Analysis of Well Performance With Multiple Shutin Periods

1
Analysis of Well Performance With Multiple
Shut-in Periods
SPE 53932

• M. Wael Helmy
• Robert A. Wattenbarger
• Texas AM University

2
Gas Well Rate Decline
3
Objectives of Analysis

• Estimate OGIP
• Estimate flow properties
• Forecast production rates

4
Well Characteristics

• High pressure gas
• Constant Pwf
• Shut-in periods in summer

5
Well Characteristics

• Very tight rock k lt 0.01md
• Very long transient periods (10-20 years)
• Linear flow

6
Problem to Solve
7
Problem to Solve
8
Gas Well Rate Decline
9
Outline

• Introduction
• Superposition
• Analytical Solution
• Production Rate Filter
• Conclusions

10
Introduction

• Linear Flow, Fractured Wells

11
Introduction

• Linear Flow, Anisotropic Reservoirs

12
Introduction
Unit slope
Exponential
½ slope
13
Introduction
From slope k1/2/Ac From time Vp
14
Introduction
15
Introduction
16
Operating Conditions

• During production
• Constant pwf
• During shut-in
• Constant rate 0

17
Outline

• Introduction
• Superposition
• Analytical Solution
• Production Rate Filter
• Conclusions

18
Superposition

• Van-Everdingen and Hurst (1949)

• Linear, closed

• Linear, infinite

• Match bottomhole pressure

19
Constant pwf Solution

• For all models

20
Application

• Excel spreadsheet, Visual Basic
• Different models
• Reservoir properties and OGIP

Run Program
21
Curve-fitting Comparison

• The method is NOT curve-fitting
• Curve fitting gives wrong answers
• Constant pwf solution

22
Curve-fitting Comparison
23
Curve-fitting Comparison
24
Curve-fitting Comparison
25
Outline

• Introduction
• Superposition
• Analytical Solution
• Production Rate Filter
• Conclusions

26
Analytical Solution
27
Analytical Solution

• Convolution integral

• Linear flow model, infinite acting

28
Analytical Solution

• Laplace space solution is difficult
• Solve using Abels Integral equation

29
Analytical Solution

• Cumulative production

30
Analytical Solution
31
Average Production
32
Average Production
Over-shoot
Under-shoot
33
Operating Conditions

• What we know
• Average monthly production
• Constant pwf (when producing)
• What we dont know
• Duration of shut-in during the month
• Time shut-in started during the month

34
Analytical Solution

• Obtain trend line
• Calculate duration of shut-in
• Determine time shut-in started

35
Application
36
Application
37
Application
38
Outline

• Introduction
• Superposition
• Analytical Solution
• Production Rate Filter
• Conclusions

39
Production Rate Filter

• Analytical solution depends on
• Shut-in period
• Time shut-in started
• Production rate filter
• Use average monthly production
• Independent of shut-in time

40
Production Rate Filter
41
Production Rate Filter

• Production rate correction

42
Production Rate Filter

• Linear flow model, infinite acting

43
Production Rate Filter
44
Production Rate Filter
45
Production Rate Filter
46
Outline

• Introduction
• Superposition
• Analytical Solution
• Production Rate Filter
• Conclusions

47
Conclusions

• Worked problem in three different and independent
  ways
• Superposition
• Analytical solution
• Rate-filtering techniques

48
Conclusions

• Superposition
• Stable, pressure not needed at all times
• Models used
• Linear, infinite acting
• Linear closed reservoir
• Obtained production trend
• Rate curve-fitting gives wrong results

49
Conclusions

• Analytical solution
• Solution for rate and cumulative
• Over-shoot and under-shoot correlation
• Determine shut-in time, if unknown
• Obtained production trend

50
Conclusions

• Production rate filter
• Filter rate independent of pressure
• Infinite acting reservoir model
• Obtained production trend
• All three methods match very well

51
Introduction
Rate -½ slope
Cumulative ½ slope
52
Problem to Solve
53
Literature Review

• Multiple shut-in º variable rate
• Literature focuses on variable-rate
  pressure-transient analysis
• Back-calculate constant rate solution from the
  measured variable rate performance --
  Deconvolution

54
Literature Review

• Bostic et al. (1979)

55
Literature Review

• Convolution
• Calculate variable rate solution
• Deconvolution
• Calculate constant rate solution

56
Literature Review

• Deconvolution before 1979
• Gladfelter et al. (1955)
• Divide pressure by rate
• Odeh and Jones (1965)
• Pseudo time function

57
Literature Review

• Deconvolution peaked in the 1980s
• Thompson et al. and Kuchuk et al.
• Different schemes to improve stability
• Kuchuk et al. (1983)
• Function deconvolution

58
Literature Review

• Kuchuk et al. (1985)
• Constrained deconvolution
• Coats et al. (1964)

59
Literature Review

• Roumboutsos et al. (1988)
• Laplace space deconvolution
• Blasingame et al. (1989)
• Power law deconvolution
• b deconvolution (exponential)

60
Literature Review

• Problems with deconvolution
• Recursive equation, unstable
• Requires monotonically decreasing rates for
  stability
• Requires rate and pressure data at each time step

61
Convolution

• Van-Everdingen and Hurst (1949)

62
Objectives

• Develop methodology to analyze performance with
  multiple shut-ins
• Superposition
• Analytical solution
• Rate-filtering techniques