evaluation the methodologies of analyzing · pdf filematerial-balance methods and history...

EVALUATION THE METHODOLOGIES OF ANALYZING PRODUCTION AND PRESSURE DATA OF HYDRAULIC FRACTURED WELLS

IN LOW PERMEABILITY GAS RESERVOIRS

Faisal S. Al-ReshedanSaudi Aramco

[email protected]

Ahamed Gawish, Hazim N. DmourPetroleum and Natural Gas Engineering Dept.

King Saud UniversitySaudi Arabia, Riyadh 11424, P.O.Box: [email protected], [email protected]

Production data analysis approaches have advanced significantly over the past few years. While many different methods have been published in the literature, there is no single method that yields the most reliable answer. Analyzing production history and pressure data of a hydraulically fractured gas well in low permeability reservoir can be an effective way to estimate the well and reservoir properties. However, fractured gas wells in low permeability reservoirs represent a challenge to petroleum engineers. This is because of the presence of wellbore storage, formation damage and Non-Darcy flow effects around wellbore.

This study uses an advanced production analysis package, Topaze software, to evaluate the most applicable methods for use in determining well and reservoir parameters, and estimating the gas in place for hydraulically fractured gas wells in low permeability reservoirs. Field and simulated examples are presented to illustrate the evaluation of these methods. Results from this study show that modern methods such as Blasingame, Normalized Pressure Integral and the Flowing Material Balance are valuable analysis tools for production history and pressure data. Both pressure transient analysis and production analysis have been studied.

The interaction of changing wellbore storage and Non-Darcy flow effects on the analysis of production and pressure data have been studied. Results show that using flowing pressure data in production analysis will be more representative and descriptive of the reservoir than using wellhead pressure data for gas well.

Keywords: Pressure Transient, Non-Darcy flow effect, wellbore storage effect, Low permeability reservoirs, hydraulically fractured gas wells, Formation damage

INTRODUCTION

Tight gas reservoirs represent a challenge to the petroleum engineer. Low

permeability slows down the response of the pressure transient test, so it is difficult to

obtain the reservoir properties. Moreover, it will slow down the production response, so

it is difficult to estimate the gas in place and to predict the gas recovery. Therefore,

there is a need for a hydraulic or acid fracture in these types of reservoirs to enhance the

conductivity of the gas wells. However, the presence of the fracture will add a comple-

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xity of pressure transient and production data analysis, because of the effect of Non-

Darcy flow, formation damage and the well bore storage.

Analyzing the production history and pressure data of a hydraulically fractured

gas well can be an effective way to estimate the well and reservoir properties. A well

test for fractured gas well in a low permeability reservoir is likely to require a long data

acquisition time for interpretation. Therefore, the low permeability delays the post-

treatment evaluation. Coupled with economic constraints, in this situation suggests that

the utilization of production history and pressure data for the evaluation of well

performance and the calculation of fracture properties [1, 2].

Production data analysis approaches have advanced significantly over the past

few years. There are many different methods published in the literature, but there is no

single method that yields the most reliable answer. However, the combination of using

all available methods will provide a full picture to the analyst in understanding what is

going on, and great level of confidence when all methods agree. The currently known

methods are:

1. Arps decline analysis (exponential, hyperbolic and harmonic) [3].

2. Fetkovich type curve analysis [2].

3. Blasingame type curve analysis [4].

4. Agarwal-Gardner type curve analysis [5].

5. Normalized Pressure Integral (NPI) type curves [6].

6. Flowing Material Balance [5].

7. Modeling [7].

Only two methods will not be considered in this study. These are the Agarwal-

Gardner type curve analysis and Modeling method. The main reason is that these two

methods are not implemented yet in the application, Topaze software..

The main objective of this study is to evaluate the most applicable methods for

use in determining well and reservoir parameters and estimating the gas in place of

hydraulically fractured gas wells in low permeability reservoirs. Also, the study will

seek to investigate the interaction of changing wellbore storage and Non-Darcy flow

effects on analyzing production and pressure data. Two production history and pressure

data for actual and simulated fractured gas in low permeability reservoir will be used to


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illustrate and demonstrate the proposed objectives of this study, using advanced

production analysis package used in petroleum industry, which is Topaze.

LITERATURE REVIEW

The basis of decline-curve analysis is to match past production performance

histories or trends (i.e., actual production rate/time data) with a "model." Assuming that

future production continues to follow the past trend, we can use these models to

estimate original gas in place and to predict ultimate gas reserves at some future

reservoir abandonment pressure or economic production rate. Alternatively, we can

determine the remaining productive life of a well or the entire field. In addition, we can

estimate the individual well flowing characteristics, such as formation permeability and

skin factor, with decline-type-curve analysis techniques [8].

Decline-curve analysis is a widely used method for analyzing the past and future

performance of production wells especially in low permeability gas reservoirs. In

addition to that, analyzing production data for hydraulic fractured low permeability gas

wells is the more practical method to due partly to the long time necessary to achieve

pseudo radial flow [9, 10]. A number of techniques have been developed by the petro-

leum industry for evaluating well performance. Unfortunately, no single methodology is

perfect and capable of handling all types of data and reservoirs. Theoretical assumpti-

ons, model applicability, and/or data requirements limit each analysis technique [7, 11].

A systematic approach to production data analysis that uses all the best methods

available enables the analyst to obtain a full picture of what is going on with regards to

both reservoir and operations. Furthermore, it provides a greater level of confidence,

when all the methods agree [7].

Decline-curve analysis techniques offer an alternative to volumetric and

material-balance methods and history matching with reservoir simulation for estimating

original gas in place and gas reserves. Application of decline-curve analysis techniques

to gas reservoirs is most appropriate when more conventional volumetric or material-

balance methods are not accurate or when sufficient data are not available to justify

complex reservoir simulation. For example, material-balance methods require estimates

of stabilized shut-in bottomhole pressures (BHP's); however, in low-permeability


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reservoirs where long times are needed for stabilization, accurate shut-in BHP's often

are not available.

Early attempts at decline-curve analysis required finding plotting techniques or

functions that would linearize the production history. Because linear functions are

simple to manipulate mathematically or graphically, the future performance could then

be estimated if we assumed that the production trend remained linear for the remaining

life of the well or reservoir. The most common conventional decline-curve analysis

technique is a linear semilog decline curve, some times called exponential or constant-

percentage decline. Most conventional decline-curve analyses are based on Arps empi-

rical rate/time decline equation,

q t =qi

1bDi t 1 /b (1.1)

Where Di = -dq(t)/dt/q(t) = initial decline rate, days-1. Note that the units of gas

flow rate, time, and initial decline rate in Eq. 1.1 must be consistent.

Depending on the value of the decline exponent b, Eq. 1.1 has three different

forms. These three forms of decline exponential, harmonic and hyperbolic-have a diffe-

rent shape on Cartesian and semilog graphs of gas production rate vs. time and gas pro-

duction rate vs. cumulative gas production.

Arps decline analysis (exponential or hyperbolic) gives reasonable answers in

many situations. One of the most attractive features of the Arps methodology is its

simplicity. Because it is an empirical method, it requires no knowledge of reservoir or

well parameters. However it has its failings, the most important one being that it

completely ignores the flowing pressure data. As a result, it can underestimate or over-

estimate the reserves [2, 3 and 7].

Fetkovich was the first to extend the concept of using type curves to transient

production. The Fetkovich methodology uses the same Arps depletion for the analysis

of boundary-dominated flow and constant pressure typecurves (originally developed by

VanEverdingen and Hurst) for transient production. The most valuable feature of type-

curves lies not in the analysis, but in the diagnostics [2, 7].

Blasingame and Agrawal-Gradner (Modern) methods are similar to Fetkovich in

that they use typecurve for production data analysis. However, the primary difference is

that the modern methods incorporate the flowing pressure data along with production


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rates and they use analytical solutions to calculate hydrocarbons-in-place. Two features

of modern analysis that improve upon the traditional techniques are:

- Normalizing rates using flowing pressure enables the effects of back pressure

changes to be accommodated in the reservoir analysis.

- Handling the changing compressibility of gas with pressure using pseudo-time,

as the time function enables the gas material balance to be handled rigorously as the

reservoir pressure decreases with time [4, 5 and 7].

Hydraulic Fractured

Most gas wells, especially those in low-permeability formations require

hydraulic fracturing to be economically feasible producers. Interpretation of pressure

and production data in hydraulically fractured wells is important for evaluating the

success of fracture treatments and predicting the performance of fractured wells.

When a well is fractured, the effect on well performance is equivalent to an

improvement of the wellbore radius. In terms of constant-pressure rate behavior, stimu-

lation yields an initial increase in rate (sometimes 10 or even 100-foot) then followed by

a rapid decline in production rate [12].

The behavior of a stimulated well can be analyzed using the radial flow model,

where the fracture is quantified in terms of an equivalent wellbore radius. Two factors

reflect the effect of stimulation on production:

1. Dimension of Fracture (w and xf), and

2. Flow Conductivity of Fracture (FCD).

In pressure and production analysis the vertical fractures are usually classified

according to one of three models:

1. Infinite Conductivity model: assumes negligible pressure loss in the fractures.

2. Uniform Flux model: assumes a slight pressure gradient in the fracture,

3. Finite Conductivity model: assumes constant and limited permeability in the

fracture.


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Skin Flow Effect

It is not unusual for materials such as mud filtrate, cement slurry, or clay

particles to enter the formation during drilling, completion or workover operations and

reduce the permeability around the wellbore. This effect is commonly referred to as a

wellbore damage and the region of altered permeability is called the skin zone. This

zone can extend from a few inches to several feet from the wellbore. Many other wells

are stimulated by acidizing or fracturing which in effect increase the permeability near

the wellbore. Thus, the permeability near the wellbore is always different from the

permeability away from the well where the formation has not been affected by drilling

or stimulation. Those factors that cause damage to the formation can produce additional

localized pressure drop during flow. This additional pressure drop is commonly referred

to as ∆pskin. On the other hand, well stimulation techniques will normally enhance the

properties of the formation and increase the permeability around the wellbore, so that a

decrease in pressure drop is observed. The resulting effect of altering the permeability

around the well bore is called the skin effect [13].

Non-Darcy Flow Coefficient

In general, the main feature that makes the interpretation of gas wells more

difficult to analyze than oil wells is the presence of non-Darcy effects due to high-

velocity flow around the wellbore and the wellbore storage effects. Non-Darcy effects

have been commonly treated as an additional rate-dependent skin. Several authors have

presented different techniques for rate-decline analysis of gas wells under the influence

of high-velocity flow effects. These techniques were based on either simulated results or

analytical methods [14, 15].

There are two main options to address the Non-Darcy flow factor [18].

First, is to focus on the impact of Non-Darcy flow on the well productivity. This

is what has been done historically using rate dependent skin. The Non-Darcy flow effect

is simulated by an additional skin using the linear function of the rate:

S total=S 0dsdq and

dsdq

=Dq (1.2)

Where D is called the linear Non-Darcy flow coefficient.


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Second, is to model Non-Darcy flow be numerically integrating the Forscheimer

equation in the mode. The non linear Non-Darcy flow effect is included in the flow

equation through the value of the non linear Non-Darcy flow coefficient ( β ) which

appears in the Forcheimer equation:

∂ p∂ x

= μk⋅uβ⋅ρ⋅u2 (1.3)

It can be evaluated from the linear assumption described above using dsdq with:

β≈ds/dq⋅2πr w⋅h⋅μ

k(1.4)

Or from an empirical equation:

β= 0 .005[φ⋅1−S w]

5.5⋅k0.5

When non-Darcy flow occurs along the fracture, analysis of the pressure

transient test data using conventional analyses methods will produce incorrect values of

fracture conductivity and fracture half-length [16, 17]. As a result, the determination of

the Non-Darcy flow coefficient presents the most challenging task that the petroleum

engineers face in hydraulically fractured low permeability gas well testing [14].

Modeling

Reservoir modeling is an essential, but often overlooked step in effective

production data analysis. Its primary purpose is as an independent confirmation that the

analysis performed is, indeed valid. The underlying model solution can be either analy-

tical or numerical, and the inputs are obtained from the diagnostics and fluid in place.

The results of a model history match will indicate whether the diagnostics and

analysis of the production data is consistent and valid. For example, if the Blasingame

typecurves indicates that boundary dominated flow has not been reached, this can be

confirmed by testing the history match sensitivity to varying the model volume (fluid in

place) [7].


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TOPAZE SOFTWARE FEATURES

Topaze is one of those applications that is used in the petroleum industry to

manage and analyze production and pressure data. Topaze is a windows-based

application for production data interpretation by KAPPA Engineering. Topaze combi-

nes traditional decline curve (old methods) that assume constant pressure or empirical

decline functions with modeling capabilities ranging from analytical single well to

numerical 2-D multi well models. Some key features of Topaze will now be

highlighted [20]:

Decline Curve Analysis and Type Curve Matching

Arps is a classical decline curve analysis on specialized scale: log(q) vs t, q vs Q,

log(q) vs Q. The automatic and user-defined regressions best fits the end of the data and

displays the best matching decline function which may be interactively changed.

Fetkovich Type-Curve plot is used to process data even in the absence of permanent

pressure gauges assuming constant producing conditions. Normalized rates and cumula-

tive production can be superimposed on the selected type curve.

Diagnostic Tools

Blasingame plot displays instant and average productivity index with respect to

material balance time. It also calculates the derivative, in a display similar to an 'upside

down' loglog plot tending to a negative unite slope when pseudo-steady state is reached.

The log-log plot can be used as a diagnostic tool with exceptionally clean data. When

data is more scattered some trends may still be detected. The simulated model can be

compared to the data on this plot.

Modeling and Non-Linear Regression

Topaze offers the unique capacity to simulate pressure from production history,

or simulate rates and cumulative production from pressure history, or both simulta-

neously. Non-linear regression allows history matching, minimizing the error in terms

of pressures, rates, cumulative production or any weighted average.

Production Forecast

Without data or after history matching, a production forecast for any analytical

or numerical model may be run based on anticipated producing pressure. Sensitivity to

improvement or decay of productivity index can also be simulated. In addition, this

forecast may then be exported in a variety of file and data base formats.


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DATA DESCRIPTION

Two fractured gas wells in low permeability reservoir are used to illustrate the

proposed objectives of this study.

WELL No. 1:

Production history and well head pressure data for a fractured gas well (field

example) in low permeability reservoir is loaded into Topaze. The production history

plot is shown in Fig. 1.1, while Table 1 shows gas and reservoir properties. Using

Topaze software, the well head pressure data was converted to downhole pressure at

11225 ft by the "Cullender & Smith" flow correlation as shown in Fig. 1.2. The objec-

tive is to find out if there is any difference between the two pressure data in processing

production data for fractured gas wells.

Buildup test was conducted on this well after the hydraulic fractured job and

pressure derivative plot is shown in Fig. 1.3. Table 2 reports the estimated reservoir and

fractured parameters from pressure transient analysis.

WELL No. 2:

Assuming that the Non-Darcy flow coefficient is negligible and using the same

employed gas and reservoir properties illustrated in Table 1. Flowing pressure and

production history are predicted using Topaze software. Fig. 1.4 shows the simulated

production history and pressure data. Table 3 captures the pre-define fracture and

reservoir parameters for pressure prediction model.

RESULTS AND DISCUSSION

WELL No. 1:

In this well, the traditional decline analysis (Arps plot) will over-estimate the

reserves. The main reason is that Arps decline analysis is tied to production constraints;

its reserve is calculated by assuming that the flowing pressure is constant with time [4].

Fig. 2.1 shows Arps's exponential plot indicating reserves of approximately 19.1 bscf.

The STGIIP estimated using Material Balance plot (Normalized Rate-Cumulative plot)

is approximately 16.3 bscf as shown in Fig 2.2. There is no way that STGIIP can be

lower than reserves. As a result, just knowing the current production constraint is not


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adequate to estimate the reserves unless the flowing pressure is relatively constant with

time, Arps decline analysis will yield to reasonable result.

Figs. 2.3 through 2.6 show the production history, Blasingame, Fetkovich and

loglog plots using well head pressure data. The data was plotted in loglog and

Blasingame plots using Normalized pressure integral function to reduce the noise level

on the pressure derivative. From the match, it is clear that the well production is

boundary-dominated. The estimated permeability and gas initially in place (SGIIP)

parameters from Blasingame Fetkovich and loglog plots are similar and they are

reported in Table 4. The estimated SGIIP value using these methods is approximately

15.6 bscf. Using the Material Balance method, the SGIIP is 16.3 bscf. There is not

much difference in estimation of the SGIIP; only 0.7 bscf difference between the

Material Balance method and the other methods.

Blasingame and loglog plots, Figs. 2.4 and 2.5 respectively, show clearly that the

early, transient and boundary flows are matched with the selected model. From the early

time in loglog and Blasingame plots, the fracture properties are estimated and they are

reported in Table 2.1. Also, from the early time of pressure derivative one should be

able to calculate the wellbore storage coefficient. However, from the Topaze's help

menu, it is stated that the calculation option of wellbore storage coefficient has not yet

been implemented. With this software limitation, the wellbore storage effect will not be

determined and investigated.

From the match, the Non-Darcy coefficient is negligible and does not affect the

production history, Blasingame and loglog plots match as shown in Figs. 2.3 through

2.5. The reason could be due to using wellhead pressure in the production interpretation.

So, Non-Darcy coefficient will not be demonstrated in this case.

In the Fetkovich plot, Fig. 2.6 shows that the transient and boundary are matched

and the estimated permeability and original gas in place are captured in Table 4. Since

the Fetkovich methodology was designed as a diagnostics tool for the analysis of transi-

ent and boundary-dominated flow at constant pressure [4, 6], the fracture properties,

Non-Darcy and wellbore storage coefficients will not be estimated using the Fetkovich

method.

Figs. 2.7 through 2.12 show matched Arps, Fetkovich, Normalized Rate-Cumu-

lative, Production history, Blasingame, and log-log plots respectively, using converted


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pressure at bottom hole depth. Table 5 captures the selected model, gas and reservoir

estimated parameters. The objective mainly is to do a comparison between wellhead

pressure calculations and flowing pressure in production analysis technique.

The estimated STGIIP using Material Balance plot (Normalized Rate-Cumula-

tive plot) as shown in Fig. 2.7 is approximately 20.3 bscf. This value is higher than the

estimated STGIIP using wellhead pressure data. The main reason is because of the

selected initial pressure in this case is higher than the defined initial pressure at well-

head pressure data. In flowing pressure the selected initial pressure is approximately

8208 psia, while the initial pressure using wellhead pressure is 6700 psia. Therefore,

this change in initial pressure will affect all the diagnostic methods Blasingame and

loglog plots as shown in Table 5 in estimating the gas in place (STGIIP) parameter.

However, the Arps and Fetkovich plots, Fig. 2.8 and Fig. 2.9 respectively, will

not be affected by the pressure change condition. We get the same reserve estimation

(19.1 bscf) in both methods compared with the wellhead pressure results. The main

reason is that these two methods assume the flowing pressure is constant with time. So,

using wellhead or flowing pressure in both method should give the same parameter

estimation.

Fig. 2.10 shows the production history plot, and that the flowing pressure data

are matched successfully with selected model. The selected model takes into account

the mechanical skin at the wellbore. Based the on selected model as captured in Table 2,

the mechanical skin is assigned positive value 0.8 to be able to match the production

history data successfully with selected model. In the previous interpretation using

wellhead pressure, the mechanical skin effect was absent and negligible.

Moreover, in the loglog plot the wellbore storage and fracture behavior usually

defined in the early time of pressure derivative as shown in the plot Fig. 2.11, where

they were defined using wellhead pressure. Table 5 illustrates the estimated parameters

of the fracture based on the selected model. Again the wellbore storage coefficient will

not be estimated due to software limitation in computing this parameter.

The estimated fracture conductivity which is approximately (Fc= 4400 md.ft) is

almost similar to the estimated fracture conductivity (Fc= 4410 md.ft) using surface

pressure data. However, the estimated fracture half length (xf= 80 ft) using downhole

pressure is higher than the estimated value (xf= 40.2 ft) using wellhead pressure data.


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The main reason is due to the presence of mechanical skin and turbulent flow near the

wellbore.

Non-Darcy flow effect becomes visible with the selected model using downhole

pressure data, while it was not shown in the wellhead pressure interpretation. The main

reason is that the well is produced with high production rate. Moreover, the presences of

mechanical skin around wellbore causes Non-Darcy flow around wellbore. However,

with the current version of Topaze, this parameter can not be estimated using linear

method, it requires Non-linear model to estimate the Non-Darcy flow. Since the damage

around wellbore and Non-Darcy flow exist in the select model, the permeability estima-

tion will be affected by these two parameters. In downhole pressure the estimated

permeability is approximately (k = 0.959 md) as shown in Table 5, while the estimated

permeability using wellhead pressure is (k = 1.06 md). There is 10 % error of estimating

permeability in the downhole pressure situation.

From Table 4 it is shown that the gas and reservoir properties estimated by

production analysis using surface pressure are almost similar to the pressure transient

analysis results as shown in Table 6. However, from Table 5 we see the difference in

estimating the gas, fracture and reservoir parameters using converted downhole pressure

with pressure transient analysis. The presence of damage and turbulence around the

wellbore in downhole pressure data interpretation, while they are not shown in the

pressure transient analysis, causing the unmatched result] we observe that. Even if there

is a difference in computing the parameters, with long-term surface production and

pressure (wellhead or downhole) history you will still be able to define the reservoir

boundary and initial gas in place without shutting the well for long times especially for

low permeability reservoir

WELL No. 2:

In this simulated well, a traditional decline analysis (Arps plot) will significantly

under-predict the reserve. The reason again, lies in the flowing pressure. Fig. 2.13

shows Arps exponential plot indicating the reserves of approximately 0.738 bscf. The

STGIIP estimated using Material Balance plot (Normalized Rate-Cumulative plot) is

approximately 125 bscf as shown in Fig. 2.14.


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Figs. 2.15 through 2.18 show the production history, Blasingame, Fetckovich

and loglog plots match. The simulated flowing pressure and production data was plotted

in log-log and Blasingame plots using Normalized pressure integral function to reduce

the noise level on pressure derivative. The log-log and Blasingame plots show that the

early, transient and boundary flow are matched with selected model. The gas, reservoir

and fracture properties estimated using these methods are reported in Table 4.

In the Fetkovich plot Fig. 2.17, the transient and boundary flow are matched but

the early time flow is absent. The reason is that Fetkovich methodology is a diagnostics

tool that is used to analysis transient and boundary dominated flow at constant pressure

[4, 6]. The fracture properties, Non-Darcy and wellbore storage factor will not be

estimated using this technique.

The radial flow (Transient flow) was easy to define in this well compared with

the field example. As shown in the production history plot Fig. 2.15. The main reason is

that this well has more build pressure period. However, in the previous well (Field case)

there is no build up pressure period shown in production history Fig. 2.3. The absence

of a properly defined transient flow period may lead to errors in the permeability

estimation.

CONCLUSIONS

From the study of production history and pressure data of fractured gas wells,

the following conclusions are drawn:

Analyzing production history and pressure data of a hydraulically fractured gas

well can be an effective way to estimate reservoir properties and gas in place without

shutting the well for long period of time, especially for low permeability reservoirs.

This conclusion is consistent with Refs. 2.

Arps decline analysis will yield reasonable estimation of reserve if the flowing

pressure is relatively constant. However, just knowing the current production constraint

is not adequate to estimate the reserves.

Fetkovich methodology was designed as diagnostics tool for analyzing transient

and boundary dominated flow at constant pressure.


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The modern methods such as Blasingame, Normalized Pressure Integral and the

Flowing Material Balance are valuable analysis tools for production history and

pressure data.

The Flowing Material Balance method provides convenient and sensitive way to

estimate Gas in place without shut-in pressure except for Pi. This method has better

resolution for boundary dominated flow than any of the production analysis methods.

Non-Darcy flow and mechanical skin effects in production analysis were defined

and estimated using converted downhole pressure, while they were not observed in the

wellhead pressure data interpretation. Due to limitation in Topaze software, the

wellbore storage and Non-Darcy flow effects were not estimated in both pressure

conditions.

Using downhole pressure data in production analysis will be more represen-

tative and descriptive of the reservoir than using wellhead pressure data for gas wells.

There is difficulty with determining the most appropriate transient interpretation

in well no. 1. However, it was easy in the simulated well due to the existence of build

up period in pressure data.

Recommendations

Agrawal-Gradner methodology should be considered for evaluating production

analysis for fractured gas well in low permeability reservoir.

Enhance Topaze functionality to handle Non-Darcy flow and wellbore storage

calculation for further study on the effect of these two parameters on production history

and pressure analysis in low permeability reservoir.

Future studies should consider the flowing pressure data on Decline-curve

analysis.

ACKNOWLEDGEMENTS

The authors of this paper would like to acknowledge the Research Center of

College of Engineering at King Saud University for providing the finance support for

this study.


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19. Palacio, J.C. and Blasingame, T.A., Decline Curve Analysis Using Type-

Curves: Analysis of Gas Well Production Data, paper SPE25909, (1993)

20. Topaze Help Manual and Brochure, Kappa Engineering Inc.

http:// www.kappaeng.com .

21. Slider, H.C. Worldwide Practical Petroleum Reservoir Engineering Methods,

Tulsa, Oklahoma (1983).

22. Jacques, H., Automatic Decline-Curve Analysis of Wells in Gas Reservoirs,

Paper SPE 77187 presented at the SPE Reservoir Evaluation & Engineering Technology

Symposium, December 2003.

23. Fetkovich, M.J., et al., Decline Curve Analysis Using Type Curves – Case

Histories, SPE (December 1987), 637-656.

24. Anderson, D., and Mattar, L., Practical Diagnostics Using Production Data

and Flowing Pressures, Paper SPE 89939 presented at the SPE Annual Conference and

Exhibition, Huston, Texas, U.S.A., 26-29 September 2004.


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NOMENCLATURE

A = drainage area, ft2

B = decline exponentBg = gas formation volume factor, ft3/scfCA = Dietz shape factorCt = total compressibility, cpDi = initial decline rate, day-1

D = linear Non-Darcy flow coefficient, [Mscf/day]-1

FCD = fracture conductivity, md.ftGi = gas initial in place, bscfh = formation thickness, ftI(te) = integral of normalized pressure, [psia2/cp]I'(te) = derivative of the integral of normalized pressure, [psia2/cp]k = permeability, mdkskin = permeability at damage zone, mdkh = well flow capacity, md.ftm(p) = pseudo pressure, [psia2/cp]mpss = slope at pseudo steady-state flow rate, 1/[bscf.cp]Np = ultimate recovery, bscfpi = initial pressure, psiapw = well flowing pressure, psiaPsc = pressure at standard condition, psiaPp = pseudo pressure, [psia2/cp]PI = normalized rate, [psia2/cp]-1

PIInt = normalized rate integral, [psia2/cp]-1

PIInt.D.= normalized rate integral derivative, [psia2/cp]-1

q = flow rate, Mscf/day qi = initial flow rate, Mscf/dayqDd = decline curve dimensionless flow rateqD = dimensionless flow rateQ = cumulative production rate, scfQDd = decline curve dimensionless cumulativeQDA = normalized rate cumulative, [Mscf/day]/[psia2/cp]rw = wellbore radius, ftre = effective wellbore radius, ftS = skin, dimensionlessStotal = total skin, dimensionlessS0 = mechanical skin, dimensionlessSw = water saturationt = time, hrtD = dimensionless timetDd = decline curve dimensionless timetcr = the constant rate time, hrte = pseudo normalized time, hrT = temperature, oFTsc = temperature at standard condition, oFwf = fracture width, ft


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xf = fracture half length, ft z = z-factor, dimensionless∆pskin = pressure drop due to skin, psiaµ = viscosity, cpφ = effective porosityπ = 3.14γ = Euler's constant, 0.577216ρ = density, gm/ccβ = turbulence factor or Forcheimer factor, ft-1

Table 1 Gas and Reservoir Properties- Field Case

Gas PropertiesGas Specific Gravity 0.73Gas Compressibility, psia-1 6.0 x 10-6

Well and Reservoir ParametersProductivity thickness, ft 50Wellbore Radius, rw, ft 0.35Porosity 0.13Reservoir Temperature, F 259Reservoir Pressure, psia 7250

Table 2 Estimated Well and Reservoir Parameters- Pressure Transient Analysis

Selected ModelWell Fracture-Finite ConductivityReservoir Radial CompositeBoundary Circle, No FlowWell and Reservoir ParametersWell bore Storage Coefficient, C, bll/psi 0.177Total Skin, S -4.28Fracture Half Length, xf, ft 52.7Fracture Conductivity, Fc, md.ft 4320Initial Pressure, Pi, psia 6729.8Flow Capacity, k.h, md.ft 55.3Permeability, k, md 1.11


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Table 3Pre-Defined Well and Reservoir Parameters

Selected ModelWell Fracture-Finite ConductivityReservoir HomogeneousBoundary Circle, No FlowWell and Reservoir ParametersTotal Skin, S -4.03Fracture Half Length, xf, ft 143Fracture Conductivity, Fc, md.ft 5220Initial Pressure, Pi, psia 5000Flow Capacity, k.h, md.ft 1630Permeability, k, md 32.5

Table 4Estimated Well and Reservoir Parameters using

wellhead pressure data Production Analysis

Selected ModelWell Fracture- Finite ConductivityReservoir HomogenousBoundary Circle, No FlowWell and Reservoir ParametersTotal Skin, S -4.02Initial Pressure, Pi, psia 6700Fracture Half Length, xf, ft 40.2Fracture Conductivity, Fc, md.ft 4410Flow Capacity, k.h, md.ft 53.1Permeability, k, md 1.06Stock Tank GAS Initially in Place, STGIIP, bscf 15.6Stock Tank GAS in Place, STGIP, bscf 13.4


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Table 5Estimated Well and Reservoir Parameters using

flowing pressure data Production Analysis

Selected ModelWell Fracture- Finite ConductivityReservoir HomogenousBoundary Circle, No FlowSkin 0.8Geometrical Skin -4.69Well and Reservoir ParametersTotal Skin, S -3.9Initial Pressure, Pi, psia 8208Fracture Half Length, xf, ft 80Fracture Conductivity, Fc, md.ft 4400Flow Capacity, k.h, md.ft 47.9Permeability, k, md 0.959Stock Tank GAS Initially in Place, STGIIP, bscf 17.4Stock Tank GAS in Place, STGIP, bscf 15.3

Table 6Estimated Well and Reservoir Parameters- Pressure Transient Analysis

Selected ModelWell Fracture-Finite ConductivityReservoir Radial CompositeBoundary Circle, No FlowWell and Reservoir ParametersWell bore Storage Coefficient, C, bll/psi 0.177Total Skin, S -4.28Fracture Half Length, xf, ft 52.7Fracture Conductivity, Fc, md.ft 4320Initial Pressure, Pi, psia 6729.8Flow Capacity, k.h, md.ft 55.3Permeability, k, md 1.11

Table 7Estimated Well and Reservoir Parameters-Simulated Case


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Selected ModelWell Fracture-Finite ConductivityReservoir HomogeneousBoundary Circle, No FlowWell and Reservoir ParametersTotal Skin, S -4.03Fracture Half Length, xf, ft 143Fracture Conductivity, Fc, md.ft 5220Initial Pressure, Pi, psia 5000Flow Capacity, k.h, md.ft 1630Permeability, k, md 32.5Stock Tank GAS Initially in Place, STGIIP, bscf 124Stock Tank GAS in Place, STGIP, bscf 124

Figure 1.1. Production history plot, well head pressure vs Time- Field Case

Figure 1.2. Production history plot, downhole pressure vs Time- Field Case

Figure 1.3. Pressure Derivative Matched plot


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Figure 1.4. Production history plot, Pressure vs Time- Simulated Case

Figure 2.1. Arps's Exponential plot-Wellhead pressure

Figure 2.2. Material Balance plot (Normalized Rate-Cumulative plot)-Wellhead pressure


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Figure 2.3. Matched Production history plot-Wellhead pressure

Figure 2.4. Matched Blasingame plot-Wellhead pressure


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Figure 2.5. Matched Loglog plot-Wellhead pressure

Figure 2.6. Matched Fetkovich plot-Wellhead pressure


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Figure 2.7. Material Balance plot (Normalized Rate-Cumulative plot)-Downhole pressure

Figure 2.8. Arps's Exponential plot-Downhole pressure


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Figure 2.9. Matched Fetkovich plot-Downhole pressure

Figure 2.10. Matched Production history plot-Downhole pressure


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Figure 2.11. Matched Loglog plot-Downhole pressure

Figure 2.12. Matched Blasingame plot-Downhole pressure


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Figure 2.13. Arps's exponential plot-Simulated Case

Figure 2.14. Material Balance plot (Normalized Rate-Cumulative plot)-Simulated Case

Figure 2.15. Matched Production history plot-Simulated Case


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Figure 2.16. Matched Blasingame plot-Simulated Case

Figure 2.17. Matched Fetkovich plot-Simulated Case


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Figure 2.18. Matched Loglog plot-Simulated Case


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