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# Types of decline analysis in production forecasting

The production forecasting guidelines will address the following types of decline analysis:

• Traditional decline — generates a forecast of future production rates based on the equations defined by Arps. This is outlined under decline curve analysis. The traditional decline analysis can also be modified to a terminal / limiting decline rate.
• Duong decline — an empirical method developed specifically for low permeability systems exhibiting long periods of transient flow.
• Multi-segment decline-generates a three-segment arps decline that allows each segment to capture distinct flow regimes, including transient flow (b > 1), boundary-dominated flow (0 < b < = 1), and exponential decline (b = 0).
• Power law decline

## Terminal / limiting decline rate

The terminal / limiting decline rate begins as a hyperbolic decline curve and transitions into an exponential decline curve at a specified limiting effective decline rate, dlim. There are two options for the dlim value: “dlimexponential” and “dlimhyperbolic”. When using the “dlimexponential” , the decline will transition such that the exponential portion of the decline will have an effective decline rate of the dlimvalue specified. When using the “dlimhyperbolic” , the decline will transition when the hyperbolic portion reaches the specified dlim value. The exponential portion will then have an effective decline rate that is different from the dlim value.[1]

## Stretched exponential decline

The stretched exponential decline method is a variation of the traditional Arps method, but is better suited to unconventional reservoirs due to its bounded nature. One of the benefits of this method is that for positive n, τ, qi, the model gives a finite value of EUR, even if no abandonment constraints are used in time or rate.[2] [3] [4] [5] [6]

## Duong decline

The duong method was developed specifically for unconventional reservoirs with very low permeability. The shape of the curve is suited for wells that exhibit long periods of transient flow. The duong method will reach a finite eur, and tends to be more conservative than traditional Arps declines with b > 1. [7] The assumption in this case is an increase in fracture density over time due to pressure depletion.

Q1 is rate at day 1, a and m are constants generated from log-log q/gp vs days while t is in days. An estimate of a and m can be derived from the intercept on y axis and the slope respectively. A plot of t versus q is made and a slope of the line’s best fit indicate rate at day 1. The intercept is q∞ which is the flow rate at time= ∞.

INSERT Figure 1 – Duong’s specialized plot for a and m. (Pending permission approval)

## Modified Duong’s model

Duong’s original model is suitable for production forecasts in tight gas reservoirs and shales and it is also related only to linear flow. Now if there exists boundary dominated flow in a shale or tight gas reservoir, Joshi (2013)[8] suggests some changes to Duong’s model:

1. The line of best fit on q versus t plot may not regress through the origin or in other words, q∞ ≠0
2. A change from transient flow to boundary dominated flow can be modeled using a hyperbolic decline of 5%

## Multi-segment decline

The multi-segment method generates a three-segment Arps decline that allows each segment to capture distinct flow regimes, including transient flow (b > 1), boundary-dominated flow (0 < b < = 1), and exponential decline (b = 0). This method is well-suited for unconventional reservoirs that exhibit multiple flow regimes.

## Power law decline (ilk)

The power law exponential was originally introduced by Ilk et al (2008)[6]. It is as defined by “loss ratio” and its derivatives originally presented by Johnson and Bollens (1927)[9] and Arps (1945)[1].

In the case of tight gas formations, the d parameter can be expressed in the form of power law function in hydraulically fractured reservoir (Matter et al 2008). The power law loss ratio decline equation by Ilk et al (2008a)[6] is represented as:

N is defined by

These equations outlined above combined with hyperbolic rate decline relation can be used to predict reserves in tight gas reservoirs. The power law denoted above can also be used to model transient, transition as well as boundary dominated flow. It is also important to match the loss ratio and its derivatives to field data using a smoothing factor similar to bourdet’s derivative (1989).

## Logistic growth model

Logistical growth models are based on the underlying principles of population growth which stipulates that growth is possible up to a certain size. Clark et al (2011) generated a growth model to predict production from single wells using the following equations:

K is the recoverable resource. A couple of examples comparing the different empirical methods are culled from Kanfar et al (2012).

### Type curve analysis

Type curve analysis methods:

• Gringarten (specifically undersaturated oil)
• Agarwal-gardner
• Blasingame
• Compound linear
• Normalized pressure integral
• Wattenbarger
• Fetkovich
• Transient

## Type curve models

Cylindrical reservoir with a vertical well in the center.

### Fracture

Cylindrical or rectangular reservoir with an infinite conductivity fracture in the center.

### Water drive

Cylindrical reservoir with a concentrically cylindrical aquifer. This model is based on a radial composite model, with the outer region representing the aquifer, characterized by several different levels of aquifer mobility, relative to the reservoir. The mobility ratios range from zero (no aquifer) to 10 (effectively constant pressure boundaries). The aquifer model assumes a water zone of infinite extent.

### Horizontal

Square reservoir with a horizontal well in the center. There are actually nine different horizontal well models. Each model represents a different penetration ratio "le /2xe"(ratio of effective wellbore length to reservoir length) and dimensionless wellbore radius "rwd" (ratio of effective wellbore radius to effective wellbore length).

### Elliptical

elliptical reservoir with a finite conductivity fracture in the center.

### Finite conductivity fracture

Cylindrical (Blasingame) or square (transient) reservoir with a finite conductivity fracture in the center.

## Gringarten type curve analysis

Gringarten presented a type curve, commonly called the gringarten type curve, that achieved widespread use. It is based on a solution to the radial diffusivity equation and the following assumptions: vertical well with constant production rate; infinite-acting, homogeneous-acting reservoir; single-phase, slightly compressible liquid flowing; infinitesimal skin factor (thin "membrane" at production face); and constant wellbore-storage coefficient. These assumptions indicate that the type curve was developed specifically for drawdown tests in undersaturated oil reservoirs. The type curve is also useful to analyze pressure buildup tests and for gas wells.

In the Gringarten type curve, pd is plotted vs. The time functiontd/cd, with a parameter cde2s Fig 2. Each different value of cde2s describes a pressure response with a shape different (in theory) from the responses for other values of the parameter. However, adjacent pairs of curves can be quite similar, and this fact can cause uncertainty when trying to match test data to the "uniquely correct" curve.

INSERT Figure 2 – Gringarten type curve with parameter (Pending permission approval)

## Agarwal-Gardner type curve analysis

The Agarwal-Gardner type curve analysis (spe 057916, 1998) is a practical tool that can easily estimate the gas (or oil) in-place, as well as reservoir permeability, skin effect, and fracture half-length (for hydraulically fractured wells). The accuracy of this analysis has been verified through numerical simulations. These modern decline type curves represent advancement over Blasingame type curves because a clearer distinction can be made between transient and boundary-dominated flow periods. This method also features curves containing derivative functions, similar to those used in the pressure transient literature, to aid in the matching process. The raw data derivative can also be used to assist in flow regime interpretation.

The Agarwal-Gardner type curve analysis method uses the following models:

• Fracture (cylindrical)
• Water drive

## Boundary-dominated match

To obtain information about reserves and drainage areas, it is recommended to focus on the boundary-dominated (depletion) stems of the type curves. The Agarwal-Gardner type curve analysis does not require hyperbolic exponent values. Instead, the data is matched on the single depletion stem.

## Transient match

To obtain information about permeability and skin, it is recommended to focus on the transient stems of the type curves. The outputs are normally:

• Skin for a radial model.
• Fracture half-length for a fracture model.
• Mobility ratio and skin for a water-drive (transient) model.

## Blasingame type curve analysis

Blasingame represents the first of the modern type curve methods.[10] It features pressure normalized rates, and introduces the concept of material balance time (i.e. boundary-dominated superposition time) to generate fully analytical constant rate type curves featuring a single depletion stem, regardless of the reservoir structure (shape and size) or drive mechanism. Blasingame analysis results include skin factor, formation permeability, in-place fluid volumes, and reservoir drainage area. The flow rate integral and flow rate integral derivative functions allow for more accurate decline type curve matches than would be possible using flow-rate data alone. These integral functions also eliminate problems associated with the analysis of field production data with erratic production rate and bottom-hole pressure behavior. Blasingame analysis is particularly useful in the modeling of suspected elliptical drainage patterns and open-hole horizontal wells, which have transitioned into boundary-dominated flow.

The Blasingame type curve analysis method uses the following models:

• Fracture (cylindrical)
• Water drive
• Horizontal
• Elliptical flow
• Finite conductivity fracture (cylindrical)

### Boundary-dominated match

To obtain information about reserves and drainage area, it is recommended to focus on the boundary-dominated (depletion) stems of the type curves. The Blasingame type curve analysis does not require hyperbolic exponent values. Instead, the data is matched on the single depletion stem.

### Transient match

To obtain information about permeability and skin, it is recommended to focus on the transient stems of the type curves. Outputs are normally:

• Permeability and skin for the radial model.
• Permeability and fracture half-length for the fracture model.
• Mobility ratio, permeability, aquifer permeability, and skin for the water-drive (transient) model.
• Vertical and horizontal permeability, and skin for the horizontal model.
• Fracture half-length, major and minor axes of the reservoir, drainage aspect ratio, and penetration ratio for the elliptical flow model.
• Permeability, fracture half-length, and fracture-equivalent skin for the finite conductivity fracture model.

## Compound linear type curve analysis

compound linear type curves are useful for analyzing horizontal multifractured wells producing from tight gas or shale wells. There are two sets of compound linear type curves:

1. Pressure-time: uses normalized pressures - the constant rate solution
2. Rate-time: uses normalized rates - the reciprocal of the constant rate solution

Rate-time and pressure-time are reciprocals of one another, and simply plot the data on the typecurves differently.

### Boundary-dominated match

As the compound linear typ curves were developed using an infinitely large reservoir, there is no boundary-dominated flow stem. However, entering a value for either ye or area (a), will produce a dashed boundary-dominated flow line that intersects the selected type curve. If boundaries have been reached, the production data will deviate from the compound linear type curve onto the boundary-dominated line.

### Transient match

Compound linear type curves were developed for a horizontal, multifractured well in an infinite reservoir. The first half slope indicates linear flow into the fractures, while the second half slope indicates linear flow into the fractured region. The two half slopes are connected by a transition period. Most production data is expected to fall in the transition zone. Matching data to a type curve will give the xs / xf ratio. Assuming a value for number of fractures (nf) will calculate the following values:

• Le
• Xfsqrt(k)
• Xs sqrt(k)
• (xf)y
• Xs

### Skin

Generally, skin effects will impact the first linear flow period, causing the data to deviate from the ideal type curve.

## Fetkovich type curve analysis

the Fetkovich[11] type curve analysis was the first analysis method to use analytical type curve matching for production data. It is a semi-analytical approach in that type curves are generated from analytical solutions of transient (infinite) radial systems at constant flowing pressure, while the boundary-dominated flow period is defined using hyperbolic decline typecurves, originally developed by Arps. In addition to reserves, calculated from the depletion stem (b-value) match, this analysis provides diagnostic power through the determination of reservoir permeability and wellbore skin factor. Rate normalization[6] has been included to account for changing operating conditions (i.e., changes in flowing pressures) to more reliably determine permeability and skin. Re-initialization allows you to analyze the transient production data signature of post-buildup production to diagnose permeability and skin. A clear advantage of this method over modern type curve methods is that it does not plot data using superposition time functions, which may bias the interpretation. It remains a popular technique for the analysis of conventional vertical oil and gas wells. Fetkovich plots are even used to describe the behavior of unconventional well production data. The limitation of this technique is that the transient type curves are restricted to radial flow systems, and the method does not directly calculate original-hydrocarbons-in-place (as is the case in modern methods); it is estimated through simple material balance.

The Fetkovich type curve analysis method uses the following models:

• Fracture (rectangular)

### Boundary-dominated match

To obtain information about reserves and drainage areas, it is recommended to focus on the boundary-dominated (depletion) stems of the type curves. Each of the depletion stems represents a different b value, identical to the b values used in the hyperbolic arps analysis. Once a b value has been selected, recoverable reserves and expected ultimate recovery can be calculated. If a sandface flowing pressure is specified drainage area and original gas-in-place can also be calculated.

### Transient match

To obtain information about permeability and skin, it is recommended to focus on the transient stems of the type curves.

### Time reinitialization

The fundamental assumption in Fetkovich transient analysis is a constant sandface flowing pressure. Although an ideal case, this assumption is rarely representative of true operating conditions, particularly in early (transient) production. A well may be subject to shut-ins or operational changes during its life. When a well is shut-in or undergoes a change in operating conditions, the constant sandface flowing pressure assumption is no longer valid. When the well resumes production, a new additional transient effect is introduced to the wellbore. Additional transient effects in the wellbore are indicated by the green arrows in the screenshot below.

Fetkovich suggested a method called "time reinitialization" to analyze a dataset with multiple transient effects. This method resets the time at the start of each additional transient effect to zero, allowing you to specify additional transient effects on the type curve plot. Once specified, the time associated with the first rate of each new transient flow period is reset to zero. As a result, the dataset is smoothed on the type curve, allowing to continue with the fetkovich type curve match.

## Normalized pressure integral type curve analysis

Normalized pressure integral type curves are the inverse of Agarwal-Gardner type curves. The NPI analysis is often preferred by those who come from a pressure transient analysis domain, and are accustomed to seeing log-log plots using normalized pressure, instead of normalized rates.

The NPI typecurve analysis method uses the following models:

• Fracture (cylindrical)
• Water drive

### Boundary-dominated match

To obtain information about reserves and drainage areas, it is recommended to focus on the boundary-dominated (depletion) stems of type curves.

### Transient match

To obtain information about permeability and skin, you should focus on the transient stems of the type curves. Outputs are normally:

• Permeability and skin for the radial model.
• Permeability and fracture half-length for the fracture model.
• Mobility ratio, permeability, aquifer permeability, and skin for the water-drive (transient) model.

## Transient type curve analysis

Transient type curves are particularly useful for data sets containing long-term transient flow. As opposed to the other modern type curve methods that feature a single depletion stem, the transient module features a single transient stem. The multiple boundary-dominated flow stems correspond to reservoirs of different sizes. It hosts multiple superposition time functions from which to choose. This flexibility is offered for advanced users who have previously diagnosed

The transient type curve analysis method uses the following models:

• Finite conductivity fracture (square)

### Boundary-dominated match

To obtain information about reserves and drainage areas, it is recommended to focus on the boundary-dominated (depletion) stems of the type curves.

### Transient match

To obtain information about permeability and skin, it is recommended to focus on the transient stems of type curves.

Outputs are normally:

• Permeability and skin for the radial model
• Permeability and fracture half length for the finite conductivity fracture model

It should be noted that selecting a type curve on the transient analysis is not a vital step for determining permeability and skin for the radial model (or permeability and fracture half length for the finite conductivity fracture model).

## Wattenbarger type curve analysis

Wattenbarger type curves are used for analyzing linear flow. They are particularly useful in the analysis of shale gas wells, which tend to exhibit long-term linear flow followed by a transition towards boundary-dominated flow.

The Wattenbarger type curve analysis method uses the following model: fracture (rectangular).

### Boundary-dominated match

To obtain information about reserves and drainage areas, it recommended to focus on the boundary-dominated (depletion) stems of type curves.

### Transient match

To obtain information about fracture half length, reservoir size, and well location in the reservoir, it is recommended to focus on the transient stems of type curves.

Outputs are normally:

• Fracture half length
• Reservoir width
• Reservoir length
• Well location

## Adsorption, geomechanical, pss water drive

The adsorption model accounts for the adsorbed portion of the total gas in place when analyzing unconventional gas reservoirs. In some unconventional gas reservoirs, the amount of adsorbed gas is significant. Failing to account for it can lead to a significant underestimation of the in-place and recoverable gas volumes.

The geomechanical model should be used when there is evidence that the reservoir is overpressured. In general, one of the key factors in identifying pressure-dependent permeability behavior is the inconsistency between the static and dynamic data analyses. As a result of compaction, flowing data is affected by the change in the magnitude of permeability of the formation during the flow period. If the geomechanical model is not used, reserves can be drastically underestimated when compared to a static gas material balance analysis. The pseudo-steady state (pss) water drive model can be used to analyze data affected by pressure support from an aquifer. For type curve analysis methods featuring material balance time, boundary-dominated flow is indicated by production data matching on the single depletion stem (unit slope). If the production data deviates from the unit slope upwards, and there is reason to believe water drive is the cause, then it can be modeled using Fetkovich’s water-drive calculations (Dake, 1978), based on two parameters: aquifer size and productivity index (i.e., transfer coefficient).

## References

1. Arps, J. J. 1945. Analysis of Decline Curves. Society of Petroleum Engineers. http://dx.doi.org/10.2118/945228-G.
2. Valko, P. P., & Lee, W. J. 2010. A Better Way To Forecast Production From Unconventional Gas Wells. Society of Petroleum Engineers. http://dx.doi.org/10.2118/134231-MS.
3. Can, B., & Kabir, C. S. 2011. Probabilistic Performance Forecasting for Unconventional Reservoirs with Stretched-Exponential Model. Society of Petroleum Engineers. http://dx.doi.org/10.2118/143666-MS.
4. Kabir, S., Rasdi, F., & Igboalisi, B. 2011. Analyzing Production Data From Tight Oil Wells. Society of Petroleum Engineers. http://dx.doi.org/10.2118/137414-PA.
5. Kabir, C. S., & Lake, L. W. 2011. An Analytical Approach to Estimating EUR in Unconventional Reservoirs. Society of Petroleum Engineers. http://dx.doi.org/10.2118/144311-MS.
6. Ilk, D., Currie, S. M., Symmons, D., Rushing, J. A., & Blasingame, T. A. 2010. Hybrid Rate-Decline Models for the Analysis of Production Performance in Unconventional Reservoirs. Society of Petroleum Engineers. http://dx.doi.org/10.2118/135616-MS. Cite error: Invalid `<ref>` tag; name "r8" defined multiple times with different content
7. Duong, A. N. 2010. An Unconventional Rate Decline Approach for Tight and Fracture-Dominated Gas Wells. Society of Petroleum Engineers. http://dx.doi.org/10.2118/137748-MS.
8. Joshi, K., & Lee, W. J. 2013. Comparison of Various Deterministic Forecasting Techniques in Shale Gas Reservoirs. Society of Petroleum Engineers. http://dx.doi.org/10.2118/163870-MS.
9. Johnson, R. H., & Bollens, A. L. 1927. The Loss Ratio Method of Extrapolating Oil Well Decline Curves. Society of Petroleum Engineers. http://dx.doi.org/10.2118/927771-G.
10. Doublet, L. E., Pande, P. K., McCollum, T. J., & Blasingame, T. A. 1994. Decline Curve Analysis Using Type Curves--Analysis of Oil Well Production Data Using Material Balance Time: Application to Field Cases. Society of Petroleum Engineers. http://dx.doi.org/10.2118/28688-MS.
11. Fetkovich, M. J. 1980. Decline Curve Analysis Using Type Curves. Society of Petroleum Engineers. http://dx.doi.org/10.2118/4629-PA.

## Noteworthy papers in OnePetro

Agarwal, R. G., Gardner, D. C., Kleinsteiber, S. W., & Fussell, D. D. 1999. Analyzing Well Production Data Using Combined-Type-Curve and Decline-Curve Analysis Concepts. Society of Petroleum Engineers. http://dx.doi.org/10.2118/57916-PA.

Fetkovich, M. J. 1980. Enlarged Type Curves Supporting Paper SPE 4629. Society of Petroleum Engineers. https://www.onepetro.org/general/SPE-9086-MS.

Fetkovich, M. J., & Vienot, M. E. 1984. Rate Normalization of Buildup Pressure By Using Afterflow Data. Society of Petroleum Engineers. http://dx.doi.org/10.2118/12179-PA.

Nobakht, M., & Mattar, L. 2012. Analyzing Production Data From Unconventional Gas Reservoirs With Linear Flow and Apparent Skin. Society of Petroleum Engineers. http://dx.doi.org/10.2118/137454-PA.

Siddiqui, A. A., Ilk, D., & Blasingame, T. A. 2008. Towards a Characteristic Equation for Permeability. Society of Petroleum Engineers. http://dx.doi.org/10.2118/118026-MS.

## Noteworthy books

Society of Petroleum Engineers (U.S.). 2011. Production forecasting. Richardson, Tex: Society of Petroleum Engineers. WorldCat or SPE Bookstore