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Reservoir Engineering 1 Course (1st Ed.)
1. Vertical Gas Well Performance
2. Pressure Application Regions
3. Turbulent Flow in Gas WellsA. Simplified Treatment Approach
B. Laminar-Inertial-Turbulent (LIT) Approach (Cases A. & B.)
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
Case C. Pseudopressure Quadratic ApproachPseudopressure 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
Case C. Graph of Real Gas Pseudo-Pressure DataThe 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
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 pressure-squared 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
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
IPR for Different Methods
Figure compares graphically the performance of each method with that of ψ-approach.
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 10
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 back-pressure 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
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
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 EquationLIT Methods
Pressure-Squared MethodPressure-Approximation MethodPseudopressure Approach
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 14
Future IPR: Back-Pressure Equation
The performance coefficient C is considered a pressure-dependent 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
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
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
Current and Future IPR Comparison
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 18
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
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
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:
Where L = length of the
horizontal well, fth = thickness, ftrw = wellbore radius, ftreh = horizontal well
drainage radius, fta = half the major axis of
drainage ellipse, ftA = drainage area, acres
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 22
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
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 rate-dependent 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
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
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
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
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
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
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
Production Data of a Solution-Gas-Drive Reservoir
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 34
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
Production Data for a Gas-Cap-Drive Reservoir
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 36
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
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
Reservoir Having Artesian Water Drive
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 39
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
Production Data for a Water-Drive Reservoir
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 41
The Gravity-Drainage-Drive MechanismThe
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
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
Combination-Drive Reservoir
The most common type of drive encountered, therefore, is a combination-drive mechanism as illustrated in Figure.
2013 H. AlamiNia Reservoir Engineering 1 Course: Gas Well Performance / Driving Mechanisms 44
1. Ahmed, T. (2006). Reservoir engineering handbook (Gulf Professional Publishing). Ch8 & 11