Calibration prerequisite for accurate PVT measurements

Nikos Varotsis, N. Pasadakis
Technical University of Crete
Chania, Greece

A calibration procedure improves PVT (pressure-volume-temperature) measurement accuracy, especially at high pressures.

This approach can be used for both the traditional setups with mercury as the displacing fluid or with the more recent mercury-free systems.

Volume is the parameter that usually varies independently during the course of PVT studies. The accuracy with which the volume variations are monitored influences directly the quality of the results.

PVT analysis

Fig. 1 shows the major parts of a typical PVT setup designed to meet the requirements for oil and gas condensate fluid studies.

The pumping device applies pressure or transfers fluids from one cell to another. Volumetric positive displacement measuring pumps are available on the market, with a precision of 0.001 cc.

In the high-pressure blind, windowed, or full view cells, the equilibrium phases formed are identified, thermodynamic behavior is determined, and individual volumes are monitored. Visual observation is considered a prerequisite for gas-condensate studies.

Low-pressure rated cells can be used as storage vessels, although, for safety reasons, it is generally recommended to maintain the same pressure rating for all equipment that may be included in any pressure loop. The fluids in the cells can be moved either with mercury acting as a floating piston or with a sealing piston driven by silicon oil.

PVT studies usually require thermocouples with a precision of up to 0.01 F. and pressure gauges with precision up to 0.01 psi. Measurement accuracy obviously depends on the sensor reliability and quality.

The temperature is controlled with air bath and oil bath heating jackets. Although oil baths are expected to maintain uniform temperature, temperature-controlled air baths are necessary when visual observations have to be made. The temperature of the cells should be controlled within 0.1 C. of the selected value

Volumetric calibration

Volume measurements of test fluids are obtained using either pump readings or indications from an optical device (kathetometer) if a through-window cell is available. The pump is usually preferred because it is applicable in all cases and does not include calculations for any dead volume between the window and the top valve. This volume may be small but is unavoidable in all full-view cells.

The recorded values should be corrected for the expansion or the contraction of the components (pumps, manifold. valves, cell, and displacing fluid) included in the pressurized loop, employed because of pressure and/or the temperature deviations from the reference conditions.

Every volume change in a pressurized loop recorded by the pump is the algebraic sum of the changes undergone by:

• The fluid volume in the loop due to its displacement

• The fluid volumes, the displacing fluid (mercury or silicon oil), and the hardware (lines, pump barrel, etc.) due to the variation of the prevailing conditions.

A precise calibration procedure needs to be followed so that the net fluid volume changes under study can be determined. This can be done by removing from the actual measurement the variations of system volume and of the displacing fluid with pressure and temperature.

Because flow loops of different configurations are employed at the various steps of a phase behavior study, the calibration procedure should include all the flow loops that may be used.

Test fluid volume

The volume of the fluid under study, present at any time in the cell, is given by the difference between the cell volume and the displacing fluid volume contained in it, as follows:

Vfluid@P,T = Vcell@P,T - VDF@P,T (1)

where:

Vfluid@P,T = Fluid volume at P, T

Vcell@P,T = Cell volume at P, T

VDF@P,T = Displacing fluid volume at P, T

Therefore, for calculating test-fluid volume change, as the conditions vary, cell volume variations and displacing fluid volume due to thermal expansion and/or compressibility should be taken into account.

Displacing fluid volume

Volume changes of a given mass of displacing fluid contained in the cell, can occur because of:

• Fluid displacement into or out of the cell because of pump piston movement and/or internal volume changes of the hardware in response to pressure and temperature changes

• Fluid density variations because of changes in the prevailing conditions.

If one considers a loop consisting of the pump, pressurized manifold, and pressure cell, the mass mDF of the displacing fluid contained in the cell at a given step can be computed as:

mDF = m'DF + DmDFcell (2)

The m'DF is the mass of the displacing fluid contained in the cell at the previous step and DmDFcell is the mass increment of the displacing fluid that enters or leaves the cell when the piston moves from the pump reading R1 to R2. This can be written as:

DmDFcell = Dmmeas + Dmpump + Dmman (3)

where:

DmDFcell = Mass increment of the displacing fluid in the cell (injected or expelled)

Dmmeas = Mass increment of the displacing fluid calculated using the recorded pump readings and the displacing fluid density at reference pressure and ambient temperature

Dmman = Mass increment of the displacing fluid in the manifold because of its expansion/contraction with pressure and/or temperature

Dmpump = Mass increment of the displacing fluid remaining in the pump as a result of its expansion/contraction because of temperature variation.

It is recommended to always record the pump reading at the same reference pressure regardless of the operating pressure. Any reasonably high value of pressure within the pressure range of operation (such as 1,500 psia) can he selected as the reference pressure.

When all components of the employed loop are maintained under the same pressure and temperature conditions, DmDFcell equals Dmmeas. Because it is more convenient to work with volume rather than with mass, Equation 3 can be expressed as follows:

VDF@P,T 3 rDFcell =

V'DF@P,T 3 r'DFcell + DVDFcell 3 rDFcell + DVmeas 3 rDFpump + DVpump 3 rDFpump + DVman 3 rDFman (4)

where:

V'DF@P,T 3 r'DFcell = Displacing fluid volume and density at the previous step

DVpump, DVman, and

DV DFcell = Displacing fluid volume change in the pump barrel, manifold, and cell

rDFcell, rDFpump, rDFman = Displacing fluid density in the cell, pump, and manifold.

DVmeas = Displacing fluid volume change in the pump barrel because of pump piston movement.

The displacing fluid volume, DVmeas, pushed out or withdrawn from a positive displacement pump barrel is determined from the readings that track piston displacement. These readings should be calibrated beforehand against the actual fluid volume in the following manner:

• Mass increments of the displacing fluid are pushed out of the pump at ambient temperature and atmospheric pressure.

• The displaced fluid is weighed at each step and its volume DVi is calculated using the precise density value at these conditions.

• A pump correction factor F, which expresses the linearity between the pump readings and the true volume displaced by the piston, is calculated as:

  Fi = DVi/DRi

The DRi is the difference in the pump reading before and after the displacement.

Once F is determined, the values of DVmeas can be calculated with Equation 5.

If there is a possibility for the pump barrel to be exposed to significant temperature variations, care has to be taken to maintain constant pump body temperature (thermoisolation, heating mantles, etc.). A change of the ambient temperature of 4 F. leads a 500 cc pump barrel to a volume change, DVpump, of 0.0132 cc.1

The manifold volume varies as pressure and/or temperature changes because of compressibility and thermal expansion of the metal. In practice, the influence of its volume variations, DVman, on the precision of volume measurements can be ig nored by including the manifold in the pressure loop and always taking the pump readings at the selected reference pressure. If the manifold employed in the flow loop configuration has a considerable volume and is subjected to significant temperature variations, the volume change from thermal expansion has to be derived using the volume calibration procedure.

The displacing fluid volume at the operating conditions P and T can be written as:

VDF@P,T = V DF@sc + DVT + DVP (6)

VDF@sc is the volume at standard conditions.

Equation 6 expressed in terms of densities has the following form:

rDF@P,T = rDF@sc/(r(1 - c(P - Psc))) (7)

where:

rDF@P,T = Displacing fluid density at pressure P, and temperature T

rDF@sc = Displacing fluid density at 60 F. and 14.7 psia

r = VDF@Patm,T/VDF@sc

c = Displacing fluid compressibility

If the displacing fluid is mercury, then its density, at the reference conditions of 60 F. and 14.7 psia, is equal to 13.5571 g/cu cm and the coefficients r and c can be obtained as follows:2

r = 1 + 1.00868 3 10-4 3

(T - 60) + 2.4 3 10-9 3

(T - 60) (8)

C = 3.544 + (2.58 3 10-7) 3

(21.68 3 103 - P) 3(T - 32)/1.8 + 8.3 3 10-6 3 (21.68 3 103 - P) (9)

The temperature is in F. and pressure in psia.

Cell volume

The cell volume at a given P and T is determined using an equation of the following form:

Vcell@P,T = f(P,T) (10)

To determine the cell volume at atmospheric pressure (P = 14.7 psia) and ambient temperature, the calibration procedure has to be conducted slowly to allow equilibrium to be established at each step. This can be confirmed by a few minutes of stable pressure.

The cell to be calibrated is filled with the displacing fluid at no pressure. The displaced fluid volume is then measured using the pump readings corrected with the procedure described previously. The fluid content of the cell can be weighed to confirm the precision of the measured volume. These steps can be done for all kinds of pressure cells.

To determine the cell volume at P = 14.7 psia as function or the temperature VPatm,T, the cell volume at P = 14.7 psia as a function of temperature T can be expressed as follows:

Vcell@Patm,T = VPatm,32F. 3 (1 + A 3 T) (11)

The VPatm,32F. is the cell volume at the arbitrary selected reference temperature of 32 F. and A is the thermal expansion coefficient.

The cell temperature is gradually set at T1, T2,...,Tn covering the temperature range expected in the PVT study. Pressure is maintained constant at P = 14.7 psia by withdrawing displacing fluid from the cell.

Where mercury is used, the cell volume change is recorded using the pump readings. If a piston cell is used, the displacing fluid expelled from the cell because of expansion is collected and weighed.

Fig. 2 is a typical plot of cell volume (at 14.7 psia)-vs.-temperature. VPatm,32F. is determined by extrapolating the volume curve to T = 32 F. The thermal expansion coefficient A is determined as a/VPatm,32F. where a is the slope of the curve in Fig. 2.

To determine the cell volume at constant temperature Ti and different pressures, the displacing fluid is gradually injected into the pressure cell at a predetermined constant temperature (preferably the last one of the previous calibration step). The change of the cell volume is measured at any pressure P1, P2,..., Pn step. This procedure is then repeated at a lower temperature until ambient temperature is reached. Fig. 3 represents the cell volume at any temperature Ti-vs.-pressure.

Each curve represents the isothermal cell volume behavior with respect to pressure and can be described by the equation:

Vcell@P,T = Vcell@Patm,32F. 3 (1 + B 3 P) (12)

The coefficient B is determined as:

B = C/Vcell@Patm,T (13)

The coefficient C is equal to the temperature dependent gradient dV/dP and is shown in Fig. 4. It can be expressed as follows:

C = a1 + a2 3 T (14)

The slope of the curve is equal to the coefficient a2, whereas the intercept is equal to al. Finally, the cell volume at any pressure and temperature is determined by:

Vcell@P,T = Vcell@Patm,32F. + A 3 T + C 3 P (15)

With equations 1, 4, and 15, the actual volume of the fluid under test in a PVT study can be accurately determined at any pressure and temperature.

Precision examples

The significance of calibration on the precision of the volume measurements is shown in the following examples from PVT tests.

Constant pressure

In the case of volume measurements at constant pressure and different temperatures, a 100 cc full-view window cell was charged with methane at 212 F. and 735 psia. After thermal equilibrium has been achieved, the pressure was set to 5,880 psia by injecting mercury in the cell in steps of 735 psia.

The actual methane volume contained in the cell at each pressure was calculated using the readings from the positive displacement mercury pump. All pump readings were taken with the pump and manifold held at the same reference pressure.

Table 1 compares the methane volumes calculated according to the proposed procedure with the volumes calculated by ignoring the variations of both the cell volume and mercury density with pressure. Deviations are in the order of 1%.

Constant temperature

In the case of volume measurement at constant temperature and different pressures, the same quantity of methane as in the previous case was charged in the cell at 1,470 psia and 176 F. The temperature was increased gradually to 482 F. in increments of 68 F. The cell pressure was maintained throughout the test at a constant 1,470 psia.

Table 2 compares the methane volumes calculated according to the proposed procedure with the volumes calculated by ignoring the variations in cell volume and in mercury density with temperature. At high pressures the relative error is in the order of 10%.

Oil compressibility

The compressibility of a heavy oil, 18 API, with an 808 psia bubble point pressure, was measured at 212 F. within the pressure range of 5,500-808 psia.

Table 3 compares the compressibility of the fluid obtained by following the proposed calibration procedure against the uncorrected values.

The uncorrected values had errors up to 70% at static pressure conditions.

References

1. Perry's Chemical Engineering Handbook, Sixth Edition, pp. 23-39.

2. Ruska's Training Manual, Ruska Instrument Corp. Houston.

The Authors