Rate Transient Analysis COPYRIGHT. Introduction. This section will cover the following learning objectives:

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1 Learning Objectives Rate Transient Analysis Core Introduction This section will cover the following learning objectives: Define the rate time analysis Distinguish between traditional pressure transient analysis and rate time analysis Describe the needs of the type of data which are typically used for rate time analysis Discuss the application of rate time analysis under transient and pseudo-steady state conditions Distinguish between the type of reservoir information we can obtain under transient and pseudo-steady state conditions Explain the use of dimensionless variables in rate time analysis Describe the limitations of the rate time analysis 1

2 Rate Time vs. Pressure Transient Analysis Pressure Transient Analysis Rate Time Analysis Typically pressure is measured at a constant rate as a function of time; the rate can be zero during the build up test The data collected has a very high resolution (seconds, minutes, etc.) using well calibrated instrumentation In most cases, the goal is to obtain reservoir parameters which influence the productivity of the well Requires an active interference with the well (i.e., shutting it for prolonged period; producing it at a fixed rate over certain duration, etc.) Typically rate is measured as a function of time assuming the pressure is constant The data collected has a poor resolution (daily, monthly, etc.) In most cases, the goal is to obtain future performance and EUR of the well Passive technique; only requires monitoring of well production as the well is producing 2

3 Important Complications Assumptions Past producing trends reflect future performance Wells are produced at or near capacity Constant drainage area Constant bottom hole pressure Important Complications Changing reservoir conditions Crossing the bubble point Crossing the dew point Stress sensitive permeability Water influx (gas reservoir) Interference from offset wells Changing well/surface conditions Flow restrictions Liquid loading Back pressure 3

4 Flow Regimes The rate transient analysis can be applied under any flow regime conditions. However, the information gained is different under different flow regimes. Data available under transient state By evaluating the data under transient conditions, we can obtain reservoir parameters such as permeability, skin factor, hydraulic fracture characteristics Data available under pseudo-steady state or boundary dominated state By evaluating the data under pseudo-steady state or boundary dominated flow conditions, we can obtain the remaining reserves, EUR and future rate predictions as a function of time See Reservoir Flow Properties Fundamentals for more information on this topic. 4

5 Important Dimensionless Variables Field Units Dimensionless Pressure SI Units Dimensionless Pressure Dimensionless Rate Dimensionless Rate q k h B o p STB/d md ft cp bbi/stb psia Important Dimensionless Variables Field Units Dimensionless Pressure Z Dimensionless Rate q Sm 3 /d k h md m Pa.s B o m 3 /Sm 3 p kpa SI Units Dimensionless Pressure Z Dimensionless Rate q k h T m(p) MSCF/d md ft R psia 2 /cp q Sm 3 /d k md h m T K m(p) kpa 2 /pa.s 5

6 Important Dimensionless Variables Field Units SI Units Dimensionless Pressure (another version) 0.75 Dimensionless Rate (another version) 0.75 = Where q D and p D are defined previously and r e and r w are drainage and wellbore radii respectively. The alternate definition for q Dd comes directly from the rate equation for q i based on Darcy s law. Dimensionless Pressure (another version) 0.75 Dimensionless Rate (another version) Important Dimensionless Variables Field Units Dimensionless time 3792ϕ Dimensionless Time (another version) = k md t hrs fraction cp c t psi -1 r e and r w ft r wa Effective well bore radius or r w e -S where S is the skin factor t Dd Can be defined in terms of decline rate, D i and t = Where q D and p D are defined previously and r e and r w are drainage and wellbore radii respectively. The alternate definition for q Dd comes directly from the rate equation for q i based on Darcy s law. SI Units Dimensionless time ϕ Dimensionless Time (another version) = k md t hrs fraction Pa.s c t kpa -1 r e and r w m r wa Effective well bore radius or r w e -S where S is the skin factor t Dd Can be defined in terms of decline rate, D i and t. 6

7 Important Dimensionless Variables Field Units Dimensionless time 3792ϕ Dimensionless Time (fractured well) 3792ϕ k md t hrs fraction cp c t psi -1 A area in ft 2 x f half fracture length in ft Important Dimensionless Variables Field Units Dimensionless cumulative production (oil) ϕ Dimensionless Cumulative Production (gas) ϕ N p MSCF fraction cp c t psi -1 A area in ft 2 p psia m(p) psi 2 /cp SI Units Dimensionless time ϕ Dimensionless Time (fractured well) ϕ k md t hrs fraction Pa.s c t kpa -1 A area in m 2 x f half fracture length in m SI Units Dimensionless cumulative production (oil) ϕ Dimensionless Cumulative Production (gas) 704 ϕ N p Sm 3 fraction Pa.s c t kpa -1 A area in m 2 p kpa m(p) psi 2 /Pa.s 7

8 Learning Objectives This section has covered the following learning objectives: Define the rate time analysis Distinguish between traditional pressure transient analysis and rate time analysis Describe the needs of the type of data which are typically used for rate time analysis Discuss the application of rate time analysis under transient and pseudo-steady state conditions Distinguish between the type of reservoir information we can obtain under transient and pseudo-steady state conditions Explain the use of dimensionless variables in rate time analysis Describe the limitations of the rate time analysis 8

9 Learning Objectives Rate Transient Analysis Core Traditional Decline Curve Analysis This section will cover the following learning objectives: Distinguish between exponential, harmonic and hyperbolic decline curves Explain the different parameters that impact the performance of a well Describe how the Economic Ultimate Recovery (EUR) is impacted by the assumptions about the type of decline method Explain how the traditional decline curve analysis can be extended to transient state conditions 9

10 Generalized Equation Arps proposed that for any well, the production decline can be represented by 1 / Initial rate hyperbolic exponent Initial decline rate Time Graphical Representation q Log-log plot of rate versus time b=0 Time b=1 The value of is always between 0 and 1. The limiting cases for b values are: When = 0, the equation can be written as:. This equation is called exponential decline When 0 < < 1, the equation takes the original form and it is called hyperbolic decline When = 1, the equation can be written as. This equation is called harmonic decline For the range of b values, the decline in q as a function of time is shown b=0 b=1 Smaller the value of b, faster the decline (exponential decline) The rate change slowest for harmonic decline (b = 1) The value of b determines the shape of decline Faster decline also translates into smaller cumulative production 10

11 Exponential Decline The unique aspect of exponential decline is that the decline rate throughout the depletion of the well is constant If we know the abandonment rate,, we can calculate the cumulative hydrocarbons production. If we know the current rate of a well,, and know the abandonment rate, we can calculate the remaining reserves. 11

12 Exponential Decline Exponential decline provides the most conservative estimation of EUR compared to other types of decline Hyperbolic Decline We can obtain the decline rate by either plotting log of rate versus time and calculating the slope, or by plotting cumulative production versus rate and calculating the slope Exponential decline allows prediction of future rate performance by using an assumption of constant decline rate For values of b between 0 and 1, we can use hyperbolic decline Unlike exponential decline, the decline rate decreases with time for hyperbolic decline. We can calculate the decline rate after 1 certain time. The cumulative production, at the time of abandonment, can be calculated

13 Harmonic Decline Similar to hyperbolic decline, for harmonic decline, the decline rate changes with time. The decline rate as a function of time can be calculated. 1 The cumulative production is calculated. Similar principles can be used to calculate EUR if we know the historical, cumulative oil produced 13

14 Fetkovich Type Curve Log-log plot of dimensionless rate vs. dimensionless time Fetkovich Type Curve The transition from transient to boundary dominated flow happens when y axis is 1 and x axis is 0.1 If the data falls in transient region (a plot of q vs. t) permeability and skin factor can be obtained If the data falls in the boundary dominated region, q i, D i and b can be obtained The boundary dominated stem also shows values of b exceeding 1.0 This can be useful for analyzing the data from unconventional wells Log-log plot of dimensionless rate vs. dimensionless time 14

15 Learning Objectives This section has covered the following learning objectives: Distinguish between exponential, harmonic and hyperbolic decline curves Explain the different parameters that impact the performance of a well Describe how the Economic Ultimate Recovery (EUR) is impacted by the assumptions about the type of decline method Explain how the traditional decline curve analysis can be extended to transient state conditions 15

16 Learning Objectives Rate Transient Analysis Core Modern Rate Time Analysis This section will cover the following learning objectives: Describe how to extend the rate time analysis when the bottom hole pressure is not constant but a variable Compare both Blasingame and Agarwal type curve methods and evaluate both oil and gas wells using both these types of curves Explain the concept of flowing material balance analysis 16

17 Blasingame Approach Blasingame used the normalized rate plot to account for both variable rate and variable pressure Instead of using rate (as in the case of Arps), we plot: on the y axis for oil wells After Palacio and Blasingame, SPE (1993) on the y axis for gas wells Instead of plotting the actual time on x axis, Blasingame recommended material balance time, which is defined as: for oil wells for gas wells The numerator represents cumulative production and the q in the denominator represents the rate at the time N p or G p hydrocarbons are produced Blasingame Plot This plot represents dimensionless normalized rate versus dimensionless material balance time; the definitions of dimensionless rate and time are already defined, except that the dimensionless time is calculated using material balance time The graph does show clear distinction between transient and boundary dominated flow There is only single stem in boundary dominated flow (unlike multiple ones for Arps equation); the slope is -1 in boundary dominated flow which corresponds to harmonic decline 17

18 Blasingame Plot Blasingame also created integral and differential plots to improve the diagnostic power of the plot The integral function provides more smoother data compared to raw data The derivative of integral function provides a better signature to identify transition between transient and boundary dominated flow When all three curves are plotted and fitted to the type curve, we can obtain reservoir parameters in transient region and EUR in boundary dominated region Example Blasingame Method This plot shows all three curves Integral function is smoother but the derivative function has more character; the derivative of integral function is smoother than the derivative of raw data By fitting the data, we can identify the data in both transient and boundary dominated regions 18

19 Normalized Rate Raw Data vs. Dimensionless Plot Normalized Cumulative Production qdd Normalized rate is / and normalized cumulative production is ( )/ ; using the graph, we can calculate maximum recovery based on the intersection on x axis if we know the bottom hole pressure To calculate oil in place, we need to assume different value of A (area) such that the intersection point on dimensionless graph goes through 1 on x axis; through trial and error we can calculate the value of A and hence oil in place if other reservoir parameters are known Q Dd 19

20 Learning Objectives This section has covered the following learning objectives: Describe how to extend the rate time analysis when the bottom hole pressure is not constant but a variable Compare both Blasingame and Agarwal type curve methods and evaluate both oil and gas wells using both these types of curves Explain the concept of flowing material balance analysis 20

21 Learning Objectives Rate Transient Analysis Core Unconventional Reservoirs This section will cover the following learning objectives: Describe the application of rate time analysis for unconventional reservoirs Identify different flow regimes which are present for multiple fractured, horizontal wells Indicate important flow regimes which are typically observed in horizontal, multi-stage fractured wells Determine the type of reservoir parameters we can obtain from evaluating rate time data for unconventional formations Indicate how the traditional decline curve analysis can be used for wells producing from unconventional reservoirs 21

22 Horizontal Well Geometry A typical horizontal well is drilled in the direction of minimum stress Multi-stage fractures are created which are perpendicular to the well Although each fracture may have different length and height, for simplicity in the model, we assume that all the fractures are uniform and have the same length and height The space between the fractures is also assumed to have some stimulation and hence alteration of permeability Fractures are transverse (perpendicular) to well direction 22

23 Flow Regimes in Horizontal Well Fracture Linear Flow Bi-linear Flow Stimulated Region Linear Flow into the Fracture Flow Regimes in Horizontal Well Fracture interference flow (Boundary dominated flow successive fracture start interfering) Half fracture length x F = L in the figure; H is the thickness of the reservoir Linear flow from unstimulated region into stimulated region 23

24 Relationship between Normalized Rate (or Pressure) versus Time Depending on the flow regime, a distinct relationship exists between normalized pressure (or rate) and time For linear flow from stimulated region into fracture, depending on whether the well is producing at constant rate or pressure, we can write the equation in terms of dimensionless form: For constant rate: For constant pressure: where t D is defined in terms of half fracture length. where t D is defined in terms of half fracture. If both pressure and rate are varying (as is more common), use the equation corresponding to constant rate but instead of using time, use superposition time. 24

25 Superposition Time What is superposition time? Superposition Time Superposition time is a way by which we can apply the constant rate equation to variable rate problem. That is, if the well is producing at three different rates, what would be equivalent time the well has to produce at the last rate so that the bottom hole pressure would be the same? q 1 q 2 q 3 Liang et al. (SPE ) 25

26 Procedure to Evaluate Well Procedure to Evaluate Well QUESTION How do you evaluate a horizontal multistage fracture well? Plot normalized pressure versus superposition time on log-log graph. Determine different flow regimes present in the reservoir. Determine the transition from linear flow in stimulated region to fracture interference (boundary dominated) flow. Note the time at which transition happens (t elf ). Plot normalized pressure versus square root of time and determine the slope of the straight line. From the slope (m) calculate x F k. From the knowledge of t elf and based on simple rectangular geometry, determine the initial oil or gas in place within the rectangle. 26

27 Equations to Estimate Parameters Oil Well Field Units 19.9 ϕ 8.96 Where: x F is in ft, k is in md m (slope) is in psi/(stb/d)/d 0.5 h is in ft, is in cp, is in fraction c t is in psi -1, t elf is in days B o and B oi are in bbl/stb Equations to Estimate Parameters Gas Well Field Units ϕ Oil Well SI Units 965 ϕ 8.96 Where: x F is in m, k is in md m (slope) is in kpa/(sm 3 /d)/d 0.5 h is in m, is in Pa.s, is in fraction c t is in kpa -1, t elf is in days B o and B oi are in m 3 /Sm 3 Gas Well SI Units Where: x F is in ft, k is in md, T is in R m (slope) is in psi 2 /cp/(mscf/d)/d 0.5 h is in ft, is in cp, is in fraction c t is in psi -1, t elf is in days S gi is initial gas saturation B gi is in ft 3 /SCF ϕ Where: x F is in m, k is in md, T is in K m (slope) is in kpa 2 /Pa.s/(Sm 3 /d)/d 0.5 h is in m, is in Pa.s, is in fraction c t is in kpa -1, t elf is in days S gi is initial gas saturation B gi is in m 3 /Sm 3 27

28 Gas Well Example Field Units , , ,000 SI Units , After Ibrahim and Wattenberger (SPE ) 28

29 Traditional Decline Curve Analysis Evaluation of a gas or oil well producing from unconventional reservoirs based on flow regimes is much more rigorous and more informative. Alternately, the wells can also be analyzed using traditional decline curve analysis such as Arps method. The main difficulty in using Arps method is the key assumption that a well is producing under boundary dominated flow is violated. When early production data from unconventional well is fitted, the value of b is much greater than 1 (close to 2 for linear flow) for transient flow regime and as the well becomes boundary dominated, the value of b gets smaller. The common practice is to use two different values of b to fit the data. The early production data are fitted using higher b value and when the decline rate reaches certain value, assume exponential decline ( b = 0). 29

30 Gas Well Example Production data are available for 565 days for a gas well The production data are fitted using Arps decline curve using a value of b = 1.65 (far exceeding the normal range) The decline rate is continuously calculated and when it reaches 0.07/year, the production is switched to exponential decline Gas Well Example q, MSCFD [MSCMD] q MSCFD 4500 [127] 4000 [113] 3500 [99] 3000 [85] 2500 [71] 2000 [57] 1500 [42] 1000 [28] 500 [14] Time, t (days) 30

31 Gas Well Example Match between production rate and Arps equation is shown here. The Arps equation for the best fit is the following: 4, /. 4,254 is the initial rate in MSCFD, b is 1.65, D i is 0.036/day and t is in days Using this equation, we can determine that switch to exponential decline will happen when t = 3,128 days Assuming that abandonment rate is 100 MSCFD [2.8 MSCMD], we can make predictions q, MSCFD [MSCMD] q MSCFD 4500 [127] 4000 [113] 3500 [99] 3000 [85] 2500 [71] 2000 [57] 1500 [42] 1000 [28] 500 [14] Time, t (days) 31

32 Learning Objectives This section has covered the following learning objectives: Describe the application of rate time analysis for unconventional reservoirs Identify different flow regimes which are present for multiple fractured, horizontal wells Indicate important flow regimes which are typically observed in horizontal, multi-stage fractured wells Determine the type of reservoir parameters we can obtain from evaluating rate time data for unconventional formations Indicate how the traditional decline curve analysis can be used for wells producing from unconventional reservoirs 32

33 Learning Objectives Rate Transient Analysis Core Integration of Material Balance This section will cover the following learning objectives: Describe the relationship between material balance and rate time analysis Explain how to combine material balance with rate equations to predict rate as a function of time Describe simple cases for single phase gas and oil reservoirs and predict the rates Indicate how the simple analysis can be extended to other complex situations 33

34 Material Balance Recall The Reservoir Material Balance Fundamentals module provided information on: How the material balance technique works Oil, gas and water rates, change in the reservoir pressure as a function of time and fluid properties as a function of pressure Important mechanisms which influence the production Using the known mechanisms and the provided data, determine the initial oil or gas in place depending on the type of the reservoir To predict the rate from a well, work backwards and assume that the initial oil or gas in place is known and determine the rate at which the well will produce as a function of time See Reservoir Material Balance Fundamentals for more information on this topic. 34

35 Black Oil Reservoirs Consider the most generalized form of black oil reservoir material balance equation: If we only consider oil reservoir producing above bubble point with no influence of water aquifer, we can simplify the equation as: 1 =, 35

36 Black Oil Reservoirs How to Predict Rate as a Function of Time? Assume that initial oil in place associated with a well is known, N foi Assume that initial pressure is known; we can calculate the initial rate at which well will produce as (assuming pseudo-steady state): Field Units.. Assume a decrement in pressure p; the new reservoir pressure is: Use the material balance equation to calculate oil produced by creating this pressure drop: SI Units.. p i p =, Black Oil Reservoirs Integration with Time Using the new average pressure, calculate the new rate: Field Units.. Calculate the average rate during a period when pressure changed from p i to The reason we used logarithmic average is it is the most appropriate for exponential decline SI Units.. Knowing the average rate during that period and the incremental oil produced, we can determine incremental time to produce that oil Δ 36

37 Black Oil Reservoirs Integration with Time Using the new average pressure, calculate the new rate: Field Units SI Units.. The Calculate same the steps average are repeated rate during at other a period pressure when decrements pressure changed from p i to By adding the time, we can calculate the cumulative time and The reason we used logarithmic average is plot rate vs. time it is the most appropriate for exponential decline Knowing the average rate during that period and the incremental oil produced, we can determine incremental time to produce that oil.. Δ 37

38 Rate Profile The figure shows the rate profile as a function of time q, STB/day Time, days Accounts for both the oil compressibility and formation compressibility Although the rate profile is predicted using pseudo-steady state assumption, it can also be predicted using transient state equation except that it will involve trial and error procedure since rate will change with time for transient state q, Sm 3 /day 38

39 Black Oil Reservoirs Below Bubble Point For black oil model, oil saturation can be calculated as a function of pressure: Once saturation is calculated, we can calculate the producing gas oil ratio as: Similar to previous example, we can assume pressure decrement and calculate R p using prior pressure Using material balance, we can calculate the produced oil and calculate the oil rate. To calculate the oil rate at a new pressure, we also need to account for oil saturation changes; hence the change in the rate. The oil rate is calculated as: Gas Reservoirs A similar procedure can also be applied for gas reservoirs Assume a simple case where the only mechanism by which gas is produced is by gas expansion only. The material balance equation can be written as: 0.75 ) If we assume the initial gas in place is known, we can calculate the amount of gas produced at a given pressure as: Field Units SI Units The rate at any given pressure is calculated using Darcy s law: / / Field Units SI Units 39

40 Rate Profile The rate is shown as a function of time Similar to oil wells, we can apply it for gas wells producing under transient conditions; however, it would require a trial and error procedure since the rate is dependent on time as well q, MSCF/D Time, days q, MSm 3 /day 40

41 Learning Objectives This section has covered the following learning objectives: Describe the relationship between material balance and rate time analysis Explain how to combine material balance with rate equations to predict rate as a function of time Describe simple cases for single phase gas and oil reservoirs and predict the rates Indicate how the simple analysis can be extended to other complex situations This is Reservoir Engineering Core Reservoir Rock Properties Core Reservoir Rock Properties Fundamentals Reservoir Fluid Core Reservoir Fluid Fundamentals Reservoir Flow Properties Core Reservoir Flow Properties Fundamentals Reservoir Fluid Displacement Core Reservoir Fluid Displacement Fundamentals Applied Reservoir Engineering Properties Analysis Management Reservoir Material Balance Core Reservoir Material Balance Fundamentals Decline Curve Analysis and Empirical Approaches Core Decline Curve Analysis and Empirical Approaches Fundamentals Pressure Transient Analysis Core Rate Transient Analysis Core Enhanced Oil Recovery Core Enhanced Oil Recovery Fundamentals Reservoir Simulation Core Reserves and Resources Core Reservoir Surveillance Core Reservoir Surveillance Fundamentals Reservoir Management Core Reservoir Management Fundamentals 41