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Water Flooding

Description of waterflooding in oilfields

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296 views41 pages

Water Flooding

Description of waterflooding in oilfields

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kerron_rekha
Copyright
© © All Rights Reserved
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Chapter 8 WATERFLOODING* GERALD L. LANGNES, JOHN 0, ROBERTSON, Jr., AMROLLAH MEHDIZADEH, JALAL TORABZADEH, T.F. YEN, ERLE C. DONALDSON and GEORGE V. CHILINGARIAN INTRODUCTION An excellent comparison of the various waterflood prediction techniques (Dykstra, 1950; Guerrero and Earlougher, 1961) was presented by Schoeppel (1968) in the Oil and Gas Journal. Table 8-1 summarizes the various predic- tion techniques presented, whereas Tables 8-2 and 8-4 provide details for the primary techniques summarized in Table 8-7. Major assumptions, data re- quirements, and comparisons of methods are presented in these tables. Tables 8-5 to 8-7 provide detailed comparisons of alternate predictive tech- niques within the major groupings. Reviewing these tables early in the life of a field, provides direction to the future gathering of data, Behavior of carbonate reservoirs is also discussed in this chapter. WATERFLOODING “RULES OF THUMB” When considering the use of waterflooding for a specific reservoir, it is often valuable to get a quick look at the overall project economics. With this in mind, the following “rules of thumb” were accumulated by the authors. Two primary sources were used: N. van Wingen’s lectures at the University of Southern California and “Practical Waterflooding Shortcuts” published in World Oil (Editorial, 1966). Rules of thumb: (1) Water requirements: 1% to 2 pore volumes. (2) Typical injection rates for wells average from 5 to 10 bbl/day ft of reser- voir for pattern flooding; a rate of 3 bbl/day ft is considered minimum. A high- er rate of 10—20 bbl/day ft can be anticipated for aquifer injection, * This chapter is a revised version of Chapters 3 and 4 of G.L. Langnes, J.0, Robertson, Jr, and G.V. Chilingar, Secondary Recovery and Carbonate Reservoirs, Elsevier, New York, N.Y., 1972. 252 TABLE 8-1 Classification of 33 waterflood prediction methods (after Sehoeppel, 1968; coutesy of Oil and Gas Journal) L Basic method Modification Methods primarily concerned with permeability heterogeneity—injectivity 1. Dykstra-Parsons (1950) (a) Johnson (1956) (b) Felsenthal-Cobb-Heuer (1962)* 2, Stiles (1949) (a) Schmalz-Rahme (1950) rT Mm. Iv. oe (b) Arps ("Modified Si (e) Ache (1957) (d) Slider (1961) 3. Yuster-Suder-Calhoun (1949) (a) Muskat (1950) (b) Prats et al, (1959)° ”) (1956) 4, Prats-MatthewsJewett-Baker (1959) Methods primarily concerned with areal sweep efficiency 1, Muskat (1946) 2. Hurst (1958) 3. Atlantie-Richfield (19521959) 4, Aronofsky (1952-1956) 5, Deppe-Hauber (1961-1964) Methods primarily concerned with the displacement process 1. Buckley-Leverett (1942) (a) Terwilliger et al. (1951) {b) Felsenthal-Yuster (1951) (ec) Welge (1952) (d) Craig-Geffen-Morse (1955)° (e) Roberts (1959) (f) Higgins-Leighton (1960-1964) 2, Craig-Geffen-Morse (1955) (a) Hendrickson (1961) 3, Higgins-Leighton (1960-1964) Miscellaneous theoretical methods 1. Douglas-Blair-Wagner (1958) 2. Hiatt (1958) 3. Douglas-Peaceman-Rachford (1959) 4, Naar-Henderson (1961) 5, Warren-Cosgrove (1964) 6. Morel-Seytoux (1965) Empirical methods 1, Guthrie-Greenberger (1955) 2, Schauer (1957) 3. Guerrero-Earlougher (1961) Also applies to Stiles method. Also applies to Yuster-Suder-Calhoun and Schauer methods. Also concerned with areal sweep problem, Also recognized as basic method, TABLE 8-2 Characteristics of the perfect waterflood prediction method (after Schoeppel, 1968; courtesy of Oil and Gas Journal) Effect Characteristic Fluid flow initial gas saturation is considered saturation gradient is considered varying injectivity is considered Pattern applies to linear systems applies to five-spot pattern applies to other patterns applicable to all mobility ratios considers areal sweep considers increased sweep after breakthrough does not require published laboratory data does not require additional laboratory data Heterogeneity considers stratified reservoirs considers crossflow considers spatial variations (8) Injection rates for sandstone reservoirs vary from 0.35 to 1.5 bbl/acre- ft with an average of 0.5 bbl/acre-ft. Rates for carbonate reservoirs should run two to three times the average. (4) Response to flood can be expected when two thirds of the fill-up has been achieved (i.e., when two thirds of the voidage created by primary pro- duction is filled by the water injected). (5) Peak oil production rate is reached at the time of fill-up. (6) Gross production rate equals 80% of water injection rate. The rest of the injected water is lost outside of the patterns or to the aquifer. (7) Approximately one half of the secondary recovery oil (primary re- covery oil left at time of flood plus increase in recovery) will be recovered prior to reaching peak production. (8) Incremental recovery due to waterflooding is equal to the primary for crude oils having gravities above 30°API. For lower crude oil gravities (15— 80°API), the incremental recovery ranges from 50 to 100% of primary re- covery. (9) The analysis of many pattern floods indicates that (Earlougher and Guerrero, 1965): (a) areal efficiency = 70—100%, (b) vertical efficiency = 40—80%, (c) combined efficiency = 28-80% (median of 60%), and (d) resid- ual oil saturation = 15—30%, TABLE 6-3 Basie assumptions in waterflood predietion methods (after Schoeppel, 1968; courtesy of Oil and Gae Yournal) 90 Method w ‘modification Date Fluidsfow effects Pattern effects Hecerogencity effects presented = considers requires considers ial gas sazara Increased pub addi: atratiied croc spatial srs om injecs system —patiora patterns ‘sweep mweep lished —thomal_— reservoirs flow variations Hon gradient deity ‘after Web data lab, data break through o 8 © ©» © & BW © ® oO OD oy Us OM ‘The perfect method yee yes yee es yes any ye meses 1, Dykstre Parsons 1950 yee nok no any no mest Johnson 1956 yes monk no any. no noth tt Petsenthal-Cobb-Heuer 1962 ye pene ao any no nemo Heh Stiles 1959 a no 0 no momo Jek mt Schmalz-Rakme 1960 no non no 0 no yes Yes Arps 1956 po hots a0 ay no no tSek om ‘Acie 1987 no mt a0 0 no on Yeh om Slider 196 yor no yas ee yen (2) nt x ee, ee ee Yuster-Seder-Calhoun 1949 ys mo yee ye mo 0 mote Muska 1950 no no Yes oe ee "ym mks Prats et ae 1989 yee ono yes ye no any yes yes yes yok yes nt. TL Muskat 196 oom + ye oye 0 yes to moto mono Burst 1983 no mo yao. 10 yen mo nom yektto AantioRichfield 1962-1959 noo ye ye gen my ye ee Seen Sh mo ‘aronotsky 1952-1986, no Ye ye mommy est me Deppe-Hauber 1961-1984 noo ye yoo yee amy Yess Ym HL Buckley-Loverett 1942 mo yes nye no mmr Welse i992 no yee eek ee Roberts 1959 no yee moth et no no yes neh Ceaig-Geffen Morse 1955 ye yee yee = yes nom yes yes yes, on Yes mono Histine Leighton 1960-1964 yes. yen yes = ye yes, any yes vos yer, mokono Hendrickson jt po yee ya apy yes Yess moh 1Y, Doughs Blair Wagnee mo yes yee = yes yee my yes yon, yes nest Miatt no ye noo po name geen ‘Douglas sta mo yeh Yee yea yes oamy yes, yess kn. [Naar-Henderson mo yee ye mony See Yes Ses mo Yes. Warren-Cosgrove mo yes nyt Ro ke ho mek ves Moret Seytous moo ye yer yes my yes yest Meet V. Schauer me Se Guerrero-Eariougher em he ys ye no monomer + Categorized secording to classification presented in Table 81, TABLE 84 Data required for waterflood prediction methods (after Sehoeppel 1968; courtesy of Of and as Journal) Method and modification® ‘Absolute Stratified Etfective Relate tnt and Initial Resid. Olland Gat Average Injection Correlation perme: bed thiek- olland —perme- resid oll gas ae ‘water viscosity Injection History for areal shilty ness illty ature fun stare viol. te sree joturae tions ton ton LDykstra-Parsons (1900) ‘Johnson (1956) Foluenthal-Cobb-Hewer (1982) Stiles (2949) ‘Schmalz-Fixhme (1950) Arps (1996) ‘Ache (1957) Slider (1961) Yuster-SuderCalhboun (1949) ‘Muskat (1950) Pratset al. (1959) UW Muskat (1946) Hurst (1983) Atlantic-Richfietd (1952) ‘Aronofsky (1952) IME, Buckley-Levecett (1942) ‘Weige (953) Craig- Geffen Morse (1966) Roberts (1989) Hiern Leighton (1360, 1962, 1968) X IV, Douglae-Blair-Wagner (1958) | prtreeee retiereis * x x * * x x x x % x KM LL 36 | OEE KID KOE HIE FL | OE | XRKARK ELL EXP OOK L EDT HOHE | D2 | OC KOE MEP RRT EET ERR ELL IKEL PORK CL | 208 | 29H PEEL CDT SLL Dare DOPE Deeper hn pnns PIER OOEXE CEPT EEE ES MILTTIELTLX * * x x xxx I * Categorized aceording 10 chassification scheme of Table hy only. SSo TABLE 8-5 ~ a a Comparison of basic methods concerned with permeability—heterogeneity—injectivity problems (after Schoeppel, 1968; courtesy of Oil and Gas Journal) Dykstra-Parsons (1950) Stiles (1949) Yuster-Suder-Calhoun (1949) stratified-linear normal probability mobility ratio Reservoir configuration Permeability distribution Injection controlled Total injection rate constant Layer injection rate variable Required mobility ratio any Gas fill-up before oil production Displacement mechanism pistonlike Areal sweep 100% at water breakthrough Vertical sweep proportional to permeability capacity and mobility ratio Solution method graphical stratified-linear rearranged actual data kit capacity constant constant 1.0 initially pistonlike 100% at water breakthrough proportional to permeability capacity graphical and numerical stratified five-spot average of permeability capacity kh capacity variable (to fill-up), constant (after fillsp) variable (to fill-up), constant (after fill-up) pistonlike sweep efficiency factor* reeovery factor* numerical * Determined as a function of throughput, (10) The costs of secondary recovery of oil in 1981 in the United States are broken down as equipment and operating costs for ten producing wells and eleven injection wells operating at a depth of 4000 ft as follows (Funk and Anderson, 1982, pp. 8, 15): Additional lease equipment 1,012,200 Injection wells 2,366,100 -$ 3,378,300 ‘Normal daily operating costs 138,300 Surface repair 64,500 Subsurface repair 73,200 $ 276,000 FLOOD DESIGN BY ANALOGY The study of existing and completed waterflood projects and natural water-drive reservoirs provides the basis for the extension of the “rules of thumb” approach to flood design. A study of the reservoirs in the Denver Basin (Nebraska and Colorado) showed that natural water-drive reservoirs in the Nebraska portion of the basin had primary recoveries of 40-45% of the initial stock tank oil-in-place (Bleakley, 1965). In the Colorado portion of the basin, 18% was considered a good primary recovery (solution gas-drive mechanism) in similar types of reservoirs. The operators concluded that waterflooding would be feasible in the Colorado portion of the basin and that the ultimate recovery for a field could reasonably be expected to be 40%, The predicted performance of the West Lisbon waterflood in Loui- ‘TABLE 8-6 Comparison of basic methods concerned with areal sweep efficiency problems (after Schoeppel, 1968; courtesy of Oil and Gas Journal) ‘Muskat (1946) Hurst (1953) Atlantic-Richfield (1952, 1955) Reservoir configuration stratified five-spot stratified five-spot stratified five-spot ‘Total injection rate constant constant variable Applicable mobility ratio 1.0 1.0 01-10 Initial gas saturation none none none Sweep efficiency at water breakthrough 12.8% 72.6% variable Sweep efficiency after water breakthrough not available not available from correlation 258 TABLE 8-7 Waterflood prediction methodsconcemed with displacement mechanism (after Schoeppel, 1968; courtesy of Oil and Gas Journal) Basic method Highlights of method Buckley-Leverett (1942) material balance on element; vai front displacement mechanism; single layer—linear model; constant injection rate; no residual gas saturation; 100% sweep at water breakthrough Modification 1, Terwilliger et al. (1951) saturations in flood front; stabilized zone concepts 2, Felsenthal-Yuster (1951) radial case 3. Welge (1952) average saturation at water breakthrough 4, Craig-Geffen-Morse (1955) —_five-spot pattern; sweep efficiency correlated with mobility ratio at breakthrough 5, Roberts (1959) allowance for stratification 6. Higgins-Leighton (1960) channel and cell displacement; any well pattern siana was based on the past performance of the waterflood of the South- west Lisbon Pettit reservoir, Louisiana. It was estimated that the recovery would be raised from 14% under primary depletion to 32% under flood (Miller and Perkins, 1960). Callaway (1959) suggested that by relating the results obtained from a waterflood to the reservoir parameters, which control the performance, a reliable set of experience factors can be obtained and the uncertainties can be greatly reduced. He divided the engineering factors involved in eva- luating waterflood recovery into two sets of variables: (1) “primary vari- ables,” which are those factors bearing a direct mathematical relation to the amount of oil to be recovered; (2) “secondary variables,” which operate in- directly through the primary variables to influence the oil recovery. The primary variables are (1) primary recovery efficiency, (2) connate water saturation, (3) sweep efficiency, (4) residual oil saturation, and (5) crude shrinkage. The secondary variables and the corresponding primary factors influenced (numbers in parentheses) are (a) oil viscosity (1, 3, 4); (b) per- meability (1, 3, 4); (c) structural considerations (1, 3); (d) uniformity of reservoir rock (3); (e) type of flood (3); {f) time for start of flood (5); and (g) economic factors (1, 3, 4). Callaway’s (1959) equation for evaluating the recovery by waterflooding is as follows: WR = 77586 (=) {1-2,- 72 [a-#.(1- =%)]] (84) where WR = waterflood recovery, bbl/acre-ft; B,; = original formation volume factor for oil, bbl/STB; B, = formation volume factor for oil during water- flood operations, bbl/STB; S,, = residual oil saturation, fraction: S, = connate water saturation, fraction; ¢ = porosity, fraction; Ey = primary re- covery efficiency, fraction of original oil-in-place; E,, = overall sweep effi- ciency, fraction of reservoir volume. This equation is based on the assumption that the unswept portion of the reservoir at the time of flood abandonment is completely saturated with oil and connate water. It is also assumed that there is no gas cap and that a free gas saturation does not exist in the swept portion of the reservoir. Goolsby (1967) suggested the following steps for flood design: (1) Characterize the reservoir geologically as completely as possible, (2) Determine the value for Callaway’s (1959) five “primary variables”. Most of these variables can be expressed with a range developed from field and laboratory data and the study of analogous fields. (3) Calculate a range of waterflood recoveries using equation (8-1). (4) Relate the maximum, average, and minimum recoveries to time by using fluid-in—fluid-out and water—oil production relationships taken from analogous fields. The effects of various injection rates can be incorporated in this step if felt necessary. ‘The “primary variables” can also be expressed as probability distributions. Equation (8-1) is then solved using these distributions yielding a probability distribution for the waterflood recovery instead of a simple range-average value, SWEEP EFFICIENCY The effectiveness of a secondary recovery process is dependent on the volume of the reservoir which will be contacted by the injected fluid. The latter, in turn, is dependent on the horizontal and vertical sweep efficiency of the process, The following factors control the sweep efficiency: (1) Patter of injectors. (2) Off-pattern wells. (3) Unconfined patterns. (4) Fractures. (5) Reservoir heterogeneity. (6) Continued injection after breakthrough. (7) Mobility ratio. (8) Position of gas—oil and oil—water contacts. Pattern selection The selection of an injection pattern is one of the first steps in the design of secondary recovery projects. When making the choice, it is necessary to 260 Solid line indicates symmetry pattern of infinite well network. Dastied line indicates symmetry element of infinite well network. ‘Code: © Injection wells, @ Producing wells DIRECT LINE DRIVE oe, 08 ee eo te 0.001536 AhAaP i ' aby tog & + 0.682 4 -0.798 1 iw ° . &40 ote 2 A oe eeoeee STAGGERED LINE DRIVE 0.001536 AAP log 2 + 0.682 § -0798 O° e ee e |. 2001838 hae tog 7 - 02688 ‘SEVEN-SPOT 5 « 2902081 ana? io: Res joo - 0.2472 a 5 ¢ pata e e NINE - SPOT 6 Heir 8 0.001538 anAp, os 1 Soot +19 --9 He fos - ones] ” a] 1 3 sh 4 = 0.003076 ana, Peat +k 2301 ‘ e e ae fog, -o.nea] - ocd Fig. 8-1. For description, see p. 262. R = Ratio of producing rates of corner well (c) to side well (s), AP),<= Ditterence in pressure between injection well and comer weil (c), APi,« = Difference in pressure between injection well and side well (s). DIRECT LINE DRIVE BOUNDARY PATTERN 0.003076 2hAFiy,q¥ SES [oa & + 0166 + ooo] + ‘2eteltem ‘ Sete) re 2g. ‘APiy’,qy = Difference in pressure between injection well iy’ and Producing well ay’. RESERVOIR BOUNDARY RESERVOIR BOUNDARY AP irq? * Difference in pressure between injection well i’ and Producing well q’ (Wells of outer row are alternating injection and producing welts.) FIVE-SPOT BOUNDARY PATTERN é 0.003076 hA(a, + 92 +2’ + 24,")4P\', ay 2qy[(3 + Ri{tog & + 0.815} -1:7216] + a1 + R4{log -Z -0.098} Fig. 8-1 (continued). pete RESERVOIR BOUNDARY AP), qr Difference in pressure between injection well i’ anc producing well q/ (Wells of outer row are all producing wells.) NINE -SPOT BOUNDARY PATTERN 0.003676 ahAP}’,5"(2ay/ + 2ar +34, + Ge) + Rofiog & + 0848} -148] + [2 Rfioa + 0885} - 0577] 0.003076 ANP). (2a,' + 2qe/+ 34, + &) d + 0204} + 0362] + a, [(3+ R){log -0.460} + O12 SP;,,y = Difference in pressure between injection weil i ond Producing well s AP), «: = Difference in pressure between injection well i’ ond producing well c/. RESERVOIR BOUNDARY Fig. 8-1, Injectivities for regular patterns for mobility ratio equal to one. h = net pay thickness, ft; r,, = wellbore radius, ft; Ap = difference in pressure between the injection well and producer, psi; and A = mobility of reservoir fluid, md/ep. (After Deppe, 1961; courtesy of the SPE of AIME.) consider all the available information about the reservoir. The adverse effects of the other factors listed above can be partially offset if they are considered during the pattern selection. Other factors which should be considered in pattern selection are as follows: (1) Flood life. (2) Well spacing. (3) Injectivity. (4) Response time. (5) Productivity. The flood life depends on the availability of water, the rate at which water can be injected, well spacing, and proration policies. The performance and economics for various well spacings and pattern sizes should be analyzed in order to arrive at the economically optimum choice. These analyses, however, cannot be made without also considering injectivity, which is best determined from pilot operations. A well-controlled pilot operation is essential to under- standing all the pattern selection factors. Empirical methods for estimating water injectivity prior to an actual test for pattern floods have been worked out by Muskat (1946) and by Deppe (1961) for a mobility ratio of unity in the case of single fluid flow; they are presented in Fig. 8-1. Prats et al. (1959) have developed a plot relating di- mensionless injectivity, Jp, to mobility ratio, My, o» for different stages of a flood in five-spot patterns, when the reservoir has an initial mobile gas satura- tion (Fig. 8-2), Dimensionless injectivity, Jp, is defined by the following equation: Solid lines -experimental Dashed lines - trom cross plots D Injectivity, 1 = 0 or 02 0304 05 06 07 08 05 10 Water cut, fraction in total ettlux Fig. 8-2, Injectivity as a function of water cut and mobility ratio. (After Prats et al., 1959, P. 98; courtesy of the SPE of AIME.) 264 iwHw ” RyhAp where i,, = water injection rate, bbi/day; u, = water viscosity, cp; k,, = per- meability to water, md; h = thickness of injection zone, ft; Ap = differential injection pressure, psi. ‘Response time is dependent on injectivity and spacing. It is further in- fluenced by reservoir heterogeneity and the oil, gas, and water saturations, which exist at the beginning of injection. The pattern chosen must above all consider the physical characteristics of the reservoir. Formal patterns, such as the 5-, 7-, or 9-spot, and the direct or staggered line drives are useful only when the reservoir is generally uniform in character. Faulting and localized variations in porosity or permeability lead to irregular patterns or peripheral injection systems. For limestone reser- voirs, the irregular pattern or peripheral system is more likely to be used. Ip (8-2) Off-pattern wells Prats et al. (1962) have calculated the effect of off-pattern wells (producers and injectors) on the performance of a regular five-spot waterflood. Data developed by their work are presented in Figs. 8-3 through 8-11. These results are strictly applicable only when the assumptions are (1) the reservoir is thin and horizontal; (2) porosity, permeability, and thickness are uniform; (8) only crude oil is mobile initially in the formation; (4) mobility ratio is one; (5) injection and production rates are the same for all wells throughout the field; (6) there is a sharp boundary between the oil and water banks; Woter fraction in eux 2 0 02.04. 06 08 10 12 14 16. 1B~ 20 Cumulative water injection in floodable regular five-spot volumes Fig. 8-3, Water-cut history of a laterally displaced production well, (After Prats et al., 1962, p. 173; courtesy of the SPE of AIME.) u A ‘ o8| & - f a rm fei £ o| é % —e2__04 0508 1013S Cumulative water injection in floodable requiar five-spot volumes Fig. 8-4, Oil-production history of a laterally displaced production well, (After Prats et al,, 1962, p, 173; courtesy of the SPE of AIME.) (7) producing wells are kept flowing even after the individual wells have reached an economic limit cut of 98%, The data developed by Prats et al. (1962) can be used, however, to estimate the impact for other conditions. These estimates would generally represent the minimum impact to be ex- pected for offset wells. Water fraction in efflux % 08 2024 28 32 36 40 Cormuatve water rection in coaable regular five-spot volumes Fig. 8-5. Water-cut history of a diagonally displaced production well. (After Prats et al., 1962; courtesy of the SPE of AIME,) 266 1 Oo 0468 24 26 32 36 40 vnrstve lec eis PUL tage elise Fig. 8-6. Oil-production history of a diagonally displaced production well, (After Prats et al., 1962; courtesy of the SPE of AIME.) 1 —— 1 x ‘ ‘ o £ e i ie A %—er 0406 08 -10-~*CS CSS ‘Cumulative water injection in floodable regular five-spot volumes Fig. 8-7, Water-cut history of five-spot patterns eaanay laterally displaced injection well, (After Prats et al., 1962; courtesy of the SPE of AIME. [2 -}- | $ — ae [yt a B Of a £ Curve A refers to oa the regular five-spot} |__| 8 o2 ol 0 02 04 06 O08 10 12 14 16 16 20 Cumulative water injection in floadable regular five-spot volumes. Fig. 8-8. Oil-production history of five-spot patterns surrounding laterally displaced injec- tion well, (After Prats et al., 1962; courtesy of the SPE of AIME.) 10 2 & 2 R Water traction in efflux 5 2 Oo 04 08 12 16 20 24 28 32 36 40 ‘Cumulative water injection in floodable regular five-spot volumes Fig. 8-9. Water-cut history of five-spot patterns surrounding diagonally displaced injection well. (After Prats et al., 1962; courtesy of the SPE of AIME.) ° 04 08 12. 16 +20 24 28 32 36. 40 ‘Cumulative water injection in floodable regular five-spot volumes Fig, 8-10, Oil-production history of five-spot patterns surrounding diagonally displaced injection well. (After Prats et al., 1962; courtesy of the SPE of AIME.) pS 2 | ‘Total 1088 in oil recovery, percent . | | | ° aon ‘Goa ‘006 ‘O08 ‘Square of the dimensioniess displacement om Fig. 8-11, Effect of displacement on total loss in oil recovery. (After Prats et al., 1962; courtesy of the SPE of AIME.) Multiple irregular patterns in a single field can be evaluated with Figs. 8-3 through 8-11 as long as the irregular patterns are separated by at least one normal five-spot pattern. In Figs. 8-3 through 8-10, the A curves rep- resent the performance of a normal five-spot flood. The other curves are keyed to the well diagrams included in the water-cut history figures, The D or L notations refer to the diagonal or lateral displacement of the wells, Unconfined patterns The principal problem associated with an unconfined pattern is the loss of injected energy to wells and/or aquifer outside of the injection pattern. The degree of pattern confinement is dependent upon the reservoir pressures around this pattern. Geologic barriers such as faults and pinchouts or the presence of high-pressure aquifers limit the loss of energy. Unconfined bound- aries include boundaries adjacent to (1) leases where the reservoir is unpres- sured, and (2) low-pressure aquifers. Exact percentages of energy loss or oil migration outside the confined pat- tern will vary with overall well configuration and estimates should be made as to the magnitude of the anticipated loss, A simple procedure often used to estimate the loss is based on the assumption of uniform radial flow of the injected water from the injector. The peripheral injectors are connected by lines on a map and the losses are calculated for each injector by measuring the exterior angle between the lines connecting the injector with the injectors on either side and dividing by 360° (an injector on the side of a project may lose around 50%, whereas a corner injector may lose about 75%). Fractures Dyes et al. (1958) studied the effect of fractures on the sweep efficiency of a five-spot pattern. Figs. 8-12 through 8-15 present a summary of their findings; in the figures, the fracture length, L, is expressed as the fraction of the distance between the fractured well and the boundary of the element in the flood pattern as shown in the small diagrams located in the figure. Fig, 8-12 shows that a vertical fracture, when located in a favorable direc- tion, has little effect on sweep efficiency. When the vertical fracture is located in an unfavorable direction, the breakthrough sweep efficiency drops with increasing fracture length, L. The ultimate sweep efficiency is unaffected if no restriction is placed on the amount of water injected or the water/oil ratio of the producer, The work of Dyes et al, (1958) was directed toward investigating the im- pact of fracturing techniques on waterflooding operations. Their work, how- ever, can also be used when considering natural fracture systems. By using the trends presented, patterns can be planned to minimize the impact of the fracture system. ve ae Mobility ratio= 14 = Fracture length 1 2 3 ‘Throughput, displaceable volumes Fig. 8-12. Sweep-out with vertical fracture of favorable direction. (After Dyes et al., 1958; courtesy of the SPE of AIME,) Fracture length, L = fraction of distance between fractured well and boundary of element in flood pattern, 100; Untractured—| 1.3/4 75) a 3 ‘y 25} =t me Mobility ratio «1.1 L=Fracture length % 1 2 3 Throughput, displaceable volumes Fig. 8-13. Sweep-out with vertical fracture having unfavorable direction, (After Dyes et al,, 1958; courtesy of the SPE of AIME.) 271 Fracture length =1/2 Memopility ratio 1 Throughout , displaceable volumes Fig. 8-14. Influence of mobility ratio and fracture on percentage of area swept. (After Dyes et al., 1958; courtesy of the SPE of AIME.) Fracture length - 1/2 M=Mobility ratio, 1 Throughput , displaceable volurnes Fig. 8-15, Influence of injection or production well fracture on percentage of area swept. (After Dyes et al., 1958; courtesy of the SPE of AIME.) 272 ‘Sweep efficiency Fig. 8-16, The effect of directional jility on sweep efficiency, (After Landrum and Crawford, 1960; courtesy of the SPE of AIME.) Oo Os 1 18 20 25 30 35 ta/hy 100, eof 60} [\ Lie he. ; Bor L — ae ror oA r

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