and Curtis H. Whitson (1991), Well Performance, 2nd Edition, Prentice-Hall

Course Content Reservoir Performance

Well Performance Equations, Darcy’s Law Factors affecting productivity index IPR for oil and gas wells Back pressure equations Well Completion effects

Flow in Pipes and Restrictions Energy equation, single and multi-phase flows Fluid Property calculations Well flow correlations:

Hagedorn and Brown Poettmann and Carpenter Duns and Ros Orkiszewski Aziz, Govier and Fogarasi

Pipe flow correlations Pressure drop through restrictions

Total System Analysis Tubing and Flow line size selection System analysis for wells with restrictions Evaluating Completion effects Nodal analysis of injection wells Effect of depletion Relating performance to time Analyzing multiwell systems

Artificial Lift Design Continuous Flow Gas lift Electrical Submersible Pump (ESP) selection Sucker rod / beam pumping Hydraulic pumping


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Course Learning Outcome

At the end of the course, students should be able to:

1. Apply fundamentals of production optimization usingcommercial software.

2. Analyze the performance of the petroleum productionsystem.

3. Understand the interaction of the reservoir system and

its effect on the overall production system.4. Design optimum petroleum production systems.

• Major segments of theproduction system

• Reservoir (InflowPerformance Relationship)

• Wellbore (Completions,Tubing etc)

• Surface Facilities (Flowlines, Separator, Pipelines

etc)

• Any one of these canadversely affect our target – to’maximize oil rate’

Let us look at the simplified production system

The 1st component is the Reservoir. So lets begin with the Reservoir >>>


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Lecture Outline

Reservoir Performance

Reservoir flow equations

Darcy equation for different fluid types and f low patterns

Reservoir – well system performance

Productivity Index

The Reservoir Most important component in the production system Relationship between flowrate and pressure drop in the reservoir can be very

complex Flow is through “porous medium”, so its formulation is very different from

other fluid f low problem, such as flow through pipes, channels, etc. Therefore, flow in the reservoir is handled differently than flow in the wellbore Parameters involved:

Rock properties (k, φ, ct, etc.) Fluid properties (PVT, µ, etc) Flow regime (Transient, Stabilized, etc) Fluid saturation (Sw, So, Sg) Formation damage/improvement (+s, -s) Drive mechanism (WDI, DDI, etc)

So lets begin with the flow in the Reservoir >>> We will learn about flow in the wellbore later in the course.


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Fluid Flow though Porous Medium (Reservoir Flow) Depending on time dependency, flow in the reservoir can be

Transient flow(pressure, f low rate etc., varying with time) Stabilized Flow (pressure, f low rate etc., NOT varying with time, or

varying at a fixed rate) Pseudo-Steady State (varying at a fixed rate)- requires NO-FLOW boundary Steady State (not varying) – requires CONSTANT PRESSURE boundary, such as

large aquifer support Both type of flows are also called “Boundary Dominated” f low

Transient flow is more relevant for Pressure Transient Analysis (WellTesting)

Stabilized flow is more relevant for Production Engineering

Therefore, we proceed with the Stabilized flow in the Reservoir >>>

Stabilized flow in the Reservoir:Linear Flow: Liquids

Basic equation to describe stabilizedflow in reservoir is the DarcyEquation.

Can be written in different forms suchas differential form, Integral form

Can be modified for different flowpattern (linear, radial, spherical, etc.)

Can be modified for different f luids(incompressible, slightlycompressible, compressible)

In the simplest form:

= =

q = flow rate

v = fluid velocity

A = area open to flow

µ = viscosity of the f luid

dp/dx = pressure gradient

It is the “differential” form of Darcy equationThere is NO variable to represent TIME- (Steady State) Valid only for LAMINAR flow Valid for incompressible/slightly compressible fluids (water, oil etc)NOT valid for GAS, or for TURBULENT flow


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Stabilized flow in the Reservoir:Linear Flow: Gas

For compressible fluid (gas), theequation can take the form:

Due to the nature of pressuredependency of gas, the pressure termsin the equation are usually expressedin 3 different forms: Average pressure Pressure quared

Pseudo-pressure This is the «pressure squared» form Notice the new terms: z, T

P = pressure, psia T = Temperature, oR µ = viscosity, cp L = length, ft K = permeability, md A = area open to flow, ft2

qsc = flow rate, SCF/D

Stabilized flow in the Reservoir:Radial Flow: Oil


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Stabilized flow in the Reservoir:Radial Flow: Oil

Fluid converging radially into the well Area open to flow is not constsnt

Area is given by: A = 2πrh

Darcy equation for radial flow, slightly compressiblefluid (oil):

=

0.00708 ℎ (−)

ln( )

qo =

Stabilized flow in the Reservoir:Radial Flow: Gas For compressible fluid (gas), and steady state flow, the equation can take the form:

2

2 = ln(

)

ℎ

It is the «pressure squared form»

Let psc = 14.7 psia & Tsc = 520 oR, and pseudo-steady state flow

=703 106 ℎ (

− )

ln(0.472

)

notice in addition to the conversion factor, the multiplier 0.472 in the ln argument for Gas, flow rate qsc is always reported/calculated/expressed in terms of standard

condition

, are evaluated at average pressure, i.e., at T and p = ½( + )


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Stabilized flow in the Reservoir:Radial Flow: Pressure Profile

The behavior of the pressure in the reservoir as a function of radius canbe analyzed by plotting pressure vs radius.

Assuming a fixed average reservoir pressure, pR at r = 0.472 re andsolving for pressure:


Figure shows that large increase inpressure gradient near the wellboreas the fluid velocity increases

Approx. one half of the pressuredrawdown occurs within 15ft radiusfrom the well.


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From the previous equation, a plot of p- vs- ln(r) will result in a straight lineof constant slope m, where

Notice the change of ’m’ withchange in ’q’Larger ’q’ results in steeper slope,assuming other variables remain thesame

Flow in the Reservoir: Recap

So far we concentrated on stabilized flow only

Become familiar with the equations for:

Steady state & pseudo-steady state flow

Linear & radial flow patterns

Liquids and gas

Pressure profile in the reservoir as a function of radial distance from the wellbore

But, how good is the reservoir? How much can be extracted from it with a given well? Where is the reservoir energy being spent??

To answer these questions, we need to learn about the performance indicator ofthe reservoir & well system>>>


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Productivity Index

Strong indicator of performance of the reservoir-well system

Defined by:

Higher values of J indicate good performance, where more oil is produced perunit draw down

Alternate definition:

Notice the impact of each variable.

Which one would you/can you change to increase J? What factors affect J?

Productivity Index...

Solving for p wf in terms of qo reveals thata plot of p wf vs qo on a Cartesiancoordinates results in a straight linehaving a slope of -1/J and an intercept ofpR at qo= 0.

J can be obtained from production test orcalculated from equation

This line is known as the InflowPerformance Relation (IPR) line

Later we will see IPR curves, not straightlines


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Sample exercise

Calculate:

The Productivity Index, J


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Lecture Summary

The reservoir is the 1st and foremost component in the production system

Fluid flow in the reservoir is described by Darcy equation, which applies forlaminar f low, and stabilized (steady and pseudo-steady) conditions

Darcy equation is expressed for linear and radial flow

It can be modified for compressible fluids such as gas

Productivity Index is the most important indicator for reservoir-wellperformance

From PI, we can derive the IPR

For production operations, and production optimization, obtaining the IPR,and studying the behavior of IPR, comprise the main part from the reservoirside.

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Reservoir Performance