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### Q913 re1 w4 lec 16

1. 1. Reservoir Engineering 1 Course (1st Ed.)
2. 2. 1. Vertical Gas Well Performance 2. Pressure Application Regions 3. Turbulent Flow in Gas Wells A. Simplified Treatment Approach B. Laminar-Inertial-Turbulent (LIT) Approach (Cases A. & B.)
3. 3. 1. Turbulent Flow in Gas Wells: LIT Approach (Case C) 2. Comparison of Different IPR Calculation Methods 3. Future IPR for Gas Wells 4. Horizontal Gas Well Performance 5. Primary Recovery Mechanisms 6. Basic Driving Mechanisms
4. 4. Case C. Pseudopressure Quadratic Approach Pseudopressure Equation can be written as: Where The term (a2 Qg) represents the pseudopressure drop due to laminar flow while the term (b2 Qg2) accounts for the pseudopressure drop due to inertial-turbulent flow effects. The Equation can be linearized by dividing both sides of the equation by Qg to yield: 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 5
5. 5. Case C. Graph of Real Gas PseudoPressure Data The above expression suggests that a plot of versus Qg on a Cartesian scale should yield a straight line with a slope of b2 and intercept of a2 as shown in Figure. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 6
6. 6. Case C. Gas Flow Rate Calculation Given the values of a2 and b2, the gas flow rate at any pwf is calculated from: It should be pointed out that the pseudopressure approach is more rigorous than either the pressuresquared or pressure-approximation method and is applicable to all ranges of pressure. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 7
7. 7. The Back-Pressure Test Rawlins and Schellhardt (1936) proposed a method for testing gas wells by gauging the ability of the well to flow against various back pressures. This type of flow test is commonly referred to as the conventional deliverability test. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 9
8. 8. IPR for Different Methods Figure compares graphically the performance of each method with that of ψapproach. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 10
9. 9. IPR for All Methods (Cont.) Since the pseudo-pressure analysis is considered more accurate and rigorous than the other three methods, the accuracy of each of the methods in predicting the IPR data is compared with that of the ψ-approach. Results indicate that the pressure-squared equation generated the IPR data with an absolute average error of 5.4% as compared with 6% and 11% for the backpressure equation and the pressure approximation method, respectively. It should be noted that the pressure-approximation method is limited to applications for pressures greater than 3000 psi. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 11
10. 10. Future Inflow Performance Relationships Once a well has been tested and the appropriate deliverability or inflow performance equation established, It is essential to predict the IPR data as a function of average reservoir pressure. The gas viscosity μg and gas compressibility z-factor are considered the parameters that are subject to the greatest change as reservoir pressure p–r changes. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 13
11. 11. Future IPR Methodology Assume that the current average reservoir pressure is p–r, with gas viscosity of μg1 and a compressibility factor of z1. At a selected future average reservoir pressure p–r2, μg2 and z2 represent the corresponding gas properties. To approximate the effect of reservoir pressure changes, i.e. from p–r1 to p–r2, on the coefficients of the deliverability equation, the following methodology is recommended: Back-Pressure Equation LIT Methods Pressure-Squared Method Pressure-Approximation Method Pseudopressure Approach 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 14
12. 12. Future IPR: Back-Pressure Equation The performance coefficient C is considered a pressuredependent parameter and adjusted with each change of the reservoir pressure according to the following expression: The value of n is considered essentially constant. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 15
13. 13. Future IPR: LIT Methods The laminar flow coefficient a and the inertial-turbulent flow coefficient b of any of the previous LIT methods, are modified according to the following simple relationships: Pressure-Squared Method • The coefficients a and b of pressure-squared are modified to account for the change of the reservoir pressure from p–r1 to p– r2 by adjusting the coefficients as follows: • (the subscripts 1 and 2 represent conditions at reservoir pressure p–r1 to p–r2, respectively.) 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 16
14. 14. Future IPR: LIT Methods (Cont.) Pressure-Approximation Method Pseudopressure Approach • The coefficients a and b of the pseudo-pressure approach are essentially independent of the reservoir pressure and they can be treated as constants. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 17
15. 15. Current and Future IPR Comparison 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 18
16. 16. Horizontal Gas Well Many low permeability gas reservoirs are historically considered to be noncommercial due to low production rates. Most vertical wells drilled in tight gas reservoirs are stimulated using hydraulic fracturing and/or acidizing treatments to attain economical flow rates. In addition, to deplete a tight gas reservoir, vertical wells must be drilled at close spacing to efficiently drain the reservoir. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 20
17. 17. Horizontal Gas Well (Cont.) This would require a large number of vertical wells. In such reservoirs, horizontal wells provide an attractive alternative to effectively deplete tight gas reservoirs and attain high flow rates. Joshi (1991) points out those horizontal wells are applicable in both low-permeability reservoirs as well as in high-permeability reservoirs. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 21
18. 18. Effective Wellbore Radius in Horizontal Gas Well  In calculating the gas flow rate from a horizontal well, Joshi introduced the concept of the effective wellbore radius r′w into the gas flow equation. The effective wellbore radius is given by: 2013 H. AlamiNia Where L = length of the horizontal well, ft h = thickness, ft rw = wellbore radius, ft reh = horizontal well drainage radius, ft a = half the major axis of drainage ellipse, ft A = drainage area, acres Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 22
19. 19. Qg Calculation from a Horizontal Gas Well Methods of calculating the horizontal well drainage area A are presented in previous lecture. For a pseudosteady-state flow, Joshi expressed Darcy’s equation of a laminar flow in the following two familiar forms: Pressure-Squared Form Where Qg = gas flow rate, Mscf/day s = skin factor k = permeability, md T = temperature, °R Pseudo-Pressure Form 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 23
20. 20. IPR Curve for Horizontal Gas Well For turbulent flow, Darcy’s equation must be modified to account for the additional pressure caused by the non-Darcy flow by including the ratedependent skin factor DQg. In practice, the back-pressure equation and the LIT approach are used to calculate the flow rate and construct the IPR curve for the horizontal well. Multirate tests, i.e., deliverability tests, must be performed on the horizontal well to determine the coefficients of the selected flow equation. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 24
21. 21. Reservoir Classification Each reservoir is composed of a unique combination of geometric form, geological rock properties, fluid characteristics, and primary drive mechanism. Although no two reservoirs are identical in all aspects, they can be grouped according to the primary recovery mechanism by which they produce. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 27
22. 22. Driving Mechanisms Characteristics It has been observed that each drive mechanism has certain typical performance characteristics in terms of: Ultimate recovery factor Pressure decline rate Gas-oil ratio Water production The recovery of oil by any of the natural drive mechanisms is called primary recovery. The term refers to the production of hydrocarbons from a reservoir without the use of any process (such as fluid injection) to supplement the natural energy of the reservoir. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 28
23. 23. Primary Recovery Mechanisms For a proper understanding of reservoir behavior and predicting future performance, it is necessary to have knowledge of the driving mechanisms that control the behavior of fluids within reservoirs. The overall performance of oil reservoirs is largely determined by the nature of the energy, i.e., driving mechanism, available for moving the oil to the wellbore. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 29
24. 24. Driving Mechanisms There are basically six driving mechanisms that provide the natural energy necessary for oil recovery: Rock and liquid expansion drive Depletion drive Gas cap drive Water drive Gravity drainage drive Combination drive 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 30
25. 25. Rock and Liquid Expansion At pressures above the bubble-point pressure, crude oil (in undersaturated reservoirs), connate water, and rock are the only materials present. As the reservoir pressure declines, the rock and fluids expand due to their individual compressibilities. As the expansion of the fluids and reduction in the pore volume occur with decreasing reservoir pressure, the crude oil and water will be forced out of the pore space to the wellbore. This driving mechanism is considered the least efficient driving force and usually results in the recovery of only a small percentage of the total oil in place. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 32
26. 26. The Depletion Drive Mechanism This driving form may also be referred to by the following various terms: Solution gas drive Dissolved gas drive Internal gas drive In this type of reservoir, the principal source of energy is a result of gas liberation from the crude oil and the subsequent expansion of the solution gas as the reservoir pressure is reduced. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 33
27. 27. Production Data of a Solution-Gas-Drive Reservoir 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 34
28. 28. Gas Cap Drive Gas-cap-drive reservoirs can be identified by the presence of a gas cap with little or no water drive. Due to the ability of the gas cap to expand, these reservoirs are characterized by a slow decline in the reservoir pressure. The natural energy available to produce the crude oil comes from the following two sources: Expansion of the gas-cap gas Expansion of the solution gas as it is liberated 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 35
29. 29. Production Data for a Gas-Cap-Drive Reservoir 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 36
30. 30. The Water-Drive Mechanism Many reservoirs are bounded on a portion or all of their peripheries by water bearing rocks called aquifers. The aquifers may be so large compared to the reservoir they adjoin as to appear infinite for all practical purposes, and they may range down to those as small as to be negligible in their effects on the reservoir performance. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 37
31. 31. Types of Aquifers The aquifer itself may be entirely bounded by impermeable rock so that the reservoir and aquifer together form a closed (volumetric) unit. On the other hand, the reservoir may be outcropped at one or more places where it may be replenished by surface water. Regardless of the source of water, the water drive is the result of water moving into the pore spaces originally occupied by oil, replacing the oil and displacing it to the producing wells. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 38
32. 32. Reservoir Having Artesian Water Drive 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 39
33. 33. Aquifer Geometries It is common to speak of edge water or bottom water in discussing water influx into a reservoir. Bottom water occurs directly beneath the oil and edge water occurs off the flanks of the structure at the edge of the oil 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 40
34. 34. Production Data for a Water-Drive Reservoir 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 41
35. 35. The Gravity-Drainage-Drive Mechanism The mechanism of gravity drainage occurs in petroleum reservoirs as a result of differences in densities of the reservoir fluids. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 42
36. 36. The Combination-Drive Mechanism The driving mechanism most commonly encountered is one in which both water and free gas are available in some degree to displace the oil toward the producing wells. Two combinations of driving forces can be present in combination drive reservoirs. These are (1) Depletion drive and a weak water drive and; (2) Depletion drive with a small gas cap and a weak water drive. Then, of course, gravity segregation can play an important role in any of the aforementioned drives. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 43
37. 37. Combination-Drive Reservoir The most common type of drive encountered, therefore, is a combinationdrive mechanism as illustrated in Figure. 2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 44
38. 38. 1. Ahmed, T. (2006). Reservoir engineering handbook (Gulf Professional Publishing). Ch8 & 11