An Approach To Predict Tarmat Breakdown in Minagish Reservoir in Kuwait Mohammed El-Sayed Osman, * SPE, Kuwait Oil Co. (KSC)

Summary

The Minagish oolite reservoir, Minagish field, Kuwait, is characterized by the presence of tarmat at the oil/water contact (OWC), so a waterflooding project was planned for the reservoir. This paper discusses the possibility of tarmat breakdown by injection of water below it. The differential pressure at the tarmat resulted mainly from water injection, and this differential pressure, a result of oil production, was negligible. This paper presents a tech­nique to predict tarmat breakdown time, response time at the nearest producer or observation well, and the time when water injection should be switched from below the tarmat to above it. Also, this technique can be used to predict the differential pressure at tarmat anywhere in the reservoir.

Introduction Asphaltic deposits and tarmats have been recognized for many years. 1-3 Tarmats normally occur near the base of oil accumulation or near the surface as oil seeps.4 Several recent geochemical studies 5 indicate that tarmats formed as a result of one or more of the following mechanisms: (1) gravitational segregation that caused the hydrocarbon fractions to stratify with the lighter petroleum at the top of the reservoir and the heavier at the base: (2) natural deasphalting where natural, buoyant gases from the source rock entered the pool and rose through the hydrocarbon column, lowering the solubility of the asphaltic fraction, which would consequently precipitate and fall to the base of the reservoir; and (3) water washing, the movement of undersaturated water that removed a portion of light hydrocarbons, leaving asphaltic fractions at the base of oil accumulation. The moving water might have carried bacteria that selectively metabolized the lighter fractions of crude oil. This might have caused a tarmat to form.

One oil reservoir with tarmat is the Minagish oolite reservoir. It is located in the west central portion of Kuwait, as shown in Fig. 1. The presence of tarmat was indicated by samples, cores, and logs that were obtained from several wells drilled in the reservoir. The mobility of the tar was almost zero. It created a zone that isolated the reservoir from its aquifer. The aquifer was a good size. The reservoir, however, resembled a depleted-drive type. Thus, a gas-injection project was begun in 1967 to maintain reservoir pressure. Since 1971, the reservoir pressure has remained about 4,200 psig [29 MPa] without any decline.

'Now at the U. of United Arab Emirates.

Copyright 1985 Society of Petroleum Engineers

NOVEMBER 1985

Pressure surveys of different wells indicated pressure support at different locations in the reservoir. Moreover, we interpreted the rapid pressure decline (450 psi [3.1 MPa]) at initial production followed by a steady pressure buildup after field shut-in as a result of breakdown in the tarmat. Both conventional and simulation studies were per­formed on the reservoir. It was impossible to explain the reservoir's behavior without considering tarmat break­down in certain locations in the reservoir.

A plan to waterflood the reservoir was enacted. The main objectives of injecting water below the tarmat were to recover some of the heavy oil (tarmat) and to increase the communication between the aquifer and the reservoir, and, consequently, to use its energy in producing the reservoir.

This paper discusses tarmat breakdown after water is injected and the duration of that injection.

MOdel Description For the purpose of this study, the Minagish oolite reser­voir was divided into five layers on the basis of permea­bility. Tarmat was present at the OWe. It acted as a complete barrier between the aquifer and the reservoir. Its thickness varied from 30 to 115 ft [9.14 to 35.1 m]. We planned to waterflood the reservoir in a peripheral flood pattern. To predict the full-scale flooding perform­ance, two waterflooding pilots were chosen-one in the north and the other in the south. The northern pilot injec­tor was located in the reservoir where the tarmat was rela­tively thick, and the southern one was located where the tarmat was relatively thin. The results of the two pilots would indicate whether to inject water above and/or be­low the tarmat throughout the rest of the reservoir. Fur­thermore, the decision had to be economically feasible. Data from the northern Pilot Injector MN-26 were used in this study. Fig. 2 presents a structural cross section of the MN-26 injector and the tarmat. The average rock properties are indicated on the figure. Clearly, Layer 3 is the thickest and most permeable layer. Data from Producer MN-4 (shown in Table 1) were used to study. the effect of oil production on the differential pressure at the tarmat.

The following assumptions were used in this study. 1. The reservoir and its aquifer behave as an infinite­

acting reservoir. This is necessary to validate the solu­tion of the diffusivity equation presented later.

2. The tarmat is a complete barrier between the reser­voir and its aquifer until it breaks down. Also, differen­tial pressure across the tarmat at the start of water injection

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TABLE 1-AVERAGE PROPERTIES OF ROCKS AT MN·4

Layer Thickness Permeability Number (ft) (md)

1 75 292 2 80 348 3 137 877 4 75 29 5 50 1.5

Ekh = 172.139 md-ft. Et/>h= 87.09 ft.

KUWAIT

Porosity (fraction)

0.18 0.24 0.22 0.21 0.17

ARABIAN GULF

Fig. 1-Location map of Minagish field.

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rla TARMAT

is neglected. Therefore, conservative predictions are ob­tained.

3. The pressure buildup in the reservoir at the tannat resulting from water entering the reservoir after the tar­mat breakdown is equal to the pressure drop in the reser­voir at the tarmat resulting from oil production.

The solution of the diffusivity equation is used to cal­culate the differential pressure at the tarmat resulting from both water injection and oil production.

The diffusivity equation is written as 7

Considering the tannat as a complete barrier, the super­position technique in space was applied to Eq. 1 to ob­tain Eqs. 2 through 5 to calculate differential pressure at the tannat:

141.2 B-xIL-xq-x /l.p=2 PD. . ................. (2)

k-xh

PD=-V2Ei( -:r:D) . ..................... (3)

O.OOO2637k-x tD = 2 t. . ...................... (4)

cecblL-Xrw

d rD=- . ................................ (5)

rw

To study the effect of oil production and water injec­tion on the differential pressure at the tarmat, initial cal­culations were made at two different points on the tarmat: at d=r w from MN-26 and at d=4,OOO ft [1219 m] (about

~ INJECTOR MN-26

4.1·

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Fig. 2-Structural cross section of northern Pilot Injector MN·26 (not to scale).

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half the distance on the tarmat to be covered by each in­jector). In these calculations, the MN-4 production rate of 6,000 STEID [954 stock-tank m3 /d] and the MN-26 injection rate of 30,000 BID [4770 m 3 / d] water were assumed. To have a valid comparison between the effects of water injection and oil production on the differential pressure across the tarmat, it was assumed that water in­jection into MN-26 and oil production from MN-4 should start at the same time and continue at constant rates. Oil production, however, could have been started long be­fore that time because the effect of such long production on differential pressure across the tarmat was assumed to be negligible. An engineer may take this into account when estimating the differential pressure required to break the tarmat (L1Pb)' Some average rock and fluid proper­ties that were used in this paper are listed in Table 2. Differential pressures at the tarmat resulting from oil pro­duction from MN-4 and water injection into MN-26 are presented in Table 3. It shows that the differential pres­sure at the tarmat resulting from oil production from MN-4 is negligible compared with that resulting from water injection into MN-26. The remainder of this paper will concentrate on the effect of water injection on the differential pressure at the tarmat.

The calculations were extended to cover wide ranges of time and injection rates. The results are shown in Fig. 3. The figure presents a family of curves of differential pressure resulting from water injection vs. injection time for different values of injection rates. Because the tarmat thickness (and, consequently, its breakdown differential pressure) at the injector and the expected injection rate were known, the duration of the injection required to break the tarmat could be determined. Thus a decision whether to inject above or below the tarmat based on the economical advantages could be made.

Response Time The response time is defined as the time at which the ef­fect of water injection on bottomhole pressure of the nearest producer or observation well is felt. The super­position technique in both time and space is applied to Eqs. 1,3, and 4. We assumed that thej", of the injected water entered the reservoir after tarmat breakdown. The logical value for j", is 0.5 in absence of data that would support any other values. Then the equation was manipu­lated to obtain a set of expressions for response time:

...... (6)

It should be noted that oil properties are used in Eqs. 6 and 7 assuming that, by the time of response, water ad­vance in the reservoir is negligible.

Time To Inject Above Tarmat Assuming that the tarmat would break down by time t b ,

additional time would be required to sweep the oil in the ring between the top surface and a plane passing by the injector of interest and parallel to the tarmat location with-

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TABLE 2-AVERAGE ROCK AND FLUID PROPERTIES

Water FVF, bbllSTB Water viSCOSity at reservoir conditions, cp Average water saturation in the reservoir Relative permeability to oil (at Sw =0.137) Oil viscosity at reservoir conditions, cp Oil FVF, bbl/STB Well bore radius, ft Relative permeability to water at residual

oil saturation Distance between MN-26 and MN-4, ft Average reservoir effective compressibility,

psi-' Average aquifer effective compressibility,

psi-'

1.029 0.48

0.137 1

0.97 1.47

0.2917

1 3,380

1.29x 10-5

5.6x10-6

TABLE 3-DIFFERENTIAL PRESSURE RESULTING FROM OIL PRODUCTION AND WATER INJECTION

Differential Pressure Differential Pressure at d=r w at d = 4,000 ft

Time t.pp t.pj t.pplt.pj t.pp t.p, t.pplt.pj (years) (psi) (psi) (%) (psi) (psi) (%) ---

1 28.4 905.6 3.1 20.7 174.4 11.9 2 33.2 922.2 3.6 25.6 201.0 12.7 3 36.1 947.8 3.8 28.4 218.3 13.0

... •• • f

- _: .... ".IItDrAYI

-~~------~u~------~ .. ~------~_~------~_. ---.-Fig. 3-Differential pressure vs. injection time for different

injection rates.

in the area of interest. The time that the oil in the ring would have been swept is given by

where V 0 is the oil volume to be displaced from the ring,

and t a is the cumulative time at which the injector should be recompleted in the oil zone to allow for water injec­tion above the tarmat.

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0_

0_ o.oa

i' o.oa

I 0.02<

oS 0.022 !§ a 0.020

~ 0.01'

i :::: ~ 0.012

= 0.010 a: i 0.001

0.001

0._

0.G02 0.0 L-______ ....L. _______ L-______ ..... ______ ~

0.01 0.1 10.0 100.0

Fig. 4-Differential pressure vs. injection time for different distances on the tarmat from the injector.

~p at Any Distance From the Injector Eqs. 2 through 5 were used to calculate the differential pressure at the tarmat resulting from water injection at any distance, d, from the injector. The results presented in Fig. 4 show a family of curves of differential pressure per barrel of injected water vs. injection time for differ­ent distances from the injector. Fig. 4 could be used to predict the differential pressure at the tarmat at any dis­tance from the injector. The main advantage of Fig. 4 is that it could be used with variable injection rates.

It should be noted that only a single water injector was considered in this study. For a multi well injection sys­tem, the superposition technique in space should be im­plemented to predict a particular injector's behavior.

The use of Fig. 3 for a constant injection rate is straight­forward. The following example shows how to use the chart presented in Fig. 4 for variable injection rates.

Let us assume that water is injected into the MN-26 with the following variable rates: 16,000 BID [2544 m3 /d) water for the first 0.5 year, 20,000 BID [3180 m3 /d] water for the next 0.5 year, and 25,000 B/D [3975 m3 /d] water to the end of the project. Assume that the average tarmat thickness around the injector is 50 ft [15.24 mI· Field pressure history shows that a differential pressure of 15 psi/ft [339 kPa/mj of tarmat thickness would be re­quired to break down tarmat anywhere in the reservoir. Thus a 750-psi [5. 17-MPa] pressure differential is need­ed to break the tarmat at this location. A more accurate figure could be obtained from laboratory experiments on cores taken from the tarmat zone. The average rock and fluid properties are given in Table 2. Assuming that i,,· is 0.5 and the pressure-gauge sensitivity ex is 10 psi [69 kPa], calculate (I) tarmat breakdown time, t,,; (2) response time at MN-4, t r; and (3) differential pressure on the tarmat at a distance, d, equal to 100 ft [30.5 m] from the injector MN-26 at time t h.

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Fig. 4 is used with superposition in time. A trial-and -error procedure should be followed. Assume t h and cal­culate t:.p. If t:.p = t:.p h =750 psi [5.17 MPa], t b assumed is correct. In this example, at t h = 1.3 years "assumed,"

t:.p=0.0305 x 1,600+0.0299 X4,OOO+0.0286

x5,ooo=750.6= t:.Ph'

Thus t h = 1.3 years. Eqs. 6 and 7 are solved to calculate response time, t r'

As the reservoir is stratified, k"h and cp/k" in the two equations were replaced by r.k"h and r.cphlr.k"h, respec­tively. From Eqs. 6 and 7, t r = 1.192 years.

By using Fig. 4 with superposition in time,

t:.p=0.015 x 1,600+0.0149 X4,ooo+0.137 x 5,000

=377.7 psi [2.6 MPa].

Thus breakable tarmat thickness at d= 100 ft [30.5 m] is about 25 ft [7.62 mI.

Conclusions

1. The differential pressure at the tarmat results main­ly from water injection rather than oil production. Thus tarmat breakage should not interfere with the oil produc­tion schedule. Figs. 3 and 4 were constructed on the ba­sis of this conclusion and are expected to give conservative answers.

2. This paper suggests a technique to predict breakdown time of the tarmat on water injection (with constant or variable rates) below the tarmat. Also, response time at the nearest observation well and time to switch injection from below the tarmat to above it were also considered. Thus a decision about whether to start the water injection in a particular injector above or below the tarmat could be based on economics.

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3. The differential pressure at the tarmat anywhere in the reservoir could also be predicted for both constant and variable injection rates. By knowing the thickness of tar­mat at a particular point in the reservoir, it is possible to predict tarmat breakage at that point at any time of water injection. For a multi well injection system, the superpo­sition technique in space should be applied for prediction of the tarmat behavior.

Nomenclature

A r = area of the ring around a particular injector sq ft [m 2 ]

Bx = FVF of liquid A, RB/STB [res m 3 /stock-tank m 3 ]

C e = effective compressibility, psi - 1 [kPa - 1 ]

d = distance from injector or producer to the tarmat, ft [m]

Ei = exponential integral defined by

-Ei( -x)= r e:u

du

x

E v = volumetric sweep efficiency fw = fraction of water injected entering the

reservoir after tarmat breakdown h = formation thickness, ft [m]

h t = average tarmat thickness, ft [m] kx = effective permeability to liquid A, md flp = pressure differential at the tarmat, psi [kPa)

flPb = breakdown differential pressure, psi [kPa] flp i = differential pressure at tarmat resulting

from water injection, psi [kPa) flPn = normalized differential pressure, psi/(BID)

[kPa/m 3 'd)] water flp p = differential pressure at tarmat resulting

from oil production, psi [kPa] P D = dimensionless pressure expressed by Eq. 3 qx = liquid rate (oil production or water

injection), STBID [stock-tank m 3 /d] r w = wellbore radius, ft [m) r D = dimensionless radius, d/ r w

S or = residual oil saturation Swi = average initial water saturation

t = time, hours t a = time of switching water injection from

below tarmat to above it, years tb = tarmat breakdown time. years t r = response time at nearest producer or

observation well, years t D = dimensionless time expressed by Eq. 4 Vo = oil volume to be displaced from ring ex­

pressed by Eq. 9, res bbl [res m 3)

Zr = average height of ring, ft [m] a = pressure-gauge sensitivity

/J- x = viscosity of liquid A, cp [Pa' s) cJ> = formation porosity

cJ> r = average porosity of ring

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Subscripts

o = oil w = water A = liquid (oil or water)

Acknowledgments The author wishes to express his appreciation to the management of the Kuwait Oil Co. and the Ministry of Oil of Kuwait State, who made it possible to publish this paper.

APPENDIX SI Metric Values for Key Equations

f1p= 1.866 x 103 BX/J-xqx PD' ............... (1) kxh

3 BX/J-xqx flp=2 x 1.866 x 10 PD. . ............ (2)

kxh

3.55XI0-6k x tD= t ....................... (4)

CecJ>/J-xr~

...... (6)

References I. Berger, W.P.: Facts about Oil. Oklahoma State U. Technology Ex­

tension, Stillwater, OK (1975). 2. Berger, W.P. and Anderson, K.E.: Modern Petroleum: A Basic

Primer of the Industry, Petroleum Publishing, Tulsa (1978). 3. Price, P.H.: "Evolution of Geologic Thought in Prospecting for

Oil and Natural Gas," Bull., AAPG (1947) 31,673-97. 4. Moore, L.V.: "Significance, Classification of Asphaltic Material

in Petroleum Exploration," Oil and Gas 1. (Oct. 8, 1984) 109-12. 5. Hunt, LM.: Petroleum Geochemistry and Geology, W.H. Free­

man & Co., San Francisco (1979). 6. Gussow, W.C.: "Differential Entrapment of Oil and Gas: A Fun­

damental Principle," Bull., AAPG (1954) 38,816-53. 7. Earlougher, R.C. Jr.: Advances in Well Test Analvsis. Monograph

Series, SPE, Richardson, TX (1977) 5.

SI Metric Conversion Factors

bbl x 1.589 873 E-Ol m3

cp x 1.0* E-03 Pa's ft x 3.048* E-Ol m

psi x 6.894757 E+OO kPa

• Conversion factor is exact. JPT Original manuscript received in the Society of Petroteum Engineers office Dec. 29, 1982. Paper accepted for publication June 27, 1985. Revised manuscript received May 20.1985. Paper (SPE 11492) first presented at the 1983 SPE Middle East Oil Techni· cal Conference and Exhibition held in Manama March 14-17.

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