Reservoir Formation Damage Episode 2 Part 8 doc

Table 14-5 Conditions of Core Flood Tests*0.30 0.21 0.34 1.0 0.48 - Deposition profile inlet -» outlet Uniform Uniform Decreasing Decreasing Decreasing - Decreasing Near core inlet accum

O BEREA SANDSTONE O100 MESH)

A DICKITE (WISCONSIN)

D DOLOMITE (DOLOCRON) OTTAWA SAND (SUPER X >325 MESH)

O CALCtTE (DOVER CHALK)

• KAOLIN MINERAL

• (LUTE (BEAVER'S BEND)

O ALUMINA

EQUILIBRIUM ASPHALTENE CONCENTRATION, ppm —•>

Figure 14-33 Adsorption isotherms for asphaltenes on clay and mineral

surfaces from toluene (Dubey and Waxman, ©1991 SPE; reprinted by mission of the Society of Petroleum Engineers)

per-Then, assuming that all oil is in contact with the porous media, the surface

excess of species i can be expressed as:

nf = n f (xl — ;c(.) : i = asphaltene or oil (14-8)They assume that the theory is applicable for both mono- and multi-layeradsorption

A balance of the oil and asphaltene adsorbed over the pore surface yields:1

0 500 1000 1500 2000 2500

A8PHALT6NE EQUILIBRIUM CONCENTRATION, ppm —*•

Figure 14-34 Hysteresis of adsorption/desorption isotherms for asphaltenes

on kaolin from toluene (Dubey and Waxman, ©1991 SPE; reprinted bypermission of the Society of Petroleum Engineers)

300 600 900 1200 Equilibrium concentration of asphaltenes (mg/1)

3000

Figure 14-35 Adsorption isotherm for Cerro Negro asphaltenes on inorganic

material surface from toluene at 26°C (reprinted from Journal of Fuel, Vol.

74, Acevedo, S., Ranaudo, M A., Escobar, G., Gutierrez, L, & Ortega, P.,

"Adsorption of Asphaltenes and Resins on Organic and Inorganic Substratesand Their Correlation with Precipitation Problems in Production Well Tubing,"

pp 595-598, ©1995, with permission from Elsevier Science)

400 600 800 1000 1200 MOO 1600 1800 2000 2200 2400 2600Equilibrium concentration of uphaitenes (mg/L)

Figure 14-36 Adsorption isotherm for Ceuta asphaltenes on inorganic material

surface from toluene at 26°C (reprinted from Journal of Fuel, Vol 74,

Acevedo, S., Ranaudo, M A., Escobar, G., Gutierrez, L, & Ortega, P.,

"Adsorption of Asphaltenes and Resins on Organic and Inorganic Substratesand Their Correlation with Precipitation Problems in Production Well Tubing,"

pp 595-598, ©1995, with permission from Elsevier Science)

In Eq 14-9, m l and ra2 denote the monolayer coverage of asphalteneand carrier oil, respectively, expressed as mass of species adsorbed perunit mass of porous solid Then, a selectivity parameter, as defined below,

As a result, the rates of adsorption or desorption are expressed

accord-ing to:

dt - n : j ' = adsorption , desorption (14-13)

where n\ and n{ a denote the amount of species 1 (asphaltene) adsorbed/desorbed and the actual surface excess of species 1 per unit mass ofporous formation The initial condition is given as:

n ea _ ea t — f\

Empirical Algebraic Model for Formation Damage

by Asphaltene Precipitation in Single Phase

Minssieux (1997) has demonstrated that the predominant mechanisms

of the asphaltene deposition can be identified by means of the Wojtanowicz

et al (1987, 1988) analytic models He also observed that the asphalteneprecipitates existing in the injected oil can pass into porous media withoutforming an external filtercake

The characteristics of the oils used are given in Tables 14-2 and14-3, and the conditions and results of the coreflood experiments aregiven in Tables 14-4 and 14-5 by Minssieux (1997) The analyses oftypical data according to Wojtanowicz et al (1987, 1988) formulae aregiven in Figures 14-37 and 14-38 by Minssieux (1997) Figure 14-37

Table 14-2 Characteristics of Stock Tank Oils*

«a

50 80 119 81

S Sat

5 Asph.

5.3 4

0.15

14

Res/Asph ratio

1.6 1.9 22 2.4

Viscosity (cP 20°)

13 7.7 1.5 (80°)

"API

29 43 43 10

* Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers

Table 14-3 Characteristics of Crude and Asphaltenes*

4

0.15

10.7

Average MW (vpo/toluene) 6000

1.00

0.88

1.14

phaltenes anal) O/C 0.025

50

80 50 80 80

id.

H Messaoud Weyburn

Weyburn

Lagrave Weyburn Lagrave

13.6 13.7

8 24.7

24.3

26 22.6

6 29

12.2

73 15.2

1.1 2

0.67

Injection rate (cm 3 /hour)

50 80 10 10 20 50 80 10 10

10 5 10 10

10 5 5

8

* Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers

Table 14-5 Conditions of Core Flood Tests*

0.30 0.21 0.34

1.0 0.48 -

Deposition profile inlet -» outlet

Uniform Uniform Decreasing

Decreasing Decreasing -

Decreasing Near core inlet accumulation

Decreasing

Uniform

Uniform

K reduction (%) after 50 PV 20 42.5 58.5 0

47 after 150 PV

88 89

Palatinat sandstone (Kaolinite) crude injected with additive

Reservoir-rock core samples from H.MD field

* Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers

shows the results of the analysis of the GF3 test data considering thepossibility of the gradual surface deposition, single pore plugging, andin-situ cake formation by pore filling mechanisms in formation damage

As can be seen, only the ^K/K 0 vs PV (pore volume) data yields a straight

line plot, indicating that the damage mechanism is the gradual surfacedeposition In the case of the GV5 data, Figure 14-38 indicates that thedamage mechanism is the in-situ cake formation by pore filling, because

KQ/K vs PV data yields a straight line plot for this case (see Table 10-1).

40 50

CRUDE PV INJECTED

Figure 14-37 Correlation of the experimental permeability reduction data

reveals a uniform surface deposition mechanism (Minssieux, ©1997 SPE;reprinted by permission of the Society of Petroleum Engineers)

30 40

CRUDE PV INJECTED

Figure 14-38 Correlation of the experimental permeability reduction data

reveals a pore blocking deposition mechanism (Minssieux, ©1997 SPE;reprinted by permission of the Society of Petroleum Engineers)

Simplified Analytic Model for Asphaltene-Induced

Formation Damage in Single-Phase

Leontaritis (1998) developed a simplified model for prediction offormation damage and productivity decline by asphaltene deposition inunder-saturated (above bubble-point pressure) asphaltenic oil reservoirs.This model consists of a set of algebraic equations In this section, theLeontaritis model is presented with some modifications for consistencywith the rest of the presentation of this chapter

As schematically shown in Figure 14-39, for analysis, Leontaritis(1998) considers the portion of the reservoir defined by the radius ofdrainage of a production well In this region, the flow is assumed radial.Figure 14-40 schematically depicts the variation of the flowing bottomhole pressure during constant rate production, while the external reservoirpressure and the onset of the asphaltene flocculation pressure remain constant.The calculational steps of this model are described briefly in the following

Step 1 The initiation time for asphaltene precipitation is referred to as

zero (i.e., ? = 0) Given the well productivity index, PI, the flowing bottom hole pressure, p w [=Q, prior to asphaltene damage is calculatedfrom the definition of the productivity index:

The asphaltene deposition is assumed to occur within the near wellbore

region, r w <r<r AF , where the pressure is below the asphaltene

floccula-tion pressure, p AF The radius of this region, r AF , is determined by Eq.

14-16 for p = p AF , according to Figure 14-41 Leontaritis (1998) assumes

that the pressure beyond this region (i.e., r AF <r<r e } is not influenced

by asphaltene deposition in the near wellbore region

The region r w < r < r AF is divided into a number of sections of finite width

Ar Steps 2 and 3 calculations are carried out over each Ar segment for atime increment by A?, consecutively, as described in the following

Figure 14-39 Producing reservoir drainage area (modified after Leontaritis,

Figure 14-40 Variation of the flowing bottom hole pressure during constant

rate production (modified after Leontaritis, 1998)

Reservoir radial drainage area

•w

Enlarged section of

a hydraulic tube

rAF

•*

Asphaltene region

No deposition region

Figure 14-41 Asphaltene deposition induced formation damage in the

near-wellbore region (modified after Leontaritis, 1998)

Step 2 Similar to Wojtanowicz et al (1987, 1988), Leontaritis considers

the porous media as a bundle of tortuous flow tubes Thus, the meanhydraulic diameter is estimated by the ratio of the total pore volume tothe total pore surface area of the flow channels according to:

ALcj)

where A, L, and <|> denote the cross-sectional area, length, and porosity

of a core plug, and A g and V g are the mean surface area and the meanvolume of the porous media grains If the mean, spherical grain diameter

is denoted by d , then Eq 14-17 can be expressed as:

Next, the tube size distribution function, f(D A ), the mole fraction, X A , and molar volume, V A , of the flocculated asphaltenes, and the moles of

reservoir fluid, m RF , at the prevailing pressure and temperature conditions

within the near wellbore region are determined according to Leontaritis(1997) Figure 14-42 shows a typical asphaltene particle size distribution

Figure 14-42 Asphaltene particle size distribution (after Leontaritis, ©1998

SPE, reprinted by permission of the Society of Petroleum Engineers)

Leontaritis (1998) assumes that permeability impairment primarilyoccurs by pore throat plugging and generalizes the one-third rule-of-thumb

of filtration as the particles larger than a certain fraction of the pore size

cannot penetrate a filter, and determines the fraction of the particles, f trap ,

which are captured and deposited at the pore throats Thus, the thumb for trapment of particles at the pore throats is generalized toestimate the critical particle diameter for plugging as a fraction of thehydraulic tube diameter as:

/,= J f(D A )dD A

(14-20)

Step 3 The incremental moles of asphaltene particles trapped and the

incremental flow area closed within the A? time interval are estimated,respectively, by:

where D A is the mean diameter of the asphaltene particles retained, p is

an empirical factor accounting for the plugging by asphaltene particles

Therefore, combining Eqs 14-20 through 23 over a number of N

consecutive, discrete time steps, Af, the cumulative flow area closed toflow by pore throat plugging is estimated by:

(14-24)

where y = 6p/oc is a combined constant

Hence, the area open to flow during damage is given by:

in which the productivity index is defined by:

Step 4 When Steps 2 and 3 over all the Ar segments are completed,

the pressure loss by skin and the skin factor are calculated as following.Note that the drawdown pressure is given during damage as:

J7M

(14-36)

where s is the van Everdingen-Hurst skin factor Thus, the loss of the

pressure by the skin effect is given by:

(14-37)

Consequently, comparing Eqs 14-16 and 36 in view of Eq 14-37 yields:

Once the pressure loss by skin is calculated by Eq 14-38, the skin factorcan then be calculated by Eq 14-37

Step 5 Another time increment, At, is taken and Steps 2-4 are repeated

until either the final time considered for the calculation is reached or theflow rate of production can no longer be kept constant, which is thecondition imposed for the above described model

Leontaritis considers that a steady-state is attained when the depositionand erosion rates equal Then, the asphaltene deposition stops and the areaopen to flow attains a certain minimum limit value Because of the lack

of a better asphaltene erosion theory, Leontaritis assumes that the area

of flow can be empirically expressed as some fraction of the initial area.His equation can be expressed in terms of Eq 14-31 as:

0<b<\ However, there is no clear evidence of the use of Eqs 14-39

through 41 in his calculational procedure

Using the data given in Figures 14-42 and 14-43 with this model,Leontaritis (1998) obtained the results presented in Figures 14-44 through14-47

Plugging-Nonplugging Pathways Model

for Asphaltene Deposition in Single-Phase

Ali and Islam (1997, 1998) considered only asphaltene deposition andresorted to a simplified, single phase formation damage modeling approachaccording to Gruesbeck and Collins (1982) Here, their model is presented

in a manner consistent with the rest of the presentation of this chapter.Also, a few missing equations are supplied Note that this model appliesfor undersaturated oils

The rate of deposition in the plugging paths is given by:

(14-42)

(text continued on page 424)

Reservoir Ten perature, 250.0

'Bubble Point'Lower Onset

Upper Onset

Figure 14-43 Asphaltene deposition envelope for an AsphWax Oil Company

reservoir oil (after Leontaritis, ©1998 SPE; reprinted by permission of theSociety of Petroleum Engineers)

9000 8800

7400

2.5 4.5Radial Distance, feet

Figure 14-44 Variation of pressure profile in the asphaltene-damaged region

(after Leontaritis, ©1998 SPE; reprinted by permission of the Society ofPetroleum Engineers)

2.5 4.5Radial Distance, feet+ at 0.0 Hrs

Figure 14-45 Variation of permeability profile in the asphaltene-damaged

region (after Leontaritis, ©1998 SPE; reprinted by permission of the Society

of Petroleum Engineers)

oI

I

2.5 4.5Radial Distance, feet

Figure 14-46 Variation of porosity profile in the asphaltene-damaged region

(after Leontaritis, ©1998 SPE; reprinted by permission of the Society ofPetroleum Engineers)

Steady s :ate flow is ac helved

0.0

20.0 40.0Time, Hrs

60.0

Figure 14-47 Variation of skin factor by asphaltene-induced damaged (after

Leontaritis, ©1998 SPE; reprinted by permission of the Society of Petroleum Engineers).

(text continued from page 421)

(14-46)(14-47)

(14-48)

Note that Ali and Islam (1997, 1998) used the original Gruesbeck and

Collins (1982) equation, which misses the f p and f np terms in Eq 14-48instead of the corrected Eq 14-48 given independently by Civan (1992)and Schechter (1992)

The flow in the nonplugging pathways is given by:

(14-49)

'np np

(14-50)

Following Gruesbeck and Collins (1982), Ali and Islam (1997) assumed

f p and f np as some characteristic values of the porous medium anddetermined them to match the model predictions to experimental data.The permeability impairments in the plugging and nonplugging path-ways were represented by the Gruesbeck and Collins (1982) empiricalexpressions, given, respectively, by:

where K po and K npo denote the permeabilities of the plugging andnonplugging pathways before damage, and oc and |3 are some adjust-able constants

Ali and Islam (1997) assumed the same concentrations in the pluggingand nonplugging pathways Thus, the mass balance of the suspendedparticles of asphaltene in the flowing fluid can be expressed as (Civan,

The mass rate of asphaltene particles added to phase L is given by:

=-p

where e p and e^ denote the retention by filtration and adsorption,respectively The formulation by Ali and Islam (1997) implies that theyexpressed the dispersion coefficient as a linear function of the interstitialvelocity of the fluid:

It can be shown that Eq 14-58 can be reformulated in the form given

by Ali and Islam (1997) However, the last term in their equation appears

to probably have a typographical error, because o in their equation should

be replaced by 3a/3r The same error has been repeated by Ali andIslam (1998)

The initial and boundary conditions for Eq 14-58 are given by:

iw P,L

(14-60)