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Bubble point pressure, pb,

Liquid [Oil] Formation Volume Factor (FVF), Bo,

Solution GOR, Rs, and

Oil and Gas Viscosity, o and g.

These correlations generally use the following set of parameters:

Oil API gravity8, API,

Gas gravity9, g,

Solution GOR at initial conditions, Rsi, and

Temperature, TR.

The correlations are therefore of the form:

(3.2)

pb f API , g , Rsi ,TR

The more commonly known correlations are due to Standing, Lasater, and Vasquez and Beggs: for more details see Chapter 22 of Bradley.

3.4 The Corresponding States Theorem

As was evident from Table 3.1, the physical properties of hydrocarbons vary with molecular weight [and shape]. Therefore, derived properties such as density, viscosity, thermal conductivity, etc., cannot be easily be deduced for one species based on measurements of those properties for another species. However, it was observed that if we work in terms of reduced properties, such as reduced temperature, Tr, and reduced pressure, pr, where:

(3.3)	T	T	p	r		p	,
	r	Tc				pc

then a more consistent picture emerges.

In particular, the Corresponding States theorem says all pure gases will have the same Z- factor10 at the same reduced temperature and reduced pressure: see the Real Gas Law in section 5.1.3.

8 API gravity is related to specific gravity, o, [density relative to water] by API

(141.5

o ) 131.5

9 Gas gravity is density relative to that of air. Since they are both measured at standard conditions, we assume the ideal gas law applies [see section 5.1] and therefore density is proportional to mole weight. Therefore, gas gravity can be equally well represented as the gas mole weight relative to that of air where Mair = 28.97.

10 We will define Z-factor in section 5.2.

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The following figure, usually known as the Standing Z-Factor chart, shows the variation of Z-Factor with reduced pressure and reduced temperature.

Figure 19: Standing Z-Factor Chart

All hydrocarbon gases [up to C6] and the inorganics N2, CO2 and H2S obey this chart to within a few percent. Mixtures of these components can also have their Z-Factor computed from this chart if instead of the pure component critical pressure and temperature in (3.3), we use the pseudo-critical pressure, ppc, and pseudo-critical temperature, Tpc, defined by:

	N	N
(3.4)	p pc yi pci	Tpc yiTci
	i 1	i 1

Here yi is the mole fraction of the ith of the N components. In the absence of a compositional analysis, the pseudo-criticals can be estimated from correlations based on gas gravity: see Appendix B of McCain.

We will see later when we study Equations of State that both pressure and temperature enter these expressions as reduced quantities. Other models utilize the Corresponding States Theorem. Amongst them are the models for estimating viscosity and thermal conductivity of hydrocarbon mixtures due to Pedersen et al., in Chapter 11 of Pedersen et al.

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3.4.1 Z-Factor Correlations

One of simplest correlations for estimating Z-factors is due to Brill and Beggs [see Beggs for details]:

(3.5)		Z A (1 A) exp( B) Cp prD
where:
	A 1.39 Tpr 0.92 0.5 0.36Tpr			0.101
				0.066				0.32 p6pr exp 20.723 Tpr 1
	B	p pr 0.62 0.23Tpr p2pr				0.037
(3.6)					0.86)
		(Tpr
	C 0.132 0.32logTpr
	D exp 0.715 1.128Tpr 0.42Tpr2

This correlation is adequate ( 1-2%) provided the temperature is 80.0 < T (oF) < 340.0 and the pressure p < 10000.0 psia. The main advantage is the expression is explicit in Z.

A more accurate expression, which can be used over a wider range of pressure and temperature, is credited to Hall and Yarborough. Here, the Z-factor is calculated from:

(3.7) Z p pr

		y
	where:	0.06125t exp 1.2 1 t 2
	(3.8)
		t 1 Tpr

In (3.7), y is the reduced density, which is found by solving the non-linear equation:

	F( y)	ppr	y y2 y3	y4	(14.76t 9.76t 2			4.58t 3 ) y2
			1 y 3
(3.9)		(90.7t 242.2t 2 42.4t 3 ) y 2.18 2.82t
		0
The derivative of (3.9) is calculated from:
	dF	1 4y 4y 2 4y3 y 4				2			3
(3.10)	dy	1 y 4		(29.52t 19.52t			9.16t			) y

2.18 2.82t 90.7t 242.2t 2 42.3t 3 y 1.18 2.82t

An initial estimate of y=0.001 when used with the Newton procedure should achieve convergence in 3 to 10 iterations for F(y) = 10-8.

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3.4.1.1 Estimating Pseudo-Criticals

In the absence of compositional information, the pressure and temperature pseudocriticals (ppc, Tpc), can be estimate by correlations dependent on the [reported] gas gravity. Standing gives two sets of correlations, one for dry gases ( gHC < 0.75):

	(3.10)	TpcHC	168.0		325.0 gHC 12.5 gHC2
		ppHC	667.0		15.0 gHC 37.5 gHC2

and a second set for wet gas mixtures ( gHC 0.75):

	(3.11)	TpcHC	187.0		330.0 gHC 71.5 gHC2
		ppHC	706.0		51.7 gHC 11.1 gHC2

When significant quantities of the inorganics CO2 and H2S are present, the pseudocriticals should be corrected to account for the mole fractions of these components. In particular,

	Tpc TpcHC
(3.12)	ppc	ppcHC TpcHC
		TpcHC yH2S (1 yH2S )
where the -correction factor is calculated from:
(3.13)	120 yCO2 yH2S 0.9 yCO2			yH2S 1.6 15 yH0.52S yH4	2S

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4.Sampling and Laboratory Analysis

Increasingly, we are using mathematical models encapsulated within software packages to predict the behaviour of hydrocarbon reservoirs and their associated production systems. The models require things:

1.Input and Initialisation

2.Calibration

For fluid property determination this necessitates we take samples of the fluids of interest. Next, we determine their composition. Finally, we perform a set of standard tests to produce data to calibrate our models.

4.1 Sampling

Before we can conduct any test, we have to acquire samples of the fluid of interest. Samples should be taken as part of the initial well testing program. There are usually conflicts in the well test program with the need to acquire reservoir parameters versus the collection of representative samples. Proper design and careful planning are the key to minimizing these conflicts.

A number of industry bodies have studied the problem of sampling, especially for more complex fluids such as gas condensates. Their recommendations can be found the reports from the API and UKOOA.

4.1.1 Well Testing

The main problems in well test design for sampling concern the producing interval and tubing size.

In large hydrocarbon columns, a significant variation in composition with depth is possible [we will discuss this effect in detail in section 6.4]. In this case, it is preferable to sample only a limited interval by restricting the perforations: the UKOOA report suggests intervals be restricted to 30-ft [10 m]. This then requires several tests be performed over a large column: over a 300-ft column, the UKOOA report suggests a minimum of three separate tests.

As we will see when we consider well conditioning, sample collection is best served by low flow rates. Low flow rates should be produced using small diameter tubing since low rate production in large diameter tubing gives rise to an unstable flow regime called slugging. However, the rate must be high enough to ensure that liquids are produced to surface: see Turner et al.: see section 4.1.4. If the flow rate of a condensate well being surface sampled is too low such that some of the liquid phase is not produced then an

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unrepresentative sample will be taken. If all the liquid falls back, the well may choke and die.

Technological advances in recent years have helped us here since it may be possible to run small diameter coiled tubing during the sampling phase, reverting back to the large diameter tubing for the other aspects of the well test.

4.1.2 Conditioning

As we shall discuss shortly, there are two ways of sampling:

Down Hole

Surface

In both cases, proper conditioning of well prior to taking the sample is essential.

Ideally, sampling should be done as soon as possible after the well is completed. The process of drilling and completion usually results in near well bore damage and contamination, which must be cleaned-up before the sample can be taken. This is best achieved by a high flow rate. However, a high flow rate may cause in a large pressure draw down that results in the bottom hole pressure falling below the saturation pressure. Then, depending on relative permeability effects, the fluid flowing into the well may be unrepresentative of the reservoir fluid.

Once the balance has been achieved between maximizing clean-up time and minimizing draw down the main aim is to achieve:

Uniform flow rate,

Uniform GOR,

Stable Top Hole Pressure (THP)

Stable Bottom Hole Pressure (BHP)

Stable bottom hole density, BH [to ensure no liquid build up], and

Stable wellhead temperature, TWH.

The UKOOA report suggests these stability conditions be satisfied for 6 hours prior to the sample being taken.

4.1.3 Down Hole Sampling

In this technique, a bottle is lowered down hole on a wire line and placed as close as possible to the open interval. At some pre-arranged time or on a command from the surface, the bottle is opened to the fluid flowing around it whereupon some of that fluid is allowed to enter the bottle.

Unlike surface sampling, the volume of fluid that can be collected is relatively small: typically 1 litre or so. Traditionally, this has precluded their use for gas condensate

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systems but with improving laboratory techniques requiring less fluid to perform the suite of analysis tests, this is less of a problem.

The sample bottle is returned to the laboratory and the fluid is flashed to atmospheric conditions. The volumes of stock tank gas and oil are measured (Vg, Vo). The normalized weight fractions of the stock tank gas and oil samples are found by gas chromatography, wgi and woi. The mole weight and density of the oil sample are measured, Mo and o. The flash GOR, Rs, in consistent units, i.e. ft3/ft3 or m3/m3, tells us:

	(4.xxx)	Rs	Vg		ngVgm
			Vo		noVom

Vgm and Vom are the molar volumes of gas and oil and ng and no are the corresponding mole numbers: by definition, in field units, Vgm = 379.4 ft3/lbmole. If we assume 1.0 mole of feed then no = 1.0 – ng. The oil molar volume is calculated from:

M

(4.xxx) Vom o

o

Combining these results allows us to calculate the gas moles as:

	(4.xxx)	ng	M o	o Rs
			Vgm M o o		Rs

Meanwhile, the oil and gas weight fractions are converted to mole fractions using the component mole weights:

xi		woi	M i
	woj	M j	wo7	M o7
(4.xxx)	j C7	wgi	M i
yi
	wgj	M j wg 7		M g 7
	j C7

The surface gas usually contains 1.0 mole percent or less of C7+ so Whitson has suggested that a good estimate for the gas’ plus fraction mole weights is Mg7+ = 105.0. The oil sample plus fraction weight is calculated by material balance from:

(4.xxx)	M o7		wo7
		1		woj
		M o		M j
			j C7

Finally, with the gas and oil sample compositions and the gas moles, the feed composition is calculated from:

(4.xxx)

zi ng yi (1 ng )xi

We will see in section 4.2.1 that the measurement of mole weight is extremely difficult

and can be subject to an error as large as 10.0%: this will clearly feed through into the determination of well stream composition. Whitson has suggested that the Watson

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characterization factor, Kw11, can be used to test the accuracy of the mole weight measurement.

4.1.4 Surface Sampling

This remains the dominant technique for collecting samples. A well is allowed to flow to surface where a fraction of the well stream fluid is re-directed to a test separator held at some pre-determined pressure and temperature. After ensuring the stability conditions outlined in section 4.1.2 are met, samples of the separator vapour and liquid are collected in a number of bottles. These are then sent to regional laboratories for analysis.

The main advantage of this technique over down-hole sampling is the ability to collect large volumes of fluid. However, there are a number of issues including:

Lifting all the produced fluids,

Ensuring a representative mix is taken from the flow line,

Accurate metering with the consequent problem of recombining the vapour and liquid streams to reconstitute the well stream fluid.

4.1.4.1 Liquid Loading in Gas Wells

The first issue is particularly important for gas wells that also produce condensate or water. The minimum [equivalent surface] rate for a given well head pressure and tubing size was predicted by Turner et al. from:

	(4.xxx)	Qmin	3.06	vmin Apwh
				TZ

The surface flow is expressed in MMscf/day, the tubing area, A, in ft2, the well head pressure, pwh, in psia, the surface flowing temperature, T, is in degrees Rankine and Z is

the gas Z-factor at (pwh, T). The minimum velocity, vmin, measured in ft/s, can be estimated from one of the two following equations depending on whether the liquid is

water or condensate:

	vminwat	5.62	67.0 0.0031pwh 0.25
	(4.xxx)			0.0031pwh 0.50
				45.0 0.0031pwh 0.25
	vmincond	4.02
				0.0031pwh 0.50

It has been reported that the Turner correlation works well for LGR ratios as high as 250 bbl/MMscf.

11 See section 7.2.

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4.1.4.2 Taking Samples

Most surface samples are taken via a test separator. Ideally, the inlet of to the test separator should be a probe inserted into the main flow line from the well head manifold. The probe should be preceded by a baffle arrangement to ensure the fluid is well mixed.

4.1.4.3 Metering

Probably the biggest source of error in surface sampling is associated with errors in metering the vapour and liquid streams emerging from the test separator.

The measurement of the gas rate is usually done by inserting a restriction into the gas flow line. The restriction is one of two types, the Venturi tube:

Figure 20: Schematic of the Venturi Tube Rate Measurement

Or the Orifice Plate:

Figure 21: Schematic of an Orifice Plate Gas Rate Device

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In both cases, the conservation of momentum is used to equate the change in pressure between the upstream [denoted ‘1’] and throat [denoted ‘2’] to the flow rate:

(4.xxx) P1 12 1v12 P2 12 2v22

where the local velocity vj = Q/Aj and Aj = dj2. After some algebra, the above equation becomes:

(4.xxx)	Qg A2	1		2 P1 P2
		1 Fd4

where A2 is the choke area, Fd = d/D and is the average density. The second term on

the right side of this expression is often known as the Approach factor. The pressure difference is often expressed in terms of the height of a column of water, hw. In this case, the Orifice Plate Equation (OPE) is expressed as:

(4.xxx) Qg C hw p f

where pf is the flowing or down stream pressure and the Orifice constant C is given by:

(4.xxx)

C Fb Fpb Ftb Fg Ftj FrYFpv Fm Fl Fa

The set of F-multipliers correct for a series of assumptions which were made in the derivation of OPE. Of particular interest are:

The Specific Gravity-factor, Fg, which must be used when the gravity is other than 1.0: Fg 1 g 0.5

The Super Compressibility factor, Fpv, which accounts for deviations from the Ideal Gas law: Fpv 1Z 0.5

Very often the during the laboratory report of the recombination process, it will be seen that the test separator or field GOR is corrected to ‘lab’ conditions by the equation:

F Lab F Lab

(4.xxx) GORLab GORField g pv FgField FpvField

More information on the OPE and its various F-multipliers can be found in Chapter 13 of the Petroleum Engineers Handbook.

A well maintained, relatively new OP or Venturi Tube meter should be capable of predicting the gas rate to an accuracy of 5.0%. However, they are easily damaged if there is liquid carry over in the form of a liquid-in-gas mist into the gas line. Even worse damage will occur if the well stream fluid contains particulates, i.e. sand production.

Most liquid measurements are done via a turbine-based meter in which a spinner turns more or less slowly depending on the flow rate and fluid properties. A well maintained

meter would be accurate to 5.0%.

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