Summary. A new method to pre-dict field performance for gas fields consisting of small reservoirs of point-bar origin was developed, imple-mented, and tested. Conventional geological and reservoir engineering modeling of this type of field is difficult and usually gives erroneous results. This paper describes the evaluation and use of exploration- and apprais-al-well data as input for a stochastic geological model and the use of out-put from that model as input for a semianalytical reservoir performance model. The semianalytical model in-cludes production constraints for well, platform, and field conditions. Example applications of the stochas-tic geological model and the semi-analytical model are also presented.

1580

Production Forecasting for Gas Fields With Multiple Reservoirs Lelf M. Mellng, SPE, Per O. M.rkeseth, and Thore Langeland, Statoil

Introduction Oil and gas fields that consist of sand deposits of fluvial origin may have extreme-ly complicated or even chaotic structures. Sand lenses are discontinuous and cannot be correlated from well to well. Fields can con-sist of thousands of separate reservoirs. The thickness of the pay intervals can be very large (e.g., up to 1000 m). Between pay in-tervals, reservoirs may be water saturated and fluid properties may change rapidly from reservoir to reservoir. Fig. 1 illustrates the complexity of this type of field.

A geological evaluation should estimate not only in-place reserves, but also reserves penetrated by wells. The evaluation must also consider the variations of reserves at all levels because averaging of volumes and properties gives overly optimistic field fore-casts. Variations usually lead to bottlenecks and surprises.

Stochastic geological models have been presented in the literature. Haldorsen and Lake 1 developed a 2D model that distrib-utes shale intervals stochastically. Augedal et az.2 developed a 3D model that distrib-utes sand bodies that are parallelpipeds. Both models assume a constant net/gross ratio over the field.

The model presented here is a 3D model designed to describe point-bar deposits in a mud-rich environment. The analytical model is designed to handle data from a large num-ber of reservoirs (> 1,0(0) with complex production controls. The models presented in the literature3,4 do pot take into account the complex production procedures and reservoir management program.

Geology of Meandering River Systems Meandering river systems are normally formed in areas of relatively low slope. Heavy vegetation and cohesive flood-plain deposits make rivers more stable and favor development of meandering rather than braided river systems. The flow pattern of meandering systems causes erosion at the outer bank and deposition at the inner bank. Thus, the position of the river changes and point bars form (Fig. 2). Copyright 1990 SOCiety of Petroleum Engineers

Each individual point bar is a fining-up sequence, with high-energy deposits (gravel and sand) at the bottom and low-energy deposits (such as silt and shale) at the top. Fig. 3 shows a typical gamma ray response from such a sequence. The vertical shift from sand to shale intervals in the wells reflects the shifting nature of rivers owing to avulsion of the meander-belt. In sand-rich meandrous environments with low subsi-dence rates, meander-belt deposits common-ly develop extensive sand bodies that are parallel to the overall transport direction of the river, where the continuity is very good.

In a more mud-rich environment with a high subsidence rate, isolated point bars form. Some amalgamated sequences may occur, but the continuity is very poor. Fig. I shows single and amalg8.!llilted sequences. The water-saturated intervals in Well B clearly demonstrate the lack of continuity for both sequences.

The dimensions of point bars are related to the size of the river system. Several papers related to this subject have been pub-lished. In this work, we used Leeder's5 correlation between channel depth and chan-nel width and assumed that the channel deposit thickness was equivalent to channel depth:

be =3.6hc 1.54. . ................ (1) We used Lorenz et at. 's6 correlation be-tween channel width and the meander-belt width to estimate the dimensions of the point bars:

bm=7.44bc 1.01 ................. (2)

Data From Exploration Wells Channel thickness can be estimated by in-specting raw logs, especially the gamma ray log. Intervals can be defined as single or amalgamated sequences of channels. Single-channel sequences are used to estimate chan-nel thickness as indicated in Fig. 3. If several channels are found, an average thickness for a given formation and a given well can be estimated. The interpreted logs are used to estimate the probability of hydrocarbons in a specific sand interval. A net sand is an in-terval with a porosity higher than and a clay content lower than predefined values.

December 1990 JPT

2000 m Well A --------- Well B

o GR 200

Fig. 1-Sand continuity in a mud-rich meandering channel system.

An additional criterion for net pay is a water saturation less than a given value. The probability of a hydrocarbon-filled interval is equal to the sum of hydrocarbon-filled in-tervals divided by the sum of net-sand in-tervals.

For each formation and well, the thick-nesses of the sand and shale intervals are estimated. On the basis of these data, dis-tribution functions are made (see Figs. 4 and 5). Distribution functions for porosity and water saturation are estimated in the same manner.

A correlation between porosity and per-meability is estimated by correlating well-test permeability to log porosity and water saturation:

k=exp(alcP+a2Sw+a3)' ........ (3) Fig. 6 shows the predicted vs. the estimated permeabilities.

Fluid data are evaluated, and depth corre-lations for gas gravity, critical pressure and temperature, and heating value and conden-sate content are made. Depth correlations

~ ...,71'"

1,64 1.01

b< 3.6 h. b m 7.44 b< (Leeder 1973) (Lorentz et al. 1985)

Fig. 2-Size estimate of a meandering river system.

can also be made for reservoir pressure and temperature. These correlations can be used to estimate fluid properties in the model.

Stochastic Geological Mode. It is impossible to duplicate the complicated field geometry with numerical models. With statistical methods, however, it is possible to design a comparable model. Our model distributes point-bar reservoirs stochastical-ly. Therefore, the results must be consid-ered to be possible geological realizations.

In the model, each formation is handled separately. A random location within the field limits is picked and distribution func-tions for shale and sand interval thicknesses, porosity, and water saturation are generated by interpolation. Distribution functions are also estimated for channel thickness and probability of hydrocarbons. The interpo-lation is performed with data from the three nearest wells.

The distribution functions are used to generate probable shale and sand thicknesses by depth. Each sand interval is registered

;, ~ ~

:;; ~ C>

;': ~

I ~

40 1 1 1

30

20

10

00 0.1 0.2 0.30.4 0505 0.70.8 0.9 1.0

OR

h I j net ray

OR

h I

Single channel Amalgamated channel sequence

net pay

l

Fig. 3-Channel thickness and net pay es-timated from gamma ray log.

as ,gas- or water-saturated according to the probability of hydrocarbons in that area. Water-bearing intervals are then deleted, as well as sand intervals thinner than a prede-fined value. For the remaining sands, porosity and water saturation are estimated with a random-number generator and the distribution functions.

The radii for the sand bodies are estimated by using the interpolated channel depth values as input for Eqs. I and 2. The addi-tional HCPV included by this event is then estimated and compared with the expected value for the whole formation. New loca-tions are picked, and the same procedure is used until the generated HCPV is equiva-lent to the value calculated by conventional geological interpretation.

A predefined well pattern and well paths are included in the model. For each well, directly and indirectly penetrated reservoirs are registered and the HCPV is calculated. Net pay, porosity, and water saturation were registered for the directly penetrated sand intervals as illustrated in Fig. 7.

CUM PROBABle i TY (FRAC.) 00 0 1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1.0

Fig. 4-Cumulatlve probability, individual sand Interval thickness.

JPT December 1990

CUM. PROBABI L I TY (FRAC.)

Fig. 5-Cumulatlve probability, Individual shale Interval thickness.

1581

10000 Permea~ility from cor!e~~!~ __________ _

1000 Permeability in md

100

10

Directly penetrated

D Indirectly penetrated D Un penetrated

10 100 1000 10000 Test permeability

Fig. 6-Permeabllity from well tests compared with correlation. Fig. 7-Directly, indirectly, and unpenetrated reservoirs.

Analytical Reservoir Model This model predicts potential production by combining material balance, bottornhole deliverability, and wellbore hydraulics.

The material balance for dry gas can be written as

p/z =(p;/z; )(1-ER) ............. (4) and rearranged to become

p2 = [z(p;!z; )(1-ER)]2. . ........ (5) The bottornhole deliverability is best de-

scribed by the laminar/inertial/turbulent flow equation:

p2 -pw/ =AF Qg+BFQg 2 . ........ (6) The pressure squared is valid only for sys-tems where 2p/Jl.g z is linear with pressure. This is normally true for low pressures, but for practical purposes the pressure squared can be used for high pressures if the draw-down is not too large.

"Our model distributes point-bar reservoirs stochastically. Therefore, the results must be considered to be possible geological realizations. "

1582

The laminar flow coefficient is defined as

(7.056re2 ) ]

x 2 +O.869s, . ..... (7) Fsrw

and the turbulent flow coefficient as

BF =3.14 x lO-6-yZT{3/h2rw ' ...... (8) Several correlations for the internal flow

coefficient have been published. This model uses Geertsma's 7 correlation:

4.85 X lO4 {3= ............ (9)

[4>(1-Sw)p5kO.5

In field studies, it is often impractical to use tables to describe pressure drop in tub-ing. Several runs on wellbore-hydraulics models are often performed to predict pres-

Gas rate potential (MMscf/d)

sure drop at different rates, wellhead pres-sures, tubing lengths, and/or gaslliquid ra-tios (GLR's). The results from these runs can often be summarized with an appropri-ate regression equation. The single-phase Smith S equation for vertical gas flow can be written as

Pwl =AT+ BTq/ ............. (lO) This equation can be used as a regression equation for predictions of wellbore hydraul-ics for more complicated models. For the example runs shown later, the depths of the different reservoirs varied considerably. Therefore, both AT and BT were correlated with reservoir depth (an average well devi-ation was used):

AT=a4 +a5D+a6D2, .......... (11) and BT=a7+asD+a9D2 . ........ (12) The correlations can also easily include var-iations in wellhead pressure and GLR.

25 -----------

20

15

10

5 -~

0 0 0.2 0.4 0.6 0.8

Recovery factor

Very good zone -j- Good zone

--Poor zone --8- Very poor zone

Fig. a-Potential gas rate vs. recovery.

December 1990 JPT

MAKE WELL POTENTIAL

CORRELATIONS

COMPLETE OR

RECOMPLETE

WELL, PLAT FORM AND

INITIALIZE MODEL

READ DATA FROM STOCHASTIC GEOLOGICAL

MODEL

FIELD CHOOSE WELLS t-t+DElTAt POTENTIAL TO BE

I RECOMPLETED

YES

REDUCE RATE FOR

WELLS THAT DO NOT MEET

SPECIFICATIONS

YES NO

PRODUCE FIELD,

PLATFORMS AND WELLS

AT MAXIMUM RATE

UPDATE MODEL

NO

NO SALES YES PRODUCE AT SPECIFICATIONS I PLATEAU I> I MAX?

OK? ACCORDING TO POTENTIAL

Fig. 9-Reservoir model flow chart.

Wellhead deliverability can be estimated by combining Eqs. 6 and 10 as follows:

(Br+BF)qgZ +AFqg +Ar-Pz =0. ................ (13)

Fetkovich9 suggested a similar procedure that replaced Eq. 13 with the backpressure equation. This is not necessary. Solving for qg and replacing pZ with Eq. 5 gives

qg=[ -AF+(AFZ -4(Br+BFHAr

-[z(p;!z;)(1-ER)]2}) 'h ]+2(Br +BF). ................ (14)

Eq. 14 gives the well potential at a given wellhead pressure as a function of recovery . In theory, an iteration procedure must be used to solve the equation. In practice, how-ever, it is possible to speed up computation time by generating decline curves.

For some selected pressures (and thus recoveries), the potential gas rates are cal-culated by solving Eq. 14 numerically. Fig. 8 shows that the maximum potential gas rate as a function of recovery exhibits a nonlinear trend. Regression analysis indicates that the cubic equation

JPT December 1990

YES

PRINT RESULTS

qg =A(ER)Z + B(ER) + C ......... (15) describes the development of maximum potential gas rate vs. recovery with good ac-curacy. Exponential decline implies that the gas rate vs. recovery is linear (A =0).

Recovery at a given economic rate can be estimated by solving the decline-curve equation:

-B-..JBZ -4A[C-(qg)min] 2A

. ............... (16) By definition,

ER=GpIG; . ................... (17) Substitution into Eq. 15 gives

Gas rate is defined as the change of cumula-tive production per time unit:

qg=dGpldt, .................. (19) which leads to

~ERCf~jT~G~ ,,0

40

20

II o 98 1 00 1 OJ ! 04

IN PLACE. RESlRVlS (PERCENT OF AVERAGfl

Fig. 10-Variations in penetrated gas reserves.

PERCENTAGE 4Q

3C

20

10

27 81 ~ 4.3

VOLUME (BSCF)

Fig. 11-Variations in reserves on a well basis.

t=JGp

[A(:Y+B(:)+Cr1dGp. ................ (20)

Eq. 20 is solved analytically with the fol-lowing substitutions:

a=AIG;Z, .................... (21) b=BIG;, ..................... (22) c=C, ........................ (23) u=Gp +b/2a, ................. (24)

and D= -(4ac-bz)/4aZ . ......... (25) The solution of the integral then becomes

1[ 1 [( luo+.JDI) t=-;; 2.JD In uo-.JD

-(lnl:~11) J], ........... (26) where Uo =b/2a. . ............... (27)

The minimum time needed to produce a given reservoir to its economic limit can be estimated by specifying (Gp ) max calculated from Eqs. 16 and 17.

1583

PERCENTAGE 40

30

20

10

o

VOLUME (BSCF)

Gas rate potential (MMscf/d) 35 -

30

25

20

15

10

5

o o 5

---------1

10 15 20 25 30 35 Cumulative production (Bscf)

Fig. 12-Varlatlons In reserves for individual reservoirs. Fig. 13-Potentlal gas rate vs. cumulative production.

The solution of the integral can be rear-ranged to become

-2-JD(I +eE) 2(1-eE)

-([2-JD (I +eE)]2 - {4(1-eE) x [-JD (I-eE)]}) 'h !2(I-eE ) -bI2a, ...................... (28)

where the superscript .

E=2(ln\:: :1\-2a-JD ~t) .. (29) and Uo =(Gp)old + (bI2a) . ......... (30)

The average potential production for a given period (~t) can then be estimated because

( )new -(Gp )old ~t

Production Control

........ (31)

Production control is designed to be autono-mous. The principles are based on the pro-duction and reservoir management most likely to optimize plateau length, well and platform startup, recovery, and sales-gas specifications. Fig. 9 is a flow chart of the model.

Both single and dual-completed wells can be handled by the model. The upper part of the well is assumed to be produced by a short string and the lower part by a long string.

Production startup for a well can be given as a fixed or floating startup time. Wells specified with a floating startup time are put on production when needed to maintain the plateau production. A time delay can be used to take into account the drilling schedule on a platform. As an initial guess, each reser-voir is assumed to be produced to the mini-mum economic rate, which is given as input. The maximum recoverable gas volume for

1584

each sand and the minimum time needed to produce these reserves can then be calcu-lated. If the minimum production time for a producing reservoir is less than the timestep length, then the reservoir is pro-duced at maximum rate in that timestep and the string is recompleted in the next reservoir.

For each string, the potential full well-stream gas production is calculated. The potential string sales-gas production is cal-culated with Eq. 32:

(qgps )string = (qgpw)string(R ws ). . ... (32) If the calculated potential string production is higher than a maximum predefmed value, the potential production is reduced to this maximum value.

If necessary, the potential string values are corrected for startup andlor shut-in within the timestep.

The potential platform-well sales-gas pro-duction is calculated by adding the poten-tial values for all wells connected to that platform:

(qgps ) plat = (Feff) platE (qgps )string' ................ (33)

The efficiency factor takes into account that all wells will not be available for produc-tion at all times and reflects downtime re-sUlting from wireline work, workovers, maintenance, etc.

If the calculated potential platform-well sales-gas production is higher than a maxi-mum predefined value, the potential platform-well sales-gas production is re-duced to this maximum value.

The potential field sales-gas production is calculated in the same manner as the poten-tial platform-well sales-gas production. The target is the sum of the sales-gas volume and the fuel gas consumed on the platforms. Both inputs are given as time-specified figures:

(qgst ) field = (qgs )field + (qfuel) field . " (34)

The potential field sales-gas production tar-get is defined as

(qgpst ) field = (qgs ) field (Fswing) + (q fuel) field' ............... (35)

The swing factor takes into account varia-tions in market demand and allows for pro-duction at higher rates for shorter periods of time if necessary.

For each timestep, sales-gas production and potential production targets are com-pared with the potential field sales-gas pro-duction. If the potential field production exceeds the target, then no optimization is necessary. If the potential production is less than the target, then optimization is per-formed if possible. Two optimization methods may be used: (I) recompletion (the first choice) and (2) drilling of new wells.

The additional field production needed to meet the targets is calculated for each timestep. For each platform, the potential spare sales-gas production is calculated with Eq.36:

(qgsS)plat = (qgsmax)plat -(qgps )plat ............... (36)

This potential production is the difference between the maximum platform production and the potential platform sales-gas produc-tion at that timestep.

A maximum recompletion rate is entered into the model. Reservoirs with potential rates lower than this rate are assumed to be available for recompletion. For strings that satisfy this criterion, the additional produc-tion that can be obtained by recompletion is then calculated with Eq. 37:

(~qgps ) string = (qgps ) newres - (qgps ) oldres . ............... (37)

Additional potential platform and field production is then calculated. The additional potential platform production is set equal to the potential spare production if the sum of the additional string production exceeds the

December 1990 JPT

PERCENTAGE 40

30

20

10

o

PERCENTAGE 30

20

10

0.750 0.753 0.756 0.759 o 0.575 0.600 0.625 0.650

MAX. RECOVERY FACTOR (FRAC.)

Fig. 14-Maxlmum field recovery.

potential spare production at a given plat-form. If the additional potential field pro-duction from recompletion plus the potential field production without recompletion ex-ceeds the production target, then recomple-tions are preferred.

Strings are recompleted according to the following guidelines.

1. Strings producing from reservoirs with the smallest remaining reserves are recom-pleted first.

2. No recompletion is performed on a platform with a potential sales-gas rate equal to or higher than the maximum rate speci-fied for that platform. .

If possible, recompletions are performed until the potential field sales-gas target is reached. If obtaining the field sales-gas pro-duction target by recompletion is not possi-ble, then new wells are put on production (if such wells are defmed) and recompletions are not performed.

Minimum platform and field rates are entered into the model. If the minimum plat-form rate cannot be obtained by recomple-tion, then the platform is shut in. If the minimum field rate cannot be obtained by recompletions or new wells, then all plat-forms are shut in.

If the potential sales-gas production is lower tlian the target sales-gas production, then the platforms and strings are produced at their potential rate. If the potential sales-gas production is higher than the target sales-gas production, then rates are allocated ac-cording to the following guidelines.

1. Strings that can produce their reser-voirs to the minimum economic rate will do so and are recompleted within the timestep.

JPT December 1990

ACT. RECOVERY FACTOR (FRAC.)

Fig. 15-Actual field recovery.

2. A field sales-gas target is set for each platform according to its potential sales-gas production.

3. A platform production target is then set for each individual string according to its sales-gas production target.

Platform rates are set according to Eq. 38:

[ (qgps ) plat ] (qgs)plat = (qgts ) field .

E(qgps ) plat ........... , .... (38)

Well rates are set with 'Eq. 39:

(qgs) string = [(qgs)plat - (dqgs)plat]

x[ (qgSp):~ps)string ] ..... (39) (dqgs)plat '.

(Feff)plat

A sales-gas specification can be entered into the model. If the sales-gas production does not meet this specification, then the model reduces the potential sales-gas pro-duction for the strings that do not meet spec-ification. Platform and string rates are reset. This optimization is performed until the specification is met or until the adjusted potential field production is equal to the tar-get field sales gas production.

Applications The models were tested in field studies. Ten simulation runs were performed. The num-ber of cases was not adequate for a complete Monte Carlo simulation, but the cases give a good indication of possible production scenarios.

The in-place HCPV was identical for all runs, but the wells penetrated various reserves. Roughly 79% of the in-place reserves were penetrated by wells. The var-iations between the different cases were rather small, ,.. 5 %, as indicated in Fig. 10.

On a well-by-well basis, however, the variations in reserves were more significant, as indicated in Fig. 11. The model predicted that about 10% of the wells were dry holes. This information is important for future field development. In an actual production situ-ation, this can be accounted for by allow-ing sidetracking or new wells.

Fig. 12 shows the volume distribution for the individual reservoirs. Note the similar-ity between Figs. 11 and 12. On average, each well penetrates 10 reservoirs. The volume distribution for the wells is there-fore scaled with a factor of 10 compared with the volume distribution for the in-dividual reservoirs.

A well may have large fluctuations in well productivity vs. time and cumulative pro-duction. Some reservoirs deplete quickly and the well must be recompleted (see Fig. 13). The large variations cause difficulties in maintaining a production plateau while optimizing recovery.

Production is optimized to maintain the plateau level as long as possible. Wells are recompleted, and new wells and platforms are put, on production. Recovery is con-trolled by the well, platform, and field pro-duction constraints. The recovery factor obtained is defined as the actual recovery factor. If the field is perfect, all reservoirs, wells, and platforms are produced to their economic limits and the recovery and recov-ery factor are maximum. In our study, a

1585

PERCENTAGE 30

20

10

o

PLA TFNO= 7

7.8 8.4 9.0 9.6

PLATFORM START UP (YEARS)

Gas rate

Gas potential

Pessimistic

Most likely

Optimistic

Fig. 16-Predlcted startup times for new Fig. 17-Slmulated productiontlme scenarios. platforms.

large difference ("" 14%) was found be-tween the actual and maximum recovery fac-tors. This difference can be seen by comparing Figs. 14 and 15. The difference was caused by the production constraint that optimizes plateau length before recovery. Variations in reserves at the reservoir, well, and platform levels enhanced the difference.

For the fields discussed in this paper, it is difficult to predict an actual time when new wells and/or platforms are needed to maintain plateau level. Fig. 16 shows pre-dicted times for new platforms.

The simulations give 10 different produc-tion scenarios. Fig. 17 shows three of these. Sales-gas production and potential sales-gas production are included in the figure. At the plateau, the struggle to maintain the produc-tion level is indicated by the erratic devel-opment of the potential production. In the most optimistic case, the potential produc-tion is obtained with fewer interventions and is less erratic.

Conclusions 1. The stochastic geological model makes

possible geological realizations for fields that consist of point-bar reservoirs.

2. A complex reservoir management pro-gram can be tested with the semianalytical performance model. Critical bottlenecks can be identified and resolved. The autonomous production control makes the simulation runs easy to perform.

3. Simulations show the importance of describing the variations in reserves at the reservoir, well, and platform levels.

4. The models give possible production scenarios resulting from different geologi-cal realizations. Differences can be large, depending on the type of field studied.

1586

Nomenclature a,b,c, A ,B, C = correlation coefficients

AF = laminar flow coefficient, LIT equation, psi2/(scf/D) [kPa2/(std m3/d)]

AT = static flow coefficient, Smith equation, psi2 [kPa2]

be = channel width, ft [m] bm = meander-belt width, ft [m] BF = turbulent flow coefficient,

LIT equation, psi2/(sef/D)2 [kPa2/(std m3/d)2]

BT = turbulent flow coefficient, Smith equation, psi2/(sef/D)2 [kPa2/(std m3/d)2]

D = depth, ft [m] ER = recovery, fraction F = factor

Fs = shape factor Gi = initial gas in place, sef

[std m3] Gp = produced gas, scf [std m3]

h = formation thickness, ft [m] he = channel thickness, ft [m] k = permeability, md [ltm2 ] p = reservoir pressure, psi [kPa]

Pwf = flowing bottomhole pressure, psi [kPa]

qfuel = fuel gas consumption, sefID [std m3 /d]

qg = gas production rate, sefID [std m3 /d]

Te = drainage radius, ft [m] Tw = well radius, ft [m]

Rws = gas well-stream ratio, scf/bbl [std m 3 /m 3 ]

s = skin factor Sw = water saturation, fraction

t = time, days Ilt = timestep, days T = reservoir temperature, OR

[K] z = gas deviation factor

ex = correlation coefficient {3 = interual resistance coefficient,

ft- 1 [m-I] l' = full well-stream gas gravity

(air = 1) Itg = gas viscosity, cp [mPa s]

tf> = porosity, fraction

Subscripts eff = efficiency

i = initial max = maximum min = minimum

P = potential plat = platform res = reservoir

s = sales S = spare t = target

w = wellstream

Acknowledgments We thank Statoil for permission to publish this paper and Olav Vikane for his helpful review.

References I. Haldorsen, H.H. and Lake, L.W.: "A New

Approach to Shale Management in Field-Scale Models," SPEJ (Aug. 1984) 447-57.

2. AugedaI, H.O., Stanley, K.O., and Omre, H.: "SISABOSA, A Program for Stochastic Model-ling and Evaluation of Reservoir Geology,"

December 1990 JPT

Report SAND 18/86 presented at the 1986 Conference on Reservoir Description and Simulation With Emphasis on EOR, Oslo, Sept. 5-7.

3. Saif, M.A., Kumar, R. , and Shanyoor, M.: "Mixed Integer Linear Programming Model for MuItireservoir Strategic Planning, " paper SPE 15759 presented at the 1987 SPE Middle East Oil Show, Bahrain, March 7-10.

4. EI-Feky, S.A.: "A Combination Gasfield De-velopment Model Evaluated With Field Data," paper SPE 16937 presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 27-30.

5. Leeder, M.R.: "Fluviatile Fining-Upward Cycles and the Magnitude of Paleochannels," Geological Magazine (May 1975) 110, No.3, 265-76.

6. Lorenz, J .C. et al.: "Determination of Widths of Meander-Belt Sandstone Reservoirs From Vertical Downhole Data, Mesaverde Group, Piceance Creek Basin, Colorado," AAPG Bulletin (May 1985) 69, No.5, 710-21.

7. Geertsma, J.: "Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media," SPFJ (Oct. 1974) 445-50.

JPT December 1990

8. Smith, R.V. : " Determining Friction Factors for Measuring Productivity of Gas Wells," Trans., AIME (1950) 189, 73-82.

9. Fetkovich, MJ.: "Multipoint Testing of Gas Wells," SPE Mid-Continent Section, Continu-ing Education Course on Well-Test Analysis (March 17, 1975).

51 Metric Conversion Factors ft x 3.048*

ft' x 2.831 685 md x 9.869233

'Conversion factor Is exact.

Provenance

E-Ol = m E-02 = m' E-04 = p.m'

Original SPE manuscript, Production Fore-casting for Gas Fields With Multiple Reservoirs, received for review Oct. 2, 1988. Paper accepted for publication Sept. 18, 1990. Revised manuscript received Dec. 21,1989. Paper (SPE 18287) first presented at the 1988 SPE Annual Technical Conferc ence and Exhibition in Houston, Oct. 2-5.'

JPT

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