Reservoir Engineering: Laboratory ReportReservoir Engineering: Performance and Modelling

Laboratory Report:Reservoir Evaluation Using Pressure Transient Analysis

Table of ContentsIntroduction3Objectives3Background4Methodology7Graphs, Calculations and Discussion9Conclusions14References15

IntroductionIn this laboratory exercise, the software Ecrin by Kappa has been used to evaluate a petroleum reservoir using Pressure Transient Analysis. Pressure Transient Analysis (PTA) is used to analyses a reservoirs response to a change in production rate. Pressure output and flowrates from a test on an oil well has been given for a period of 84 hours. The drawdown happened at a rate of 10,000 barrels of oil per day for 12 hours followed by a shut in period for 72 hours. ObjectivesBased on the theoretical work covered in the lecture course, the aim was to carry out all appropriate checks and estimates to validate the results of Kappa computations. Appropriate plots had to be produced for the purposes of comparison.

Background

Figure 1: Rate and pressure profile during a pressure buildup testThe pressure build-up test (PBU) is the most common form of well testing. The well is flowed at a constant rate (drawdown), q, for a period of time, t, after which it is closed in and the pressure allowed to build-up. During the test, flow rate, q, and flowing pressure, pwf, are measured. After Shut-in the pressure, pws, is measured as a function of the shut-in time, t [1].

Also, it is important to distinguish between different flow types that can occur in a reservoir during PTA:1) Wellbore StorageWellbore Storage is the effect that takes places when the flow from a reservoir into the wellbore (Sandface Flow Rate) is not constant, while the flow rate at the surface might be constant. It can be found on Log-Log plots as the early time unit slope where the hump starts. There are two main types of wellbore storage. The first one is modelled by the compression or decompression of the wellbore fluid in the wellbore volume. The second type of wellbore storage is linked to the rise of the liquid level present in the wellbore.2) Infinite Acting Radial Flow (IARF)The main flow regime of interest is the Infinite Acting Radial Flow (IARF), which occurs after well effects have faded and before boundaries are detected. IARF may not always be seen. IARF provides an average reservoir permeability around the well, the well productivity (Skin). When the well is shut in we also get an estimate of the reservoir static pressure (p* or pi). The first PTA methods were specialised plots (Horner, etc.) introduced in the 1950s to identify and quantify IARF. IARD can be characterised as the stabilised region of the Bourdet derivative in the Log-Log plot. 3) Pseudo-Steady State (PSS)During production, when the boundary is detected, the behaviour deviates from IARF to reach Pseudo-Steady State according to the Circular PSS equation (that s not necessary in this report). PSS is characterised by linearity between the pressure change and the elapse time on the linear scale. On the loglog plot PSS is characterised by a unit slope of the Bourdet derivative. Though it is slower, the pressure change also tends towards marking with the pressure derivative on the same unit slope. Horner PlotThe Horner Plot is important in this experiment. The following table has been shortened to show an overview over a couple of values after closing the well (after 12 hours).t(t+t)/tlog((t+t)/t)Pressure

hr--psia

0.0008150014.176120211815.906

0.00177059.823533.848793845852.907

10.0892.189414210.3403279335409.83

20.1691.594972480.2027531955600.67

30.2491.396707330.1451054125700.53

40.3291.297552630.1131249825764.84

50.4091.238052730.0927391425810.75

60.9091.197015220.0780996725846.94

721.166666670.066946795876.85

Table 1: Shortened Table of calculated values for Horner Plot

Figure 2Plotting the approximate trendline on the Horner Plot, the slope can be taken as m = 1437. Other reservoir data can be found under Methodology. Now the formula for permeability can be derived:Equation 1

MethodologyFirst, the module Saphir had to be opened in Kappa and the well and reservoir data had to be put in.

Figure 3: Overview of options in Ecrin

Figure 4: Putting in values in EcrinThe well and reservoir data: The radius of the vertical well is 0.3 ft The payzone (H) is 100 ft The Oil Formation Volume Factor (Bo) is 1.1 and the viscosity is 5 cp. The reservoir is homogeneous with porosity of 0.2Then the pressure and flow rate data from the Excel file had to be imported into the program which resulted in the graphs. Following each of the steps in the manual Kappa manual, graphs have been created.

Graphs, Calculations and DiscussionIn this section, different graphs and findings from KAPPA are described in terms of how they were created and their meaning.

Figure 5: Formation Data found by KAPPAIn the above screenshot we can see all the Data that has been found by Kappa. Rate, Pressure and TimeThe first graph has been created by taking the welltest data from the excel file and plotting it in Kappa as it can be seen in the History Plot in Figure 5.

PavgIARFWSPSSFigure 6: Pressure [psia], Liquid Rate [STB/D] vs Time [hr]

PSSIARFWSFigure 7: Log-Log PlotFigure 6 shows the Log-Log plot. The early time hump of the derivative (red line) is the transition between pure wellbore storage (early time unit slope, the magnitude of the hump is the skin). IARF corresponds to the stabilisation of the Bourdet derivative. At late time, the production (drawdown) period shows a unit slope corresponding to Pseudo-Steady State, whilst during the Shut-In the pressure stabilises at the average pressure and the derivative takes a dive.

Time PSSIARFWSFigure 8: Semi-Log Plot Pressure [psia] vs Superposition Time

TimeIARFWSFigure 9: Horner PlotFigure 7 (Semi-Log Plot) and Figure 8 (Horner Plot) can also be used to find the magnitude of storage. The Horner Plot shows the response of the reservoir during well shut-in. In Figure 8 we can see how WS turns into IARF and turns into a solid green line where we can see that the reservoir finds its equilibrium at the average reservoir pressure.

Other Logs

Figure 10: Log-Log Plot with changed SkinConsidering that Skin is an important property of the reservoir Ive drawn a few plots with varying skin in KAPPA. It affects the transition phase from WB to IARF and delays it.

Figure 11: K.I.W.I. PlotThe Kappa Intelligent Well Test Interpretation (K.I.W.I.) function in Kappa is used to find the best model for the real data.

ConclusionsLooking at the calculated value (62.23 mD) for permeability (k) and the one that KAPPA has given us (105 mD), we can see that there might be a big difference in some calculations. This may be due to different approximation methods that Kappa is using, plus the line on the excel graph is not exact. Also, it is important to note that changing different values (for example skin) can have tremendous effects on the performance of the reservoir. In this report, not all different variations have been done, as this would have taken up more time. To make this lab better, it could be made a necessary instruction to change known as well as unknown variables and plot different graphs. For reference, they can be taken from [2]. An important observation was that the fast transition from IARF to PSS can be interpreted as the well being closely located to boundaries. This might be parallel faults. This can be tested through decreasing the well drainage radius.

References

[1] Reservoir Engineering II: Performance and Modelling. Well Testing 1 & 2. Lecture Notes. [2] Kappa Dynamic Data Analysis. Handbook.

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