SPE 139118

Production Analysis and Well Performance Forecasting of Tight Gas and Shale Gas Wells D. Ilk, Texas A&M University/DeGolyer and MacNaughton, S.M. Currie, Texas A&M University/Devon Energy Corp., and T.A. Blasingame, Texas A&M University

Copyright 2010, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Eastern Regional Meeting held in Morgantown, West Virginia, USA, 12–14 October 2010. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Estimation of reserves in tight gas and shale gas reservoirs is problematic due to the low to ultra-low permeability characteristics of these reservoir systems. The sole application of conventional decline curve analysis methodologies often yields erroneous reserve estimates. Therefore, the use of theoretically-based production analysis techniques has become a must to analyze well performance and estimate reserves.

The primary objective of this work is to develop a systematic workflow, which integrates model-based production analysis and rate-time relations, for the analysis/interpretation of well performance data in unconventional reservoirs. The major steps in the proposed workflow are:

● Diagnosis of production data. ● Construction of a base well/reservoir model utilizing static well/reservoir data as well as completion/stimulation

parameters. ● Extrapolation of the model to predict well performance along with the use of rate-time decline relations.

The proposed methodology is demonstrated using data from unconventional reservoirs, including a horizontal well with multiple fractures. We present the application of rate-time relations to provide estimates of time-dependent reserves. The use of βq,cp-derivative is also illustrated in distinguishing data characteristics as well as identifying issues associated with data. Rationale for This Work

Unconventional reservoir systems such as tight gas sands, shale gas, tight/shale oil, and coalbed methane reservoirs have currently become a significant source of hydrocarbon production and offer remarkable potential for reserves growth and future production. Unconventional reservoir systems can be described as hydrocarbon accumulations which are difficult to be characterized and produced by conventional exploration and production technologies. Complex geological and petrophysical systems describe unconventional reservoirs in addition to heterogeneities at all scales similar to conventional reservoir systems. Because of the low to ultra-low permeability of these reservoir systems, well stimulation operations (e.g., single or multi-stage hydraulic fracturing, etc.) are required to establish production from the formations at commercial rates.

Gas-in-place/reserves estimation in unconventional (low/ultra-low permeability) reservoirs has recently become a topic of increased interest as advanced technology permits the production and development of these resources domestically and internationally. Production data from unconventional reservoirs exhibit extensive periods of transient flow behavior due to the low/ultra-low permeability characteristics of these systems which often lead to the over-estimation of gas-in-place/reserves with the use of conventional rate-time relations (i.e., exponential and hyperbolic rate-time relations). Because of the uncertainty associated with reserves well/reservoir parameter estimation in unconventional reservoirs, a comprehensive workflow has to be developed. In this work we develop a workflow which includes using both rate-time and production data analysis methodologies (i.e., analytical/semi-analytical solutions) in conjunction to estimate well/reservoir properties and forecast production into future.

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Literature Review

In this section we provide reference on production data analysis of wells completed in low to ultra-low permeability reservoirs. For a hydraulically fractured vertical well in a low permeability reservoir (in particular, tight gas sands), elliptical flow regime should be expected as a transitional flow regime between bi-linear and/or linear flow and pseudoradial flow (Thompson 1981; Roberts 1981). Cipolla, Lolon, and Mayerhofer (2009) also indicate that elliptical drainage areas would exist as a result of long hydraulic fractures based on microseismic mapping results. Riley, Brigham, and Horne develop an elliptical flow solution for the case of an infinite acting reservoir and Amini, Ilk, and Blasingame (2007) provide type curve solutions for hydraulically fractured vertical wells in elliptical drainage areas. The application of elliptical flow type curves is presented in the work by Ilk et al. (2007a). Moreover, plentiful solutions in the literature can be found on hydraulically fractured vertical wells. Therefore, we can conclude that existing production data analysis techniques should be reliable to obtain well/reservoir parameters for hydraulically fractured vertical wells in low to ultra-low permeability reservoirs.

The advances in technology to produce and develop ultra-low permeability reservoirs such as shale gas reservoirs bring the difficulties and uncertainty associated with well performance. The uncertainty is mainly due to the lack of our fundamental understanding of the production mechanisms and behavior of these reservoirs. Currently a handful of diagnostic methods, which are based on linear/compound linear flow concepts exist to diagnose the flow behavior of this type of wells. The solutions based on the "linear flow" concept (Wattenbarger et al. 1998; El-Banbi and Wattenbarger 1998) are frequently used with the inclusion of effective fracture network length accounting for a single vertical fracture. Bello and Wattenbarger (2010) extend the previously mentioned linear flow solutions to account for the natural fracture network in shale gas reservoirs by proposing a linear dual porosity solution. Bello and Wattenbarger state that transient linear flow regime (drainage from matrix to fracture system) should generally be the case for field data in shale gas reservoirs. Consequently, slope of the straight line exhibited by the data, in the rate versus square root of time plot yields the matrix drainage area provided that the matrix permeability is known during transient linear flow regime. The deviations from linear flow can be attributed to skin factor effects. We note that establishing the linear flow trend could often be subjective and the conductivity of fractures might affect the production behavior.

Regardless of diagnostics, for horizontal wells completed with multiple fractures in ultra-low permeability reservoirs, we suggest that multiple-fractured horizontal well model should be used for analysis. The references on this particular well model in fact extend to late 1980s. van Kruysdijk and Dullaert (1989) provide an analytical solution based on "boundary-element method". van Kruysdijk and Dullaert show that at early time dominant flow is linear, perpendicular to the fracture face until pressure transients of the individual fractures begin to interfere leading to a compound linear flow regime at late times (linear flow is seen towards the collections of fractures during compound linear flow regime). Eventually, pseudoradial flow should occur, however we must note that the occurrence of pseudoradial flow regime should not be expected in ultra-low permeability shale gas reservoirs. Other analytical solutions for horizontal wells with multiple fractures include the works by Soliman, Hunt, and El Rabaa (1990), Larsen and Hegre (1991), Guo and Evans (1993), Larsen and Hegre (1994), Horne and Temeng (1995), Chen and Raghavan (1997), and Raghavan, Chen, and Agarwal (1997).

Ozkan et al. (2009) and Brown et al. (2009) present an analytical trilinear flow solution including dual porosity idealization to simulate the pressure transient and production behavior of horizontal wells with multiple fractures. The trilinear solution given by Ozkan et al. (2009) and Brown et al. (2009) is based on coupling of individual "outer reservoir, inner reservoir, and fracture" solutions using the pressure and flux continuity conditions on the interfaces between the regions. We note that dual porosity idealization is used to account for natural fracture network. Meyer et al. (2010) provide an approximate analytical solution for horizontal wells with multiple finite-conductivity transverse fractures. The solution by Meyer et al. is based on a trilinear flow solution (Lee and Brockenbrough 1986) and includes fracture interference.

Medeiros, Ozkan, and Kazemi (2006) present a semi-analytical approach to obtain pressure-transient solutions for heterogeneous systems — this approach gives the ability to model various kinds of well responses in many types of heterogeneous reservoirs including shale gas reservoirs. Amini and Valkó (2010) use a semi-analytical solution, namely the method of "distributed volumetric sources", to predict the performance of a horizontal well with multiple transverse fractures in a bounded reservoir. Amini and Valkó solution includes non-Darcy flow effect in fracture.

For reserves assessments and fluid-in-place estimations, methods based on material balance and pseudosteady-state flow (or boundary-dominated flow) concepts should not be applied for wells in ultra-low permeability reservoirs as the ultra-low permeability nature of the reservoir prevents the occurence of the boundary-dominated flow regime. To conclude, we again note that unconstrained application of Arps' relations to estimate reserves will always yield significant overestimates as these relations are only applicable for the boundary-dominated flow regime.

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Development of the Methodology

As mentioned earlier our workflow includes using rate-time and production data analysis methodologies. Conceptually, our main goal is to obtain consistent results (e.g., reserves estimates) using different techniques. In addition, diagnostics of production data is a major component of our workflow as we seek to understand the behavior/character of data prior to perform analysis. Specifically, diagnostics of production data is important for verifying the correlation between data (i.e., correlation of rates and pressures) and identifying flow regimes (i.e., bilinear/linear flow, boundary-dominated flow, etc.). Once correlation of rates and pressures is verified and flow regimes are identified, a reservoir model can be constructed and model parameters are calibrated to obtain the optimum history match of rates and pressures. We can obtain a production forecast using the reservoir model with calibrated parameter values. Furthermore, we use rate-time relations to supplement the production forecast obtained by the analytical solution. For our purposes we use the methodologies below:

● Diagnostics:

■ Data correlation check (pwf or ptf vs rate, rate and pressure vs time plots) ■ Data review/editing (e.g., well cleanup, recompletions) ■ Data filtering for clarity (elimination of spurious data) ■ Flow regime identification (βq,cp-derivative function) ■ Flow regime identification (pressure drop normalized rate vs material balance time and square root of time plots)

● Rate-Time Analyis:

■ Exponential rate decline relation (Arps 1945 — yields the most conservative reserves estimate) ■ Hyperbolic rate decline relation (Arps 1945 — generally yields the most liberal reserves estimate) ■ Semi-analytical rate decline relation (Ansah et al. 2000 and Ilk et al. 2009) ■ Stretched exponential rate decline relation (Ilk et al. 2008 and Valko 2009)

● Model-Based Production Analyis:

■ Analytical solution for a horizontal with multiple transverse fractures (van Kruysdijk and Dullaert 1989) ■ Analytical solution for a horizontal with multiple transverse fractures (Larsen and Hegre 1991 and 1994) ■ Analytical solution for a horizontal with multiple transverse fractures (Chen and Raghavan 1997)

Our workflow consists of the methodologies summarized above. As indicated, using this workflow yields consistent reserves estimates and reliable well/reservoir parameter values. We demonstrate the use of this workflow with a shale gas field example. Prior to the field example, we describe the βq,cp-derivative function in the next section. βq,cp Derivative Function for Data Diagnostics

Our previous work (Hosseinpour-Zoonozi et al. 2006; Ilk et al. 2007b) has presented the application of the constant-rate formulations of the βq,cr-derivative and βq,cr-integral-derivative functions for the analysis and interpretation of pressure transient and production data, respectively. For production data analysis purposes, constant-rate form of the βq,cr-derivative is obtained by differentiation of rate data with respect to material balance time (i.e., Gp(t)/q(t)). As noted, βq,cr-derivative formulations in the previous work were based on constant-rate solutions. In this work we formulate the βq,cr-derivative as the "constant pressure" form of the βq,cr-derivative and henceforth, we refer to it as the βq,cp-derivative function. The only difference of the constant-pressure form of the βq,cp-derivative is the character of the boundary-dominated flow regime where βq,cp-derivative function exhibits unit slope on log-log scale as opposed to the constant value (i.e., βq,cr(t)=1) for constant-rate form of the βq,cr-derivative function.

For reference the βq,cp-derivative function (constant-pressure form) is given as:

dttdq

tqt

tdtqdtcpq

)()(]ln[

)](ln[)(, −=−=β .................................................................................................................................. (1)

Our goal is to introduce a practical tool for production data diagnostics. The βq,cp-derivative function has significant diagnostic value as the power-law type flow regimes such as linear flow, bilinear flow, etc. appear as constants on log-log scale. For example, if the βq,cp-derivative data indicate a constant value of 0.5, then one can interpret that production data exhibit linear flow. In addition since the βq,cp-derivative is dimensionless, it can be utilized to differentiate the performance of the wells producing in a same field.

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In Fig. 1 we present the computed βq,cp-derivative function data for the wells producing in a shale gas reservoir (Field A). We observe two different production trends in Fig. 1 — Wells A and B follow the same trend, and rest of the wells have the similar βq,cp-derivative response. We can conclude that two distinct production trends are exhibited by the wells producing in this reservoir. Most probably this difference is due to the contrast in permeability as we know that completions are more or less the same for these wells. Furthermore, we note that early time data are affected by non-reservoir effects (e.g., well clean-up, water production, etc.). Field Example

In this section we provide a field example as a means of demonstrating the use of our proposed workflow. Our field example includes data of a horizontal well with multiple fractures obtained from a shale gas reservoir. Fig. 2 presents the rate and the calculated bottomhole pressure data for this well. As observed in Fig. 2, high-frequency rate and pressure data are available. Visual inspection of the data set suggests unusual rate and pressure behavior. Between 300-340 days, rates follow a smooth decline behavior whereas pressures drop drastically. Also, rate and pressure behavior after 360 days exhibit more scatter which might be related with operational issues. In addition, we present the pwf vs q plot in Fig. 3 for only data quality checking purposes. We note that we do not perform analysis in this plot. We observe a general declining trend of the pressures with some scattered data points. The declining trend might be indicative of the depletion of the "stimulated reservoir volume" as we investigate this signature later in the diagnostic and analysis plots. We also note that the bottomhole pressure data are calculated using the casing and tubing pressures.

In Fig. 4 we present the pressure drop normalized rate functions versus material balance time. It is worth to mention that we eliminate the spurious data prior to computing the integral and integral-derivative functions. For this case we observe excellent diagnostic character of the normalized rate functions. The merging trend of the rate-integral and rate-integral derivative functions indicates the depletion of the "stimulated reservoir volume". We do not observe a strong evidence of linear flow for this case as the βq,cr-derivative function data do not clearly exhibit a constant value at 0.5. Also from another point of view, the βq,cp-derivative function data (see Fig. 5) for rate-time data diagnostics indicate a steep increasing trend which also supports the conclusion that the depletion of stimulated reservoir volume is being established.

Next, we employ the horizontal well with multiple fractures model to analyze the data. Fig. 6 presents the pressure drop normalized rate data and model functions versus material balance time. We observe good matches of the data functions with the reservoir model except for early time. Fig. 7 presents the history match of the rate and bottomhole pressure data with the horizontal well with multiple fractures model. As seen in Fig. 7, very good match of the data with the model is obtained until 300 days. The mis-matches after 300 days validate our assumption that pressure and rate data are not correlated after 300 days. The model includes a horizontal well with 36 transverse fractures (well completion indicates 9 stages with 4 clusters) in an infinite-acting reservoir. Therefore, no gas-in-place (i.e., volume) value can be obtained, however we can forecast production to a desired time limit (typically 30 years) to estimate maximum gas production. For this case our production forecast only includes the depletion of the stimulated reservoir volume. The results of model-based analysis are summarized in Table 1 below:

Table 1 — Model-based analysis results and model parameters for the shale gas well.

Effective permeability, k = 360 nd Fracture half-length, xf = 180 ft Fracture conductivity, FcD = Infinite Number of fractures, nf = 36 Skin factor, sf = 0.06 (dimensionless) Gas-in-place, G = N/A Maximum gas production, Gp,max = 5.0 BSCF

To complement model-based production analysis, we use rate-time relations to estimate maximum gas production at 30 years. For our purposes we have developed a spreadsheet* which includes the implementation of the rate-time relations in our workflow. Fig. 8 and 9 present the results for exponential and hyperbolic rate decline relation, respectively. As noted earlier our matches for analyses are dictated by the character of data — that is we do not perform regression or any statistical method for fitting purposes. Figs. 10 and 11 present the results for stretched exponential (or power-law exponential) rate decline relation. We observe similar reserves estimates values using all the rate-time decline relations. However, we must note that this observation is specific to this case and can not be generalized as exponential rate decline relation predicts the most conservative reserves estimate and hyperbolic rate decline relation with b-parameter values higher than 1 generally predicts the highest reserves estimate. For this case the b-parameter value is set to 0.26. For reference, Table 2 provides the results for the rate-time decline relations.

______________________

*The spreadsheet is publicly available at http://www.pe.tamu.edu/blasingame/data/z_Rate_Time_Spreadsheet

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Table 2—Maximum gas production at 30 years using all rate-time relations.

Exponential rate decline relation, Gp,max = 4.32 BSCF Hyperbolic rate decline relation, Gp,max = 4.92 BSCF Stretched exponential rate decline relation, Gp,max = 4.58 BSCF

Summary and Conclusions

Summary: This work presents the development and application of a workflow to estimate reserves and well/reservoir properties of the wells producing in unconventional reservoirs. This workflow is mainly based on production data diagnostics and model-based production analysis. Rate-time relations are used to supplement the reserves estimate obtained using model-based production analysis. Finally, we achieve a systematic procedure, which yields consistent results for reserves estimate as well as well/reservoir parameter estimates.

Conclusions:

We state the following conclusions based on this work:

1. Diagnostic plots are indispensable in the characteristic evaluation and analysis of production data. The analysis of production data is uniquely tied to the quantity and quality of data — diagnostic plots assist in assessing the quality and character of the production data.

2. The application of model-based analysis for production data is the most important task — all other efforts support or compliment this effort. Model-based analysis is not regression-based, but rather, a product of a systematic diagnosis process — where such a process includes revisions (updates), but ultimately the analysis is dictated by the diagnostic efforts, not by the model itself.

3. The uncertainty and non-uniqueness associated with reserves and model parameter estimation for wells in unconventional reservoirs can significantly be reduced using the workflow proposed in this work.

Nomenclature

Variables

b = Arps' decline exponent, dimensionless EUR = Estimate of ultimate recovery, BSCF Fc = Fracture conductivity, md-ft G = Original (contacted) gas-in-place, MSCF or BSCF Gp,max = Maximum gas production (at a specified time limit), MSCF or BSCF k = Formation permeability, md Lw = Horizontal well length, ft nf = Number of transverse hydraulic fractures intersecting the horizontal wellbore. ptf = Flowing tubing pressure (surface), psia pwf = Flowing bottomhole pressure, psia q = Production rate, MSCF/D or STB/D sf = Skin factor, dimensionless t = Production time, days tmb = Material balance time function ((Gp(t)/qg(t) or (Np(t)/qo(t)), days xf = Fracture half-length, ft

Dimensionless Variables

FcD = Dimensionless fracture conductivity

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References

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Ilk, D., Hosseinpour-Zonoozi, N., Amini, S., and Blasingame, T.A. 2007b. Application of the �-Integral Derivative Function to Production Analysis. Paper SPE 107967 presented at the SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, CO, 16-18 April.

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Ilk, D., Rushing, J.A., Perego, A.D., and Blasingame, T.A. 2008. Exponential vs. Hyperbolic Decline in Tight Gas Sands — Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves. Paper SPE 116731 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 21-24 September.

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Fig. 1 — βq,cp-derivative function data for the wells completed in a shale gas reservoir (Field A).

Fig. 2 — Rate and calculated bottomhole pressure versus production time.

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Fig. 3 — Calculated bottomhole pressure versus rate.

Fig. 4 — Pseudopressure drop normalized rate and auxiliary functions versus material balance pseudotime.

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Fig. 5 — βq,cp-derivative versus production time.

Fig. 6 — Pseudopressure drop normalized rate and auxiliary functions versus material balance pseudotime data and model match.

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Fig. 7 — History match of the rate and calculated bottomhole pressure data with horizontal well with multiple fractures model.

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Fig. 8 — Rate-time relations: Exponential rate decline match.

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Fig. 9 — Rate-time relations: Hyperbolic rate decline match.

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Fig. 10 — Rate-time relations: Stretched exponential rate decline match (qDb plot).

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Fig. 11 — Rate-time relations: Stretched exponential rate decline match.