The Use of MIDA-QRC Software in the Analysis of Unconventional Oil and Gas Wells Introduction

Transcription

1 The Use of MIDA-QRC Software in the Analysis of Unconventional Oil and Gas Wells Introduction Mannon Associates is pleased to announce an upgrade to our MIDA decline curve analysis software that now includes the capability of analyzing unconventional oil and gas reservoirs. The new software, MIDA-QRC, also applies to hydraulically-fractured low-permeability vertical wells as well as horizontal wells. The methods employed in the analysis contain features proposed by Nobakht et al, 2010 for the production forecasting of unconventional gas reservoirs and the calculation of gas well drainage areas, The technique has been expanded in the software to apply also to unconventional oil reservoirs. A prime advantage of MIDA-QRC is the ability to provide quick and reliable production forecasts and well drainage area calculations for wells in a manner of minutes rather than hours with other petroleum software currently in use. This has been accomplished by replacing the traditional flowing material balance (FMB) method of diagnoses which is a very powerful tool for use in conventional reservoirs with a technique that is now becoming recognized as superior overall to the FMB method in the analysis of unconventional reservoirs. This simplified method is supported by linear flow theory and is based principally on a plot of the inverse of gas or oil rate vs. the square root of time during the linear flow period (Wattenbarger,1998), followed by Arps (1945) hyperbolic flow during the boundary determined flow period. Provision is also made for the occurrence of transitional flow and compound linear flow. The quickness and reliability is accomplished by eliminating iterative and time-consuming functions in the analysis, such as pseudo-time and flowing material balance functions, that are unnecessary and can add bias. The program is best suited for oil and gas wells producing at relatively constant flowing pressure. A large segment of the unconventional wells on production today fall into this category. Reservoir Characteristics of Unconventional Wells A major factor in the wide difference between conventional and unconventional reservoir characteristics is related to the permeability of reservoir rock. The magnitude of producing zone permeability in a conventional reservoir usually permits the operator to drill either a vertical or horizontal well with a relatively limited degree of well stimulation. However, commercial unconventional reservoir development requires horizontal wells and extensive hydraulic fracturing, which is being done very successfully. The massive effort by industry in this regard has had a dramatic effect on oil and gas leasing and related oil and gas activity in the U.S. The manner in which the unconventional oil and gas accumulations reside in the reservoir has caused this. The normal sequence of a structural/stratigraphic trap and source rock for commercial

2 production is not a requirement as in the case of conventional reservoirs. The reservoir rock is the shale bed itself, which is also the source rock for the oil and gas. In addition, since shale has such an extremely low permeability, the oil and gas is immobilized in place. As a result the existence of a trap is not mandatory, and the productive of limits of unconventional development reservoirs extend over a much broader area. This has served to open up huge areas on the order of multiple hundreds of thousands of acres for development. Fluid Flow Characteristics Figure 1 depicts plan views of boundary-dominated flow in a conventional reservoir versus a fractured shale reservoir. The productive limits of the conventional reservoir (Fig. 1a) represent the actual no-flow exterior boundary of the reservoir. The internal noflow boundaries outline the respective drainage area limits of the producing wells. Fig 1b is also a plan view of a vertical well containing a single bi-wing hydraulic fracture where x f is the fracture half-length and y e /2 is the distance to the no-flow boundary. The fluid flow in the matrix to the fracture is linear. Fig. 1c represents a horizontal well with multiple hydraulic fractures of equal fracture half-length forming a rectangular drainage area. The dashed lines represent the no-flow boundaries midway between the fractures. Here again the fluid flow in the matrix to the fractures is linear. Fractured Shale Reservoir (two geometries shown) b. Bi-wing Hydraulic Fracture x f a. Conventional Reservoir y e c. Multiple Hydraulic Fractures Figure 1. Boundary-Dominated Flows in a Conventional Reservoir versus a Fractured Shale Reservoir (Figures from Anderson, D. M. et al SPE , and Liang, P. et al SPE ) Mannon Associates 2

3 Unconventional Reservoir Analysis This massive program of unconventional reservoir development has been accompanied by a concentrated effort to develop methods and procedures to analyze the behavior of these horizontal wells specifically in the areas of (1) production forecasting, (2) reserve estimation and (3) estimate of the drainage area of the wells. A major body of work exists in the Society of Petroleum Engineers technical papers produced in the last fifteen years that is focused in these three areas. MIDA-QRC is designed to provide quick, reliable, and comprehensive answers to questions in these three areas. The forthcoming presentation on the use of MIDA-QRC in horizontal well analysis draws heavily on the SPE literature. To gain a clearer understanding of the role of MIDA-QRC in unconventional reservoir analysis it is recommended that the engineers and geoscientists refer to as many of the SPE papers cited in the references as possible. The MIDA-QRC Methodology of Analysis Fundamental Considerations Primarily through the use of equations and analytical and empirical methods, MIDA- QRC provides the user with these quick and reliable oil and gas production forecasts, EUR s and well spacing data and related reservoir information on unconventional wells. Reservoirs of this type characteristically exhibit linear flow behavior initially which transitions to boundary dominated flow (BDF) to eventual well abandonment with reversion back to linear flow in some cases as discussed below. A key factor in the analysis is the fact that a plot of 1/q vs. square root of time of the early linear portion is a straight line. The equation for the straight-line plot combined with fluid flow equations for both gas and oil provide a means to measure the interplay of key reservoir parameters that largely govern reservoir performance. Some of these parameters may be known and others may not be known. Through the use of these equations the engineer or scientist is able to quickly produce a forecast or a series of forecasts if desired for a well by coupling together the mix of known and unknown parameters values in various ways. In the actual drilling of the well, the lateral section of the horizontal well is normally oriented in the direction of the minimum horizontal compressive stresses in the shale section to provide for the hydraulic fractures to be orthogonal to the lateral section. The result ideally promotes an alignment of parallel and equally spaced fractures along the horizontal section of the well as depicted in Fig.1c. The area contributing to production is defined by the length of the bi-winged fractures that comprise the width of the drainage area and the number and spacing of the fractures that determines the length of the perforated interval. It is assumed that the fractures all have the same half-length. The dotted line is the no flow line separating the two flow directions. The Linear Flow Equations In practice, tight gas and shale gas and shale oil wells typically exhibit linear flow initially which may continue for several years. The wells are normally produced under high drawdown for maximum production and the equations presented here assume constant bottom hole flowing pressure. The slope (m) of the plot of inverse gas rate vs. the square root of time on Cartesian coordinates is a straight line as seen in Fig. 2. Mannon Associates 3

4 Linear-flow theory by (Wattenbarger et al. 1998; El-Banbi and Wattenbarger 1998) represents this flow behavior as 1 m t b' q (1) where the intercept, b ', is a constant that represents near-well effects (e.g., skin, finite fracture conductivity, and any extra pressure drops) and the slope m (for gas wells) is given by (Wattenbarger et al. 1998) 315.4T 1 1 m h c ppi ppwf xf k g t i. (2) m Figure 2. Square root-time plot for the linear flow period of a well In Eq. (2) T is the reservoir temperature, h is the net-pay thickness, x f is the fracture half-length, k is the reservoir permeability, is the reservoir porosity, is gas viscosity, c t is total compressibility, subscript i refers to initial pressure, and P i and P wf are pseudo-pressures at initial pressure and bottom hole flowing pressure, respectively. Duration of Linear Flow When the well in Fig. 1b is producing under constant flowing pressure, the end of linear flow is given by Eq.3 (Wattenbarger et al 1998) g Mannon Associates 4

5 ye 2 ktelf 0.159, (3) c g t i where y e is reservoir length and t elf is the duration of linear flow. Eq. (3) can be rewritten as t elf ye gc t i k 2. (4) It is not practical to use Eq. (4) to calculate t elf because y e and k are usually not known explicitly. The drainage area (or surface area of the stimulated reservoir volume) (SRV) A x y is given by 2 f e, where y e and x f are reservoir length and fracture half-length, respectively as shown in Fig. 1b.and Fig. 1c. The end of linear flow designated by t elf is indicated in Fig. 3. t elf Figure 3. A plot of inverse gas rate versus square root of time. The end of linear flow is estimated to be 370 days (dashed vertical line) based on the time at which the data diverge from the linear flow line Nobakht et al, 2012 have shown that a workable equation for t elf can be developed as follows: The quantity y e A 2x can be substituted into Eq. (4), which results in f Mannon Associates 5

6 t elf A gct i x f 1 k 2, (5) where xf k 1 is related to slope m of the q vs. t plot and can be calculated by rearranging Eq. (2) as x f k 315.4T 1 1. (6) h c ppi ppwf m g t i Substituting x f k from Eq. (6) into Eq. (5), the following equation is obtained for calculating the duration of linear flow and, hence, the beginning of boundary-dominated flow (Wattenbarger et al. 1998; El-Banbi and Wattenbarger 1998): t elf 2 g t pi pwf Ah c m p p i 200.6T (7) Eq. 7 is used in the MIDA-QRC procedure to determine the duration of the linear flow period of the well and does not require that x f or k be known explicitly. The values for these parameters along with the other major unknowns of zone thickness h, and zone porosity φ are imbedded in Eq. 2 for the value of m, the slope of the square root of time plot. The other major unknown in calculating the duration of linear flow t elf is area A of the SRV as defined above and by the flow geometries shown in Fig. 1. The value for A can be calculated by Eq. 8 below if t elf is evident from the square root of time plot indicating the well has reached boundary dominated flow (BDF). If not, t elf is unknown in which case either A or t elf are estimated to proceed with the forecast of future production. Appropriate values for A may be obtained from the analysis of analog wells or from well spacing studies. Equation (7) is rearranged to solve for A as follows: Boundary-Dominated Flow 200.6T telf A h c m p p g t pi pwf i The progression of a shale gas well moving from linear flow to boundary-dominated flow (BDF) is illustrated in the sequence of Figs. 4a and 4b. In cases of extremely low matrix permeability common to many gas shale reservoirs of approximately 1-10 nanodarcies (nd) the area beyond the tips of the hydraulic fractures does not contribute to the production from the well during the linear flow period. Accordingly, the end of linear flow in the well (Fig.4b) marks the formation of the SRV (Stimulated Reservoir Volume) and the advent of the depletion period of the well. The occurrence of a second later linear Mannon Associates 6 (8)

7 flow period (compound linear flow) in cases of higher matrix permeability is discussed below. x f x f Figure 4 (a) Schematic of a multifractured horizontal well in a rectangular reservoir. b) SRV for the multifractured horizontal well shown in Fig. 4a. (c) The region that each fracture in Fig. 4b drains. [from Nobakht and Clarkson (2011)]. To maintain simplicity and practicality in the process, the traditional Arps hyperbolic decline equation (Arps 1945) is employed in the depletion period. This relationship is given by q q 1 bdt 1 i i b, (9) where q i is the production rate at the start of the hyperbolic forecast period, b is the hyperbolic-decline exponent (usually between zero and 0.5 for gas and oil wells), D i is the decline rate corresponding to q i, and t is time since the start of the hyperbolic forecast. Case Studies To familiarize the engineer and scientist with the theory and use of MIDA-QRC the procedure for analysis is illustrated by three case studies employing a series of steps Mannon Associates 7

8 and screen shots. Additional details on the execution of MIDA-QRC (for unconventional reservoirs) can be found in the Appendix to the MIDA-QRC help file. Case Study 1 is a Barnett shale gas well in the East Newark area in Johnson County, Texas currently producing in the depletion period. Case Study 2 is a Bakken shale oil well in Mountrail County, North Dakota currently exhibiting initial linear flow characteristics. Case Study 3 is a Granite Wash well in the Anadarko Basin in Texas demonstrating initial linear flow and subsequent transitional flow or compound linear flow. Case Study 1 The selection of a well will bring up a graph plot window on the right hand side of the computer screen. STEP 1 Click the Y-Axis button on the upper left hand side of the window to select the desired production plot (Fig. M1) Although the plot in Fig.1 represents actual production, this well is an idealized case seldom seen in practice with very little data scatter, etc. It was chosen to illustrate some principles in the interpretation process not always evident in actual field examples. Figure M1 Mannon Associates 8

9 STEP 2 Change the plot coordinates to linear 1/q vs. square root of time (Fig. M2). The plot indicates a point of departure of the linear trend at about 35 days 0.5. STEP 3 Figure M2 Click the Linear-Arps button next to the Y-Axis button (Fig. M3) and use the start and end markers to visually align the red line with the data to determine m, the slope of the straight-line portion of the plot. The goodness of fit of the alignment is determined by how close the R 2 factor is to 1.0. This can be done, if desired, by positioning the start and end markers at or close to upper and lower limits of the linear portion of the data plot. Placing the t elf arrow as indicated yields a value of t elf = days 0.5. The slope of the straight-line linear trend is seen as The linear trend of the square root of time plot will normally represent a b factor in the Arps equation of 2. The abrupt break in slope at t elf in (Fig. M3) is a clear indication of the change in flow regime from linear flow to BDF flow. Mannon Associates 9

10 STEP 4 Figure M3 Use the Alt-2 key combination, or the Window menu, to pull up the reservoir parameters window (Fig. M4) in order to assemble the reservoir data to calculate the value for A of the well using Eq. 8. This window is used both for conventional and unconventional reservoir calculations. The data intended for unconventional reservoirs are highlighted and consist of five factors in the upper tier; namely P i, P wf, gas gravity Γ g, reservoir temperature T[R], and temperature at standard conditions T(s)[R]. Values for porosity φ, and zone thickness h are in the middle tier. The remaining factors in Eq. 8 are calculated by MIDA-QRC and reside in the lower tier and consist of initial gas compressibility (c g ) i, initial gas viscosity(μ g ) i, and the m(p i ) and m(p wf ) pseudo-pressures Mannon Associates 10

11 STEP 5 Figure M4 Click the Copy button in the lower left hand corner of the reservoir parameters window (Fig. M4) to bring up the copy parameters dialog box (Fig. M5). This allows you to copy selected parameter values to all the wells in the file, if desired. Figure M5 Mannon Associates 11

12 STEP 6 Click the calculate button on the square root of time graph (Fig. M3) to bring up a calculation window entitled End of Linear Flow (Fig. M6). Click the calculation button below the Area box to calculate the drainage area, A (Fig. M7). This window facilitates sensitivity studies of the parameters of the equation that are often difficult to measure, such as zone thickness (fracture height) h, porosity φ, drainage area, A, and t elf. Figure M6 STEP 7 Figure M7 The next step in the process is the production forecast. Click the Enable Arps check box on the square root of time plot (Fig. M3) to add a hyperbolic production curve along with a red triangle marker showing an unmatched plot (Fig. M8). The production data and the hyperbolic curve are then matched by sliding the red triangle up or down the linear trend along with setting an appropriate value for the Arps b factor, in this case b=0.3 (Fig. M9) Values for D min and well abandonment production rate are set by the user. The D min feature allows the forecaster to modify the reserves in cases of extended Mannon Associates 12

13 production times. If and when D min is reached the hyperbolic trend reverts to exponential (b=0). Figure M8 STEP 8 Figure M9 After adjusting the forecast line and parameters, the forecast can be viewed with a variety of graph settings, by clicking the Y-Axis tab to select the desired coordinates. Mannon Associates 13

14 Check the Show Forecast box to view the forecast values in red. For example, Fig. M10 shows the rate-time production (q) forecast for the well. STEP 9 Figure M10 The forecast is saved by clicking the save forecast to spreadsheet button. This causes a comma-separated value (.csv) file to be saved with the production forecast for the well. Fig. M11 shows this forecast as seen from within the Microsoft Excel program. Mannon Associates 14

15 Case 2 Figure M11 Case 2 is for a Bakken oil well in North Dakota. The analysis of unconventional oil wells also involves the use of the square root of time plot as in the case of unconventional gas wells. The equation for the slope m this plot for oil wells is: From a calculation point, the equation is simpler than the gas equation in that reservoir temperature and pseudo-pressures are not required, and the oil viscosity is expressed in a form so that oil viscosity drops out of the final equation for t elf. The formation factor for oil (B o ) i is added. In addition, in the oil case the compressibility is the total compressibility which includes formation compressibility and the compressibility of the reservoir fluids. For gas wells the gas compressibility is so dominant that the other elements of compressibility can be ignored. The equations assume single phase flow from an undersaturated reservoir that remains in that state throughout the linear flow period. Equation 5 mentioned above for gas reservoirs also applies to oil reservoirs. t elf A gct i x f 1 k 2 (9), (5) Substituting the quantity x f k 0.5 from Eq. 9 into Eq. 5 yields t elf, the duration of linear flow for oil wells. Mannon Associates 15

16 Equation 10 is arranged to solve for drainage area A d : (10) The stepwise procedure for the analysis of an unconventional oil well is essentially the same as for a gas well except for the differences in the equations and the reservoir parameters going into the equations. Fig. M12 and Fig. M13 display the oil reservoir parameters and copy parameters windows. Case 2 will also require additional steps to complete the analysis due to the fact that the well is still producing in the linear flow period (11) Figure M12 Figure M13 STEP 1 The form of the square root of time plot (Fig. M14) confirms the status of the well in the linear flow period with the t elf arrow set at the last production data point. The corresponding value for t elf of days 1/2 assumes that the well will enter the depletion period (BDF).in the next month of production. A click of the calculate button on Mannon Associates 16

17 the graph window (Fig. M14) indicates a drainage area of acres as shown in the End of Linear Flow window (Fig. M15). Figure M14 STEP 2 Figure M15 The next step in the process is to forecast the future production from the well. Unlike Case 1, the engineer or scientist has multiple options in this regard. One option is to Mannon Associates 17

18 employ the drainage area calculated in Step 1 and forecast minimum well reserves all of which are in the depletion period. STEP 3 Other options to generate multiple production forecasts are available for the well by assuming a series of drainage areas in excess of the minimum drainage calculated in Step1. This is accomplished by increasing the acreage in the acreage box in Fig.15 in one instance to say 250 acres. The result is an increase in t elf from to Days 1/2 (Fig. M16) and the automatic repositioning of the red t elf arrow on the square root of time plot as indicated in Fig. M17. Figure M16 Mannon Associates 18

19 STEP 4 Figure M17 The next step mirrors the procedure taken in Case 1. The Enable Arps box on the graph window is clicked to pull up Fig. M18, and the production data and the hyperbolic Arps curve are matched by sliding the red triangle up or down the linear trend along with setting an appropriate value for the Arps b factor (Fig. M19).The procedure is completed by assigning the desired values for D min and well abandonment rate and clicking the save forecast to spreadsheet button to save the production forecast to a comma-separated-value file, readable by Microsoft Excel. Mannon Associates 19

20 Figure M18 Figure M19 Mannon Associates 20

21 Alternative Interpretation of Figure M17 An alternative interpretation of Fig. M17 is depicted in Fig. M20 below in which the first 23 months of production data of the well from 5/31/2008 to 4/31/2010 are taken as representing the initial linear flow period with a b value of 2.0. The latter straight-line portion which has a 1.70 b factor would then be considered a form of compound linear flow, which is discussed in some detail in Case Study 3. Case 3 Figure M20 Case Study 3 is a Granite Wash well in the Anadarko Basin in Texas demonstrating initial linear flow and a subsequent linear flow period known as compound linear flow. Case studies 1 and 2 illustrate the production performance of unconventional oil and gas wells that typically exhibit an initial linear portion followed by a depletion portion to well abandonment. Case 3 is an example of wells that demonstrate a more complicated production profile consisting of this second linear flow period after the initial flow period. The second linear flow or compound linear flow represents fluid flow in the reservoir beyond the limits of the SRV into the SRV region. There are various reasons for compound linear flow. A common one as stated by Thompson et al 2012 occurs when an unconventional completion is performed in a conventional reservoir (e.g. 10,000 ft. MFHW in a 0.1 md oil reservoir). In the case of gas reservoirs the permeability could be on the order of at least ten-fold less than that. There is a long history of Granite Wash Mannon Associates 21

22 vertical well development in the Texas portion of the Anadarko Basin where the Case 3 well is located. STEP 1 Fig. GW1 illustrates the initial linear flow period of the well with an estimated t elf of approximately 26.5 days.5 to represent the beginning of the depletion period. Figure GW1 Mannon Associates 22

23 STEP 2 Fig. GW2 shows the production forecast based on an Arps b = 0.4 and economic limit = 200Mcf/D for reserves of 0.482BCF. STEP 3 Figure GW2 Fig. GW3 indicates the existence of a subsequent linear portion that could represent compound linear flow or possibly a transitional flow period between the initial linear flow period and compound linear flow. In either case the red arrow has been placed at the last month s production of the second linear trend. Mannon Associates 23

24 STEP 4 Figure GW3 Positioning the red arrow as shown in Fig,GW4 would anticipate the beginning of the depletion period at that point and yield minimum P90 reserves of Bcf for an increase of 37.6% over the reserves calculated in step 2 above. The operator could also calculate P50 and P10 reserves by prolonging the second linear trend. Mannon Associates 24

25 Summary and Conclusions Figure GW4 The goal of MIDA-QRC is to conduct Reservoir Transient Analysis (RTA) on both oil and gas unconventional wells in such a way to achieve quicker, more reliable and comprehensive production forecasts and drainage area calculations. This is accomplished by combining linear flow equations with the square root of time plot to forecast transient oil or gas production along with transition to the Arps BDF forecast. Adopting this quick, simplified, yet rigorous, theoretically sound methodology in the interpretation of unconventional oil and gas well data can be of substantial value to both large and small oil and gas companies. It can provide a platform of performance and better understanding of this ever growing segment of the oil and gas industry. Technical Note Methodology The methodology adopted by MIDA-QRC combines quickness with reliability. Superposition time functions are not employed which insures an absence of flow regime bias. In addition reliability was achieved without the use of pseudo time and the accompanying complexities and time-consuming iterations. The procedure assumes constant flowing pressures operating at high degrees of drawdown which is an acceptable assumption for a large segment of the unconventional oil and gas reservoirs. The reader is referred to Stubhar et al 1975 and Thompson et al 2012 and others for a discussion of bi-linear and radial flow regimes that may occur in Multi-Fractured Horizontal Well (MFHW) type completions on occasion. Experience has shown they can Mannon Associates 25

26 usually be ignored for RTA purposes. The focus can then be placed on the normally recognizable early linear, transitional, compound linear, and BDF flow periods to gain a better understanding of the character of the reservoir-well system under examination. Technical Notes Example Well Files Example well files of conventional wells as well as unconventional wells are included in the MIDA-QRC software package. The production data for the unconventional well files was obtained from the Lasser, Inc. US data base, and contains Barnett, Marcellus, and Eagle Ford (Webb and Dimmit Counties) gas well examples together with Bakken, Elm Coulee, Niobrara, and Eagle Ford (Lavaca and Frio Counties) oil well examples. The main purpose of the unconventional well files is to illustrate the utility of the software in preparing quick and reliable forecasts of future production from unconventional wells. The reader will notice in reviewing the well files that a straight-line match of the linear flow period of all the wells has been made. In a few cases the match is applied to a linear flow period in the well subsequent to the initial flow period which may represent compound linear flow or instances of an abrupt decrease in the bottom hole flowing pressure of the well. A forecast of future production is shown for wells that have reached depletion flow conditions. No attempt was made to calculate drainage areas due to the lack of appropriate reservoir data. The red arrow is employed by the user to pick the point of departure of the square root of time plot from linear flow to depletion flow. The red triangle signifies the change from the linear flow equation to the Arps depletion flow equation. Ideally, the two markers should be superimposed on each other, however, this usually reflects an improper placement of the Arps model. Apparently the net effect of the movement of the pressure transients within the complex fractured matrix system as they move outward and eventually contact the boundaries of the SRV is not characterized by such an abrupt change, but is transitional even though the departure on the square root of time plot may not appear to reflect this. In any case experience has shown that positioning the red triangle upstream from the red arrow, i.e. at an earlier time provides a more realistic and appropriate production data match. Bibliography Anderson, D.M. et al Analysis of Production Data from Fractured Shale Reservoirs 2010 SPE Anderson, D.M. et al, How Reliable is Production Data Analysis? 2014 SPE Chu, P., et al, Characterizing and Stimulating the Non-Stationariness and Non-Linearity in Unconventional Oil Reservoirs: Bakken Application 2012 SPE Ibrahim, M. et al, Analysis of Rate Dependence in Transient Linear Flow in Tight Gas Wells 2006 SPE Liang, P. et al, Analyzing Rate/Pressure Data in Transient Linear Flow in Unconventional Gas Reservoirs 2011 SPE Liang, J.M., et al, Importance of Transition Period in Compound Linear Flow in Unconventional Reservoirs 2012 SPE Mannon Associates 26

27 Moghadam, S., et al, Pitfalls of Superposition When Analyzing Production Data 2011 SPE Neal, D.B., Early-Time Tight Gas Production Forecasting Technique Improves Reserves and Reservoir Description 1989 SPE Nobakht, M., et al, Simplified Yet Rigorous Forecasting of Tight/Shale Gas Production in Linear Flow 2010 SPE Nobakht, M. et al, Case Studies of a Simplified Yet Rigorous Forecasting Procedure for Tight Gas Wells 2010 SPE Nobahkt, M. et al, Analyzing Production Data from Unconventional Gas Reservoirs with Linear Flow and Apparent Skin 2012 SPE Nobakht, M. et al, A New Analytical for Analyzing Production from Shale Gas Reservoirs Exhibiting Linear Flow: Constant Pressure Case 2011 SPE Nobakht, M., et al, Estimation of Contacted and Original Gas in Place for Low Permeability Reservoirs Exhibiting Linear Flow 2011 SPE Rasri, F., et al, Diagnosing Fracture Network Pattern and Flow Regime Aids Production Performance Analysis in Unconventional Oil Reservoirs 2012 SPE Thompson, J.M., et al, What s Positive About Negative Intercepts 2012 SPE Tran, T., et al Production Characteristics of the Bakken Shale Oil 2011 SPE Wattenbarger, R.A., et al, Production Analysis of Linear Flow into Fractured Tight Gas Wells 1998 SPE Ye, P., et al, Beyond Linear Analysis in an Unconventional Oil Reservoir 2013 SPE Mannon Associates 27