Inflow Performance 1

Transcription

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2 Contents 1. Introduction 2. The Radial Flow Equation 3. Straight Line Inflow Performance Relationship 4. Vogel Inflow Performance Relationship 5. Other Inflow Performance Relationship 6. Establishing the Well's IPR 7. Use of the Inflow Performance Relationship 2

3 1. INTRODUCTION 3

4 The rate at which fluid will flow towards the wellbore depends upon The nature of the fluid, The type of reservoir rock and the Driving force. This is driving force is not the reservoir pressure but the difference in pressure between the reservoir and the wellbore, and is called The Drawdown (ΔP DD ) 4

5 The Inflow Performance Relationship (IPR) quantifies the flow-rate from a well as a function of the drawdown. 5

6 2. THE RADIAL FLOW EQUATION 6

7 Consider radial inflow into a well as depicted in the Figure. The change in pressure profile and the pressure at the outer boundary (p e ) depend on the initial and boundary conditions imposed. 7

8 Three different f1ow conditions can be distinguished: Transient flow Semi Steady State flow Steady State flow 8

9 Transient flow This condition is only applicable for a relatively short period after some pressure disturbance has been created in the reservoir. Transient flow conditions are applied to the analysis of well tests. 9

10 Semi Steady State flow This condition is applicable to reservoir which has been producing for a sufficient period of time so that the effect of the outer boundary has been felt. It is considered that the well is surrounded at its outer boundary by a solid "brick wall which prevents flow of fluids into the radial cell (Figure). r e = drainage radius r w = well bore radius 10

11 Steady State flow Inflow Performance This condition applies to a well draining a cell which has a completely open outer boundary. It is assumed that, for: q A constant production rate, q Fluid withdrawal from the cell will be exactly balanced by fluid entry across the open boundary. 11

12 This condition is appropriate when pressure is being maintained in the reservoir due to either: Natural water influx, or The injection of displacing fluid. 12

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14 Radial inflow equation for steady state flow Inflow Performance Assuming that the reservoir is homogeneous in all reservoir parameters, Darcy's law for the radial flow of a single phase fluid can be expressed as: Where: k = Permeability A = Flow area μ = Viscosity 14

15 More realistically, for a well located in a reservoir containing other wells, the radius from which liquid is being drained is known and is called the drainage radius r e. The inflow equation for Steady State flow may be written; 15

16 The radial flow model is therefore adapted to express the drawdown in terms of the average reservoir pressure P. This value would be obtained if the producing field was shut in until the pressure in the reservoir had equalize, and the average reservoir pressure is found by analyzing individual well shut-in bottom hole pressures. 16

17 3. STRAIGHT-LINE INFLOW PERFORMANCE RELATIONSHIP 17

18 When we consider the parameters in the equation for the Productivity Index the following comments can be made: h, r e and r w are constant. k, μ and B o are pressure dependent. The criteria is the flowing bottom hole pressure with respect to the phase envelope of the fluid considered. For single phase flow, which occurs when the flowing pressure is above the bubble point pressure, these parameters can be considered constant (independent of pressure). 18

19 Under the above conditions the Productivity Index (J) is constant and is called "PI". The equation q = PI x ΔP dd describes a straight line. 19

20 4. VOGEL INFLOW PERFORMANCE RELATIONSHIP 20

21 When the flowing bottomhole pressure is below the bubble point pressure, two phase liquid and gas flow occurs in the reservoir and the linear relationship defined above is no longer valid. When the pressure declines below Pb. The permeability decrease, Oil formation volume factor will decrease, The viscosity will increase. 21

22 This type of behavior has been observed in solution gas drive reservoirs, as depletion precedes the productivity of a typical well decrease. Under these conditions, a plot of flowing bottom hole pressure against production rate results in a curved, rather than a straight line and there is a progressive deterioration in the inflow performance relationships as the reservoir is depleted. 22

23 The inflow performance relationships shown in the previous Figure may be redefined as no dimensional IPR's. This is done by expressing the bottom hole flowing pressure as a fraction of the maximum shut-in pressure, and the relevant flow rate as a fraction of the maximum production rate for that curve, at very similar throughout most of the producing life of the reservoir. 23

24 It is shown that non-dimensional IPR's apply to many different reservoirs. Exceptions are wells with: q Large positive skins, q High viscosity crudes, and q Very high rate producers. Because of the similar nature of the nondimensional IPR's, it is possible to group them into one representative curve which closely approximates them all. 24

25 The curve giving the best fit to the nondimensional IPR's shown above is called the reference IPR curve, or the Vogel IPR. 25

26 The equation of the reference curve is: If q/q max is plotted against p Wf / p, the reference curve will result. Having established the maximum possible flow rate and the reservoir pressure, plotting q against p wf will give the actual inflow performance relationship for a particular well. 26

27 For comparison to the Vogel IPR, the relationship for a straight line (PI) IPR would be; 27

28 5. OTHER INFLOW PERFORMANCE RELATIONSHIPS 28

29 5.1 IPR or reservoirs with static pressures above bubble point pressure 5.2 Gas Well IPR's 29

30 5.1 IPR or reservoirs with static pressures above bubble point pressure The IPR's described in the previous sections dealt with either above or below bubble point conditions. It is more realistic to define an IPR which is valid for both conditions. 30

31 Above P b the IPR will respond linear and when the P wf is below P b a curved IPR will occur. 31

32 The solution for P wf < P b is then: Where J* is the Productivity Index for the straight line part of the IPR. 32

33 5.2 Gas Well IPR's Inflow Performance The IPR's described in the previous sections are applicable to oil wells only. In gas wells, fluid velocity around the well bore is much higher than that found in oil wells. Due to this high velocity, turbulent flow will occur resulting in an additional pressure drop. In addition the gas viscosity and compressibility are highly dependent on pressure and temperature. 33

34 The resulting non-linear IPR of gas wells is often expressed as: Where Q = the pressure drop due to laminar (Darcy) flow and bq 2 = the pressure drop due to inertial turbulent (non-darcy) flow. The constants a, and b can be derived from known reservoir and gas properties. 34

35 6. ESTABLISHING THE WELL'S IPR 35

36 The inflow performance relationship for a given well has to be established by a well test. Inflow Performance In theory, one production rate with corresponding bottom hole pressure and the shut-in pressure will define the inflow performance relationship. 36

37 In practice a number of flow rates may be taken to confirm the well performance. If a sample of formation fluid is taken and analyzed to establish the bubble point pressure, it will be possible to decide whether to use the straight line, the Vogel or the Vogel / Glass inflow performance relation hit. 37

38 During well testing, it should not be necessary to draw the well bore pressure down very low in order to establish the maximum inflow potential of the well, the IPR may be used to establish this value. In the case that the formations being tested are friable, unconsolidated sands, it is unwise to apply a high drawdown for a fear of collapsing the formation and getting no test data at all. 38

39 7. USE OF THE INFLOW PERFORMANCE RELATIONSHIP 39

40 The inflow performance relationship is useful as a tool to monitor well performance and predict the stimulation and artificial lift to requirements of a number of wells. The IPR for a well must be known in order to size the well tubular correctly. 40

41 Based on interpolation between wells, if the initial IPR for a well is lower than expected in a particular part of the reservoir, it may then be suspected that the formation has been badly damaged during the drilling and completion phase. Mapping the IPR's across the field may highlight this situation. When well bore damage is confirmed by a buildup survey the well may require stimulation. 41

42 Even with stimulation, the inflow performance of a well will decline with falling reservoir pressure. Plotting this decline will indicate approximately when the wells will have to be artificially lifted in order to maintain the required off take rate from the field. 42