1. Optimizing In Fill Well Drilling - Wamsutter Field
Mohan Kelkar
The University of Tulsa
Akhil Datta-Gupta
Texas A & M University

2. Outline Background Objectives Project Management Project Deliverables
Progress to Date
Summary

3. Wamsutter Field

4. Wamsutter Field
Over 2,000 square miles
Two main units – Lewis and Almond
Tight gas reservoir, k < 0.1 md
Currently developed on 80 acre spacing

5. Wamsutter Field Static Continuity

6. Static vs. Dynamic Continuity
Static continuity appears to be strong indicating a significant and efficient drainage using 160 acre spacing
Small scale heterogeneities in the reservoir indicate significant dynamic discontinuities
The presence of small scale heterogeneities is verified by performance of 80 acre spacing wells
Average performance of 80 acre spacing wells is 50 to 70 % of the performance of 160 acre spacing wells

7. Objectives
Determine and quantify the importance of small scale heterogeneities on the performance of wells
Quantify the potential recovery from in fill wells using production data analysis as well as simulation
Identify sweet spots for possible locations for 40 acre spacing wells

8. Project Management Principal Investigator – The University of Tulsa
Subcontractors
Devon Energy
Texas A & M University
Based on the results of the study, Devon is planning to drill seven new wells in the field

9. Project Deliverables
Methodology to determine the incremental vs. acceleration gas production from in fill wells
Methodology to account for and, preservation of, sand connectivity in coarse scale models
Procedures for high and low grading areas for in fill well potential

10. Progress to Date Area of Concentration

11. Data Collected
Area of interest is 3x3 sections in 16N 93 W township with one additional section on all sides which covers 5 x5 sections (total of 25 sections)
A total of 83 wells are drilled in the area
Log data as well as production data are available from most of the wells

12. Production Data Analysis
University of Tulsa

13. Introduction
Homogeneous and heterogeneous reservoirs will exhibit different behavior when in fill wells are drilled:
Initial production rates will indicate access to new reserves
Difference in decline rates from the surrounding wells will indicate communication
First, let’s look at two basic models, homogeneous and heterogeneous reservoirs. What is the difference between these two reservoirs when infill wells are drilled.
‘Initial production rates will indicate access to new reserves’ that means when the in fill wells are drilled in the reservoir, if the in fill well access new reserves, the rate would be higher; if the in fill well produces from depleted reservoir, the rate is lower.
‘Difference in decline rates from the surrounding wells will indicate communication’ means after drilled infill wells, the decline rates of the original wells are affected by infill wells. Normally, the production rate of the parent well will decline faster. This is because there is communication between first well and infill wells, so a part of the production of the infill wells is ‘steal’ from the first well.
Let me illustrate it in the next two slides

14. Homogeneous Reservoir
Drill new wells
In this homogeneous reservoir, the first well is drilled in the center of the reservoir, and four infill wells are drilled surrounding the original well. The production rate of those wells are shown in the graph. If there are no infill wells, the production rate of the first well is like the blue dash curve. But we can see that after in fill wells are drilled, the decline rate of the first well is much higher, this is because it has been affected by infill wells. The amount of the declined production is produced by those infill wells. So in this case, the production of the infill wells are acceleration production. Also, notice that because the reservoir is homogeneous, the initial rates of in fill wells are very similar to the current rate of the parent well.
×: Original well
○: Infill wells

15. Heterogeneous Reservoir
In this heterogeneous reservoir, we also have original well and infill wells. And this reservoir is too heterogeneous that all the wells are drill in isolated compartment, so there is no communication between the wells, as shown in this chart. So the production rate of those wells are different with homogeneous reservoir. The production rate of the first well is not influenced by the infill wells. More, the infill well’s initial production rates are similar to the first well. This indicates infill wells have access to the new reserves and the production of the infill wells are all incremental production.
×: Original well
○: Infill wells

16. Objectives
Develop a methodology to predict the gas which is “stolen” by new wells.
Using the existing production data, determine the in fill well EUR
Determine the contribution of acceleration and incremental potential.
So, the objective of this presentation is:
‘Develop a methodology to predict the gas which is “stolen” by new wells’, so we want to estimate how much gas from parent wells is taken away by children wells
‘Using the existing production data, determine the in fill well EUR’, By plotting the cum production vs. proper function of time, we can get a linear relationship and extrapolate this straight line to determine the infill well EUR. I will show examples of the extrapolation later on.
Then we can calculate the contribution of acceleration and incremental components.

17. Approach
Determine an appropriate time function such that cumulative production is linearly related.
Divide the data into chronological groups so that average behavior can be predicted.
Plot cum production vs. time function and examine inflection in the graph as successive groups of wells are drilled.
Compare EUR calculated from this method with the EUR reported by companies.
First step of this method is to determine an appropriate time function to get linear relationship with cumulative production. It is important to note that linear relationship is very important. Non-linear relationships – traditionally used for decline curve analysis – are very difficult to extrapolate to understand the difference between “before” and “after” in fill drilling. Fortunately, for tight gas reservoirs, we often observe linear or bi-linear production. These relationships are ameanable to linear relationship between cum production and some function of time. We validate our theory by using the production data which is provided on website of some companies. We validate it for both tight gas and shale reservoirs.

18. Southwest Energy
This is the type curve chart of Fayetteville Shale, provided by Southwest Energy. There are tree type curves: 3.0, 2.5, 2.0 bcf type curves. We digitize the data and consider linear flow – which means a graph of cum production vs. square root of time.

19. Type Curve Extrapolation
Southwest Energy
So, in the plot we can get three approximate straight lines. And we have to pick an arbitrary end time. As you can see the comparison of EUR, the reported EUR on the left is the same with the estimated EUR on the right. This is based on extrapolation using linear relationship.

20. Chesapeake Energy
This is another example, the type curve is provided by CHK. The curves are representative of different field. We do the same thing for type curve…

21. Type Curve Extrapolation
Chesapeake Energy
And for those six type curve from different fields, we can get straight lines. Then we pick a time and extrapolate. The comparison of the EUR are shown in the chart.

22. Approach
Determine a function of time such that cumulative production is directly related.
Divide the data into chronological groups so that average behavior can be predicted.
Plot cum production vs. time function and examine inflection in the graph as successive groups of wells are drilled.
Compare EUR calculated from this method with the EUR reported by companies.
Once we establish that we can get linear relationship, we can proceed further. We will show additional examples of linear relationships for tight gas reservoirs as well. In the next step, we will sort all the wells in the chronological order. Then divide them into normally 3-5 groups based on the start date of production. This grouping is important since we want to get average results of in fill wells. More wells we have within a group, more robust results we will get. Let me show you an example.

23. Field Data
This is the part of the field map of Pinedale Field. The data is provided by Williams. We have the ability to evaluate any area. So, we select section 5 for our analysis.

24. Grouping
These are all the wells in section 5. We sort those wells in chronological order and divide them into 3 groups. It is possible to divide them into more groups. However, all these wells are drilled so close to each other that it is not necessary. This decision is arbitrary; however, we have found that fewer the groups we have, more robust are the results.

25. Approach
Determine a function of time such that cumulative production is directly related.
Divide the data into chronological groups so that average behavior can be predicted.
Plot cum production vs. time function and examine inflection in the graph as successive groups of wells are drilled.
Compare EUR calculated from this method with the EUR reported by companies.
Next, we will use production data to plot cumulative production vs. certain time function, usually we have two choices of time functions which are linear and bilinear. If it is linear, we will plot cum production vs t^0.5, and for bilinear flow, we plot cum production vs. t^0.75. we will use the most appropriate function which provides linear relationship and then we will examine the inflection point on the graph as other wells are drilled.

26. Example
This is an example from Pinedale field…..As can be seen, after the parent wells are drilled, there are two generations of wells drilled in the field. This results in an inflection point on the production data which we extrapolate to calculate the new EUR. The difference between original EUR and the new EUR is the amount of gas produced by new wells.

27. Example Another example….
We will apply this procedure to every individual well and determine the gas stolen from it by subsequent wells

28. Approach
Determine a function of time such that cumulative production is directly related.
Divide the data into chronological groups so that average behavior can be predicted.
Plot cum production vs. time function and examine inflection in the graph as successive group of wells are drilled.
Compare EUR calculated from this method with the EUR reported by companies.
After we extrapolate those straight lines and get the estimated EUR, next thing we do is compare these EUR s
with the reported EURs by companies which provided us the data. If the results are similar, we are more confident about the EUR number used in the analysis, and the results are more reliable.

29. EUR Comparison
In this EUR comparison graph, we can see the EUR number from Williams and TU are pretty close. This means that our procedure for extrapolating cum production is reasonable since the EUR predicted matches reasonably well with conventional EUR

30. Group EUR Comparison 3.31 3.32 3.01 3.07 2.32 2.34 EUR(ours)
EUR(Operator)
1st group
3.31
3.32
2nd group
3.01
3.07
3rd group
2.32
2.34
This is the average EUR in every group. The numbers are still very close to each other.

31. Approach
For every “child” well, calculate average Incremental and Acceleration components.
Plot Acceleration percentage, Incremental percentage and total EUR as a function of spacing.
Recommend potential sections where in fill well potential is the greatest.
Once we compute the EUR for each well, by knowing how much incremental gas came from parent well, we can determine incremental EUR for each well

32. Calculation Acceleration vs. Incremental
Total EUR for 2nd group per well = 3.57 BCF
Acceleration EUR for 2nd group per well
= Decreased EUR = 0.24 BCF
Incremental EUR for 2nd group per well
= Total EUR - Acceleration EUR
= = 3.33 BCF
This is how we calculate incremental and acceleration EUR per well. We calculate average EUR for the 2nd group of wells. Based on parent wells, we know the acceleration component from those wells. By dividing that number with total number of wells in the second group, we can calculate acceleration EUR per well. The difference provides the incremental EUR. The result is from section 5 of Pinedale field. Then we need to do the similar calculation for next infill groups and get incremental and acceleration EUR per well for every group ….

33. Approach
For every “child” well, calculate average Incremental and Acceleration component.
Plot Acceleration percentage, Incremental percentage and total EUR as a function of spacing.
Recommend potential sections where in fill well potential is the greatest.
After calculate the total EUR, acceleration and incremental EUR, we plot acceleration, incremental percentage and total EUR together as the function of spacing. This is better to observe the tendency of incremental and acceleration production as wells are drilled closer in spacing.

34. Wamsutter Field Multiple Section Analysis
This is the field map of Wamsutter Field in WY. Because this field may have directional trends, we did multiple section analysis in this field. So we combine three sections in both EW and NS directions. Then we do the same procedure for these sections to calculate total EUR, acceleration and incremental EUR.

35. ACC vs. INC E-W direction
This is the plot of Acceleration vs. incremental for section EW-7,8,9. In this plot, we can see as spacing decreases, we have increasing acceleration EUR and decreasing incremental EUR. Also notice that EUR per well also declines in subsequent generation wells.

36. ACC vs. INC N-S direction
Section NS-9,14,19. The trend in EUR change is not perfect. However, the declining trend is obvious.

37. Extrapolation at 80 acre spacing
Result:
1.35 bscf
Then, we can extrapolate acceleration and incremental curve at any spacing. In this case, we show the extrapolation of section EW-7,8,9 at 80 acre spacing. The extrapolation method is arbitrary. However, as long as we do it for the next generation wells, our results should be reasonable.

38. Approach
For every “child” well, calculate average Incremental and Acceleration component.
Plot Acceleration percentage, Incremental percentage and total EUR as a function of spacing.
Recommend potential sections where in fill well potential is the greatest.
Then, compare the extrapolation results and find out which section has the greatest potential for infill well.

39. Extrapolation Results
Total (bscf)
%(ACC)
%(INC)
EW-7,8,9
1.350
88%
12%
EW-12,13,14
2.300
43%
57%
EW-17,18,19
2.140
84%
16%
NS-7,12,17
0.900
70%
30%
NS-8,13,18
1.750
91% 9%
NS-9,14,19
2.150
64%
36%
This table shows the extrapolation results of Wamsutter field. We can compare the total EUR, acceleration percentage and incremental percentage. We prefer high EUR with higher percentage of incremental production. Then the recommendation is shown in the next slide.

40. Recommended Sections Total (bscf) %(ACC) %(INC) EW-7,8,9 1.350 88% 12%
2.300
43%
57%
EW-17,18,19
2.140
84%
16%
NS-7,12,17
0.900
70%
30%
NS-8,13,18
1.750
91% 9%
NS-9,14,19
2.150
64%
36%
This is the two recommendation sections. The criterion of determining better section is looking at the higher incremental percentage as well as the higher total EUR of the section. Based on our recommendation, Devon has agreed to drill seven more wells in this area with most wells in section 14. we will know the results after the summer.

41. Summary
Using a newly developed methodology, we determined the acceleration and incremental contributions for in fill wells
We have developed user friendly VBA program which is given to Devon for testing
We validated our method in Wamsutter and Pinedale gas fields.
Based on our recommendation, Devon would drill seven wells in Wamsutter field starting August.
For this slide, just read the conclusions!

42. Streamlines to Determine Connected Volume
Texas A & M University

43. Why Streamline?
Advantages of streamline tracing for gas reservoir characterization
Easier and less expensive
Better visualization of flow in the reservoir
Calculating drainage volume based on streamlines
Optimizing well spacing
Optimizing well completion design and fracturing specially for tight gas reservoirs
My motivation in this research is to fully use the advantages of streamline tracing. Streamline tracing is much easier and less expensive than Pressure transient test and we don’t need to shut down wells during testing. Another reason is there are need for efficient approaches to field scale transient pressure history matching. Especially, sometimes we need to calculate drainage area or volume in reservoir. But there is no previous research in one phase gas reservoirs. This drainage volume calculation also will be applied in tight gas reservoirs for planning completion and well locations.

44. Diffusive TOF
DTOF is similar to the TOF but it uses diffusivity coefficient instead of velocity in TOF equation.
: Diffusive Time of flight can be analytically calculated with single flow simulation. Front of DTOF represents the volume drained.
DTOF is more efficient if Multi-well testing is needed.
: The sensitivities are calculated in each well with single simulation, so drainage volume is calculated without perturbation or shutting wells down.
DTOF can be used in compressible flow
: Diffusive Time of flight calculated based on flux, so we can easily use it for compressible flow.
As discussed. Diffusive time of flight can be analytically calculated with single flow simulation, thus this approach is computationally cheap. And for the sensitivities are calculated in each well with single simulation. So drainage volumes of each well are calculated without perturbation or shutting down l wells. Diffusive time of flight can be obtained with flux calculation, we can easily calculate even in compressible flow.

45. Diffusive TOF formulation
Fourier transform of diffusivity equation
... (1)
... (2)
Asymptotic solution (Vasco et al. 2000)
Here, I will explain about numerical background. The transient pressure response from a heterogeneous permeable medium can be described by the diffusivity equation (1). Using Fourier transformation, we can obtain the following equation (2) in the frequency domain. The solution of diffusivity equation can be obtain as equation (3). The asymptotic solution of diffusivity equation is considered only the first terms which correspond to high frequency in the series. this high frequency term describe the physical propagation of a ‘pressure front’.
: From this solution we just keep the high frequency part which implies propagation of the sharp front (Only K=0)
... (3)
... (4)

46. Diffusive TOF Diffusive TOF
:Substitute equation 4 in equation 2 and equate coefficients:
... (5)
... (6)
: Diffusive TOF is the function of model parameters (Invariant with time)
If we insert this solution (4) into Fourier equation (2), we can obtain the equation for the front preparation in an isotropic permeable media. And the diffusivity alpha is given as a function of k over phi mu ct. This equation (5) explain a variety of propagation behavior and has a similar form of streamline time of flight equation which describes the propagation of a neutral tracer. In equation (7), tau hat x is the streamline time of flight and v is velocity of a neutral tracer. Note that diffusive time of flight is the function of model parameters which is invariant with time but time of flight is the function of a given field changing with time as shown in equation (8).
TOF
... (7)
: TOF is the function of given velocity field (function of time)

47. Peak Arrival Time Constant rate production at the producer
When derivative of the pressure in a grid block reaches to a maximum is assumed as pressure peak arrival time for that grid block.
Early studies have proven the similitude between peak arrival time and diffusive time of flight in oil-water phase. The pressure front arrival time can be calculated from the maximum of the time derivative of the pressure response at each grid block location as shown right above. First we scan the pressure history at each grid block and then compute its time derivatives. The time when the derivative reaches a maximum indicates the pressure front arrival time and it correspond to diffusive time of flight. This peak arrival time will be used for proving validity in gas phase, too.
... (8)
Equation (8) is used to go from time of flight domain to physical time domain in 3-D model.
For 2-D case this equation changes to:

48. Peak Arrival Time (Oil Case) Permeability Field DTOF
This shows that we can use Diffusive TOF calculations to represent the peak arrival time to calculate drainage volume.
This is the time that pressure front reaches to producer #1.
*JongUk,Kim et al (2009)

49. Advances
To be able to use this approach for gas fields same calculations can be done based on the ( pressure square approach) . Accordingly we can show that the equation (1)-(8) still holds for gas reservoirs.
The only modification is that compressibility has to be addressed correctly, so we modified the diffusivity coefficient in each grid block as follow:
- Previously : use constant oil compressibility
- Now : Calculate total compressibility from restart file
This modification allows to correctly calculate DTOF when multiple phases exist.

50. Diffusive TOF vs. Peak Time (2-D Single Phase GAS)
Homogeneous Model
Heterogeneous
Model
DTOF
P.A.T
DTOF
P.A.T
0.01 day
0.05 day
This page show the effect of coefficient. I can get consistent result with peak arrival time if we use coefficient 12. Hence we can verify our derivation in synthetic case.
0.1 day

51. Field Case (Wamsutter Field- Tight Gas Reservoir) UPGRIDDING
Reduce the number of grid blocks from four million to about 700,000 (Faster Simulations)
Preserving the fine scale model dynamic behavior as good as possible.

52. Field Case (Wamsutter Field)
Statistical Upgridding of the field
We use Pressure Based Method upgridding (CONNECT – UpGrid)
This method is based on combining layers with similar pressure profile and minimum velocity difference
In Design Factor graph we use the maximum points. (Biggest contrast to proportional model)
Original Size : 98 × 112 × 361
= 3,962,336
Coarse scale Size : 98 × 112 × 65
= 713,440 (18% of original size)

53. Field Case (Wamsutter Field)
Section of the reservoir (18× 15× 65)
Original Size : 98 × 112 × 65
Permeability Field
( md)
This is my field case. This gas reservoir is located Southwest Wyoming and named Wamsutter field. This model has 4 million cells and 85 wells, so we did upscaling in z- direction to run in PC.

54. Section of Wamsutter Gas Field ( DTOF)
1 year
This figure shows the preliminary result of streamline tracing. The calculation of Diffusive time of flight is running on my machine until now from yesterday morning.

55. Section of Wamsutter Gas Field ( DTOF)
5 year
This figure shows the preliminary result of streamline tracing. The calculation of Diffusive time of flight is running on my machine until now from yesterday morning.

56. Drainage Volume Calculations

57. Drainage Volume Calculations

58. Field Case (Wamsutter Field- Tight Gas Reservoir)
Southwest Wyoming ( Number of the Wells : 85)
This is my field case. This gas reservoir is located Southwest Wyoming and named Wamsutter field. This model has 4 million cells and 85 wells, so we did upscaling in z- direction to run in PC.
Permeability Field

59. Wamsutter Gas Field (Diffusive TOF)
25 year
This figure shows the preliminary result of streamline tracing. The calculation of Diffusive time of flight is running on my machine until now from yesterday morning.

60. Total Drainage Volume Calculations

61. Drainage Volume Whole Field
# 20222
# 20032
# 20196

62. Well location and Streamlines
# 20032

63. Drainage Volume – # 20032

64. Summary
We can use streamlines to visualize the pressure propagation in the gas reservoirs.
Diffusive time of flight is a useful tool to calculate the pressure front.
By calculating the drainage volume changes, we can quantify effect of new infill wells on the current producers.
DTOF can facilitate the integration of the high resolution pressure data into history matching process.

65. Future Work Optimized well placement based on the drainage volume
Optimized well completion based on the drainage volume Including multi-stage fracturing
High resolution transient pressure history matching for gas fields
For future study, I have to finish this Wamsutter case and verify this diffusive time of flight with peak arrival time. This filed is one phase gas field, we also expect to apply this result to less permeable tight gas field. Also we can plan well location and completion planning with using production optimization technique from Diffusive time of flight result.