Advance Reservoir Engineering

ADVANCE RESERVOIR

ENGINEERING

ARE310

Mohamed Ali

Chapter 1: Type Curve Analysis

Agenda

WTA overview

Log-Log type curves

Derivative type curves

Type curves as qualitative diagnostic tools

2 Advance Reservoir Engineering 2014 Dr. M.Ali

WTA overview

What Is A Pressure Transient Test?

A pressure transient test is a field experiment, that is like any

experiment, partially controlled.

It cannot be repeated under the same conditions, but can be rerun

using the results from earlier test (experiments).

There are many ways to interpret pressure transient test data;

There are many models with a set of parameters that may match

the observed data, but there is only one correct and more than a

few probable answers.


What Is A PTT…?

A tool for well and reservoir evaluation and characterization

– Investigates a much larger volume of the reservoir than cores or logs

– Provides estimate of porosity, permeability under in-situ conditions

– Provides estimates of near-wellbore condition

– Provides estimates of distances to boundaries


Primary Objective of PTT

o To obtain the productivity of a well and properties of the formation

from down-hole and/or surface pressure and flow-rate

measurements.

o The formation and reservoir information obtained from pressure

transient measurements are essential (Why)

– They reflect the in-situ dynamic properties of the reservoir under

realistic production/injection conditions.




Well Testing vs. Formation Testing

• A well test may last from several days to several weeks and

even months, and hence provide information on reservoir

over a large scale. Large volumes are produced/injected.

• On the other hand, WFTs refer to small scale tests with low

flow rate and short duration (e.g., from a few minutes to a

few hours).

Both are subsets of PTT. Both obey the same law of

physics and can theoretically be interpreted in the same

way, but note their scales are different.




Tools for Reservoir Characterization

• Well/Formation/Reservoir Evaluation:

– Core Analysis/Petrophysics

– Wireline Well Logs

– Production Logging (Flowmeter)

– Pressure Transient Formation and Well Testing

– Measurement While Drilling (MWD)

– Borehole Geophysics

• Siesmics (2D, 3D, or even 4D)

• Geostatistics (stochastic modeling)

• Upscaling and Numerical Reservoir Simulation


PTT Objectives

• Define reservoir limits

• Estimate average drainage area pressure

• Characterize reservoir

• Diagnose productivity problems

• Evaluate stimulation treatment effectiveness

• Determination of the Productivity Index


Productivity Index

Productivity Index is a measure of the well's

ability to produce fluids under an imposed

reservoir pressure drop.

Function of many parameters

– Transmissibility, kh/μ

– Storativity, фcth

– “Skin” damage, s

– Drainage area of the well, A

– Reservoir and well geometry

Can we determine individual values of these

parameters?


Basic Steps of PTT Interpretation

• It involves three basic steps:

– Step 1: Model Identification

– Step 2: Estimation of model parameters

– Step 3: Validation of results


Interpretation Methodology…

• Is to identify the “appropriate” interpretation model(s) and obtain

“reasonable” estimates of the formation (or reservoir) parameters of interest

from indirect measurements of pressure and rate data.

• These estimates are defined in terms of a mathematical well/reservoir model,

derived based on simplified assumptions, yet from physical principles

(conservation laws) governing the behavior of the system under observation.

• All monitored pressure transients in porous media are governed by some form

of the diffusivity equation with appropriate initial and boundary conditions.


Interpretation Methodology…

• Pressure transient interpretation sequence is applications of

inverse/forward(direct) problems:


STEP 1: Model Identification

• Find a model SM which behaves in the same way as the real system S given the

input and output.


STEP 2: Model Parameter Estimation

• Adjust the parameters of the MODEL Sm so that Om matches O “quite

well.”


STEP 2: MP Estimation…

• Tools for Model P. Estimation

– Straight line methods (semi-log, Cartesian plots, etc.)

– Type-curve matching based on Pressure and/or Pressure-Derivative

responses

– Non-linear regression

• To reduce non-uniqueness:

– Calculated parameters should be very similar independent of the

method (or tool) used.


STEP 3: Validation of Results

• Verify the consistency of the interpretation model by:

– matching with test observed data (log-log, Horner, simulation)

– matching results from other well tests

– matching with other knowledge (geology, petrophysics, cores, fluids,

completion)

– common sense (range of plausible parameter values).

– Inspect confidence intervals, correlation coefficients, RMS errors if

non-linear regression is used.


PTT Interpretation Models


History of PTT Analysis

Modified from Gringarten (SPE 102079)


Type Curve Analysis

Overview

Type curves are plots of theoretical solutions to diffusivity

equation, they can be generated for virtually any kind of

reservoir model for which a general solution describing

the flow behavior is available.

Type curves are always presented in terms of

dimensionless variables.

Type curves are derived from solutions to the flow

equations under specific assumptions, initial and boundary

conditions.


History of Type Curves Analysis

Type curves first appeared in oil industry literature in the seventies.

Several kinds, as listed below, are used to interpret a test in a vertical

well with a infinite homogeneous reservoir:

– Agarwal et al. type curves;

– McKinley type curves;

– Earlougher and Kersch type curves;

– Gringarten et al. type curves;

- Bourdet’s derivative type curves;

- Ramey’s type curves.


Gringarten et al. type curves

Let us remember the dimensionless solution of diffusivity equation at the

wellbore:

o During wellbore storage dominant period

o During infinite acting transient period


Gringarten et al. type curves

Gringarten A.C.,1987, Type-Curve Analysis: What It Can and Cannot Do,

Journal of Petroleum Technology. 27 Advance Reservoir Engineering 2014 Dr. M.Ali

Problem….

The classical type curves have very similar shapes for high

values of CDe2s which lead to the problem of finding a

unique match by a simple comparison of shapes and

determining the correct values of k, s, and C.


Solution….

Bourdet et al.(*) addressed the problem by proposing that

flow regimes can have clear characteristic shapes if the

“pressure derivatives” rather than pressure is plotted

versus time on the log-log coordinates. Since the

introduction of the pressure derivative type curves in

1983, well test analysis has been greatly enhanced by its

use.

(*) Boudet D. et al.:”ANew Set of Type Curves that Simplifies Well Test Analysis”,

World Oil , May 1983, p: 95


Advantages of derivative type curves

•Heterogeneities hardly visible on the conventional plot of well test

data are amplified on the derivative plot.

•Flow regimes have clear characteristic shapes on the derivative plot.

•The derivative plot is able to display in a single graph many separate

characteristics that would otherwise require different plots.

•The derivative approach improves the definition of the analysis plots

and therefore the quality of interpretation

•It is possible to make qualitative interpretation regarding the porous

medium and the flow system in the formation by just looking at the

shape of the derivative plot.


Bourdet’s derivative type curves

Boudet D. et al.:”ANew Set of Type Curves that Simplifies Well Test Analysis”, World

Oil , May 1983, p: 95 31 Advance Reservoir Engineering 2014 Dr. M.Ali

Gringarten-Bourdet Type Curves




The Analysis Procedure

1. Using the actual well test data, calculate the pressure difference ΔP and the

pressure derivative plotting functions as defined below for drawdown and

build-up tests.

For Build-up Tests

For Drawdown Tests



2. On tracing paper with the same size log cycles as the Bourdet-

Gringarten type curve graph plot:

•(ΔP) and (tΔP’)as a function of the flowing time t when analyzing

drawdown test data. There will be two sets of data on the same log-

log graph; the first is the analytical solution and the second is the

actual drawdown test data.

•The pressure difference ΔP versus the equivalent time Δte and the

derivative function ΔteΔP’ versus the actual shut in time Δt. Again

there are two sets of data on the same graph.



3. Check the early time pressure points for the unit-slope line. If it exists

calculate the wellbore storage coefficient C as follows:



4. Calculate the dimensionless wellbore storage coefficient CD by applying

equation :

5. Check the late time data points on the actual pressure derivative plot to see

if they form a horizontal line which indicates the occurrence of transient

flow. If it exists, draw a horizontal line through these derivative plot points.

6. Place the actual two sets of plots, i.e. the pressure difference plot and the

pressure derivative function plot, on the Gringarten-Bourdet type curve and

force a simultaneous match of the two plots to type curves. The unit slope

line should overlay the unit slope on the type curve and the late-time

horizontal line should overlay the horizontal line on the type curve which

correspondence to a value of 0.5.



7. From the match of the best fit, select a match point MP and record

the corresponding values of the following:

• From the Gringarten type curve, i.e. (PD vs tD/CD); determine

(PD, ΔP)MP and the corresponding (tD/CD, Δt)MP or(tD/CD, Δte)MP

• Record the value of the type curve dimensionless group (CDe2s)MP from the

Bourdet type curves, i.e. (P’D tD/CD vs tD/CD);


The Analysis Procedure 8. Calculate the permeability from equation:

9. Recalculate the wellbore storage coefficient and dimensionless wellbore

storage coefficient from equations, and compare the values of C and CD with

those calculated in steps 3 and 4.

For Build-up Tests

For Drawdown Tests



10. Calculate the skin factor s as follow:



Type Curves as

Qualitative Diagnostic

Tools

Infinite Acting Radial Flow

Semi-log plot (dimensioned) Log-log plot (dimensionless)


Closed Outer Boundary

Cartesian plot (dimensioned) Log-log plot (dimensionless)


Constant Pressure Boundary

Cartesian plot (dimensioned) Log-log plot (dimensionless)


IARF with wellbore storage and skin

Log-log plot (dimensioned) Log-log plot (dimensionless)


Infinite conductivity fracture

Log-log plot (dimensioned) 0.5 Log-log plot (dimensionless) 0.5


Finite conductivity fracture

Log-log plot (dimensioned) 0.25 Log-log plot (dimensionless) 0.25


Dual porosity system

Semi-log plot Log-log plot


Horizontal Wells


Linear Impermeable Boundary

Semi-log plot Log-log plot


Final Comments

I. A maximum: This is found at early times and indicates wellbore storage and

skin. The higher the maximum (or the hump) the more damaged the well. The

absence of a maximum indicates an undamaged or a stimulated well.

II. A minimum: This indicates heterogeneous/dual porosity behavior.

III. Stabilization: Stabilization indicates semi-log radial flow and corresponds to

the semi-log straight line on a Horner plot.

IV. An upward or downward trend at the end: These indicate the influence of

the reservoir boundary.


NEXT SESSION

2 MATERIAL BALANCE FOR OIL AND GAS RESERVOIRS

• The General Form of the Material Balance Equation • Derivation of the Material Balance Equation • The Material Balance Expressed As A Linear

Equation • Initial Steps in Applying the Material Balance • Solution Gas Drive • Gas Cap Drive • Natural Water Drive • Material Balance Applied to Gas Reservoirs 54 Advance Reservoir Engineering 2014 Dr. M.Ali

Advance Reservoir Engineering

Documents

reservoir information

reservoir limits

imposed reservoir pressure

numerical reservoir

ali tools

ali ptt objectives

ali wta overview

pressure transient test