Dimensionless Wellbore Storage Coefficient: Skin Factor: Notes:

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1 This problem set considers the "classic" Bourdet example for a pressure buildup test analyzed using derivative type curve analysis. For completeness, the Bourdet, et al. paper is also attached however, you must provide your own analysis you are to only use the Bourdet analysis as a guide, there are considerable differences of opinion as to what the "right" answers should be. Be sure to work the problem using BOTH shut-in time (Δt) and effective shut-in time (Δt e ). Recall that Δt e is the time function for the equivalent pressure drawdown case. A Horner plot is provided, as well as the semilog Δt and effective shut-in time Δt e plots you are to use all of these plots. Finally, for some reason, Bourdet, et al. chose not to work in terms of pressure, p ws, but instead to work in terms of the pressure drop, Δp. This is not a limitation, but it does require that you use Δp 1hr rather than p ws,1hr -p wf (Δt=0) in the semilog skin factor relation. For your convenience, the governing relations for type curve analysis using the "Bourdet -Gringarten" type curves are: Formation Permeability: Notes: qbμ k = h [ ' p wd or p wd ] [ ' Δp or Δp ] MP MP Dimensionless Wellbore Storage Coefficient: k [ Δt or Δte] C MP D = 2 φμc r [ td / CD ] Skin Factor: 1 s = ln 2 [ C 2s De ] MP CD t w MP a. The Bourdet-Gringarten type curves for radial flow behavior, including wellbore storage and skin effects, are provided in a 1 inch-by-1 inch format in this handout. b. You have also been provided with log-log "pressure and pressure integral RATIO function" plots and type curves. Use of these materials is at your discretion, BUT you should note that these functions may significantly improve your ability to assess the transition and end of wellbore storage effects. You are strongly encouraged to use these resources. You are NOT required to use these pressure and pressure integral RATIO functions, they are provided to assist your analysis and are not intended to confuse you. c. You are to provide a comprehensive HAND ANALYSIS of these test data type curves are provided for hand analysis. You are also permitted to perform SUPPLEMENTARY analyses of these data using software (e.g., your own software, Saphir, FAST, etc.) HOWEVER, YOU ARE REQUIRED TO SUBMIT HAND ANALYSES OF THESE DATA.

2 Bourdet-Gringarten Type Curve Dimensionless Pressure and Pressure Derivative Functions Bourdet-Gringarten Type Curve: Dimensionless Pressure and Pressure Derivative Functions 2

3 Bourdet-Gringarten Type Curve Dimensionless Pressure Integral and Pressure Integral-Derivative Functions Bourdet-Gringarten Type Curve: Dimensionless Pressure Integral and Pressure Integral-Derivative Functions 3

4 4 Problem Definition and Requirements Given: These data are taken from the Bourdet, et al. reference and are to be considered accurate enough for engineering analysis. Assume that wellbore storage and skin effects are present. Reservoir properties: φ=0.25 r w =0.29 ft c t =4.2x10-6 psia-1 h=107 ft Oil properties: B o =1.06 RB/STB μ o =2.5 cp Production parameters: p wf (Δt=0) =? psia q o =174 STB/D (constant) t p =15.33 hr References: 1. Bourdet, D.P., Ayoub, J.A., and Pirard, Y.M.: "Use of Pressure Derivative in Well Test Interpreta-tion," SPEFE (June 1989) Required: 1. For this problem, you are to perform the following analyses: "Preliminary" log-log analysis. Cartesian analysis of "early" time (wellbore storage distorted) data. Semilog analysis of "middle" time (radial flow) data. Log-log type curve analysis. Cartesian analysis of "late" time (boundary-dominated) data (i.e., the "Muskat Plot"). You are to complete the table on the next page provided for you to tabulate your results.

5 5 Required Results Required: You are to estimate the following: "Preliminary" log-log analysis: a. The wellbore storage coefficient, C s. b. The dimensionless wellbore storage coefficient, C D. c. The formation permeability, k. Cartesian analysis of "early" time (wellbore storage distorted) data: a. The pressure drop at the start of the test, Δp wi (Δt=0) this should be 0 psi. b. The wellbore storage coefficient, C s. c. The dimensionless wellbore storage coefficient, C D. Semilog analysis of "middle" time (radial flow) data: (use both Horner and MDH methods) a. The formation permeability, k. b. The near well skin factor, s. c. The radius of investigation, r inv, at the end of radial flow or the end of the test data. Log-log type curve analysis: (use both Δt and Δt e methods) a. The formation permeability, k. b. The near well skin factor, s. c. The wellbore storage coefficient, C s. d. The dimensionless wellbore storage coefficient, C D. Cartesian analysis of "late" time (boundary-dominated) data: "Muskat Plot" a. Average pressure DIFFERENCE, Δp = p pwf ( Δt = 0) (if applicable). Results: Log-log Analysis: Wellbore storage coefficient, C s = RB/psi Dimensionless wellbore storage coefficient, C D = Formation permeability, k = md Cartesian Analysis: Early Time Data Pressure drop at the start of the test, Δp wi (Δt=0) = psi Wellbore storage coefficient, C s = RB/psi Dimensionless wellbore storage coefficient, C D = Semilog Analysis: Horner or Δt e Δt (MDH) Formation permeability, k = md = md Near well skin factor, s = = Radius of investigation, r inv (end of radial flow or end of test) = ft = ft Log-Log Type Curve Analysis: Δt e Δt Formation permeability, k = md = md Near well skin factor, s = = Wellbore storage coefficient, C s = RB/psi = RB/psi Dimensionless wellbore storage coefficient, C D = = Cartesian Analysis: Late Time Data ("Muskat Plot" if applicable) Average pressure DIFFERENCE, Δp = p pwf ( Δt = 0) = psia

6 6 Well Test Data Functions Well Test Data Functions: Point Δt, hr Δt e, hr Δp, psi Δp'(Δt), psi Δp'(Δt e ), psi E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

7 7 Well Test Data Functions (continued) Well Test Data Functions: (continued) Point Δt, hr Δt e, hr Δp, psi Δp'(Δt), psi Δp'(Δt e ), psi E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

8 Cartesian Plot: Early-Time Pressure Data Cartesian Plot Early-Time Pressure Data 8

9 Semilog Plot: "MDH" Plot Pressure Data versus Shut-In Time Semilog Plot "MDH" Plot Pressure Data versus Shut-In Time 9

10 Semilog Plot: "Horner" Plot Pressure Data versus Horner Time Semilog Plot "Horner" Plot Pressure Data versus Horner Time 10

11 Semilog Plot: "Agarwal" Plot Pressure Data versus Effective Shut-In Time Semilog Plot "Agarwal" Plot Pressure Data versus Effective Shut-In Time 11

12 Log-log Plot Pressure Drop and Pressure Drop Derivative Data versus Shut-In Time (1 inch x 1 inch) Log-log Plot: Pressure Drop and Pressure Drop Derivative Data versus Shut-In Time (1 inch x 1 inch) 12

13 Log-log Plot Pressure Drop and Pressure Drop Derivative Data versus Effective Shut-In Time (1 inch x 1 inch) Log-log Plot: Pressure Drop and Pressure Drop Derivative Data versus Effective Shut-In Time (1 inch x 1 inch) 13

14 Log-log Plot Pressure Ratio and Pressure Integral Ratio Data Functions versus Shut-In Time (1 inch x 1 inch) Log-log Plot: Pressure Ratio and Pressure Integral Ratio Data Functions versus Shut-In Time (1 inch x 1 inch) 14

15 Log-log Plot Pressure Ratio and Pressure Integral Ratio Data Functions versus Effective Shut-In Time (1 inch x 1 inch) Log-log Plot: Pressure Ratio and Pressure Integral Ratio Data Functions versus Effective Shut-In Time (1 inch x 1 inch) 15

16 Late-Time Cartesian Plot ("Muskat Plot"): Pressure Buildup Case Late-Time Cartesian Plot ("Muskat Plot") Pressure Buildup Case 16