søndag 8. januar 2012
Relative permeability
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Relative permeability is a dimensionless term that has importance when two or more fluids move through the pore spaces—for example, oil and water. Specific or absolute permeability is the permeability of a porous medium to one fluid at 100% saturation. Effective permeability is the permeability to a given phase when more than one phase saturates the porous medium. The effective permeability, then, is a function of saturation. Relative permeability to a given phase is defined as the ratio of effective permeability to the absolute or, in some cases, a base permeability. Relative permeability, then, is also a function of saturation.
In data that were generated prior to 1973, the specific permeability to air was often used as the base permeability. Since that time, the common base has been the hydrocarbon permeability in the presence of irreducible water. For an oil-water reservoir, this would mean the base permeability would be effective permeability to oil at irreducible water. For a gas reservoir, the base permeability would be that to gas in the presence of irreducible water. Figure 1 (Gas-water relative permeability curves) illustrates gas-water relative permeability data when water displaces gas.
-----------------------Figure 1---------------------------------
Imbibition versus Drainage
The terms imbibition and drainage are also employed when discussing relative permeability tests. Their meanings imply what is happening in the pore space to the wetting phase as relative permeability tests are measured. If the wetting phase is decreasing, that phase is draining and the curve is called a drainage curve. If the wetting phase is increasing or being imbibed during the test, the curve is referred to as an imbibition curve ( Figure 1 ).
For a water-wet reservoir, the drainage curves apply during the time that water is draining from the reservoir and hydrocarbons are accumulating. Once the reservoir rock or laboratory sample has attained an equilibrium water-saturation value and the water is subsequently increased by natural water influx or the introduction of coring or test fluids, the imbibition curves apply. (In oil-wet rock, a reduction in the oil phase by water flooding would be referred to as a drainage curve.) These data are required in many reservoir engineering calculations, and the laboratory tests that develop them should follow the same saturation history as that in the reservoir.
Laboratory Methods for Measuring Relative Permeability
Two major laboratory methods have evolved to measure relative permeability. These are referred to as the steady-state and nonsteady-state techniques.
STEADY STATE: The steady-state test, the older of the two methods, is made at low flow rates, and the test apparatus contains upstream and downstream mixer heads to remove capillary end effects. Most research groups prefer data obtained from this test. Two fluids are injected simultaneously into a core sample and the water saturation is increased slowly. This simulates the slow increase in water saturation that would occur in the formation between the injection and producing wells. Saturation increase is monitored by measuring the gain in weight occurring in the sample or by X-ray technique.
NONSTEADY STATE: The nonsteady-state technique uses a viscous oil and is normally made at a higher flow rate than that present in the reservoir. It is this higher rate that sometimes yields pessimistic estimates of recovery from rocks of intermediate wettability. Heaviside and Black (1983) have analyzed the two techniques and presented recommendations on the most appropriate way to measure water-oil relative permeability depending upon the wetting characteristics of the rock.
Wettability Effects
The natural preference of a porous medium, which causes one fluid to adhere to its surfaces rather than another, is referred to as wettability. A water-wet porous medium causes water to adhere to its surfaces. The wettability of a rock has a dramatic influence on relative permeability curves. It is therefore necessary that the core samples tested in the laboratory reflect the actual formation wettability, and that initial water saturation in the test sample be of the same magnitude and have the same spatial location as it has in the reservoir. This need has led to the recovery of "native state" cores. These are cores taken with crude oil or with other oil-base fluids that do not alter the wettability or water saturation present in the recovered core.
Figure 2 (Effects of wettability on water-oil relative permeability: imbibition data for Torpedo sandstone) illustrates the effects of core wettability on water-oil relative permeability measurements (Owens and Archer 1971).
-----------------------------Figure 2--------------------------
These data indicate that as the rock becomes more oil-wet, the relative permeability to oil decreases and the relative permeability to water increases at any given saturation. This results in unfavorable recovery efficiency. It also indicates that the residual oil saturation in intermediate to oil-wet rocks is a function of the volume of water that flows through the core sample, and that the relative permeability to water existing at floodout will be much higher for the oil-wet formation. An interesting observation is that the reduction of capillary retentive forces in the oil-wet rock allows a lower residual oil saturation to be achieved in the oil-wet rock if economics would support continued water injection.
Wettability may be estimated from shapes of relative permeability curves; however, it should be remembered that a similar shift in the relative permeability curves can also be caused by changes in other rock properties. This was documented by Morgan and Gordon (1970).
Relative permeability is a dimensionless term that has importance when two or more fluids move through the pore spaces—for example, oil and water. Specific or absolute permeability is the permeability of a porous medium to one fluid at 100% saturation. Effective permeability is the permeability to a given phase when more than one phase saturates the porous medium. The effective permeability, then, is a function of saturation. Relative permeability to a given phase is defined as the ratio of effective permeability to the absolute or, in some cases, a base permeability. Relative permeability, then, is also a function of saturation.
In data that were generated prior to 1973, the specific permeability to air was often used as the base permeability. Since that time, the common base has been the hydrocarbon permeability in the presence of irreducible water. For an oil-water reservoir, this would mean the base permeability would be effective permeability to oil at irreducible water. For a gas reservoir, the base permeability would be that to gas in the presence of irreducible water. Figure 1 (Gas-water relative permeability curves) illustrates gas-water relative permeability data when water displaces gas.
-----------------------Figure 1---------------------------------
Imbibition versus Drainage
The terms imbibition and drainage are also employed when discussing relative permeability tests. Their meanings imply what is happening in the pore space to the wetting phase as relative permeability tests are measured. If the wetting phase is decreasing, that phase is draining and the curve is called a drainage curve. If the wetting phase is increasing or being imbibed during the test, the curve is referred to as an imbibition curve ( Figure 1 ).
For a water-wet reservoir, the drainage curves apply during the time that water is draining from the reservoir and hydrocarbons are accumulating. Once the reservoir rock or laboratory sample has attained an equilibrium water-saturation value and the water is subsequently increased by natural water influx or the introduction of coring or test fluids, the imbibition curves apply. (In oil-wet rock, a reduction in the oil phase by water flooding would be referred to as a drainage curve.) These data are required in many reservoir engineering calculations, and the laboratory tests that develop them should follow the same saturation history as that in the reservoir.
Laboratory Methods for Measuring Relative Permeability
Two major laboratory methods have evolved to measure relative permeability. These are referred to as the steady-state and nonsteady-state techniques.
STEADY STATE: The steady-state test, the older of the two methods, is made at low flow rates, and the test apparatus contains upstream and downstream mixer heads to remove capillary end effects. Most research groups prefer data obtained from this test. Two fluids are injected simultaneously into a core sample and the water saturation is increased slowly. This simulates the slow increase in water saturation that would occur in the formation between the injection and producing wells. Saturation increase is monitored by measuring the gain in weight occurring in the sample or by X-ray technique.
NONSTEADY STATE: The nonsteady-state technique uses a viscous oil and is normally made at a higher flow rate than that present in the reservoir. It is this higher rate that sometimes yields pessimistic estimates of recovery from rocks of intermediate wettability. Heaviside and Black (1983) have analyzed the two techniques and presented recommendations on the most appropriate way to measure water-oil relative permeability depending upon the wetting characteristics of the rock.
Wettability Effects
The natural preference of a porous medium, which causes one fluid to adhere to its surfaces rather than another, is referred to as wettability. A water-wet porous medium causes water to adhere to its surfaces. The wettability of a rock has a dramatic influence on relative permeability curves. It is therefore necessary that the core samples tested in the laboratory reflect the actual formation wettability, and that initial water saturation in the test sample be of the same magnitude and have the same spatial location as it has in the reservoir. This need has led to the recovery of "native state" cores. These are cores taken with crude oil or with other oil-base fluids that do not alter the wettability or water saturation present in the recovered core.
Figure 2 (Effects of wettability on water-oil relative permeability: imbibition data for Torpedo sandstone) illustrates the effects of core wettability on water-oil relative permeability measurements (Owens and Archer 1971).
-----------------------------Figure 2--------------------------
These data indicate that as the rock becomes more oil-wet, the relative permeability to oil decreases and the relative permeability to water increases at any given saturation. This results in unfavorable recovery efficiency. It also indicates that the residual oil saturation in intermediate to oil-wet rocks is a function of the volume of water that flows through the core sample, and that the relative permeability to water existing at floodout will be much higher for the oil-wet formation. An interesting observation is that the reduction of capillary retentive forces in the oil-wet rock allows a lower residual oil saturation to be achieved in the oil-wet rock if economics would support continued water injection.
Wettability may be estimated from shapes of relative permeability curves; however, it should be remembered that a similar shift in the relative permeability curves can also be caused by changes in other rock properties. This was documented by Morgan and Gordon (1970).
Long and short scales
- Long scale is the English translation of the French term échelle longue. It refers to a system of large-number names in which every new term greater than million is 1,000,000 times the previous term: billion means a million millions (1012), trillion means a million billions (1018), and so on.[1][2]
- Short scale is the English translation of the French term échelle courte. It refers to a system of large-number names in which every new term greater than million is 1,000 times the previous term: billion means a thousand millions (109), trillion means a thousand billions (1012), and so on.[1][2]
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D-exponent method
Jordan and Shirley (1966) approximated a solution to Bingham's
equation for a single unknown, the d-exponent, by eliminating variable
K (assuming it to be constant as in a uniform shale). They also inserted
constants in the equation to in-corporate American oilfield units of measurement.
(2)
where:
R = penetration rate, ft/hr
N = rotary speed, rpm
W = weight on bit, lb
D = diameter of bit, inches
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(2)W = weight on bit, lb
D = diameter of bit, inches
Continue reading at source...
Heave compensation
Heave compensation: control of offshore cranes and drilling equipment.
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Compensating heave motion requires a control system, a number of sensor inputs and proper machinery to control the motion of the load. A typical system is indicated below:Obtaining good heave compensation requires that we solve several problems that directly affect the performance of the system:
The ultimate goal is to adjust the compensator so that the movements of the vessel-crane assembly is perfectly compensated for at the load.
- Measuring, calculating and estimating the movements of the vessel, or more precisely: the wave induced movements of the tip of the crane. A rule of thumb is that compensation performance is limited by the quality of the motion sensor system.
- The heave machinery has a dynamic behavior of its own as well as a number of nonlinearities due to friction, valve characteristics etc, that complicates control design. A thorough understanding of these phenomena is vital to achieving good overall system performance.
- A load hanging at the end of a long elastic wire, an umbilical or a drill string behaves like a spring-mass system. In unfortunate cases this system has resonant behavior, ie. the load's motion may be amplified and become larger than that of the vessel.
- Eventually, the controller makes all the above subsystems work together in an optimal way. It extracts the essence of the sensor inputs, makes use of vital model parameters and calculates the control signals to the machinery. Depending on the system at hand, a number of different techniques may be applied: position feedback, velocity feed forward, force control by pressure and/or tension feedback, self-tuning control, repetitive control.
Heave compensation: modelling and simulation of offshore cranes and drilling equipment.
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