Petroleum Reservoir Simulation

Production data analysis of unconventional gas wells: Review of theory and best practices

Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States’ oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet.

https://www.pnas.org/content/pnas/110/49/19731.full.pdf

Gas production in the Barnett Shale obeys a simple scaling theory

A Better Way to Forecast Production from Unconventional Gas Wells

Traditional decline methods such as Arps’ rate/time relations and their variations do not work for wells producing from supertight or shale reservoirs in which fracture flow is dominant. Most of the production data from these wells exhibit fracture-dominated flow regimes and rarely reach late-time flow regimes, even over several years of production. Without the presence of pseudoradial and boundary-dominated flows (BDFs), neither matrix permeability nor drainage area can be established. This indicates that matrix contribution is negligible compared with fracture contribution, and the expected ultimate recovery (EUR) cannot be based on a traditional concept of drainage area. An alternative approach is proposed to estimate EUR from wells in which fracture flow is dominant and matrix contribution is negligible. To support these fracture flows, the connected fracture density of the fractured area must increase over time. This increase is possible because of local stress changes under fracture depletion. Pressure depletion within fracture networks would reactivate the existing faults or fractures, which may breach the hydraulic integrity of the shale that seals these features. If these faults or fractures are reactivated, their permeabilities will increase, facilitating enhanced fluid migration. For fracture flows at a constant flowing bottomhole pressure, a log-log plot of rate over cumulative production vs. time will yield a straight line with a unity slope regardless of fracture types. In practice, a slope of greater than unity is normally observed because of actual field operations, data approximation, and flow-regime changes. A rate/ time or cumulative production/time relationship can be established on the basis of the intercept and slope values of this log-log plot and initial gas rate. Field examples from several supertight and shale gas plays for both dry and high-liquid gas production, and for oil production were used to test the new model. All display the predicted straightline trend, with its slope and intercept related to reservoir types. In other words, a certain fractured flow regime or a combination of flow types that dominate a given area or play because of its reservoir-rock characteristics and/or fracture-stimulation practices all produce a narrow range of intercepts and slopes. An individualwell performance or EUR can be derived that is based on this range if the best 3-month average or the initial production rate of the well is already known or estimated. The results show that this alternative approach is easier to use, gives a reliable EUR, and can be used to replace the traditional decline methods for unconventional reservoirs. The new approach is also able to provide statistical methods to analyze production forecasts of resource plays and to establish a range of results of these forecasts, including probability distributions of reserves in terms of P90 (lower side) to P10 (higher side).

Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs

This Faper shows that the decline-curve analysis approa~h does have a solid fundamental basis. The exFonent.ialdecline is shown to be a longtime soluticm of the constant-pressure caie. The constant-pressureinfinite and finite reservcir solutions are placed on a common dimensionless curve with all the standard “empirical” expmential, hyperbolic, arid harmoni> decline-curve equations. Simple combinations of material balance equations and new forms of oil well rate equaticms fo: solution-gas drive reservoirs illustrate under what circumstances speoifis values of the hyperbolic de:line exponent (l/b) or “b” should result. kg-log type curve analysis can be performed Gn declining rate data (constant-terminal pressure case) completely analogous to the loglog type curve matching procedure presently teing employed with constant-rate case pressure transient data. Production forecasting is done by extending a line drawn through the rate-time data cverlain along the uniquely matched or best theoretical type curve. Future rates are then simply read from the real time scale on which the rate-time data is plotted. The ability to calzulate kh from decline-curve dzta by tyFe .-.eferen:es and illustrationsat end o? yapr, curve matching is demonstrated. This paper demonstrates that decline-curve analysis not only has a solid fundamentalbase, but provides a tool with more diagnostic power than has previouslybeen suspected. The type curve approach provides unique eolutions upon whish engineers can agree, or shows when a unique solution is not pssible with a type curve only. INTRODUCTION Fiate-timedecline-curve extrapolationis one of the oldest and most often used tools of the petroleum engineer. The various methods used have always been regarded as strictly empirical and not very scientific. Results obtained for a well or lease are subject to a wide range of alternate interpretations,mostly as a function of the experience and objectives of the evaluator. Recent efforts in the area of decline-curve analysis have been directed towards a ~urely computerized statistical approach. Its basic objective being to arrive at a unique “unbiased”interpretation. AS pointed out in a com rehensive review of the !? literature by R2msa , “in the period from 1964 to date, (1968 , several additional papers were publishedwhich contribute to the understanding of decline-curvesbut add’litt.lenew JIECL.INE CURVE ANALYSIS USI technology”. A new direction for decline-curve analysis was given by Slider2 with his development of an overlay method to analyze rate-time data. Because his method was rapid and easily apFlied, it was used extensivelyby Ikunsayin his evaluation of some 200 wells to determine the distribution o the decline-curve exponent term “b”. GentryIsJ Fig. 1 displaying the Arps’4 exponential, hyperbolic, and harmonic solutions all on one curve could also be used as an overlay to match all of a wells’ decline data. He did not, however, illustrate this in his example application of the zurve. The overlay method of SMder is similar in principal to the log-log tyFe zurve matching procedure presently being employed to analyze constant-rata Fressure build-up and drawdown data 5-$’. The exponential decline, often used in decliae-curveanalysis, can be readily shown to be a long-time solution of the constant-pressurezase10-13● It followed then that a log-lo~pe curve matching procedure could be develcFed to analyze decline-zurve data. This pap?r demonstrates that both the analytical 3onstant-pressureinfinite (early transient pericd for finite systems) and finite reservoir solutions ~an be placed on a common dimensionless log-log type curve with all the standard “empirical“ exponential, hyperbolic, and ha~monic decline curve equations developed by Arps. Simple combinations of material balance equations and new forms of oil well ratt equations from the recent work of Fatkovich~ illustrate under what circumstances specific values of the hyperbolic decline expnent “b” should result in dissolved-gas drive reservoirs Log-log type curve analysis is then Ferformed using these curves with declining rate data completely analogous to the log-log type curve natcliingprocedure presently being employed with constant-rate case pressure transient data BASIC EQUATIONS AIISl RATE-TIWW4U ATIONS Nearly all conventional decline-curve analysis is based on the empirical rate-time 3quations qi.venby Arps4 as For b = 0, we aan obtain the exponential declin aa.uationfrom E@. 1 4JLJ_ ‘ “ “ “ “ ● ‘(2) . D:t TYPE CURVES SPE 4% — nd for b = 1, referred tc as harmonic decline, e have y=.— (3) i [l+;it] “ “ “ ● , ● A unit solution (Di = 1) of Eq. 1 was eveloped for values of “b” between O and 1 n 0.1 increments. The results are lotted as 7 set of log-log type curves (Fig. 1 in t~~s f a decline-curve dimensionless rate ‘Dd ES&l ● ● ● * ● ● “(k) i nd a decline-curve dimensionless time ‘Od =Dit . . . . . . . . (5) From Fig. 1 we see that when all the basic lecline-curvesand normal ranges of “b” are Iisplayedon a single graph, all cur~es coincide md become indistinguishableat t 9 =0.3. Any Iataexisting prior to a t,~dof O. till ,&P~T ;Obe an exponential decline regardless of the ;ruevalue of b and thus plot as a straight lin< )n semi-log paper. A statistical or leastSquaresapproach could calculate any valus of J between O and 1. \NALYTICALSOLUTIONS (CONSTANT-Pi’iSSURE AT [NNERBOUNDARY) Constant well pressure solutions to prediziecliningproduction rates with time were first pklished in 1933 b l;iore,Schilthui.sand I fiesultswere pssented {u::stlO,and Hurstl . fcr infinite and finite, slightly compressible, ~in.gle-phaseplane radial flow systems. The rf2SUltS were presented in graphical fcrm in Lerms of a dimensionless flow rate and a ji,mensionlesstime. The dimensionless flow rat ~D ,?anbe ex~ressed as %++&+&v””””(’) and the dimensionless time tu as t = 0.00634 kt . . . . . (7) D !J~~trw2 The original publication did not inulude tabular values of q and t . For use in this ?? paper infinite SOIU ion va ues were obtained from Ref. 15, while the finite values were obtained from Ref. 16. The infinite solution, and finite solutions for r /r from 10 to 100,000, are Tlot.tedon Fif$~.w2-a ant!~-b.

Decline Curve Analysis Using Type Curves

The purpose of this paper is to present case history studies that demonstrate methods of analyzing rate-time data to predict future production and to determine reservoir variables. Constant wellbore pressure analysis techniques are demonstrated, using existing q /SUB Dd/ - t /SUB Dd/ type curves along with developing new q /SUB Dd/ - t /SUB Dd/ type curves from actual field data. Case histories for individual oil and gas wells are presented, along with groups of wells in a field and total field studies. The field studies include a one-well full water drive field, a low permeability solution gas drive field, and a field with both primary and secondary (waterflood) history. Field shutins and backpressure changes are shown to retrace the early time rate data as would be expected from superposition principles. Reservoir variables developed from a total field rate-time match are compared to early well pressure buildup analysis results. Comparisons are excellent. This work not only demonstrates the technique of analyzing rate-time data, it also presents a method whereby a reservoir or formation dimensionless type curve can be developed from rate-time field data. The resulting type curve can then be used to forecast wells or fields in the samemore » reservoir or formation. Because such a type curve is dimensionless, changes in stimulation, spacing, and reservoir properties can also be accounted for.« less

Decline Curve Analysis Using Type Curves: Case Histories

Decline-curve analysis, based on the Arps equations, has always been considered to be purely empirical with no basis on physical laws governing the flow of oil and gas through the formation. The purpose of this paper is to give engineers responsible for making forecasts and determining reserves for numerous operated or nonoperated wells some guidelines and fundamental concepts to allow them to make these forecasts and determinations more quickly and accurately.

Useful concepts for decline-curve forecasting, reserve estimation, and analysis

All gas and oil reservoirs are associated to varying extents with formation waters. The inclusion of the effects of expansion or invasion of this water into oil and gas reservoirs has ta.ken many forms, from recognizing the effects of the expansion of the connate water within the gas or oil reservoir itself, to calculating water influx or effiux across a boundary (with the boundary usually being that of an oil or gas reservoir). There are four currently popular methods used for calculating water influx into reservoirs. They are: 1. Schilthuis, steady state13 2. Hurst Simplified, unsteady state • 2 3. Resistance or Influence Function, unsteady state•-5 4. van Everdingen-Hurst Radial, unsteady state7 The first three methods have proved useful for predicting water drive performance after sufficient historical data have been obtained to fix the necessary influx constants. With what some consider to be disappointing results,1· 8 the van Everdingen-Hurst Radial method is often used with geological and core data when little or no performance history is available. It has also been used to predict reservoir perfonnance after enough historical data have been accumulated to develop values of the influx constants, to and C. In an attempt to include geometries other than radial, derivations for both limited and infinite systems have been made to cover linear, 7 • 9 • 10 spherical, 11 elliptical,12 thick-sand, and wedge-shaped reservoir-aquifer models. The many rigorous geometrical representations that have been developed cannot readily handle the effect of interference between reservoirs. Electric analyzer studies of the Smackover Limestone aquifer in Arkansas by Bruce,14 of the Woodbine aquifer in East Texas by Rumble et al., 15 and of the Ellenberger in West Texas by Moore and Truby have shown that reservoirs sharing a common aquifer can severely interfere with each other, and that, for individual reservoirs in a common aquifer, water drive perfonnance calculations that do not consider interference can be greatly in error. Mortada developed a mathematical method with which to handle interference in a basically infinite radial aquifer system. The method has been applied to field cases.• 19 Coats concluded from his own study that, \"In predicting the pressure-volume behavior of gas reservoirs situated on the common aquifer the effect of interference from other reservoirs on the common aquifer must be accounted for.\" Another aquifer problem more recently presented in the literature is that of flank water injection for pressure maintenance, either to initiate or to supplement edge-water influx. A case history shows that we need to be able to study the effects of injecting water into the aquifer instead of merely including it in the hydrocarbon material balance equation.

M.J. Fetkovich

Papers

Decline Curve Analysis Using Type Curves

Decline Curve Analysis Using Type Curves: Case Histories

Useful concepts for decline-curve forecasting, reserve estimation, and analysis

A Simplified Approach to Water Influx Calculations-Finite Aquifer Systems

Decline Curve Analysis Using Type Curves