Section 1

CHAPTER 1 GAS RESERVOIRS & INTRODUCTORY TOPICS

Gordon R. Petrie, Thru-u.com.

Contents:

Page

1.1

Introduction

3

1.2

Estimation of GIIP

4

1.3

Location of Fluid-Fluid Contacts

5

1.4

Primary Recovery Mechanism

10

1.5

Estimation of Expansion Factor

12

1.6

Gas Material Balance

13

1.7

Plotting Production Data

20

1.8

Gas Physical Properties

26

1.9

Gas Condensation

31

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1 -

GAS RESERVOIRS & INTRODUCTORY TOPICS

For nearly a century there was remarkable oil price stability at around $3-$4 per barrel. In this situation most fields were exploited with a minimum of technology: -

Primary recovery involved simply producing fluids to the surface using the stored energy within the reservoir system itself.

-

In the event of natural pressure maintenance from the expansion of aquifer or gascap fluids, then reasonable recoveries could be obtained.

-

However, in the absence of these factors, the reservoir produced by a depletion drive type mechanism, during which average reservoir pressure declined rapidly as pore fluids were produced.

-

Once the pressure dropped below the bubble-point, then free gas evolved from the oil within the reservoir; due to the preferential flow of gas to the wellbore the technique was known as Solution Gas Drive.

-

Solution gas drive was an extremely wasteful, low technology technique, but was common practice at a time of cheap oil prices.

-

In such a low technology era there was a modest role for Reservoir Engineers as part of the overall exploration & production team.

NOTE -

Since the oil price rise, from 1973 onwards, high technology recovery techniques and the advent of computer simulation have dramatically increased the importance of Reservoir Engineers.

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1.1 -

INTRODUCTION From 1973-1986 oil prices ranged from $30-$40 per barrel. These high prices stimulated exploration in high cost regions and encouraged the adoption of Secondary Recovery methods (water and gas drive).

-

Reservoir Engineers now play a central role throughout both field appraisal and development phases. Briefly, their pivotal relationship with the rest of the exploration & production team can be summarised below: GEOLOGISTS: - Preparation of subsurface maps. - Location of faults and fractures. - Inspection of core samples, drilling logs; lithology determination. - Development of depositional and geological models.

PETROPHYSISTS: - Inspection of drilling logs; lithology determination. - Log & core interpretation and deveolopment of correlations. - Determination of lithology, pore fluids and saturations. - Estimation of porosity, permeability and net rock volume.

RESERVOIR ENGINEERS: - Central co-ordination role for data collection and interpretation, i.e. collection of cores and running logs. - Fluid sampling, GIIP or STOIIP determination. - Selection of rock and fluid input property data for reservoir simulator runs. Well testing, pressure-depth data and analysis. - Flowrates, PI, number/location of wells, recovery factor and recovery timescale. - Determination of drive mechanisms, pressure communication, vertical layering and permeability distribution. - History matching reservoir simulator output. Use of simulator to predict production profiles. - Operational and production decisions, i.e. high WOR/GOR.

ECONOMISTS: - Project equipment costings. - Economic studies and determination of project viability. - Sensitivity analysis to identify critical factors for profitability. - Cash flow projections, financial controls and budget preparation.

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FACILITY ENGINEERS: - Engineering of downhole and surface production facilities. - Engineering of Secondary Recovery plant. - Engineering of export facilities. - Engineering of infrastructural requirements.

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1.2 -

ESTIMATION OF GIIP For gas reservoirs, the equation used to estimate, G , the Gas Initially In Place, expressed in terms of standard surface volumes, is as follows:

G = Vbφ (1 − SWC ) Ei

................................................(1.1)

where, G = Gas Initially In Place (SCF).

Vb = Net bulk volume of the reservoir (rcf).

φ = Average porosity, or fraction of Vb which is pore space (-). SWC = Average connate water saturation, or fraction PV occupied by water (-). Ei = Initial Gas Expansion Factor (SCF/rcf).

-

The net bulk volume (rcf) is Vb . The Pore Volume, PV (rcf), is the product Vbφ . The Hydrocarbon Pore Volume, HCPV (rcf), is the product Vbφ (1 − S wc ) .

-

The gas expansion factor ( Ei ) simply converts reservoir volumes (rcf) into surface volumes at standard conditions (SCF). Its definition, and how to calculate its value, will be discussed later in this section.

NOTE -

There are two principal ways of finding GIIP, G: First, prepare a geological map and estimate Vb then solve (1.1); this is the so-called Volumetric Method.

-

Second, use gas material balance equation to predict G directly from production-decline information; see methods later in this section.

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1.3 LOCATION OF FLUID-FLUID CONTACTS -

The Volumetric Method for finding Vb starts with a contour plot shown below:

GWC

-

-

The green lines or contours connect lines of constant elevation to a marker bed – usually sealing shale.

-

These are similar to contour lines on a map except shallowest contours are at the top and deepest contours at the base. Such a map indicates structure.

-

The orange line represents the GWC. This diagram should be prepared by geologists/petrophysists.

-

This contour plot is then converted into an net isopachous map; i.e. contours are now isopachs or lines of constant net formation thickness. The zero isopach corresponds to the GWC.

From isopachous map Vb is found. However, errors in locating the GWC will cause errors in Vb . This will lead to knock-on errors in GIIP or G. Consider two types of trapping structure below:

WELL WELL Sealing Fault

GWC

GWC

(a)

-

(b)

In the case of (a) most wells penetrating this structure will pass through the GWC. Hence cores/logs will identify the GWC. However, in the case of structure (b) the GWC cannot be located by logs/cores.

NOTE -

In such cases only the Gas Down To depth (GDT) is known. The GWC must be inferred by pressure-depth measurements.

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Accurate knowledge of the hydrostatic pressure gradient for water in the vicinity of the hydrocarbon deposits is vital. For normally pressured sands the pressure-depth relation for water is given by

⎛ dp ⎞ pW = ⎜ W ⎟ D + 14.7 ………………………….....……(1.2) ⎝ dD ⎠ where, pW = Pressure in water bearing sand at any depth (psia).

D = Depth of interest (ft). ⎛ dpW ⎞ ⎟ = Water hydrostatic pressure gradient (psi/ft). ⎜ ⎝ dD ⎠

-

If the water bearing sand is abnormally pressured, for whatever reason, equation (1.2) must be modified as shown below

⎛ dp ⎞ pW = ⎜ W ⎟ D + ( p A + 14.7) …………………....……(1.3) ⎝ dD ⎠ where, p A = Abnormal pressure factor (psi).

-

p A is positive for overpressured and negative for underpressured sands. For a

sand to be abnormally pressured, it must be sealed by impermeable strata, otherwise the abnormal pressure will equilibrate vertically or aerially.

NOTE -

Once the pressure-depth line for water is constructed, the pressuredepth line for the gas column may also be constructed.

-

Where the two lines intersect identifies the depth of the GWC.

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Consider some typical values for fluid hydrostatic pressure gradients. Obviously actual values will be affected by a variety of factors such as depth, GOR, temperature, salinity, composition, etc.

⎛ dpW ⎞ ⎟ = 0.44 …………………......................….......(1.4)a ⎜ ⎝ dD ⎠ ⎛ dpO ⎞ ⎟ = 0.32 ………………………..................…...(1.4)b ⎜ ⎝ dD ⎠ ⎛ dpg ⎞ ⎟⎟ = 0.07 …………………….............................(1.4)c ⎜⎜ ⎝ dD ⎠

-

Consider the case where an exploration well has been drilled up-dip in a target structure shown below. A DST survey has been carried out at 5900 ft; the measured pressure and density of the gas was 2721.7 psia, and 0.07 psi/ft respectively.

-

Other measurements in surrounding water-bearing sands indicate that they are normally pressured and the calculated hydrostatic pressure gradient of 0.44 psi/ft is consistent with the known salinity/temperature in this region.

5800 ft

2566.7 psia

Sealing Fault

2714.7 psia

×

×

5900 ft

WELL

0.07 psi/ft

pg = 2721.7 psia ⎛ dp g ⎞ ⎟⎟ = 0.07 psi/ft ⎜⎜ ⎝ dD ⎠

D = 5900 ft GDT

6020 ft 0.44 psi/ft

6200 ft

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2742.7 psia

GWC

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-

From the DST test the pg = 2721.7 psia @ 5900 ft. From the gas sample the

downhole hydrostatic pressure gradient is calculated from the measured gas gravity to be (dpg / dD ) = 0.07 psi/ft.

-

Hence, since any hydrocarbon column must be overpressured with respect to the surrounding water-bearing sands, the constant for the hydrostatic pressure gradient equation can be found. The equation for pg is therefore

pg = 0.07 D + 2308.7 .......................................................(A)

-

Substituting D = 5900 ft into above expression returns the measured DST pressure within the gas at this depth. The water bearing sands are known to be normally pressured. The equation for pW is therefore

pW = 0.44 D + 14.7 ..................................................…....(B)

-

These two lines could be drawn on a pressure-depth graph. The point of intersection will indicate the depth of the GWC. The same result can be obtained algebraically from (A) and (B) without drawing the graph.

-

At GWC, pg = pW , and depth of the GWC is easily found by equating (A) and (B); assuming only gas below the GDT depth. The GWC is at 6200 ft.

NOTE -

GDT from cores/logs is known to be 6020 ft. However to estimate Vb & G using Volumetric Method the depth to the GWC is needed.

-

Using hydrostatic pressure information the GWC can be located at 6200 ft. This assumes there is no oil between 6020 & 6200 ft!

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The crest of the structure is at 5800 ft. The pressure immediately above the sealing shale, in the water bearing sand, can be found from equation (B). Substituting D = 5800 ft into (B) yields pW = 2566.7 psia.

-

The pressure immediately below the sealing shale in the gas reservoir can be found from equation (A). Substituting D = 5800 ft into (A) yields pg = 2714.7 psia; neglecting for the time being the shale thickness.

-

On drilling a crestal well through the sealing shale the formation pressure will rise suddenly from 2566.7 psia to 2714.7 psia.

-

Hence, the drilling overbalance will be reduced by 148 psi, which may be sufficient for the well to kick and take an influx.

-

If drilling were taking place in a new region the water pressure gradient may be unknown. Consider now that the surrounding water bearing sands are actually overpressured by 10 psi. Equation (B) now yields

pW = 0.44 D + 24.7 .........................................................(C)

NOTE -

In this case the GWC would be at 6173 ft instead of 6200 ft. Ignoring this overpressure would have the effect of overestimating Vb & G .

-

One significant question from this exercise is how can the presence or absence of an oil column be determined below the GDT depth?

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The only way to answer this question is to drill an exploration well down-dip or plug-back and sidetrack the existing well.

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It is not always best idea to drill an exploration well targeted at the crest of the structure!

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1.4 -

PRIMARY RECOVERY MECHANISM This section and the next one deal with Primary Recovery. That is, the situation where the energy stored within the fluid itself is used to produce the hydrocarbons to the surface.

-

Later sections deal with Secondary Recovery, where external energy is used to displace the oil out of the pore space and to the surface. The most common secondary recovery methods are water or gas drive.

-

In the case of Primary Recovery, the quantity of interest is the Isothermal Coefficient of Compressibility, which is defined as

c=−

-

1 ⎛ ∂V ⎜ V ⎜⎝ ∂p

⎞ ⎟⎟ ……………………………………......(1.5) ⎠T

Since a fluid will expand as the pressure falls the partial derivative is negative. Hence, a negative sign is needed to keep the compressibility coefficient a positive number. For reservoir engineering purposes (1.5) is usually written as

dV = cVΔp

NOTE -

……………………………..(1.6)

The negative sign can be dropped so long as the fluid expansion dV and the pressure drop Δp are both taken as positive.

-

Above equation states that production (LHS) equals expansion (RHS).

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Primary production in a gas reservoir is affected by two main factors, namely expansion of gas in the reservoir and expansion of water in the aquifer: -

There are also other more minor effects due squeezing of the pore space itself; as the pore pressure declines, the overburden pressure remains constant. There is also the expansion of small amounts of connate water.

Gas production:

dV = dVg + dVW

Gascap expansion:

dVg = cgVg Δp

Aquifer expansion:

dVW = cW VW Δp

-

The subsurface expansion of these two fluids must be equal to the cumulative volume of pore fluid production, or

dV = cgVg Δp + cW VW Δp

NOTE

-

…………………..(1.7)

cg >> cW so that primary recovery will only be significantly affected by water expansion if the aquifer is large with good hydraulic diffusivity.

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1.5 -

ESTIMATION OF EXPANSION FACTOR The real gas law can be used to determine gas volumes under any combination of temperature, pressure, or composition. The well-known expression is

pV = ZnRT ..................................................................(1.8)

-

Taking n moles of gas, equation (1.8) can be used to predict the volume under

reservoir conditions ( VRES ). Equation (1.8) can then be used to give the new volume of the same n moles at standard surface conditions ( VSC ). Hence

E=

VSC ⎛ Z SC nRTSC =⎜ VRES ⎜⎝ pSC

E=

pTSC Z SC pSCTZ

⎞⎛ p ⎞ ⎟⎟⎜ ⎟ ⎠⎝ ZnRT ⎠

or,

-

The subscript “SC” means Standard Conditions. The unsubscipted variables are at Reservoir Conditions. Substituting PSC = 14.7 psia, TSC = 520 R and Z SC = 1 gives the analytical expression for E (SCF/rcf) shown below

E = 35.37

p ZT

..................................................(1.9)

where, p = Pressure of gas at reservoir conditions (psia). T = Temperature of the gas at reservoir conditions (R). Z = Compressibility Factor of the gas at reservoir conditions (-).

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1.6 -

GAS MATERIAL BALANCE Recall GIIP (G) can be calculated by the Volumetric Method or by suitable analysis of the Gas Material Balance equation. Both methods are used.

-

The Material Balance equation can be used not only to find G, but also to determine the drive mechanism (the method involves graphically “history matching” known production data). There are two main cases to consider: -

Little or no natural water influx.

-

Significant expansion of water from adjoining aquifer into reservoir.

1.6.1 -

Gas Material Balance – Schilthuis Form

The Material Balance equation involves the following: determine the total volumetric expansion of pore fluids from initial conditions to the current stage of depletion; equate this expansion with cumulative volumetric production.

PRODUCTION

-

Consider initial condition with reservoir charged at initial pressure pi .

-

At this stage no fluids have been produced.

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At later stage, reservoir pressure has depleted to lower pressure p .

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Cumulative production must equal expansion of original pore fluids from pi to lower pressure

pi RESERVOIR

PRODUCTION

p RESERVOIR

p.

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-

Ignoring water influx, the derivation of the gas material balance commences by first re-arranging equation (1.1) to get an expression for Pore Volume PV

PV = Vbφ =

-

G …………………………..….(1.10) Ei (1 − SWC )

Expansion of the gas dVg (rcf) from initial reservoir pressure pi to any lower pressure p , at some future stage of depletion, is simply the notional expanded volume (rcf) of all the original gas at lower pressure less initial gas volume (rcf)

dVg =

G G − ………………………………………….(A) E Ei

where, G = Gas Initially In Place or GIIP (SCF).

Ei = Gas expansion factor at initial pressure pi (SCF/rcf). E = Gas expansion factor at any later stage of depletion (SCF/rcf).

-

Expansion connate water dVCW (rcf) from initial reservoir pressure pi to any lower pressure p , at some future stage of depletion, is therefore given by

dVCW = cWVW Δp = cW

G SWC Δp ……………..(B) Ei (1 − SWC )

where, cW = Isothermal compressibility of water (psi-1).

Δp = Pressure drop from pi to p (psi).

⎛ ⎞ G ⎜⎜ SWC ⎟⎟ = VW or connate water volume (rcf). ⎝ Ei (1 − SWC ) ⎠

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-

As pore pressure declines, overburden pressure remains constant and grain pressure increases; the result is a shrinkage in Pore Volume dV f (rcf). This “squeezing” of the PV has the same effect as expansion of pore fluids.

dV f = c f VPV Δp = c f

-

G Δp ……………..(C) Ei (1 − SWC )

Now the basis of the material balance is to equate this expansion of the pore fluid, and compression of pore volume, to cumulative production. Hence (A), (B), (C) must all appear on the RHS of material balance expression.

-

Notice dVg & dVCW & dV f must all be multiplied by the gas expansion factor E , in order to keep volumes in (SCF) throughout.

(SCF)

(SCF)

(SCF)

(SCF)

⎛G G ⎞ ⎛ ⎞ ⎛ ⎞ G G GP = ⎜⎜ − ⎟⎟ E + ⎜⎜ cW SWC Δp ⎟⎟ E + ⎜⎜ c f Δp ⎟⎟ E ⎝ E Ei ⎠ ⎝ Ei (1 − SWC ) ⎠ ⎝ Ei (1 − SWC ) ⎠

where, GP = Cumulative gas produced at the surface (SCF).

-

Re-arranging the above expression gives the usual form of the gas material balance equation assuming no natural water influx.

GP = G − G

NOTE -

E E ⎛ cW SWC + c f + G ⎜⎜ Ei Ei ⎝ (1 − SWC )

⎞ ⎟⎟Δp ………….….(1.11) ⎠

Above expression ignores water influx and therefore applies to a volumetric depletion-type reservoir with no pressure maintenance.

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-

Next take the more general case of natural water influx into the HCPV from an adjoining aquifer. The following small adjustments need to be made to our hydraulic model: -

A second “aquifer” chamber must be attached to the RHS of the “Reservoir” chamber. It contains water at the same pressure as the oil in the “reservoir”, but there is a partially closed valve between them.

-

As the piston rises on LHS (production), expansion of the oil takes place as before. However, now water enters the “reservoir” chamber through the partially closed valve from the “aquifer” chamber.

-

Hence, an extra “expansion” term needs to be added to the RHS of the material balance equation to account for the expansion of the aquifer fluid. The last term on RHS takes below care of this natural water influx term:

⎛G G ⎞ ⎛ ⎞ ⎛ ⎞ G G GP = ⎜⎜ − ⎟⎟ E + ⎜⎜ cW Δp ⎟⎟ E + (5.615 × We )E SWC Δp ⎟⎟ E + ⎜⎜ c f ⎝ E Ei ⎠ ⎝ Ei (1 − SWC ) ⎠ ⎝ Ei (1 − SWC ) ⎠

where, We = Cumulative water influx into HCPV (rb). 5.615 = Conversion factor (rcf/rb)

-

And re-arranging the above expression as before leads to the general Schilthuis form of the Gas Material Balance equation, which includes water influx:

⎞ ⎛ E E ⎜ cW SWC + c f 5.615 × We ⎟ GP = G − G + G ⎜ Δp + ⎟ G Ei Ei ⎜ (1 − SWC ) Ei ⎟⎠ ⎝

NOTE -

….(1.12)

Above expression applies to natural waterdrive gas reservoirs.

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-

A number of simplifications and re-arrangements are usually applied to the above general expression:

-

The connate water expansion and pore volume shrinkage term is usually negligible – often contributing around only 1% to the RHS of the material balance equation.

-

The exception is in shallow unconsolidated sands g where high formation compressibility, c f , can result from a compaction-drive mechanism.

-

Assuming that this term can be ignored then equation (1-12) reduces to, after some re-arrangement

⎞ ⎛ GP E ⎜ 5.615 × We ⎟ = 1 − ⎜1 − ⎟ G G Ei ⎜ Ei ⎟⎠ ⎝

-

……………….(1.13)

Substituting equation (1.9) into the above twice ( E and Ei ), then cancelling out common terms (reservoir always assumed isothermal), leads to

⎛ ⎜ G 1− P p pi ⎜ G = ⎜ 5 . 615 × We Z Zi ⎜ 1 − ⎜⎜ G Ei ⎝

NOTE -

⎞ ⎟ ⎟ ⎟ ⎟ ⎟⎟ ⎠

……………….(1.14)

The above two equations are the most commonly applied Gas Material Balance equations. They include natural water drive effects but exclude pore shrinkage and connate water expansion effects.

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1.6.2 -

Gas Material Balance – Havlena & Odeh Form

With the Schilthuis formulation of the gas material balance equation all the terms have units of (SCF). On the other hand, the Havlena & Odeh form applies to the same basic equation, but uses reservoir volumes (rcf) instead.

-

In the Schilthuis form, the We term is actually ( We − WP BW ) or net water influx; WP is cumulative volume of water produced at surface (STB) and BW is water

formation volume factor (rb/STB). In gas reservoirs, with little produced water, We is often close to ( We − WP BW ).

-

The basic Havlena & Odeh formulation is obtained from equation (1.12). The WP term is brought to the LHS, while the We term is kept on RHS

rcf

rcf

rcf

rcf

rcf

⎛ 1 1 ⎞ G ⎛ cW SWC + c f ⎞ GP + 5.615 × WP BW = G⎜⎜ − ⎟⎟ + ⎜⎜ Δp ⎟⎟ + 5.615 × We …..(A) E ⎝ E Ei ⎠ Ei ⎝ (1 − SWC ) ⎠

-

Next, Havlena & Odeh’s method involves defining the following groups:

F=

GP + 5.615 × WP BW = Production gas + water (rcf)……….(B) E

Eg =

1 1 = Expansion of gas (rcf/SCF)…………………..(C) − E Ei

E fW =

⎞ 1 ⎛ cW SWC + c f ⎜⎜ Δp ⎟⎟ = Expansion of connate water/shrinkage Ei ⎝ (1 − SWC ) ⎠ of pore volume (rcf/SCF)……(D)

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18 Rev 1.0

-

Substituting (B), (C) & (D) into (A) leads to basic Havlena & Odeh formulation

F = G (Eg + E fW ) + 5.615 × We

-

……….…..…(1.15)

Again E fW , for reasons already discussed, can often be neglected, leading to

5.615 × We F =G+ Eg Eg

NOTE -

………….………..…(1.16)

Both equation (1.16), Havlena & Odeh formulation, or equation (1.14), the Schilthuis formulation, can be used to represent productionpressure history in a graphical form.

-

Such plots serve three vital purposes. First, production-pressure data can be tested against particular assumptions, GIIP can be verified and checked against the value obtained from the Volumetric Method.

-

Second, the existence and strength of natural water drive can be verified. Moreover, models for We can be tested - “Aquifer fitting”.

-

Third, this independently verified value of G and “aquifer model” can now be raised to the status of known in the reservoir simulator. The simulator can then be used to “history match” other field unknowns.

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1.7 -

PLOTTING PRODUCTION DATA The gas material balance equation using the Schilthuis formulation (1.14), ignoring pore and connate water effects, but including natural water drive is

⎛ ⎜ G 1− P ⎜ p pi G = ⎜ Z Z i ⎜ 1 − 5.615 × We ⎜⎜ G Ei ⎝

-

⎞ ⎟ ⎟ ⎟ ………..………………….(1.14) ⎟ ⎟⎟ ⎠

If the gas reservoir was of a volumetric depletion type (1.14) becomes

p pi ⎛ GP ⎞ = ⎜1 − ⎟ …………………..……………….(1.17) Z Zi ⎝ G ⎠

1.7.1 -

P/Z Type Plot

Equation (1.17) shows that, for a volumetric depletion type reservoir, i.e. no water influx, a plot of p/Z versus GP must be a straight line as shown below:

⎛ pi ⎞ ⎜⎜ ⎟⎟ ⎝ Zi ⎠

* *

-

By examining (1.17), when cumulative production GP = 0 , then p / Z = pi / Z i .

-

As gas is produced, then p / Z vs GP production data must fall on a straight line.

-

If reservoir pressure could be depleted to zero then GP = G .

-

Hence G can be found by extrapolating production-pressure data to zero pressure.

Volumetric Depletion

* *

⎛ p⎞ ⎜ ⎟ ⎝Z⎠

*

0 0

Section 1 © Copyright: Thru-u.com Ltd 2000.

G

(GP )

20 Rev 1.0

-

The problem with the ( p / Z ) versus GP plot is that even when the reservoir has natural waterdrive, the production-pressure data can appear to plot up as a straight line: -

This is because initially We can be quite small. Hence, during this early period, data will only deviate slightly from a straight line.

-

Later the points only gradually deviate from a straight line, with the result that the engineer is often tempted to draw the best straight line through the points. The error only becomes noticeable only after several years.

-

Consider a p/Z versus GP plot for a natural waterdrive reservoir:

⎛ pi ⎞ ⎜⎜ ⎟⎟ ⎝ Zi ⎠

*

*

EXTRAPOLATION OF ALL AVAILABLE DATA.

* *

⎛ p⎞ ⎜ ⎟ ⎝Z⎠

-

Examining the production-pressure data points closely they are aligned on a slight “S” shape.

-

This is not immediately apparent if the axes are scaled as shown.

-

The solid line shows that after a couple years of production data the points appear to lie on a straight line. The value of GIIP = G′ .

* EXTRAPOLATION OF EARLY DATA ONLY.

obtained by the volumetric method. -

0 0

NOTE -

(GP )

G′ is usually much larger than the figure

G

G′

If the axes were scaled better, or the data was considered over a longer period of time, the non-linear nature of the plot becomes apparent.

Not only is GIIP ( G′ ) overstated, but also the reservoir drive is wrongly predicted to be a volumetric depletion type.

-

Notice, extrapolation of early data points only (dotted line) give a better valued for G , although it is still too high.

-

A more sensitive type of pressure-production plot is needed.

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1.7.2 -

Havlena & Odeh Type Plots

The basic expression on which the Havlena & Odeh plot is based is equation (1.16).

5.615 × We F =G+ ………………….………….…(1.16) Eg Eg

-

In analysing pressure-production data from a gas reservoir the first step should be to produce a plot of ( F / E g ) versus GP , as shown below:

-

If the gas reservoir is truly a volumetric depletion type, the data will plot as a horizontal straight line as shown. The intercept will be G .

-

Curve A is typical of a gas reservoir with a modest aquifer response.

-

Curve B is typical of gas reservoir with large aquifer response.

-

Curves A and B could be extrapolated back to find G on y-axis, but since curves are highly non-linear, this procedure is unreliable.

B

⎛ F ⎜ ⎜E ⎝ g

⎞ ⎟ ⎟ ⎠

A

G

Volumetric Depletion

0 0

-

(GP )

The purpose of this plot is to determine the reservoir drive mechanism: -

If production-pressure data plots as a straight line there is no waterdrive. Any deviation above the straight-line case indicates water influx.

-

The shape of the curve qualitatively indicates the strength of the aquifer.

-

However to find the correct model for We requires another plot.

Section 1 © Copyright: Thru-u.com Ltd 2000.

22 Rev 1.0

-

The next question, assuming the field has an active waterdrive, is to find an appropriate mathematical model for the aquifer. The Havlena & Odeh plot is shown below:

AQUIFER MODEL GIVING TOO LOW A VALUE FOR We.

-

( F / E g ) data is plotted versus (5.615 × We BW / Eg ) data.

AQUIFER MODEL OK

F Eg AQUIFER MODEL GIVING TOO HIGH A VALUE FOR We.

G

-

If a straight line is obtained of slope 45o, then the correct aquifer model has been applied.

-

The intercept of this straight line is GIIP, G .

-

Lines deviating above or below from this case indicate wrong aquifer model.

5.615 × We Eg

-

The procedure is to first assume a mathematical model for the aquifer; that is model predicts We as a function of pressure decline. Next, use productionpressure data from field observations to predict We from the assumed model. -

If above plot is non-linear then the assumed aquifer model is predicting the wrong value of We . The aquifer model is then altered in some way and another “history match” is attempted.

-

The process is repeated until the correct model is identified. That is the predicted production-pressure- We data falls on above straight line.

NOTE -

This “history matching” must be carried out under the guidance of geologists & petrophysicists; they will assist with a logical & scientific identification of the aquifer model’s geometry and properties.

Section 1 © Copyright: Thru-u.com Ltd 2000.

23 Rev 1.0

1.7.3 -

p/Z Plot for General Waterdrive Case

Equation (1.14) gives the general gas material balance for the waterdrive case. Obviously in the absence of water drive the denominator inside the brackets reduces to unity. In this case p/Z versus GP must plot as straight line.

⎛ ⎜ G 1− P ⎜ p pi G = ⎜ 5 . 615 × We Z Zi ⎜ 1 − ⎜⎜ G Ei ⎝

-

⎞ ⎟ ⎟ ⎟ ………..……………….….(1.14) ⎟ ⎟⎟ ⎠

For waterdrive the term after the minus sign on the denominator represents the fraction of the HCPV invaded by water. The term in parenthesis is then always bigger for the waterdrive case, than for the volumetric depletion case.

⎛ pi ⎞ ⎜⎜ ⎟⎟ ⎝ Zi ⎠

⎛ p⎞ ⎜ ⎟ ⎝Z⎠

1 2

The dotted line represents the no waterdrive case.

-

For waterdrive the pressure at a given GP must be higher than without waterdrive case.

-

Solid lines 1, 2, 3 represent increasing strength of aquifer.

-

Hence, aquifer 1>aquifer 2>aquifer 3.

3

⎛ p⎞ ⎜ ⎟ ⎝ Z ⎠ ABAN

(GP )ABAN

(GP )

-

-

For moderate aquifer responses (curves 2 and 3), GP at abandonment pressure increases as compared to the no waterdrive case.

Section 1 © Copyright: Thru-u.com Ltd 2000.

24 Rev 1.0

-

However, for strong aquifer case (case1), although the pressure in the reservoir is higher for given values of GP , nevertheless the ultimate recovery at abandonment is lower: Produce gas at as high a rate as possible, so that We is minimised.

Convert downdip gas producers to water production. This also minimises We. by siphoning off water to surface. NEW GWC

As water influx enters the reservoir there is a trapped residual gas saturation in the flooded portion of the reservoir; S gr ≈ 0.30 − 0.40 .

-

This residual gas saturation is immobile.

-

Abandonment does not now occur when pressure drops below sales contract level.

-

Abandonment occurs when water breakthrough occurs at crestal producing wells.

-

Recovery is limited because gas is trapped in flooded section at S gr and because part of the reservoir is unswept by water influx.

ORIGINAL GWC

-

-

The Sweep Efficiency EV , defined as the fraction of the Moveable Gas Volume that is contacted by water influx, is generally about 0.65 - 0.75 at abandonment. Both EV and ( p / Z ) ABAN versus GP relation are given below:

EV =

5.615 × We G (1 − S gr − SWC ) Ei (1 − SWC )

⎛ p⎞ ⎜ ⎟ ⎝ Z ⎠ ABAN

-

…………………..…(1.18)

⎛ ⎞ GP ⎜ ⎟ − 1 ⎟ pi ⎜ G = ⎜ ⎟ …………..….(1.19) Z i ⎜ ⎡ S gr 1 − EV ⎤ ⎟ + ⎥ ⎜ EV ⎢1 − S EV ⎦ ⎟⎠ WC ⎣ ⎝

Where the straight line, described by equation (1.19), intersects the non-linear pressure-production curve denotes “abandonment point”. A high gas offtake rate blows down pressure rapidly, limits We and trapped/by-passed gas.

Section 1 © Copyright: Thru-u.com Ltd 2000.

25 Rev 1.0

1.8 -

GAS PHYSICAL PROPERTIES The real gas law and the analytical expression for the gas expansion factor have already been discussed:

pV = ZnRT ................................................................(1.8)

E = 35.37

-

p ……….................................................(1.9) ZT

To use either of the above expressions the compressibility factor is needed at pressure p and temperature T . As we shall see Z is also a function of gas composition.

1.8.1 -

Compressibility Factor - Z

In most Reservoir Engineering problems the reservoir temperature T is constant. Hence, Z is needed as function of pressure and composition. There are three main ways of finding compressibility factor:

-

-

Experimental measurement.

-

From manual graphical correlation – knowing composition.

-

From computerised EOS correlation – knowing composition.

The laboratory method involves taking a gas sample and choosing suitable experimental equipment/methods so that equation (1.8) can be solved. In this way the isothermal Z vs. P relationship can be physically measured.

-

Although this experimental method is accurate, Z is more usually predicted from knowledge of gas composition. One of the most widely used manual method is the correlation by Standing & Katz.

Section 1 © Copyright: Thru-u.com Ltd 2000.

26 Rev 1.0

-

Standing & Katz correlation involves the following:

-

Obtain a sample of gas and analyse hydrocarbon and non-hydrocarbon components (often H2S , CO2 and N2). C7+ fraction is often found.

-

Correlation can also be used if only the gas gravity γ g is known.

-

Calculate psuedo-critical pressure p pc and the psuedo-critical temperature Tpc as follows: p pc = ∑ yi pci ……………………………....…(1.20) Tpc = ∑ yiTci ……………………………….....(1.21)

Note, yi is the gas phase mole fraction, pci the critical pressure and Tci

-

the critical temperature of component i .

-

Once the psuedo-critical properties of the mixture have been calculated from (1.20) and (1.21) the psuedo-reduced pressure p pr and pseudoreduced temperature Tpr are calculated from equations below:

-

p pr =

p ……………………………........…(1.22) p pc

Tpr =

T ………………………………..........(1.23) Tpc

Enter Standing & Katz correlation and determine Z . Note, p pr and Tpr can also be found from γ g - apply corrections for CO2 H2S & N2.

NOTE

-

If C7+ fraction has been found – its MW and γ g must be measured

Section 1 © Copyright: Thru-u.com Ltd 2000.

27 Rev 1.0

1.8.2 -

Gas Density and Gas Gravity

Density is mass divided by volume. The mass is simply the number of moles, n , times the molecular weight of the gas, MWg . The real gas law (1.8) gives

the volume. After cancelling out the number of moles, n , we get

ρg =

-

MWg × p ZRT

…………..…………….......(1.24)

The gas gravity, γ g , is the ratio of the density of the gas at p & T , to the density of air at the same p & T ; usually atmospheric pressure and 60oF are used for p & T . Hence, γ g (60/60, air = 1) is given by

MWg ⎛ρ ⎞ ………………….…….......(1.25) = γ g = ⎜⎜ g ⎟⎟ 28.97 ⎝ ρa ⎠ p, T

-

Where the factor (28.97) is the molecular weight of air. Equation (1.24) is used to find gas density at any temperature, pressure and composition as follows:

-

If the composition of the gas has been analysed then MWg is readily calculated from:

MWg = ∑ yi MWi

Section 1 © Copyright: Thru-u.com Ltd 2000.

28 Rev 1.0

-

Once MWg is known, then ρ g is recovered from (1.24) – notice Z can be found using Standing & Katz correlation. Consult the standard reference textbooks for these correlations.

-

Alternatively, if the gas gravity γ g has been measured, then MWg is first obtained from equation (1.25) and then ρ g from equation (1.24) – notice Z can be found from Standing & Katz by looking up p pr and Tpr if γ g is known. These charts are presented in the standard reference textbooks.

-

Remembering that the density of air at standard conditions is 0.0763 Ib/cu. ft, then the density of gas at standard conditions is simply

(ρ )

g SC

-

= 0.0763 × γ g ………………………………....(1.26)

To calculate the gas hydrostatic gradient (psi/ft) at any temperature and pressure, the starting point is to express the gas density in terms of the gas gravity. That is substitute equation (1.25) into equation (1.24)

ρg =

-

28.97 × γ g × p ZRT

…………..……………..……....(1.27)

If standard field units are used, then substitute R = 10.73 (ft3)(psia)/(Ib-mol)(R) into denominator, and recognising that, in order to change (Ib/cu ft) into (psi/ft), then equation (1.27) needs additionally to be divided by 144, giving

0.01875 × γ g × p ⎛ dp ⎞ ⎟ = ⎜ ZT ⎝ dD ⎠ g

Section 1 © Copyright: Thru-u.com Ltd 2000.

…………..…..(1.28)

29 Rev 1.0

1.8.3 -

Coefficient of Isothermal Compressibility

The definition of the coefficient of isothermal compressibility was given earlier by equation (1.5). The real gas law, i.e. equation (1.8), is stated as

ZnRT p

V =

-

The partial derivative can be obtained by differentiating the above expression

⎛ ∂V ⎜⎜ ⎝ ∂p

-

⎞ ⎛ Z 1 ∂Z ⎞ ⎟⎟ = nRT ⎜⎜ − 2 + ⎟ p ∂p ⎟⎠ ⎠T ⎝ p

Substituting real gas law and above expression into equation (1.5), then cancelling common terms gives

cg =

-

1 1 ∂Z − p Z ∂p

At reservoir temperatures the partial derivative ( ∂Z / ∂p ) tends to be so small that, as a first approximation, it can be ignored. Hence, we get

cg ≈

1 p

…………….…………………(1.29)

where, C g = Isothermal compressibility of the gas (psia)-1. Not to be confused with Z , which is the gas compressibility factor.

Section 1 © Copyright: Thru-u.com Ltd 2000.

30 Rev 1.0

1.9 -

GAS CONDENSATION Everything discussed so far assumes that the gas produced is dry within the reservoir and dry at the surface. Dry in this context does not refer to water but implies an absence of liquid hydrocarbons.

-

Consider a typical p − T diagram for hydrocarbon gas; remember the gas is a mixture of several individual components and so a two-phase envelope will be produced:

Critical Point

-

The BPC is 100% liquid. First bubble of vapour formed just inside envelope.

-

The DPC is 0% liquid. First drop of liquid formed just inside envelope.

-

Critical Point is where BPC and DPC meet.

-

Note lines of constant liquid 0% - 100%.

-

CT is Cricondentherm. Above this temperature twophase behaviour is impossible.

A

p LIQUID Bubble Point Curve

100

CT

75 50

25

0

GAS Dew Point Curve

TR

T

-

Reservoir temperature is TR and reservoir pressure is initially at point “A”. As pressure falls, it does so isothermally - along the dotted line. This line is to the right of the Cricondentherm and the two-phase envelope.

NOTE -

This type of reservoir is called a dry gas reservoir. That is, there is no deposition of liquid hydrocarbons, condensate, within the reservoir itself.

Section 1 © Copyright: Thru-u.com Ltd 2000.

31 Rev 1.0

1.9.1 -

Dry Gas Reservoirs – Surface Condensate

Consider the same situation as before, i.e. a dry gas reservoir “A”. However, now the surface separator is operating at point “S” as shown in p − T diagram below:

-

If reservoir conditions are initially at “A” then as pressure falls no liquid drop out will occur within reservoir.

-

However, for separator conditions at “S” condensate liquid will drop out in the surface separator.

-

Such surface condensate normally occurs in most dry gas reservoirs.

p

A LIQUID

S GAS T

-

All the equations derived thus far assume dry gas in the reservoir and dry gas in surface separation equipment.

-

The question is how do we include the liquid condensate volumes produced at the surface into the gas material balance equation?

-

The answer is first to convert daily liquid condensate collected at the surface, ΔN P , which is usually expressed in STB, into Ib-moles of liquid ( n )

n=

ΔN P × 5.615 × γ o × 62.43 .........................................(A) MWo

Section 1 © Copyright: Thru-u.com Ltd 2000.

32 Rev 1.0

-

Mass conservation requires that Ib-moles of liquid at the surface be equal to Ibmoles of gas in the reservoir. Then simply convert this Ib-moles of gas at reservoir conditions into SCF of gas at surface conditions, ΔGP

n=

-

ΔGP × pS ΔGP × 14.7 = = 0.002635 × ΔGP ........…..(B) RTS 10.73 × 520

Equating the above two equations and solving for ΔGP leads to

0.002635 × ΔGP =

ΔN P × 5.615 × γ o × 62.43 MWo

∴ ΔGP = 1.33 × 105 ×

ΔN P × γ o MWo

................….(1.30)

where, ΔGP = Gas equivalent to surface liquid condensate (SCF). ΔN P = Liquid condensate collected at surface (STB).

γ o = Liquid condensate gravity ( γ =1.00 water). MWo = Liquid condensate molecular weight (lbs/Ib-mol).

NOTE -

The above quantity ΔGP is added to the actual cumulative gas produced GP .

-

The same gas material balance equations can then be used as if all the gas in the reservoir appeared as only as dry gas at the surface.

Section 1 © Copyright: Thru-u.com Ltd 2000.

33 Rev 1.0

1.9.2 -

Gas Condensate Reservoirs

If reservoir conditions are such that the gas in the reservoir is initially at point “B” then, as pressure declines isothermally, conditions in the reservoir eventually enter two-phase region:

-

B p

In the case of a dry gas reservoir, the temperature in the reservoir exceeds the cricondentherm. - As pressure declines no phase change occurs within reservoir fluid.

CP -

In the case of a gas condensate reservoir, the reservoir temperature is between the critical temperature and the cricondentherm. - As pressure declines reservoir fluid eventually reaches dew-point pressure.

-

T

-

The liquid volume deposited in reservoir is small so that it is usually immobile. Hence, this valuable liquid hydrocarbon remains trapped in reservoir pore volume.

Such a reservoir is called a Gas Condensate reservoir. As the pressure decreases within two-phase region, there is an increase in percentage liquid; a phenomenon called Retrograde Condensation.

-

The dry gas material balance equation can be used in this case

⎛ ⎜ G 1− P ⎜ p pi G = ⎜ 5 . 615 × We Z Zi ⎜ 1 − ⎜⎜ G Ei ⎝

NOTE -

⎞ ⎟ ⎟ ⎟ ………..…………………(1.14) ⎟ ⎟⎟ ⎠

Two-phase Z-factor, determined experimentally in transparent gas condensate p − v − T studies, must be used in above equation.

Section 1 © Copyright: Thru-u.com Ltd 2000.

34 Rev 1.0

1.9.3 -

Dry Gas Recycling

Dry gas recycling is an elegant way of recovering valuable liquid condensates at the surface, by preventing them from being deposited & trapped in the reservoir.

Wet Gas Produced for Surface Separation.

-

Recovered Condensate to Stock Tank.

Dry Gas Reinjected after Condensate Removal.

-

Wet gas is produced to surface and separated.

-

Valuable liquid condensate is recovered to Stock Tank.

-

Dry gas is separated and reinjected into reservoir.

-

Reservoir pressure is maintained above the dew-point pressure.

-

Hence, no liquid condensate in reservoir pore volume.

-

Once dry gas breakthrough into production well, reinjection is stopped and reservoir is depleted as in dry gas case.

Hence, gas condensate is produced and recovered at the surface. Once all the “wet” gas is swept out, re-injection is stopped and dry gas is produced in the normal way. This is called dry-gas recycling.

B p

Maintain reservoir pressure above the dew point pressure during re-injection phase.

-

Stop re-injection once dry gas breakthrough occurs; pressure then falls along dotted line.

-

The two-phase envelope is shifted to the left (condensates extracted).

-

So temperature now is greater than cricondentherm.

CP Dew Point Pressure

T

NOTE -

-

Treat this as dry gas reservoir and calculate ΔGP during recycling phase.

Section 1 © Copyright: Thru-u.com Ltd 2000.

35 Rev 1.0