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Abstract

This paper presents results from an evaluation of water-based hydraulic fracture stimulation treatments (or "waterfracs") performed in the Bossier tight gas sand play in the East Texas Basin. The primary objectives of our study were to not only assess stimulation effectiveness, but also to compare recovery efficiencies of various waterfrac technologies. Our primary evaluation tool is a set of new decline type curves developed specifically for the analysis of production data acquired from the elliptical flow period commonly observed in hydraulically-fractured wells completed in tight gas sands [Amini et al (2007)].

In this study we evaluated 12 gas wells from three Bossier tight gas fields located in Freestone County, Texas. Stimula-tion treatments for the wells in this study include water-based hydraulic fracture stimulation treatments with little or no sand, cases with large sand concentrations, as well as "hybrid water-fracs." "Hybrid waterfracs" are defined as fracture stimula-tion treatments where water is pumped initially to create the fracture geometry (i.e., width and length), followed by sand-laden gels to transport and place sand in the fracture (presently low concentration gels are used as opposed to large concen-tration gels used in the 1980s).

Results from our study confirm that "hybrid waterfracs" yield longer, more conductive hydraulic fractures and are more effective at recovering gas-in-place for a given well spacing. Although less expensive to implement, small "waterfracs" (with little or no sand/proppant) are less efficient at gas recovery — which suggests more wells may be required to maximize gas recovery when "waterfracs" are employed.

Introduction

The practical goal for oil and gas operators exploiting any type

of hydrocarbon resource is to maximize economic returns by optimizing field development activities. More specifically, the key to effective exploitation of tight gas sands is to develop the field at a sufficiently dense well spacing that maximizes gas recovery while avoiding drilling more wells than is necessary (i.e., establishing the optimum well spacing as early as possible during field development).

In addition, significant reductions in capital expenditures may be achieved by optimizing well stimulation treatments. Most wells completed in tight gas sands require some type of stimulation (i.e., hydraulic fracturing) to achieve economic production. Depending on the type and size of stimulation treatment, hydraulic fracturing may be very expensive — often representing a significant portion of the total well completion costs.

In the past, hydraulic fracture treatments utilized polymer gels combined with large proppant volumes in an attempt to create long, conductive fractures. Although gels are very efficient for transporting proppant, these gels often damage the frac-ture, are difficult to clean-up (i.e., remove from the forma-tion), and often yield high net fracturing pressures — and are expensive. Under these conditions, minimal effective stimula-tion was achieved, sometimes resulting in sub-economic or even uneconomic wells.

"Waterfrac" technologies were developed in the 1980s as less expensive alternatives to gel treatments. Waterfracs initially ranged from low fluid volume treatments with little or no sand to larger treatments with higher sand concentrations. The industry has recently demonstrated considerable success using hybrid waterfrac technologies that combine advantages of both large gel and waterfrac treatments. Although slightly more expensive, field evidence indicates that hybrid waterfracs generate longer, more conductive effective fractures than smaller water-fracs [Rushing and Sullivan (2003)].

Published case histories make evident the relationship between stimulation effectiveness and gas recovery — i.e., wells with longer, more conductive fractures recover more gas over a larger drainage area. This concept seems obvious, but from a practical (i.e., economic) standpoint, this issue must be revisited continuously — particularly at present, as more and more marginal plays (tight gas/shale gas) are exploited.

As the economic viability of tight-gas-sand fields depends (almost exclusively) on minimizing drilling and completion

SPE 110187

Evaluating the Impact of Waterfrac Technologies on Gas Recovery Efficiency: Case Studies Using Elliptical Flow Production Data Analysis D. Ilk, SPE, Texas A&M University, J.A. Rushing, SPE, Anadarko Petroleum Corp., R.B. Sullivan, SPE, Anadarko Petroleum Corp., and T.A. Blasingame, SPE, Texas A&M University

2 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

costs, it is crucial that we find the proper balance between well spacing, stimulation treatment selection, and gas recovery efficiency. To that end, we have evaluated the production performance for wells in the Bossier tight gas sand play where different types of stimulations were used — including:

● small waterfracs with no proppant. ● small waterfracs with 20/40 or 40/70 proppant. ● large waterfracs with 20/40 or 40/70 proppant. ● hybrid waterfracs.

Specifically, we provide 2 example analysis cases for each well type (total of 12 examples). We have employed decline type curves developed specifically for the case of an ellipti-cally bounded reservoir system with a finite conductivity vertical fracture (this model is characteristic of hydraulically-fractured wells completed in tight gas sands) [Amini et al (2007)]. During transient flow, elliptical flow occurs as a transitional flow regime between the end of bilinear/formation linear flow periods and the onset of pseudoradial flow. The model we have used considers the entire range of flow regimes but imposes an elliptical flow geometry to ensure the most appropriate representation for the performance of a fractured well in a bounded, tight gas reservoir.

The elliptical flow period is important since it represents the time period when both reservoir and effective hydraulic fracture properties affect the production response. Our choice of an elliptical flow geometry — over, say, a circular or rectangular flow geometry — was based on our objective of obtaining the best estimate of contacted gas-in-place. Results from evaluations based on the elliptical flow model allow us to correlate drainage area (and gas recovery efficiency) with created hydraulic fracture properties.

In this work, gas recovery efficiency is quantified in terms of the elliptical boundary characteristic parameter (ξ0) (which relates the drainage area (dimensions of the ellipse) and the fracture half-length), while stimulation effectiveness is quan-tified specifically in terms of the effective fracture half-length and fracture conductivity.

Waterfrac Technologies: An Historical Perspective

As we noted earlier, water fracturing technologies were developed as a less expensive alternative to conventional gel treatments. Water fracturing or "waterfracs" were initially designed to generate hydraulic fractures by injecting water with little or no proppant. "Slick-water fracs" added linear gels or friction reducers to the water. Previous studies have suggested that, when compared to conventional gel treatments, waterfracs can generate similar or sometimes better production responses (refs. 1, 4-7, 10). Furthermore, even when conven-tional gel treatments generate longer propped fracture lengths than a waterfrac, the presence of damaging gels may adversely affect well performance (refs. 6-7, 10).

Microseismic imaging has shown that waterfracs may generate very long fractures during treatment [Mayerhofer et al (2000)]. However, the propped or effective fracture half-lengths may vary significantly depending on both proppant concentration and placement effectiveness. The use of little or no proppant in a waterfrac may (and probably will) result in low to very low fracture conductivities. Recent laboratory

studies [Fredd et al (2000, 2001)] have shown fracture conductivity may be either proppant- or asperity-dominated — depending on proppant concentration, proppant size and strength, and the rock mechanical properties.

Under asperity-dominated conditions, the fracture conducti-vity is a function of fracture face asperities created when the rock is fractured. High conductivity waterfracs can be gener-ated in the absence of proppant only when rock displacement creates ample surface roughness to provide sufficient fracture width. Similar observations were made with low-strength and/or low-concentration proppants [Fredd et al (2000, 2001)]. As a result, effective fracture conductivities are often difficult to predict when little or no proppant is used. These experimental studies also suggest that proppant-dominated conditions could be achieved more consistently using high proppant concentrations.

Hybrid waterfracs were developed to improve small waterfrac effectiveness (i.e., increase both effective fracture conductivity and length) while still maintaining the low costs. The hybrid technology uses slick water to generate fracture width and length while keeping net pressures low. Following creation of the fracture geometry, gels with relatively low proppant concentrations are used to transport proppant down the fracture more effectively. Lower settling rates associated with the gels also allow a more uniform and consistent distribution of proppant placement prior to fracture closure.

Bossier Tight Gas Sand Stimulation Practices

Stimulation practices in Anadarko's Bossier tight gas sand play have progressed since initial field development activities began in the early-1990s. Wells were initially drilled on a spacing of 80 acres during the primary field development period. Following detailed production performance analyses, Anadarko initiated an infill drilling program during which well spacing was reduced to 40 acres per well in most areas.

Initially the sand stimulation treatments used for the Bossier tight gas play consisted of high polymer-loading, cross-linked fluids carrying large proppant volumes. Typical guar concen-trations ranged from 40-50 lbs. polymer (HPG) per 1000 gal fluid. These fluids were cross-linked with zirconate and usually contained several hundred thousand pounds of 20/40 sand proppant.

The objective of these early treatments was to create optimal conductivity by packing the fracture and creating tip screen-outs. Unfortunately, the stimulated well performance, as measured by initial production and decline rates, was periodically disappointing. We attribute the poor results to short effective fracture half-lengths — which is probably a result of both uncontrolled fracture height growth and gel damage. These treatments were also very expensive.

In an effort not only to reduce stimulation costs but also improve well performance in the Bossier tight gas sand play, Anadarko initially applied the same "waterfrac" technologies that were being employed in one of Anadarko's tight gas sand fields in Oklahoma. Initially, Bossier waterfrac treatments were composed of 5,000 to 10,000 bbls of water with friction reducers but (typically) no proppant. These slick-waterfracs were significantly less expensive than the cross-linked gel

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 3 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

treatments, and initial gas production rates were often as high as wells stimulated with conventional gel treatments. Well performance analyses for Bossier cases indicated that we had generated fractures with effective half-lengths of 30 to 60 ft and an effective conductivity on the order of 10 md-ft.

The next progression of stimulation treatments in the Bossier sands continued to be slick-waterfracs, but included some 20/40 sand at low concentrations. Because of the limited fracture widths generated with the slick water treatments, only 20,000 to 40,000 pounds of 20/40 proppant could be placed in the formation. Although we generally observed higher initial production rates than the slick-waterfracs with no proppant, we continued to seek improvements — in particular to im-prove the effective fracture lengths being generated by the stimulation treatment.

In the next phase of sand-laden waterfrac treatments, we used even larger proppant volumes (greater than 100,000 lbs), but we also began experimenting with smaller proppant/sand sizes. In particular, we found 40/70 proppants were very effective. The use of smaller proppant sizes allowed a much larger quantity (often exceeding 200,000 lbs.) of proppant to be placed with the slick water. Not only did we observe a significant increase in the initial production rates, but the production performance behavior suggested we had generated longer, more effective fracture half-lengths. Well perfor-mance analyses indicated that effective fracture half-lengths ranged from almost 100 ft to as much as 230 ft. We did not, however, observe a significant increase in effective fracture conductivity.

The objective of the most recent phase of Bossier sand stimulation treatments was to increase both effective fracture conductivity and half-length using a hybrid stimulation technique. This hybrid technology uses slick water to generate fracture width and length, while keeping net pressures low. Following creation of the fracture geometry, gels with relatively low proppant concentrations are used to transport proppant down the fracture more effectively. Lower settling rates associated with the gels also allow a more uniform and consistent distribution of proppant placement prior to fracture closure. The typical Bossier sand hybrid treatments include pumping slick water initially to create fracture geometry and followed by relatively low (30-35 lbs. per 1000 gals) borate cross-linked gel carrying 20/40, 40/70, or a mixture of proppant sizes for increased fracture length and conductivity. Overview of Decline Type Curves for Evaluating Elliptical Flow

It is well-known from pressure transient testing concepts that elliptical flow patterns exist for hydraulically fractured wells in low permeability and ultra-low permeability formations. The elliptical flow period is regarded as a transitional flow regime which takes place between linear and/or bilinear formation flow and the beginning of pseudoradial flow, but as can be shown in modeling, elliptical flow is "universal" for low/ultra-low permeability formations. Specifically, elliptical flow represents the phase when the reservoir properties (k, xf,

wfkf, etc.) dominate the reservoir performance. The study of elliptical flow has an important history in the petroleum engineering literature (see our Reference section for Well Performance Aspects of Elliptical Flow).

We recently developed and validated a series of "type curve" solutions for a system consisting of a hydraulically fractured well in a bounded elliptical shape reservoir [Amini et al (2007)]. The type curves are generated from the (constant rate) pressure solution which was obtained by using an analytical technique. The type curves were generated for different values of fracture conductivity and as a function of elliptical boundary characteristic parameter (ξ0).

The elliptical boundary characteristic parameter (ξ0) is a variable that correlates all the aspects of the drainage area and the fracture half-length. The schematic of the elliptical reser-voir model is provided in Fig. 1.

Figure 1 — Schematic of the elliptical reservoir model (Amini et al, 2007)

The elliptical outer boundary is assumed to have the same focal length as the hydraulic fracture length — which allows us to write the following equations (where these relations correlate all aspects of the drainage area into a single para-meter (ξ0)):

)cosh( 0ξfxa = ................................................................ (1)

)sinh( 0ξfxb = ................................................................. (2)

20 )2sinh(

2 fxabArea ξππ == ............................................ (3)

)coth(RatioAspect Drainage 0ξ==ba ............................. (4)

10 )cosh( Ration Penetratio −== ξ

ax f ............................... (5)

For our work, we utilize type curve solutions in terms of the equivalent constant rate case in "decline" form (i.e., qD and its auxiliary functions qDi and qDid versus tDA). We have previously provided diagnostic examples [Amini et al (2007) and Ilk et al (2007)] to demonstrate the value of the elliptical boundary model.

In this work, our approach goes beyond diagnostics — in addition to diagnostics, we estimate the relevant reservoir properties (i.e., k, xf, FE, G, A) using the type curve solutions we have generated for the case of an elliptically-bounded reservoir. As a reference, we follow similar diagnostic and analysis procedures as those given by Pratikno et al [Pratikno

4 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

et al (2003)]. We again note that we use qD versus tDA format for elliptical flow cases.

Estimation of Reservoir Properties:

The following reservoir properties are estimated using the "decline type curve analysis" (type curve matching) approach:

● Contacted gas-in-place (G):

MP

MP

MP

MP)(

)/()()(

211

D

pg

DA

mbg

gi qpq

tt

cG

Δ=

π................................ (6)

● Reservoir drainage area (A):

)1(6148.5

wi

giSh

GBA

−=

φ.................................................... (7)

● Formation permeability (k):

MP

MP)(

)/(2.141

D

pggigiq

pqh

Bk

Δ=

μ........................................ (8)

● Fracture half-length (xf):

5.0

0 )2sinh(12

⎥⎦

⎤⎢⎣

⎡=

ξπAx f .................................................. (9)

The dimensionless fracture conductivity (elliptical boundary model) (FE) is estimated based on the specific type curve used to perform the analysis — i.e., for the construction of the elliptical flow type curves, only a single FE-value is used for any particular type curve. The pseudopressure (pp) and pseudotime (tmbg) functions, as well as all of the variables used in this work are defined in the Nomenclature section. Field Examples

As mentioned earlier, we have utilized the type curves for a bounded elliptical flow system with a hydraulic fracture for the evaluation of 12 wells from three different Bossier tight gas sand fields. Our study includes waterfracs with little to no sand, waterfracs with large sand concentrations, and hybrid waterfracs. We provide two example wells for each type of waterfrac treatment for a total of 12 example cases, where these cases are itemized in Table 1 and the details on the each water fracture treatment (e.g., volume of sand, volume of fracturing fluid, etc.) are presented in Table 2. Our evaluation mechanism does not solely depend on "type curve" analysis results — in addition to this work, we also verified our results using numerical simulation.

In the remainder of this section we provide the following plots for each example:

● Production history plot — qualitative diagnostic plot used for assessing the flowrate and pressure data. Used in this work to identify liquid-loading or other production problems.

● Diagnostic log-log plot — diagnostic "pre-analysis" plot used to characterize the performance of the well/reservoir and to esta-blish a base model from which we begin the analysis process.

● Elliptical boundary decline type curve match — primary analy-sis plot for this work, matches the production performance the presumed well/reservoir model.

● Production history plot with model match — compares the "matched" well reservoir model to the entire production history. As a general comment, the "rate" matches are typically good to excellent; while the "pressure" matches range from poor/fair to

good. This performance is generally due to the quality (or accu-racy of the pressure data).

Table 1 — Example field cases based on the fracture stimulation method.

Example Cases

Fracture Stimulation Method

Well SW1 Small Water (No Proppant) Well SW2 Small Water (No Proppant) Well SW3 Small Water (20-40 Proppant) Well SW4 Small Water (20-40 Proppant) Well SW5 Small Water (40-70 Proppant) Well SW6 Small Water (40-70 Proppant) Well LW1 Large Water (20-40 Proppant) Well LW2 Large Water (20-40 Proppant) Well LW3 Large Water (40-70 Proppant) Well LW4 Large Water (40-70 Proppant) Well HW1 Hybrid Water Well HW2 Hybrid Water

This "four plot" process is designed to ensure that we consider data quality and diagnostic observations at every step. Our goals are to establish the most appropriate well/reservoir model — and to compare this model to the production data functions in several different ways to ensure uniqueness (if possible) in the diagnosis/analysis process.

Ex. 1 — Well SW1: Small Waterfrac (No Proppant) Example 1 is a "small waterfrac (no proppant) case and the plots for this case are presented in Figs. 2-5. In Fig. 2 we note some disparity in the production rate and pressure functions, the character of which suggests modest liquid loading effects.

Figure 2 — Ex. 1 (Gas Well SW1) — Production history plot.

The "diagnostic" functions for this case are presented in Fig. 3 and except for some minor variations in the first couple of months of data (where well clean-up and liquid loading appear to be most influential (see Fig. 2)), we note good to excellent diagnostic data functions. In particular, we can clearly observe the character of a fractured well with boundary effects in Fig. 3.

The "analysis" plot for this case is presented in Fig. 4 (type curve match), where we also note some minor discrepancies between the model and data functions at early times (as diagnosed in Fig. 3). Otherwise, we can and should consider the match shown in Fig. 4 to be very good (approaching

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 5 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

excellent), and we should conclude that this interpretation is both reasonable and accurate.

Figure 3 — Ex. 1 (Gas Well SW1) — Diagnostic log-log plot (dimensionless rate decline integral functions).

Figure 4 — Ex. 1 (Gas Well SW1) — Elliptical boundary decline type curve match [FE=10 (moderate conductivity), ξ0=2.0 (near-circular drainage geometry)].

Figure 5 — Ex. 1 (Gas Well SW1) — Production history plot with model match [excellent flowrate match, ac-ceptable pressure match].

The model/data history comparison for this case is shown in Fig. 5. As we suggested earlier, we will most likely see a very good match of the flowrate history, but not necessarily for the pressure history — this conjecture is confirmed in Fig. 5 as we note an excellent match of the rate function, but only an acceptable (or fair) match of the pressure history. This obser-vation is typical of the wells considered in this study, and the most likely culprits with regard to the pressure data are: liquid loading, the accuracy of the measured surface pressure, and (to a lesser degree) the surface-to-bottomhole pressure conversion algorithm.

Ex. 2 — Well SW2: Small Waterfrac (No Proppant) Example 2 is also a "small waterfrac (no proppant) case and the plots for this case are presented in Figs. 6-9. The pro-duction history plot (Fig. 6) also shows apparent well clean-up effects at early times, and considerable distortion caused (presumably) by liquid loading throughout most of the pro-duction history.

Figure 6 — Ex. 2 (Gas Well SW2) — Production history plot.

The "diagnostic" functions for this case are presented in Fig. 7. We note that the diagnostic functions are well-defined, and we observe the character of a fractured well with boundary effects.

Figure 7 — Ex. 2 (Gas Well SW2) — Diagnostic log-log plot (dimensionless rate decline integral functions).

6 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

In Fig. 8 we present the type curve match for this case. We consider the "weak" match of the model and data at earliest times to be an "artifact" of the well clean-up effects. We note a very good match of the "rate" functions (black symbols (data) and black line (model)) in Fig. 8, and suggest that we could have matched the "integral" (blue data/line) and "integral-derivative" (red data/line) trends better with some judicious editing, but this was not our objective. Based on the "rate" functions, this case suggests (and the model match confirms) the character of a high conductivity vertical fracture.

Figure 8 — Ex. 2 (Gas Well SW2) — Elliptical boundary decline type curve match [FE=100 (high conductivity), ξ0=3.0 (circular drainage geometry)].

The model/data history comparison for this case is shown in Fig. 9, where we again note a good match of the model and the rate history, but a fair (to poor) match of the pressure history. As with Example 1 (see Fig. 5), we believe that liquid loading is the primary reason behind this poor correlation of the model and pressure history.

Figure 9 — Ex. 2 (Gas Well SW2) — Production history plot with model match [good flowrate match, fair/poor pressure match].

Although other "small waterfrac (no proppant)" cases were reviewed and analyzed, we present these particular cases due to the consistency of the data and the clarity of the analyses.

We believe that these two cases (Examples 1 and 2) are sufficient to represent the behavior of the "no proppant" cases, and in Examples 3-6 we do consider "proppant" as a com-ponent of the "small waterfrac" cases.

Ex. 3 — Well SW3: Small Waterfrac (20/40 Proppant) In Example 3 we again present a "small waterfrac" case, but now we consider the influence of proppant (sand). The diagnostic and analysis plots for this case are presented in Figs. 10-13. In Fig. 10 we note very smooth and consistent character in production rate and pressure functions — liquid loading (if it exists) appears to be limited to the latter portion of the data (2200-2700 days).

Figure 10 — Ex. 3 (Gas Well SW3) — Production history plot.

The diagnostic (rate and pressure) functions are presented in Fig. 11, and we note excellent performance of these functions — suggesting (in advance) that we will obtain a good match of the model and data functions. We will qualify our enthusiasm for this case by noting that the erratic nature of the pressure data at early times (Fig. 10) — where this behavior has (ap-parently) yielded an artifact in the data functions (at early times (Fig. 11). Regardless, we expect a good match at late times — and further, we should also expect a good match of the flowrate and pressure histories with the well/reservoir model (again, due to the consistent character of the flowrate and pressure histories as seen in Fig. 10).

Figure 11 — Ex. 3 (Gas Well SW3) — Diagnostic log-log plot (dimensionless rate decline integral functions).

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 7 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

The type curve model/data match is shown in Fig. 12 — and as we noted, we do observe a discrepancy at early times. We did match this case with a lower conductivity (FE-value) but this caused more of a mismatch in the rate/pressure match (Fig. 13). We believe that the well/reservoir model as match-ed to the data in Fig. 12 is appropriate, and we note that the overall match for this case could likely be improved, but this would come at the expense of "fitting the errors" in the pres-sure history.

Figure 12 — Ex. 3 (Gas Well SW3) — Elliptical boundary decline type curve match [FE=10 (moderate conductivity), ξ0=2.0 (near-circular drainage geometry)].

As noted above, we are satisfied with the well/reservoir model match presented in Fig. 12 (in type curve format) as well as in Fig. 13 (raw flowrate and pressure data matched with the well/reservoir model). In Fig. 13 we note an excellent match of the flowrate history and a good (actually very good) match of the pressure history. This case represents a "balance" of analysis between the diagnostic functions (Fig. 12) and the production history (Fig. 13) — we utilize this "balanced app-roach" for each case considered in this work.

Figure 13 — Ex. 3 (Gas Well SW3) — Production history plot with model match [excellent flowrate match, good pressure match].

Ex. 4 — Well SW4: Small Waterfrac (20/40 Proppant) In Example 4 we present another "small waterfrac" case with 20/40 (large size) sand. The diagnostic and analysis plots for this case are presented in Figs. 14-17. The production history plot is presented in Fig. 14 and as a comment; we note that the flowrate and pressure functions appear well-correlated (with the exception of the pressure (increasing) for the first 100 days (well clean-up effects)).

Figure 14 — Ex. 4 (Gas Well SW4) — Production history plot.

In Fig. 15 we present the log-log diagnostic plot for this case and note that only the early portion of the data (perhaps the first log cycle) appears affected by well clean-up effects.

Figure 15 — Ex. 4 (Gas Well SW4) — Diagnostic log-log plot (dimensionless rate decline integral functions).

The "type curve" match for this case is presented in Fig. 16, and we note a good match of the "rate" functions (black data/line) but a weaker match of the "rate integral" (blue data/line) and "rate integral-derivative" (red data/line) func-tions at early times (due, as we believe, to well cleanup ef-fects).

As with Example 3, we have some mismatch at early times on the type curve match (Fig. 16), but as shown in Fig. 17, we obtain a very good match of the flowrate and pressure history with the well/reservoir model. These comparisons confirm the validity of our "balanced" approach to matching both the diag-

8 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

nostic functions (use type curves) and the "history match" of the production history (flowrate and pressure data).

Figure 16 — Ex. 4 (Gas Well SW4) — Elliptical boundary decline type curve match [FE=10 (moderate conductivity), ξ0=2.0 (near-circular drainage geometry)].

Figure 17 — Ex. 4 (Gas Well SW4) — Production history plot with model match [excellent flowrate match, very good pressure match].

Ex. 5 — Well SW5: Small Waterfrac (40/70 Proppant) In Example 5 we consider another "small waterfrac" case, but now 40/70 (small size) sand is used. The smaller sand size is used to assess an economic issue (smaller size sand is cheaper than larger size sand). We have no expectation of smaller sand being better or worse in performance than larger size sand as this is a function of many variables, not the least of which is the efficiency of the fracture treatment. Our goal is to assess the well performance, not make recommendations as to one sand sizing over another.

The history plot for this case is presented in Fig. 18, and we immediately note a high degrees of liquid loading in the rate and pressure history (the erratic "noise" in the flowrate data are indicative of liquid loading). In addition, the pressure history shows a "jumping" character (1300-2700 days) that is indicative of remediation (plunger lift, soaping, surging, etc.).

Figure 18 — Ex. 5 (Gas Well SW5) — Production history plot.

Figure 19 — Ex. 5 (Gas Well SW5) — Diagnostic log-log plot (dimensionless rate decline integral functions).

Figure 20 — Ex. 5 (Gas Well SW5) — Elliptical boundary decline type curve match [FE=10 (moderate conductivity), ξ0=1.75 ("fat" elliptical drainage geometry)].

The main issue with the character of the pressure data at late times is not the cause, but the effect — specifically, this be-

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 9 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

havior casts doubt on the accuracy of the pressure history during that time. We can (and do) address this issue with editing of the diagnostic functions (see Figs. 19 and 20), but we suspect (and confirm) that it will be difficult to match the pressure history with the reservoir model at late times (see Fig. 21).

In Fig. 19 we note an extraordinary character in the diagnostic functions, this is small part to some judicious data editing (of the base "rate function" (black symbols), not the production history itself) — but, we believe that this strong signature for a fractured well of moderate conductivity is unique. Carrying forth to the type curve analysis (Fig. 20), we note an extra-ordinary match of the data and well/reservoir model functions, this is, perhaps, the best match in this work.

Figure 21 — Ex. 5 (Gas Well SW5) — Production history plot with model match [excellent flowrate match, good/ acceptable pressure match].

As noted above, the "history match," shown in Fig. 21 is excellent for the flowrate function (factoring in that the model trend is an average within the spectra of the effects of liquid loading on the flowrate history). The pressure history match is good at early times and "acceptable" at later times (where the remediation for liquid loading is evident).

Ex. 6 — Well SW6: Small Waterfrac (40/70 Proppant) Example 6 is our second "small waterfrac"/small sand size case and we should (logically) expect very similar perform-ance to the previous case (Example 5). The production history plot is presented in Fig. 22 and we note very similar performance to that of the previous case (see Ex. 5, Fig. 18), albeit the liquid loading effect is distributed a bit differently for this case. In particular, as seen in Fig. 22, the flowrates appear to be most distorted in the 700-1200 day timeframe, while the pressure data appear to be most affected in the 200-400 and 1000-1700 day timeframes.

We (again) address the liquid loading issue by careful editing (beforehand) of the "rate" function shown on the diagnostic plot, Fig. 23. Having done this, we note an excellent set of diagnostic data trends in Fig. 23, and we expect (and confirm) an excellent model match on the type curve plot (Fig. 24) of which is the efficiency of the fracture treatment.

Figure 22 — Ex. 6 (Gas Well SW6) — Production history plot.

Figure 23 — Ex. 6 (Gas Well SW6) — Diagnostic log-log plot (dimensionless rate decline integral functions).

Figure 24 — Ex. 6 (Gas Well SW6) — Elliptical boundary decline type curve match [FE=100 (high conductivity), ξ0=1.75 ("fat" elliptical drainage geometry)].

10 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

Our final task in this example is to assess the "history match" of the flowrate and pressure functions with the well/reservoir model. In Fig. 25 we note an extraordinary match of the flow-rate data, and a fair match of the pressure history (poor at late times — due to the uncorrelated pressure/rate behavior after 1700 days).

Figure 25 — Ex. 6 (Gas Well SW6) — Production history plot with model match [excellent flowrate match, fair pressure match].

As closure for Examples 1-6, these were all "small waterfrac" cases — general expectations would be that small fracture half-lengths are achieved and that (relatively) small drainage volumes are accessed. The complete suite of results for all analyses is presented in Table 3, and we note that we do confirm the expectations given above.

Ex. 7 — Well LW1: Large Waterfrac (20/40 Proppant) Starting with Example 7, we begin our review of the "large waterfrac" cases — where Example 7 is a "large" sand size case (20/40). In this case we will expect large fracture pene-trations (half-lengths) and high fracture conductivities.

The production history plot for Example 7 is presented in Fig. 26. The most obvious feature in Fig. 26 is the effect of liquid loading in the flowrate data for the period of about 100-500 days — the pressure data are less-affected, and the calculated bottomhole pressure profile is more or less constant over the life of the well.

Figure 26 — Ex. 7 (Gas Well LW1) — Production history plot.

The diagnostic plot for this case is presented in Fig. 27 and we note a very strong signature of high fracture conductivity (1/2 slope during transient flow on the all of the diagnostic "rate" functions. This is an extraordinary case — one which con-firms our conjecture that a large fracture stimulation treatment with a large sand volume will yield a long and conductive hydraulic fracture.

Figure 27 — Ex. 7 (Gas Well LW1) — Diagnostic log-log plot (dimensionless rate decline integral functions).

The "type curve analysis" plot for this case is presented in Fig. 28 and we note, as suggested earlier, that the data are matched with a very high (essentially infinite) conductivity vertical fracture solution. Further, despite the liquid loading issues discussed in Fig. 26, we note (via judicious editing of the base "rate" function (black symbols)) excellent data trends for all "rate" functions, which match the well/reservoir model uniquely and consistently (see Fig. 28).

Figure 28 — Ex. 7 (Gas Well LW1) — Elliptical boundary decline type curve match [FE=1000 (very high conducti-vity), ξ0=1.5 (elliptical drainage geometry)].

In Fig. 29 we present the "history match" plot for this case, where the production data and well/reservoir model responses are compared directly. We note an excellent match of the

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 11 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

flowrate data and a very good match of the pressure data. There are minor discrepancies in both matches — the rate model provides an "average" trend that (certainly) does not match the liquid loading-affected flowrate data at early times; nor does the well/reservoir model match the pressure data during the first 2 months of production. However, this case remains an extraordinary example of the clarity and unique-ness of data diagnostics and model-based analyses (i.e., the type curve and history matches).

Figure 29 — Ex. 7 (Gas Well LW1) — Production history plot with model match [excellent flowrate match, very good pressure match].

Ex. 8 — Well LW2: Large Waterfrac (20/40 Proppant) Example 8 is similar to Example 7 in terms of the production histories as it is presented in Fig. 30. The obvious feature in this plot is the erratic pressure and rate data which are observ-ed from 600-1200 days (according to the well completion report, a workover was performed to remedy a "tubing or packer leak," which resolved this behavior). We also note sig-nificant well clean-up effects in the pressure data during the first 2 months of production.

Figure 30 — Ex. 8 (Gas Well LW2) — Production history plot.

In Fig. 31 we present the diagnostic data functions for this case — as with Example 7, we note a strong transient flow signature which suggests high fracture conductivity. In addition to the transient signature, we also note a good boundary-dominated flow signature in the "rate" function (i.e., the black symbols). Given the strength of these signatures, we

expect a very good to excellent type curve match using an elliptical flow model with a high fracture conductivity.

Figure 31 — Ex. 8 (Gas Well LW2) — Diagnostic log-log plot (dimensionless rate decline integral functions).

The type curve match for this case is presented in Fig. 32, and we note that the match is excellent, with only minor deviations at very early times in the "rate integral-derivative" function (i.e., the red data/trends). This early time issue does not affect the overall match, and we are confident that this match is unique and appropriate.

Figure 32 — Ex. 8 (Gas Well LW2) — Elliptical boundary decline type curve match [FE=1000 (very high conducti-vity), ξ0=1.5 (elliptical drainage geometry)].

The overall history match for this case is shown in Fig. 33, and we observe an excellent match of the flowrate history with the well/reservoir model. The pressure history match is good overall, with the exception of a period from 100 to 700 days, where this could be due to an issue with the well completion. It is noted in the well file that there was a "tubing or packer" leak during this time, so the surface pressure data (as measur-ed) may not be representative of the bottomhole condition.

12 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

Figure 33 — Ex. 8 (Gas Well LW2) — Production history plot with model match [excellent flowrate match, good pressure match].

Ex. 9 — Well LW9: Large Waterfrac (40/70 Proppant) Example 9 is a "large waterfrac" case that employs small size sand as proppant (40/70 sand). The production history for this case is presented in Fig. 34. The pressure profile shown in Fig. 34 appears to be consistent and there is little evidence of liquid loading. On the other hand, the flowrate profile is af-fectted (sometimes severely) by liquid loading, and as this behavior is not reflected in the pressure data, this is cause for (minor concern). The primary issue is the character of the data, which appears to be good.

Figure 34 — Ex. 9 (Gas Well LW3) — Production history plot.

The diagnostic data functions for this case are presented in Fig. 35, and somewhat as expected (due the use of small sand), the transient signature suggests a moderate to low conductivity vertical fracture. There is also a strong boun-dary-dominated flow signature, so we should expect a good type curve match for this case.

In Fig. 36 we present the "type curve match" for this case, and as noted, we find the best match to be that of a well with a low/moderate conductivity vertical fracture in an elliptically-bounded reservoir. The match as shown in Fig. 36 suggests that the conductivity (FE) should probably be lower than 10, but this is the "nearest" type curve that we have to match this particular case.

Figure 35 — Ex. 9 (Gas Well LW3) — Diagnostic log-log plot (dimensionless rate decline integral functions).

Figure 36 — Ex. 9 (Gas Well LW3) — Elliptical boundary decline type curve match [FE=10 (moderate conductivity), ζ0=1.5 (elliptical drainage geometry)].

Figure 37 — Ex. 9 (Gas Well LW3) — Production history plot with model match [excellent flowrate match, good pressure match].

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 13 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

The final history match for this case is shown in Fig. 37. We note an excellent (albeit average) match of the flowrate history with the prescribed well/reservoir model. The pressure history match is also good, with the exception being the period from 200-800 days, but this is also a period where the model solution also over predicts the flowrate history. We believe that these features confirm that our fracture conductivity value may be slightly high (as we noted for the type curve analysis match (Fig. 36).

Ex. 10 — Well LW10: Large Waterfrac (40/70 Proppant) Example 10 is the second "large waterfrac with small size sand" (analogous to Example 9). The production history for this case (flowrates and pressures) is presented in Fig. 38, and we note very good rate and pressure correlation, with little (apparent) mismatch. That is, virtually all features observed in the flowrates are also observed in the pressures.

Figure 38 — Ex. 10 (Gas Well LW4) — Production history plot.

The diagnostic data functions for this case are presented in Fig. 39 and we observe very strong data trends — in particu-lar, the transient signature suggests a low (to very low) frac-ture conductivity for this case. The late-time data confirm the boundary-dominated flow signature. Based on these observa-tions, we can expect a very good to excellent match of these data functions on the appropriate type curve.

Figure 39 — Ex. 10 (Gas Well LW4) — Diagnostic log-log plot (dimensionless rate decline integral functions).

In Fig. 40 we present the "type curve match" for this case, and as expected, we achieve our best match of these data functions using the well/reservoir model for the case of a well with a vertical fracture of low (to very low) conductivity in an elliptically bounded reservoir system. In short, Fig. 40 il-lustrates an excellent (if not extraordinary) match of the data and the well/reservoir model.

Figure 40 — Ex. 10 (Gas Well LW4) — Elliptical boundary de-cline type curve match [FE=1 (low conductivity), ξ0=1.5 (elliptical drainage geometry)].

The final "history match" for this case is presented in Fig. 41, and the most striking feature is the poor pressure match at early times. This was not expected based on the "type curve match," but close inspection of the early time flowrate match on Fig. 41 also indicates an under prediction of the flowrate during this time. We suspect that a slight increase in the fracture conductivity should improve this match. Except for this early-time discrepancy, the remainder of the flowrate and pressure history match is acceptable.

Figure 41 — Ex. 10 (Gas Well LW4) — Production history plot with model match [very good flowrate match, ac-ceptable pressure match].

14 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

Ex. 11 — Well HW1: Hybrid Waterfrac In this example and the next we consider the case of a "hybrid frac" which combines the slick water fracture initiation with a low concentration gel for the placing the proppant. In theory, these cases should show the highest production potential — in practice, the reality may be different.

The production history for Example 11 is presented in Fig. 42 — we observe (immediately) the erratic nature of the flowrate profile. Based on the nature of the "noise" — i.e., the flowrate data oscillate about a mean trend, we strongly believe that this is a liquid loading affect. Unfortunately (as with some of our previous examples), the liquid loading features observed for the flowrate data are not well-correlated with the pressure data.

Figure 42 — Ex. 11 (Gas Well HW1) — Production history plot.

Despite the severity of the liquid loading observed in the flowrate data shown in Fig. 42, we do obtain (via some judicious editing of the "rate" function (black symbols) shown in Fig. 43), very clear diagnostic data trends in Fig. 43. From the trends observed in Fig. 43, we suggest that this case will be matched very well by the solution for a well with a high conductivity vertical fracture producing in a bounded elliptical reservoir.

Figure 43 — Ex. 11 (Gas Well HW1) — Diagnostic log-log plot (dimensionless rate decline integral functions).

The "type curve match" for this case is provided in Fig. 44 and we note an excellent (if not extraordinary) match of the diagnostic data functions with the imposed well/reservoir model.

Figure 44 — Ex. 11 (Gas Well HW1) — Elliptical boundary decline type curve match [FE=1000 (very high conductivity), ξ0=1.0 ("thin" elliptical drainage geometry)].

The production "history match" for this example is presented in Fig. 45. The flowrate match is very good, and the pressure match is fair. The surprising aspect of this history match is that the model flowrate response actually corresponds quite well with the observed flowrate data. This is most likely due to the measured pressures being "better" than they appear. The pressure match is not as poor as it may seem given the very erratic nature of the rate function (which is used in the model to produce the model pressure response).

Figure 45 — Ex. 11 (Gas Well HW1) — Production history plot with model match [very good flowrate match, fair pressure match].

In closing, this example has some contradiction in the type curve and the production history matches — however; most of the discrepancies can be attributed to the liquid loading. The type curve analysis methodology is very "error tolerant" (based on the plotting functions) and is less affected by "data

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 15 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

noise." The production history match (which is generated using numerical simulation tuned by the "type curve" match) is less tolerant to errors, each flowrate or pressure data has an impact on the modeled solution responses.

Ex. 12 — Well HW2: Hybrid Waterfrac Example 12 is the second "hybrid waterfrac" case and the production data for this case are shown in Fig. 46. These data appear to be quite consistent, with some liquid loading effects (primarily exhibited by the flowrate data).

Figure 46— Ex. 12 (Gas Well HW2) — Production history plot.

The diagnostic plots for this case are shown in Fig. 47 and it is apparent that this well has a low (or very low) fracture con-ductivity. We also note a strong boundary-dominated flow signature, so we should expect a good match of these data functions on the elliptical boundary type curve.

Figure 47 — Ex. 12 (Gas Well HW2) — Diagnostic log-log plot (dimensionless rate decline integral functions).

The "type curve match" for this case is shown in Fig. 48, the match is very good (if not excellent), except at very early times. This weak performance at early times is almost cer-tainly an artifact due to the "clean-up" effects evident in the production pressures during the first 100 days of production (see Fig. 46). Perhaps the most important aspect of the type curve match is that it confirms our conjecture (based on Fig. 47) that the fracture is of low conductivity.

Figure 48 — Ex. 12 (Gas Well HW2) — Elliptical boundary decline type curve match [FE=1 (low conductivity), ξ0=1.5 (elliptical drainage geometry)].

The "history match" for this case is presented in Fig. 49. The match of the flowrate data and the well/reservoir model is excellent, one of the best cases we have had in this work. Similarly, the pressure match is also good — better than most of the cases that we have considered in this work. We note that even the early-time pressure match is better than expected (but certainly not perfect).

Figure 49 — Ex. 12 (Gas Well HW2) — Production history plot with model match [excellent flowrate match, good pressure match].

Discussion of Results

We compile the results from the previous section as shown in Table 3. A superficial review of the data in this table con-firms what one would expect — higher reservoir permeabili-ties (k) correlate (or should correlate) with higher contacted gas-in-place (G) estimates. Plotting these data (G versus k) as shown in Fig. 50, we observe a strong correlation for the "large waterfrac" and the "hybrid waterfrac" cases, while the "small waterfrac" cases are clearly off-trend (with a couple of noted exceptions).

16 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

The high contacted gas-in-place "on-trend" point for the "small water-frac" case (Fig. 50) is a "high" permeability case (and also has the shortest fracture half-length observed in this study). It is not surprising that this case correlates as well it does (i.e., the effectiveness of the fracture is less of an issue than for the other cases).

Figure 50 — Correlation of results — G versus k.

The low contacted gas-in-place "on-trend" point for the "small water-frac" case (Fig. 50) is the lowest permeability case — but it has a good estimate of fracture half-length and fracture conductivity. In other words, this case is likely just a coinci-dence — the low permeability nature of this case dominates the behavior of this well.

As another correlation of these results, we present Fig. 51 where the contacted gas-in-place (G) is plotted versus the frac-ture half-length (xf). In this case we note an extraordinary correlation of G with xf, regardless of the effectiveness/-efficiency of the fracture stimulation treatment. In short, Fig. 51 confirms the concept that "the fracture defines the reserves" in low permeability gas reservoirs.

Figure 51 — Correlation of results — G versus xf.

In Fig. 52 we show another correlation — in this case we compare the permeability (k) and the drainage aspect ratio (ξ0). We note a clear correlation of increasing permeability with increasing values of the drainage aspect ratio. In particular, small waterfracs exhibit the highest values of permeability — which is probably a consequence of field development strategies, as the small waterfrac wells are the oldest wells in our study, and would (presumably) be located in the best part(s) of the reservoir.

Figure 52 — Correlation of results — k versus ξ0.

In Fig. 53 we present our correlation of results for the fracture half-length (xf) compared to the drainage aspect ratio (ξ0).

Figure 53 — Correlation of results — xf versus ξ0.

Similar in form to the k versus ξ0 data (Fig. 52), but opposite in trend, we note that the xf versus ξ0 data provide very strong evidence of an inverse correlation of xf versus ξ0. Fig. 53 sug-gests that we can envision the dimensions of the ellipse boun-

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 17 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

dary from the fracture half-length — which is logical and consistent with our other observations.

Summary and Conclusions

Summary: In this work we have demonstrated the application of a rigorous model for the diagnosis and analysis of well performance data — specifically the bounded elliptical reser-voir solution applied as "decline type curves" to data from hydraulically fractured gas wells where the stimulation treat-ment method was considered as a variable. All of the cases considered (12 examples) were successfully analyzed using the elliptical boundary model, and we were also able to correlate the influence of the stimulation treatment on the results.

For example, the hybrid and the large waterfracs were shown to be the most effective treatments in terms of fracture half-length and conductivity delivered to the formation. This study was performed to provide a quantitative assessment of the in-fluence of the type/size of hydraulic fracture treatment on the formation and well performance, and we believe that the results support the conjecture that a "better fracture treatment yields better recovery."

On the basis of the 12 cases evaluated to date, the results suggest that the value of the drainage aspect ratio tends to de-crease with more effective stimulation treatments, i.e., as ef-fective fracture half-length and conductivity increase. De-creasing drainage aspect ratios (i.e., ξ0 approaching 0) indica-tes the dimensions of the fracture are approaching the dimen-sions of the ultimate drainage area, thus maintaining formation linear flow and elliptical drainage geometry for long time pe-riods. Conversely, increasing drainage aspect ratios (i.e., ξ0

approaching 3) indicates smaller fracture dimensions relative to the ultimate drainage area. These larger drainage aspect ratios are also characterized by relatively short formation li-near flow periods and the onset of pseudoradial flow (i.e, more of a circular drainage area shape) much sooner in the well's productive life.

We should note that the drainage area size and shape have implications for the optimum well spacing. Wells with small-ler drainage aspect ratios will ultimately recover a larger per-centage of the gas-in-place, thus requiring fewer wells to de-velop a field, while wells with larger drainage aspect ratios will be less efficient at gas recovery.

Another conclusion that may be put forward based on the cases analyzed to date is the relationship between proppant size and effective fracture properties for the same type of stimulaition treatment. The results shown in Table 3 suggest that we can, in general, achieve longer, more conductive frac-tures with 40/70 rather than 20/40 proppant. For example, the average effective fracture half-length for the small waterfracs with 40/70 proppant was 170 ft while that for small waterfracs with 20/40 proppant was 135 ft. These observations seem to be validated with the values of drainage aspect ratios which range from an average of 1.75 to 2.00 for small waterfracs with 40/70 and 20/40 proppant, respectively. We should note that this conclusion is based on a limited number of cases ana-

lyzed so far. We continue to evaluate more cases to validate our claim.

Conclusions:

1. Large waterfracs tend to deliver very good fracture half-lengths and excellent fracture conductivities.

2. Hybrid waterfracs tend to consistently provide the largest fracture half-lengths, and good fracture conductivity.

3. Small waterfracs (with or without proppant) tend to provide the smallest fracture half-lengths and the lowest fracture conductivities.

Acknowledgments

We would like to express our thanks to Anadarko Petroleum Corp. for their permission to publish this paper.

Nomenclature

Field Variables a = Major axis of the ellipse, ft A = Area of the ellipse/reservoir drainage area, ft2 b = Minor axis of the ellipse, ft Bgi = Gas formation volume factor at pi, RB/MSCF cgi = Gas compressibility at pi, psi-1 φ = Porosity, fraction G = Contacted gas-in-place, MSCF h = Pay thickness, ft k = Formation permeability, md kf = Fracture permeability, md μg = Gas viscosity, cp μgi = Gas viscosity at pi, cp pi = Initial reservoir pressure, psia ppi = Initial reservoir pseudopressure, psia pp = Pseudopressure function, psia Δpp = (ppi-ppwf) = Pseudopressure difference, psi pwf = Flowing bottomhole pressure, psia ppwf = Flowing bottomhole pseudopressure, psia qg = Gas flowrate, MSCF/D rw = Wellbore radius, ft Swi = Gas compressibility at pi, psi-1 t = Time, D tmba = Gas material balance time, D wf = Fracture width, ft xf = Fracture half-length, ft z = Gas compressibility factor, dimensionless zi = Gas compressibility factor at pi, dimensionless

Dimensionless Variables FE = Elliptical fracture conductivity, dimensionless qD = Dimensionless flowrate, dimensionless qDi = Dimensionless rate integral, dimensionless qDid = Dimensionless rate integral derivative, dimensionless tDA = Dimensionless time (drainage area), dimensionless ξ0 = Elliptical boundary characteristic variable, dimensionless

Mathematical Functions coth = Hyperbolic cotangent function cosh = Hyperbolic cosine function sinh = Hyperbolic sine function

Gas Pseudofunctions:

dpz

pp

ppz

pgbasei

igip

i

μ

μ

∫=

dtpcp

tqt

tqc

tgg

g

g

gigimbg

)()()(

0)( μ

μ

∫=

18 D. Ilk, J.A. Rushing, R.B. Sullivan, and T.A. Blasingame SPE 110187

References

Hydraulically Fracturing:

1. Craddock, D.L., Goza, B.T., and Bishop, J.C.: "A Case History - Fracturing the Morrow in Southern Blaine and Western Canadian Counties, Oklahoma," paper SPE 11567 presented at the 1983 SPE Production Operations Symposium, Oklahoma City, OK, February 27-March 1.

2. Fredd, C.N., McConnell, S.B., Boney, C.L., and England, K.W.: "Experimental Study of Fracture Conductivity Demonstrates the Benefits of Using Proppants," SPE paper 60326 presented at the 2000 SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium, Denver, CO, March 12-15.

3. Fredd, C.N., McConnell, S.B., Boney, C.L., and England, K.W.: "Experimental Study of Fracture Conductivity for Water-Fracturing and Conventional Fracturing Applications," SPE Journal, v. 6, no. 3 (September 2001) 288-298.

4. Kundert, D.P. and Smink, D.E.: "Improved Stimulation of the Escondido Sandstone," paper SPE 7912 presented at the 1979 SPE Low-Permeability Gas Reservoirs, Denver, CO, May 20-22.

5. Mack, D.J. and Myers, R.R.: "Proppants: Is Bigger Better or Is Placement The Key?," paper SPE 72381 presented at the 2001 SPE Eastern Regional Meeting, Canton, OH, October 17-19.

6. Mayerhofer, M.J., Richardson, M.F., Walker, Jr., R.N., Meehan, D.N., Oehler, M.W., and Browning, Jr., R.R.: "Proppants? We Don't Need No Proppants," paper SPE 38611 presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, TX, October 5-8.

7. Mayerhofer, M.J. and Meehan, D.N.: "Waterfracs-Results from 50 Cotton Valley Wells," paper SPE 49104 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 27-30.

8. Mayerhofer, M.J., Walker, Jr., R.N., Urbancic, T., and Rutledge, J.T.: "East Texas Hydraulic Fracture Imaging Project: Measur-ing Hydraulic Fracture Growth of Conventional Sandfracs and Waterfracs," paper SPE 63034 presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, TX, October 1-4.

9. Rushing, J.A. and Sullivan, R.B.: Evaluation of a Hybrid Water-Frac Stimulation Technique in the Bossier Tight Gas Sands Play," paper SPE 84394 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, CO, October 5-8.

10. Walker, R.N., Hunter, J.L., Brake, A.C., Fagin, P.A., Steinsber-ger, N.: "Proppants, We Still Don't Need No Proppants - A Per-spective of Several Operators," paper SPE 49106 presented at the 1998 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 27-30.

Well Performance Aspects of Elliptical Flow:

11. Amini, S., Ilk, D. and Blasingame, T.A.: "Evaluation of the Elliptical Flow Period for Hydraulically-Fractured Wells in Tight Gas Sands — Theoretical Aspects and Practical Considerations," paper SPE 106308 presented at the 2007 SPE Hydraulic Fracturing Technology Conference, College Station, TX, January 29-31.

12. Hale, B.W.: Elliptical Flow Systems in Vertically Fractured Gas Wells, M.S. Thesis, U. of Wyoming, Laramie, Wyoming (1991).

13. Kuchuk, F., and Brigham, W.E.: "Transient Flow in Elliptical Systems," SPEJ (December 1979), 401-10, Trans., AIME, 267.

14. Liao, Y.: Well Production Performance and Well Test Analysis for Hydraulically Fractured Wells, Ph.D. Dissertation, Texas A&M U., College Station, Texas 1993).

15. Obut, S.T., and Ertekin, T.: "A Composite System Solution in Elliptic Flow Geometry," SPEFE (September 1987), 227-38.

16. Prats, M.: "Effect of Vertical Fractures on Reservoir Behavior— Incompressible Fluid Case," SPEJ (June 1961), 105-18; Trans., AIME, 222.

17. Prats, M., Hazebroek, P., Strickler, W.R.: "Effect of Vertical Fractures on Reservoir Behavior— Compressible Fluid Case," SPEJ (June 1962), 87-94; Trans., AIME, 225.

18. Riley, M.F.: Finite Conductivity Fractures in Elliptical Coordinates, Ph.D. Dissertation, Stanford U., Stanford, California (1991).

19. Stanislav, J.F., Easwaran, C.V., and Kokal, S.L.: "Analytical Solutions for Vertical Fractures in a Composite System," J. Cdn. Pet. Tech. (September-October 1987), 51-6.

20. Stanislav, J.F., Easwaran, C.V., and Kokal, S.L.: "Elliptical Flow in Composite Reservoirs," J. Cdn. Pet. Tech. (December 1992), 47-50.

Production Data Analysis:

21. Pratikno, H., Rushing, J.A., and Blasingame, T.A.: "Decline Curve Analysis Using Type Curves — Fractured Wells," paper SPE 84287 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, CO, 05-08 October.

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

SPE 110187 Evaluating the Impact of Waterfrac Technologies on Gas Recovery 19 Efficiency: Case Studies Using Elliptical Flow Production Data Analysis

Table 2 — Details on the Types of Waterfrac Treatments.

Example

Well

Fracture Type

Fluid Type

Volume (bbl)

Proppant Quantity & Size

(lbs) SW1 Small Water (No prop) Slick Water 9,264 None SW2 Small Water (No prop) Slick Water 9,512 None SW3 Small Water (20-40) Slick Water 7,745 33,000 (20/40) SW4 Small Water (20-40) Slick Water 17,147 63,000 (20/40) SW5 Small Water (40-70) Slick Water 8,539 50,200 (40/70) SW6 Small Water (40-70) Slick Water 4,915 48,000 (40/70) LW1 Large Water (20-40) Slick Water 7,743 206,900 (20/40) LW2 Large Water (20-40) Slick Water 7,300 247,500 (20/40) LW3 Large Water (40-70) Slick Water 9,439 181,460 (40/70) LW4 Large Water (40-70) Slick Water 12,545 254,600 (40/70) HW1 Hybrid Water Slick Water + X-link Gel 2,082 + 4,827 510,140 (20/40) HW2 Hybrid Water Slick Water + X-link Gel 7,750 + 15,959 98,000 (20/40)

Table 3 — Results for Elliptical Flow Type Curve Analyses.

Example

Well

Fracture Type

Permeability

(md)

Gas-in- Place

(BSCF)

Fracture Half-Length

(ft)

Fracture Conductivity

(dimensionless)

Aspect Ratio (ξ0)

(dimensionless)

Drainage Area (acre)

SW1 Small Water (No prop) 0.0093 1.92 163 10 2.00 26.26 SW2 Small Water (No prop) 0.0157 3.27 69 100 3.00 34.45 SW3 Small Water (20-40) 0.0097 1.28 129 10 2.00 16.45 SW4 Small Water (20-40) 0.0125 1.63 142 10 2.00 20.05 SW5 Small Water (40-70) 0.0075 1.68 195 10 1.75 22.85 SW6 Small Water (40-70) 0.0030 1.62 145 100 1.75 12.61 LW1 Large Water (20-40) 0.0021 1.46 134 1000 1.50 6.51 LW2 Large Water (20-40) 0.0039 3.31 184 1000 1.50 12.21 LW3 Large Water (40-70) 0.0053 1.66 193 10 1.50 13.44 LW4 Large Water (40-70) 0.0118 2.97 212 1 1.50 16.28 HW1 Hybrid Water 0.0030 1.60 200 1000 1.00 5.25 HW2 Hybrid Water 0.0235 3.65 290 1 1.50 30.43