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• 1. Reservoir Engineering 1 Course (2nd Ed.)
• 2. 1. Superposition A. Multiple Well B. Multi Rate C. Reservoir Boundary 2. Productivity Index (PI) 3. Inflow Performance Relationship (IPR)
• 3. 1. Generating IPR for Oil Wells A. Vogel&#x2019;s Method B. Vogel&#x2019;s Method (Undersaturated Reservoirs) a. Future IPR Approximation C. Wiggins&#x2019; Method D. Standing&#x2019;s Method E. Fetkovich&#x2019;s Method
• 4. Vogel&#x2019;s Method &#xF0FC;Vogel (1968) used a computer model to generate IPRs for several hypothetical saturated-oil reservoirs that are producing under a wide range of conditions. &#xF0D8;Vogel normalized the calculated IPRs and expressed the relationships in a dimensionless form. He normalized the IPRs by introducing the following dimensionless parameters: &#xF0FC;Where (Qo) max is the flow rate at zero wellbore pressure, i.e., AOF. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 5
• 5. Vogel&#x2019;s IPR &#xF0FC;Vogel plotted the dimensionless IPR curves for all the reservoir cases and arrived at the following relationship between the above dimensionless parameters: &#xF0FC;Where Qo = oil rate at pwf &#xF0FC;(Qo) max = maximum oil flow rate at zero wellbore pressure, i.e., AOF &#xF0FC;p&#x2013;r = current average reservoir pressure, psig &#xF0FC;pwf = wellbore pressure, psig &#xF0FC;Notice that pwf and p&#x2013;r must be expressed in psig. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 6
• 6. Vogel&#x2019;s Method for Comingle Production of Water and Oil &#xF0FC;Vogel&#x2019;s method can be extended to account for water production by replacing the dimensionless rate with QL/(QL) max where QL = Qo + Qw. &#xF0D8;This has proved to be valid for wells producing at water cuts as high as 97%. &#xF0FC;The method requires the following data: &#xF0D8;Current average reservoir pressure p&#x2013;r &#xF0D8;Bubble-point pressure pb &#xF0D8;Stabilized flow test data that include Qo at pwf Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 7
• 7. Vogel&#x2019;s Methodology Applications &#xF0FC;Vogel&#x2019;s methodology can be used to predict the IPR curve for the following two types of reservoirs: &#xF0D8;Saturated oil reservoirs p&#x2013;r &#x2264; pb &#xF0D8;Undersaturated oil reservoirs p&#x2013;r &gt; pb Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 8
• 8. Vogel&#x2019;s Method: Saturated Oil Reservoirs &#xF0FC;When the reservoir pressure equals the bubblepoint pressure, the oil reservoir is referred to as a saturated-oil reservoir. &#xF0FC;The computational procedure of applying Vogel&#x2019;s method in a saturated oil reservoir to generate the IPR curve for a well with a stabilized flow data point, i.e., a recorded Qo value at pwf, is summarized below: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 9
• 9. Vogel&#x2019;s Method: Saturated Oil Reservoirs (Cont.) &#xF0FC;Step 1. Using the stabilized flow data, i.e., Qo and pwf, calculate (Qo)max from: &#xF0FC;Step 2. Construct the IPR curve by assuming various values for pwf and calculating the corresponding Qo from: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 10
• 10. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs &#xF0FC;Beggs (1991) pointed out that in applying Vogel&#x2019;s method for undersaturated reservoirs, there are two possible outcomes to the recorded stabilized flow test data that must be considered, as shown schematically in next slide: &#xF0D8;The recorded stabilized Pwf is greater than or equal to the bubble-point pressure, i.e. pwf &#x2265; pb &#xF0D8;The recorded stabilized pwf is less than the bubble-point pressure pwf &lt; pb Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 12
• 11. Stabilized flow test data Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 13
• 12. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs (Pwf&#x2265;Pb) &#xF0FC;Beggs outlined the following procedure for determining the IPR when the stabilized bottomhole pressure is greater than or equal to the bubble point pressure: &#xF0FC;Step 1. Using the stabilized test data point (Qo and pwf) calculate the productivity index J: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 14
• 13. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs (Pwf&#x2265;Pb) (Cont.) &#xF0FC;Step 2. Calculate the oil flow rate at the bubblepoint pressure: &#xF0D8;Where Qob is the oil flow rate at pb &#xF0FC;Step 3. Generate the IPR values below the bubblepoint pressure by assuming different values of pwf &lt; pb and calculating the corresponding oil flow rates by applying the following relationship: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 15
• 14. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs (Pwf&#x2265;Pb) (Cont.) &#xF0FC;The maximum oil flow rate (Qo max or AOF) occurs when the bottom hole flowing pressure is zero, i.e. pwf = 0, which can be determined from the above expression as: &#xF0FC;It should be pointed out that when pwf &#x2265; pb, the IPR is linear and is described by: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 16
• 15. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs (Pwf&lt;Pb) &#xF0FC;When the recorded pwf from the stabilized flow test is below the bubble point pressure, the following procedure for generating the IPR data is proposed: &#xF0D8;Step 1. Using the stabilized well flow test data and combining above equations, solve for the productivity index J to give: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 17
• 16. Vogel&#x2019;s Method: Undersaturated Oil Reservoirs (Pwf&lt;Pb) (Cont.) &#xF0D8;Step 2. Calculate Qob by using: &#xF0D8;Step 3. Generate the IPR for pwf &#x2265; pb by assuming several values for pwf above the bubble point pressure and calculating the corresponding Qo from: &#xF0D8;Step 4. Use below Equation to calculate Qo at various values of pwf below pb, or: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 18
• 17. IPR Prediction &#xF0FC;Quite often it is necessary to predict the well&#x2019;s inflow performance for future times as the reservoir pressure declines. &#xF0FC;Future well performance calculations require the development of a relationship that can be used to predict future maximum oil flow rates. &#xF0FC;Several methods are designed to address the problem of how the IPR might shift as the reservoir pressure declines. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 20
• 18. IPR Prediction (Cont.) &#xF0FC;Some of these prediction methods require the application of the material balance equation to generate future oil saturation data as a function of reservoir pressure. &#xF0D8;In the absence of such data, there are two simple approximation methods that can be used in conjunction with Vogel&#x2019;s method to predict future IPRs. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 21
• 19. IPR Prediction: 1st Approximation Method &#xF0FC;This method provides a rough approximation of the future maximum oil flow rate (Qomax)f at the specified future average reservoir pressure (pr)f. &#xF0D8;This future maximum flow rate (Qomax) f can be used in Vogel&#x2019;s equation to predict the future inflow performance relationships at (p&#x2013;r)f. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 22
• 20. IPR Prediction: 1st Approximation Method (Cont.) &#xF0FC;Step 1. Calculate (Qomax)f at (p&#x2013;r)f from: &#xF0D8;Where the subscript f and p represent future and present conditions, respectively. &#xF0FC;Step 2. Using the new calculated value of (Qomax)f and (p&#x2013;r)f, generate the IPR by: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 23
• 21. IPR Prediction: 2nd Approximation Method &#xF0FC;A simple approximation for estimating future (Qomax)f at (p&#x2013;r)f is proposed by Fetkovich (1973). The relationship has the following mathematical form: &#xF0D8;Where the subscripts f and p represent future and present conditions, respectively. &#xF0D8;The above equation is intended only to provide a rough estimation of future (Qo)max. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 24
• 22. Wiggins&#x2019; Method &#xF0FC;Wiggins (1993) used four sets of relative permeability and fluid property data as the basic input for a computer model to develop equations to predict inflow performance. &#xF0FC;The generated relationships are limited by the assumption that the reservoir initially exists at its bubble-point pressure. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 27
• 23. Wiggins&#x2019; Method (Cont.) &#xF0FC;Wiggins proposed generalized correlations that are suitable for predicting the IPR during three-phase flow. &#xF0FC;His proposed expressions are similar to that of Vogel&#x2019;s and are expressed as: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 28
• 24. Vogel&#x2019;s vs. Wiggins&#x2019; IPR Curves Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 29
• 25. Standing&#x2019;s Method &#xF0FC;Standing (1970) essentially extended the application of Vogel&#x2019;s to predict future inflow performance relationship of a well as a function of reservoir pressure. &#xF0FC;He noted that Vogel&#x2019;s equation can be rearranged as: &#xF0FC;Standing introduced the productivity index J as defined by J=Qo/ ((p&#x2013;r)-pwf) into above Equation to yield: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 31
• 26. Standing&#x2019;s Zero-Drawdown Productivity Index &#xF0FC;Standing then defined the present (current) zero drawdown productivity index as: &#xF0FC;Where J*p is Standing&#x2019;s zero-drawdown productivity index. The J*p is related to the productivity index J by: &#xF0FC;J=Qo/ ((p&#x2013;r)-pwf) Equation permits the calculation of J*p from a measured value of J. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 32
• 27. Standing&#x2019;s Final Expression for IPR Prediction &#xF0FC;To arrive at the final expression for predicting the desired IPR expression, Standing combines Equations to eliminate (Qo)max to give: &#xF0FC;Where the subscript f refers to future condition. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 33
• 28. Standing&#x2019;s Drawdown Productivity Index (J*P) &#xF0FC;Standing suggested that J*f can be estimated from the present value of J*p by the following expression: &#xF0FC;Where the subscript p refers to the present condition. &#xF0FC;If the relative permeability data are not available, J*f can be roughly estimated from: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 34
• 29. Summary of Standing&#x2019;s Method &#xF0FC;Standing&#x2019;s methodology for predicting a future IPR is summarized in the following steps: &#xF0FC;Step 1. Using the current time condition and the available flow test data, calculate (Qo)max from Equations below. &#xF0FC;Step 2. Calculate J* at the present condition, i.e., J*p. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 35
• 30. Summary of Standing&#x2019;s Method (Cont.) &#xF0FC;Step 3. Using fluid property, saturation, and relative permeability data, calculate both (kro/&#x3BC;oBo)p and (kro/&#x3BC;oBo)f. &#xF0FC;Step 4. Calculate J*f by using below Equation. Use the other equation if the oil relative permeability data are not available. &#xF0FC;Step 5. Generate the future IPR by applying below equation. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 36
• 31. Disadvantages of Standing&#x2019;s Methodology &#xF0FC;It should be noted that one of the main disadvantages of Standing&#x2019;s methodology is that: &#xF0D8;It requires reliable permeability information; &#xF0D8;In addition, it also requires material balance calculations to predict oil saturations at future average reservoir pressures. &#xF0FC;It should be pointed out Fetkovich&#x2019;s method has the advantage over Standing&#x2019;s methodology &#xF0D8;In that, it does not require the tedious material balance calculations to predict oil saturations at future average reservoir pressures. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 37
• 32. Fetkovich&#x2019;s Method &#xF0FC;Muskat and Evinger (1942) attempted to account for the observed nonlinear flow behavior (i.e., IPR) of wells &#xF0D8;by calculating a theoretical productivity index from the pseudosteady-state flow equation. &#xF0FC;They expressed Darcy&#x2019;s equation as: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 39
• 33. Pressure Function Concept Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 40
• 34. Fetkovich&#x2019;s Method: 1st Case &#xF0FC;In the application of the straight-line pressure function, three cases must be considered: &#xF0D8;Case 1: p&#x2013;r and pwf &gt; pb &#xF076;Where Bo and &#x3BC;o are evaluated at (p&#x2013;r+ pwf)/2. &#xF0D8;Case 2: p&#x2013;r and pwf &lt; pb &#xF0D8;Case 3: p&#x2013;r &gt; pb and pwf &lt; pb Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 41
• 35. Fetkovich&#x2019;s Method: 2nd Case, Present IPR &#xF0D8;The term (J/2pb) is commonly referred to as the performance coefficient C, or: &#xF076;To account for the possibility of non-Darcy flow (turbulent flow) in oil wells, Fetkovich introduced the exponent n to yield: &#xF076;The value of n ranges from 1.000 for a complete laminar flow to 0.5 for highly turbulent flow. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 42
• 36. Fetkovich&#x2019;s Method: 2nd Case, Calculation of C and N &#xF0FC;There are two unknowns in the Equation: &#xF0D8;The performance coefficient C and the exponent n. &#xF076;At least two tests are required to evaluate these two parameters: &#xF076;A plot of p&#x2013;2r&#x2212; p2wf versus Qo on log-log scales will result in a straight line having a slope of 1/n and an intercept of C at p&#x2013;2r&#x2212; p2wf = 1. &#xF076;The value of C can also be calculated using any point on the linear plot once n has been determined to give: Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 43
• 37. Fetkovich&#x2019;s Method: 2nd Case, Future IPR &#xF0FC;To construct the future IPR when the average reservoir pressure declines to (p&#x2013;r)f, &#xF0D8;Fetkovich assumes that the performance coefficient C is a linear function of the average reservoir pressure and, &#xF076;Therefore, the value of C can be adjusted as: &#xF076;Fetkovich assumes that the value of the exponent n would not change as the reservoir pressure declines. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 44
• 38. Fetkovich&#x2019;s Method: Comparison between Current and Future IPRs Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 45
• 39. Fetkovich&#x2019;s Method: 3rd Case &#xF0FC;Case 3: p&#x2013;r &gt; pb and pwf &lt; pb &#xF0FC;&#x3BC;o and Bo are evaluated at the bubble-point pressure pb. Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 46
• 40. 1. Ahmed, T. (2010). Reservoir engineering handbook (Gulf Professional Publishing). Chapter 7
• 41. 1. 2. 3. 4. 5. Horizontal Oil Well Performance Horizontal Well Productivity Vertical Gas Well Performance Pressure Application Regions Turbulent Flow in Gas Wells A. Simplified Treatment Approach B. Laminar-Inertial-Turbulent (LIT) Approach (Cases A. &amp; B.)