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Agarwal-Gardner Typecurve Analysis TheorySubtopics:

Rate-Cumulative Production AnalysisRate-Time Production AnalysisCalculation of ParametersMethodology

Agarwal and Gardner have compiled and presented decline typecurves for analyzing production

data. Their methods build upon the work of Fetkovich, Palacio, and Blasingame, utilizing the

concepts of the equivalence between constant rate and constant pressure solutions. Agarwal and

Gardner present typecurves with dimensionless variables based on the conventional welltest

definitions, as opposed to the Fetkovich dimensionless definitions used by Blasingame et al. They

also include primary and semi-log pressure derivative plots (in inverse format for decline

analysis). Furthermore, they present their decline curves in additional formats to the standard

normalized rate vs. time plot. These include the rate vs. cumulative, and cumulative vs. time

analysis plots.

Rate-Cumulative Production Analysis

Dimensionless Typecurves

Agarwal et al. propose the use of rate-cumulative typecurves for estimating gas- or oil-in-place.

Dimensionless rate (qD) is plotted against dimensionless cumulative production (QDA), which is

defined as follows:

The resulting typecurves are straight lines on a Cartesian graph, which are anchored at the point

0.159, as shown in the following figure. A plot of dimensionless rate vs. dimensionless cumulative

production yields a straight line that passes through QDA = 0.159 at qD = 0, provided that fluid-in-place

has been estimated correctly.

Modifications in RTA

The presentation of rate-cumulative analysis in RTA is modified significantly from that of Agarwal

and Gardner. See Methodology: Rate-Cumulative.

Data Preparation

The rate vs. cumulative production analysis is performed to estimate the hydrocarbons-in-place.

Oil Wells

Plot pressure-drop normalized flow rate (q / Δp) vs. modified cumulative production on Cartesian

coordinates, where:

Gas Wells

Estimate original gas-in-place (a lower bound estimate can be obtained by performing a straight line

extrapolation on a rate vs. cumulative production plot. Another estimate is the volumetric gas-in-

place).

Plot pressure-drop normalized flow rate vs. modified cumulative production on Cartesian

coordinates, where:

Analysis

Oil Wells

Perform a straight line extrapolation of the data. The value where the extrapolated line crosses the

x-axis is the original oil-in-place.

Gas Wells

Perform a straight line extrapolation of the data. If the extrapolated line crosses the x-axis short of

the estimated gas-in-place, choose a smaller gas-in-place input value. If the extrapolated line

crosses the x-axis beyond the estimated gas-in-place, choose a larger gas-in-place input value.

Then, re-calculate the material balance pseudo-time function and re-plot the data.

Rate-Time Production Analysis

Dimensionless Typecurves

The Agarwal-Gardner rate-time analysis plot includes dimensionless typecurves, based on the

constant rate solution. Unlike Blasingame, these typecurves are graphed using the well-test

variables dimensionless rate and dimensionless time. Agarwal and Gardner also include typecurves

for the primary pressure derivative and semi-logarithmic (well-test) derivative (plotted as an

inverse). The result is a diagnostic analysis that clearly shows the transition point from transient to

boundary-dominated flow. The dimensionless pressure for standard well-test analysis is defined as:

The dimensionless flow rate is simply the inverse of the previous equation (note that in the well-test

literature, dimensionless rate has a slightly different definition):

The primary and semi-log (inverse) derivative typecurves are as follows:

The resulting dimensionless typecurve plot is shown below.

Modifications in RTA

In RTA, this analysis has been modified slightly; In addition to the semi-log derivative, a semi-

log integral derivative curve is included. The advantage of the integral derivative curve is that the

data has far less scatter, while retaining a shape identical to the semi-log derivative, only offset in

the time scale.

The RTA rendition of the Agarwal-Gardner Rate-Time plot is shown below. Note that the primary

pressure derivative plot is not included in the RTA presentation.

Data Preparation

The horizontal axis is material balance time (pseudo-time for gas); the vertical axis is either

normalized rate or inverse of semi-log derivative.

Oil Wells

Gas Wells

Analysis

The normalized rate and inverse semi-log derivative data are plotted against material balance time

on a log-log scale of the same size as the typecurves. This plot is called the "data plot". Any

convenient units can be used for normalized rate or time because a change in units simply causes a

uniform shift of the raw data on a logarithmic scale. It is recommended that daily operated-rates be

plotted, and not the monthly rates; especially when transient data sets are analyzed.

The data plot is moved over the typecurve plot, while the axes of the two plots are kept parallel, until

a good match is obtained. Several different typecurves should be tried to obtain the best fit of all the

data. The typecurve that best fits the data is selected and its re/rwa (re/xf for fractured case) value is

noted.

Typecurve analysis is done by selecting a match point, and reading its coordinates off the data plot

(q/∆p and tc)match, and the typecurve plot (qD and tDA)match. At the same time the stem value re/rwa (re/xf for

fracture typecurves) of the matching curve is noted. To create a forecast, the selected typecurve is

traced on to the data plot, and extrapolated. The future rate is read from the data plot, off the traced

typecurve.

In the modified (RTA) plot, the inverse pressure integral derivative is also included.

Calculation of Parameters

Radial Typecurves

Oil Wells

Using the definition of dimensionless rate:

Permeability is calculated as follows, where pressure-drop normalized flow rate and dimensionless

rate are read off each of the raw data and typecurve graphs at a selected match point:

From the definition of dimensionless time based on area (tDA):

Reservoir radius is calculated as follows:

Substituting the equation for permeability into the above:

Additional reservoir parameters are now calculated:

Gas Wells

For gas wells, dimensionless rate is defined as follows:

According to this equation, the permeability can be calculated as:

From the definition of dimensionless time based on area:

Reservoir radius is calculated as follows:

Substituting the equation for permeability into the above:

Additional reservoir parameters are now calculated:

Fracture Typecurves

Oil Wells

Using the definition of dimensionless rate:

Permeability is calculated as follows, where pressure-drop normalized flow rate and dimensionless

time are read off each of the raw data and typecurve graphs at a selected match point:

From the definition of dimensionless time based on area:

Reservoir radius is calculated as follows:

Substituting the equation for permeability into the above:

Additional reservoir parameters are now calculated:

Gas Wells

For gas wells, dimensionless rate is defined as follows:

The permeability is calculated from above, as follows:

From the definition of dimensionless time based on area:

Reservoir radius is calculated as follows:

Substituting the equation for permeability into the above, we get:

Additional reservoir parameters are now calculated:

Methodology: Rate-CumulativeCumulative-time typecurves have a similar purpose to the rate-time typecurves, but have the added

advantage of smoothing noisy production data. As such, they often help to provide a more unique

type curve match, when used in conjunction with the other Agarwal-Gardner typecurves. The

following figure is an example of a cumulative-time typecurve for an unfractured well in a circular

reservoir:

Plotting rate vs. cumulative production is a widely accepted and simple method for estimating

movable reserves. In the absence of more sophisticated decline analysis techniques, many analysts

use this method as a quick and effective way of estimating reserves. A straight-line extrapolation is

equivalent to fitting the data to the exponential (b = 0) stem of the Arps decline typecurves. This

method will almost always give a lower-bound estimate of recoverable hydrocarbons (this can be

clearly seen when looking at the Arps decline typecurves, as the exponential stem has the steepest

slope). A more rigorous decline analysis can be performed by fitting data to one of the full set of

Arps decline typecurves. This type of analysis provides an empirical fit of the data to estimate the

recoverable reserves.

There are two main limitations of the Arps decline analysis technique:

The analysis does not account for changing production conditions, and thus cannot always provide a reliable estimate of recoverable hydrocarbons-in-place.

Changing gas properties with time (reservoir pressure) are not accounted for; thus gas reserves are usually underestimated.

These limitations can be overcome through modification of the rate vs. cumulative production

plotting functions. Changing production conditions are accommodated by incorporating variations in

flowing pressure as well as production rate, and by normalizing the production data using material

balance time. Changing gas properties are handled using gas pseudo-time.

 

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