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Development mechanisms and influencing factors of dump flooding
PETROLEUM EXPLORATION AND DEVELOPMENT Volume 42, Issue 5, October 2015 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2015, 42(5): 691–696.
RESEARCH PAPER
Development mechanisms and influencing factors of dump flooding SU Haiyang1,*, MU Longxin1, HAN Haiying1, LIU Yongge2, LI Bo1 1. PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China; 2. China University of Petroleum (East China), Qingdao 266580, China
Abstract: Aiming at the problem that the theory of dump flooding is not mature, this study examined the suitable reservoir conditions for dump flooding, defined the concept of “dump flooding threshold pressure” and its expression based on fluid mechanics and reservoir engineering fundamentals, and proposed the computing method of water injection rate, producing rate, water layer pressure, oil layer pressure, cumulative injection and cumulative production. It gave the corresponding computing program according to the proposed computing method, and made a case study and analyzed the factors affecting dump flooding using the program. The dump flooding computing methods are reasonable and applicable; when water reserve-oil reserve ratio is less than 60, production plateau extends with and oil recovery increases with the increase of water reserve-oil reserve ratio, when water reserve-oil reserve ratio is more than 60, the effect of the ratio of water reserve to oil reserve is negligible; the timing of dump flooding has a significant effect on production plateau and oil recovery, the later the dump flooding injection timing, the more completely the formation energy will be used, the longer the production plateau and the higher the recovery will be. Key words: dump flooding; development pattern; threshold pressure; stable production duration; recovery rate; water injection timing
Introduction
1.
Mechanism of dump flooding
Dump flooding refers to the process in which water in high-pressure water layer flows into low-pressure oil layer under pressure differential through casing to maintain reservoir pressure and displace oil[1]. At present, dump flooding is mainly used to supplement energy before water flooding, and is suitable for regions where ground water is scarce[2−3]. This technique has been rarely used in China, with only precedent in the Pinghu oilfield[4]; while the research in this aspect has been started since the 1970s, and the technique has been used mostly in the Middle East[5−8]. The published papers on dump flooding are mainly on its application, while the mechanisms of dump flooding haven’t been examined systematically. Davies C A[1] discussed the calculation method of dump flooding injection rate without considering the situation after water breakthrough. In this study, the mechanisms of dump flooding have been studied further, a method of calculating water injection rate, oil production rate, oil layer pressure and water layer pressure in the process of dump flooding has been worked out, and the application effect of this method has been analyzed.
1.1.
Threshold pressure of dump flooding
Dump flooding needs enough differential pressure between water layer and oil layer to overcome differential pressure between water layer and wellbore, friction pressure loss in wellbore, water column pressure in wellbore and water injection differential pressure between wellbore and oil layer[9−10]. In order to quantify this process, according to the research achievement of document [11], the concept of “threshold pressure of dump flooding” is defined in this paper, that is the water layer pressure which can maintain the balance of injected and produced fluid in oil layer at designed production rate through dump flooding, and likewise, the “threshold water injection rate of dump flooding” is defined as water injection rate which can keep the injected and produced fluid balance in oil layer at designed production rate through dump flooding. Based on the definition, threshold pressure of dump flooding can be expressed as follows: pth = poi + pob + pf + pwb + ph (1) The differential pressure between water layer and wellbore is
Received date: 31 Aug. 2014; Revised date: 27 May 2015. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the PetroChina Science and Technology Major Project. Copyright © 2015, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
pwb = qth J w
(2)
The differential pressure between wellbore and oil layer is pob = qth I w (3) Based on Darcy-Weisbach equation[12], the friction pressure loss in wellbore is
pf = a ρ w g λ
h v2 h ⎛ qth ⎞ = aρw λ ⎜ ⎟ d 2g 2d ⎝ A0 ⎠
2
(4)
The friction factor is
λ=
0.316 4 μw Aμ = 0.316 4 4 = 0.316 4 4 0 w 4 ρ w vd ρ w qth d Re
(5)
Water column pressure in wellbore is ph = bρ w gh
The critical pressure can be calculated as q pc = pwf + c JL
(6)
Substituting equations (2)-(6) into equation (1) we can get 2
qth qth h ⎛ qth ⎞ + + aρw λ (7) ⎜ ⎟ + bρ w gh Iw Jw 2d ⎝ A0 ⎠ The threshold pressure of dump flooding can be computed by equation (7). The reservoir can be developed at the designed production rate by dump flooding technology only if the water layer pressure is above the threshold pressure. pth = poi +
1.2.
sure and the differential pressure between water layer and oil layer will decrease constantly, based on equation (9), the water injection rate will decrease too. When water injection rate is lower than oil production rate, the oil layer pressure also begins to decrease. When the oil layer pressure decreases to a critical pressure that can’t maintain the stable liquid production, the production will turn to produce at a stable bottom hole pressure, at this point, the liquid production rate can be expressed as qL = qo + qw = J L ( po − pw f ) (16)
Calculation of dump flooding
During dump flooding, the water injection rate is controlled by the water layer pressure and oil layer pressure, conversely, the water injection rate affects the water layer pressure and oil layer pressure, and the production plateau and recovery, so the calculation of water injection rate is very important. Assuming at a time t, water injection rate is qiw, oil production rate in the oil layer is qo, water production rate is qw, water layer pressure is pw, oil layer pressure is po, based on pressure relationship we can get pw = po + pob + pf + pwb + ph (8)
(17)
Before water breakthrough, qw=0, Wp=0, qL=qo, the production index is constant. Based on equations (9)-(13), (15) or (16) we can get the 6 unknown parameters: qiw, Wiw, qo, Np, po, pw, the computing process is shown in Fig. 1. At the point of water breakthrough, based on Buckley-Leverett theory[14] we can get f ′( S ) T L = w wf ∫ qi w dt (18) 0 φA The cumulative water injection at the point of water breakthrough is T φ AL Wiw(T ) = ∫ qiw dt = (19) 0 f w ′( S wf ) Based on oil-water relative permeability curve we can get
With the same derivation as equations (2)-(7), we can get 2
h ⎛ qiw ⎞ q q pw = po + iw + iw + a ρ w λ (9) ⎜ ⎟ + bρ w gh Iw Jw 2d ⎝ A0 ⎠ The cumulative water injection, cumulative oil production and cumulative water production at time t are t
Wiw = ∫ qiw dt 0
t
N p = ∫ qo dt 0 t
Wp = ∫ qw dt 0
(10) (11) (12) [13]
For the oil layer, based on material balance equation we can get Wi w − N p Bo − Wp = N o BoiCto ( po − poi ) (13)
For the water layer, based on material balance equation we can get Wiw = N w Bw Ctw ( pwi − pw ) (14) If the oil layer is producing at constant liquid production rate, then qL = qo + qw = qc (15) With the ongoing of dump flooding, the water layer pres− 692 −
Fig. 1.
Schematic of dump flooding computing program.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
the relationship fw-Sw and fw′-Sw, and then the fw′(Swf) value can be worked out, finally the Wiw(T) value is obtained based on equation (19). Based on the Wiw(T) value we can get the water breakthrough time. After water breakthrough, equation (18) can be written as f ′( S ) t L = w wo ∫ qiw dt (20) 0 φA So we can get f w ′( S wo ) =
φ AL t
∫q 0
iw
dt
=
φ AL
(21)
Wiw
Based on oil-water relative permeability curve we can get the relationship fw-Sw and fw′-Sw, in combination with fw′(Swo) value from equation (21) we can get the water cut at exit end fw(Swo), so the water production rate and oil production rate at a point after water breakthrough are qw = q L f w (22) qo = qL (1 − f w )
(23)
After water breakthrough, the production index JL changes with the water cut. According to the document [15], the ratio of production index at a point after water breakthrough to production index at the point with water cut of 0 is J L K ro ( S w ) K rw ( S w ) μo = + (24) J L0 K ro ( S wi ) K ro ( S wi ) μ w The production index at different water cut after water breakthrough can be calculated based on equation (24). After water breakthrough, based on the 11 equations (9)-(15)(or (16)), (21)—(24) and permeability curve we can get the 11 unknown parameters: qiw, Wiw, JL, qL, fw, qo, Np, qw, Wp, pw, po, the computing process is shown in Fig. 1. From the process of computing the dump flooding parameters, we can find that the difference between artificial water flooding and dump flooding is embodied in equation (9), that is the water injection rate in dump flooding is controlled by the water layer pressure and oil layer pressure. Equation (9) is a nonlinear equation about qiw which can be solved by Newton iterative method [16]. Let F (qiw) be the function of qiw: F ( qiw ) = po − pw +
pressure, oil layer pressure, cumulative water injection, cumulative water and oil production at any time during dump flooding.
2. Application of dump flooding computing method 2.1.
A case study
The N reservoir in the Middle East is in a desert with scarce ground water. There is an M water layer 1478 m above the N reservoir (shown in Fig. 2). The N reservoir consisting of quartz sandstone of weak heterogeneity, has a porosity of 18%−21%, permeability of about 500−700×10−3 μm2, initial reservoir pressure of 39.34 MPa, saturation pressure of 19.24 MPa, thickness of 15 m, the injectivity index of 116.74 m3/(d·MPa), and production index of 104.87 m3/(d·MPa). The M water layer has water reserves 15 times of the oil reserves in N reservoir, a porosity of about 22.4%, permeability of 600×10−3 μm2, initial formation pressure of 25.48 MPa;, and the injectivity index of 137.16 m3/(d·MPa). The fluid properties are as follows: the oil volume factor at initial reservoir pressure is 1.49, formation water viscosity is 0.68 mPa·s, oil viscosity is 0.90 mPa·s, compressibility coefficient of oil is 24.5×10−4 MPa−1, compressibility coefficient of formation water is 5.66×10−4 MPa−1, and compressibility coefficient of rock is 8.73×10−4 MPa−1. The well pattern is row pattern, with well spacing of 500 m, row spacing of 500 m, and the wellbore diameter is 0.1778 m. The minimum pressure during reservoir development must be higher than saturation pressure, so the minimum bottom hole pressure pwf is set to be 20 MPa. From the above reservoir conditions, it can be seen the N reservoir and the M water layer have high porosity, high permeability, weak anisotropy, high production index and high injectivity index, and the oil viscosity is low, so the N reservoir is suitable for dump flooding (Fig. 3). 2.1.1.
Calculation of dump flooding threshold pressure
The initial pressure of N reservoir was 39.34 MPa which is
2
qiw qiw h ⎛ qiw ⎞ + + aρw λ ⎜ ⎟ + bρ w gh (25) I w Jw 2d ⎝ A ⎠ 2
h h ⎛ qiw ⎞ 1 1 + + a ρ w λ 2 qiw + a ρ w ⎜ ⎟ λ ′(qiw ) I w Jw dA 2d ⎝ A ⎠ (26) Give equation F(qiw)=0 an initial solution qiw(n=0), then
F ′ ( qiw ) =
qiw ( n +1) = qiw ( n ) −
F ⎡⎣ qiw ( n ) ⎤⎦ F ′ ⎡⎣ qiw ( n ) ⎤⎦
(n=0, 1, …, N)
Fig. 2.
Profile of N reservoir and M water layer.
(27)
Set an error bond ε, if |qiw(n+1)−qiw(n)|≤ε, then qiw(n+1) is the solution of F(qiw)=0, that’s the solution of equation (9). Finally, we get the water injection rate at any time. A computing program of dump flooding has been made based on the above mechanism, the program can compute water injection rate, oil and water producing rate, water layer − 693 −
Fig. 3.
Schematic of dump flooding in N reservoir.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
much higher than saturation pressure of 19.24 MPa and initial water layer pressure of 25.48 MPa, so firstly an expansion drive was taken for the reservoir to decrease the reservoir pressure and build a differential pressure between N reservoir and M water layer, then dump flooding was taken. In this case, the development mode was converted from expansion drive to dump flooding when the N reservoir pressure decreased to the critical pressure that can’t maintain the stable liquid production, from equation (17) we can get the critical pressure is 23.79 MPa, this is also the pressure poi at the beginning of dump flooding. The plateau production was 397.5 m3/d. Based on the definition of dump flooding, to satisfy injection and production balance under designed production rate during dump flooding, the injection and production rate should be 592 m3/d. Other parameters needed are as follows: reservoir injectivity index of 116.74 m3/(d·MPa), differential pressure between N reservoir and wellbore of 5.07 MPa, production index of M water layer of 137.16 m3/(d·MPa), differential pressure between wellbore and M water layer of 4.31 MPa, wellbore length between M water layer and reservoir of 1 478.9 m, friction pressure loss in wellbore of 0.01 MPa, water column pressure in wellbore of 14.48 MPa. Based on equation (7) and the above parameters, the calculated threshold pressure of dump flooding for the N reservoir is 18.69 MPa, much lower than the M water layer pressure of 25.48 MPa, so N reservoir can be developed by dump flooding. 2.1.2.
Calculation of dump flooding parameters
The dump flooding parameters of N reservoir were calculated based on the dump flooding computing program to evaluate the development effect of dump flooding in the N reservoir. The changes of water injection rate, oil production rate, oil layer pressure, water layer pressure with time were computed and compared with the results computed by Eclipse software (Figs. 4 and 5) . The friction pressure loss in wellbore was computed by multiple well model in Eclipse model:
Fig. 5. Curve of injection rate, production rate with time during dump flooding.
h ρwv2 (28) d The calculation method of friction pressure loss used in equation (28) is a little different from that used in equation (4), but the friction pressure loss in the wellbore is very small, so the difference of these two methods had little effect on the computing results. The result computed by the model in this paper and that computed by Eclipse software are nearly the same, indicating the computing method in this paper is reliable. Dump flooding was started in N reservoir when the reservoir pressure decreased to 23.79 MPa. In the initial phase, the differential pressure between oil layer and water layer was high, so the dump flooding rate was large and the oil layer pressure increased a little; then as the dump flooding rate decreased constantly and the production rate of the oil layer stayed the same, the oil layer pressure decreased slowly. The oil layer pressure had been kept above 60% of initial pressure for 2.92 years and the water layer pressure continuously decreased (Fig. 4). The dump flooding rate was 1 005.77 m3 at maximum in the beginning, and then it gradually decreased as the differential pressure between oil layer and water layer decreased. Water broke through 1.78 years after the dump flooding, then water cut increased and oil production decreased rapidly (Fig. 5). Five years after the dump flooding started, the cumulative oil production was 438 891 m3, cumulative water production was 167 759 m3. The production plateau would only last for 0.6 years if the reservoir was developed by expansion drive. Dump flooding make the production plateau 1.78 years longer and the recovery 6.37% higher (Fig. 6). The calculation results show that, the dump flooding in N reservoir was good at keeping reservoir pressure, maintaining production plateau and improving oil recovery. pf = 2 f
2.2. Fig. 4. Curve of reservoir pressure, water layer pressure with time during dump flooding.
2.2.1.
− 694 −
Factors affecting dump flooding Water-oil reserve ratio
In the above case, water reserves is 15 times the oil reserves,
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
Fig. 6. drive.
Oil production curve of dump flooding and expansion Fig. 8. Effect of dump flooding timing on production plateau and recovery.
Fig. 7. Effect of water-oil reserve ratio on dump flooding production plateau and recovery.
assuming the water-oil reserve ratio is 1, 15, 30, 45, 60, 75, 90, 105, 120 respectively, the effect of different water-oil reserve ratio on dump flooding development is investigated (Fig. 7). To find out the effect of different water-oil reserve ratio on production plateau, the program was changed to produce at a constant oil rate. The results show that when water-oil reserve ratio is less than 60, production plateau extends with the increase of water-oil reserve ratio, when water-oil ratio is more than 60, its effect is negligible. The longest production plateau is about 5.46 years. Then the effect of different water-oil reserve ratio on recovery was studied. The results show that when water-oil reserve ratio is less than 60, oil recovery increases with the increase of water-oil reserve ratio, when water-oil ratio is more than 60, its effect is also negligible. The highest recovery of dump flooding is 19.08%. 2.2.2.
Timing of dump flooding
In the above case, the N reservoir was developed by expansion drive firstly, when the reservoir pressure decreased to the critical pressure that couldn’t maintain the production plateau (60% of the initial reservoir pressure), it was converted to dump flooding. At the water-oil reserve ratio of 15, assuming the development mode was converted from expansion drive to dump flooding when the reservoir pressure decreased to 100%,
90%, 80%, 70%, 60% of the initial reservoir pressure respectively, the effect of dump flooding conversion timing on development result was studied (Fig. 8). The program was improved to consider the two phases of expansion drive and dump flooding. The results show that the later the timing of dump flooding conversion, the longer the production plateau and the higher the recovery of expansion drive + dump flooding, that’s because the formation energy is more fully used. Therefore, the later the timing of dump flooding conversion will be better. But the time shall not be too late because the dissolved gas will release and have an adverse effect on the development. So the best timing of dump flooding conversion should be before the reservoir pressure decreases to the saturation pressure.
3.
Conclusions
Dump flooding needs enough differential pressure between water layer and oil layer to overcome differential pressure between water layer and wellbore, friction pressure loss in wellbore, water column pressure in wellbore and water injection differential pressure between wellbore and oil layer. That is to say the water layer pressure should be higher than the threshold pressure of dump flooding. Based on fundamental of fluid mechanics and reservoir engineering, the expression of dump flooding threshold pressure was built, the computing method of water injection rate, oil and water producing rate, water layer pressure, oil layer pressure, cumulative water injection, cumulative water and oil production during dump flooding have been proposed, and the computing program was compiled by VB. A case study of the dump flooding computing method show that the method simple in principle, reasonable and reliable in calculation results, is suitable for calculating dump flooding parameters. The factors affecting dump flooding were analyzed by using the computing program. The results show that when water-oil reserve ratio is less than 60, production plateau extends and oil recovery increases with the increase of water-oil reserve ratio, when water-oil reserve ratio is more than 60, its effect is negligible; the timing of dump flooding conversion
− 695 −
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
has a significant effect on production plateau and oil recovery, the later the timing of dump flooding conversion, the longer the production plateau and the higher the recovery of the reservoir will be.
T—water breakthrough time, d; v —flow velocity of water in wellbore, m/s; Wiw—cumulative water injection, m3; Wiw(T)—cumulative water injection when water breaks through, m3; Wp—cumulative water production, m3; λ—hydraulic friction coefficient, f; μo—oil viscosity, mPa·s; μw—water viscosity, mPa·s; ρw—formation water density, kg/m3; φ —porosity of oil layer, %.
Nomenclature A—sectional area of the flow region, m2; A0—sectional area of the wellbore, m2; a, b—unit conversion factor, a is 2.296 68×10−15, b is ±1×10−6, b is negative when the water layer is above the oil layer, b is positive when water layer is below the oil layer; Bo—volume factor of oil, m3/m3; Boi—initial volume factor of oil, m3/m3; Bw—volume factor of water, m3/m3; Cto—total compressibility of the oil layer, MPa−1; Ctw—total compressibility of the water layer, MPa−1; d—wellbore diameter, m; f—Fanning factor; fw—water cut; fw′—derivate of water cut; g —acceleration of gravity, m/s2; h—the length of the wellbore between water layer and oil layer, m; Iw—injectivity index of the oil layer, m3/(d·MPa); JL—production index of the oil layer, m3/(d·MPa); JL0—production index when water cut is 0, m3/(d·MPa); Jw—production index of the water layer, m3/(d·MPa); Kro—relative permeability of oil phase; Krw—relative permeability of water phase; L—well spacing between injection and production well, m; n—number of iterations; N—end number of iterations; No—reserves of the oil layer, m3; Np—cumulative oil production, m3; Nw—reserves of the water layer, m3; pc—critical pressure, MPa; pf —friction pressure loss in wellbore, MPa; ph—water column pressure in wellbore, MPa; po—oil layer pressure, MPa; pob—differential pressure between wellbore and oil layer, MPa; poi—initial oil layer pressure at the beginning of dump flooding, MPa; pth—threshold pressure of dump flooding, MPa; pw—water layer pressure, MPa; pwb—differential pressure between water layer and wellbore, MPa; pwf —minimum bottom hole pressure, MPa; pwi—initial water layer pressure, MPa; qc—stable liquid production rate of the oil layer, m3/d; qiw—water injection rate of dump flooding, m3/d; qL—liquid production, m3/d; qo—oil production, m3/d; qth—threshold water injection rate of dump flooding, also threshold water production rate of water layer, m3/d; qw—water production rate of water layer, m3/d; Re—Reynolds number; Sw—water saturation, f; Swf —frontal water saturation of water flooding, f; Swi—initial water saturation, f; Swo—water saturation at exit end, f; t —water injection time, d;
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RESEARCH PAPER
Development mechanisms and influencing factors of dump flooding SU Haiyang1,*, MU Longxin1, HAN Haiying1, LIU Yongge2, LI Bo1 1. PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China; 2. China University of Petroleum (East China), Qingdao 266580, China
Abstract: Aiming at the problem that the theory of dump flooding is not mature, this study examined the suitable reservoir conditions for dump flooding, defined the concept of “dump flooding threshold pressure” and its expression based on fluid mechanics and reservoir engineering fundamentals, and proposed the computing method of water injection rate, producing rate, water layer pressure, oil layer pressure, cumulative injection and cumulative production. It gave the corresponding computing program according to the proposed computing method, and made a case study and analyzed the factors affecting dump flooding using the program. The dump flooding computing methods are reasonable and applicable; when water reserve-oil reserve ratio is less than 60, production plateau extends with and oil recovery increases with the increase of water reserve-oil reserve ratio, when water reserve-oil reserve ratio is more than 60, the effect of the ratio of water reserve to oil reserve is negligible; the timing of dump flooding has a significant effect on production plateau and oil recovery, the later the dump flooding injection timing, the more completely the formation energy will be used, the longer the production plateau and the higher the recovery will be. Key words: dump flooding; development pattern; threshold pressure; stable production duration; recovery rate; water injection timing
Introduction
1.
Mechanism of dump flooding
Dump flooding refers to the process in which water in high-pressure water layer flows into low-pressure oil layer under pressure differential through casing to maintain reservoir pressure and displace oil[1]. At present, dump flooding is mainly used to supplement energy before water flooding, and is suitable for regions where ground water is scarce[2−3]. This technique has been rarely used in China, with only precedent in the Pinghu oilfield[4]; while the research in this aspect has been started since the 1970s, and the technique has been used mostly in the Middle East[5−8]. The published papers on dump flooding are mainly on its application, while the mechanisms of dump flooding haven’t been examined systematically. Davies C A[1] discussed the calculation method of dump flooding injection rate without considering the situation after water breakthrough. In this study, the mechanisms of dump flooding have been studied further, a method of calculating water injection rate, oil production rate, oil layer pressure and water layer pressure in the process of dump flooding has been worked out, and the application effect of this method has been analyzed.
1.1.
Threshold pressure of dump flooding
Dump flooding needs enough differential pressure between water layer and oil layer to overcome differential pressure between water layer and wellbore, friction pressure loss in wellbore, water column pressure in wellbore and water injection differential pressure between wellbore and oil layer[9−10]. In order to quantify this process, according to the research achievement of document [11], the concept of “threshold pressure of dump flooding” is defined in this paper, that is the water layer pressure which can maintain the balance of injected and produced fluid in oil layer at designed production rate through dump flooding, and likewise, the “threshold water injection rate of dump flooding” is defined as water injection rate which can keep the injected and produced fluid balance in oil layer at designed production rate through dump flooding. Based on the definition, threshold pressure of dump flooding can be expressed as follows: pth = poi + pob + pf + pwb + ph (1) The differential pressure between water layer and wellbore is
Received date: 31 Aug. 2014; Revised date: 27 May 2015. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the PetroChina Science and Technology Major Project. Copyright © 2015, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
pwb = qth J w
(2)
The differential pressure between wellbore and oil layer is pob = qth I w (3) Based on Darcy-Weisbach equation[12], the friction pressure loss in wellbore is
pf = a ρ w g λ
h v2 h ⎛ qth ⎞ = aρw λ ⎜ ⎟ d 2g 2d ⎝ A0 ⎠
2
(4)
The friction factor is
λ=
0.316 4 μw Aμ = 0.316 4 4 = 0.316 4 4 0 w 4 ρ w vd ρ w qth d Re
(5)
Water column pressure in wellbore is ph = bρ w gh
The critical pressure can be calculated as q pc = pwf + c JL
(6)
Substituting equations (2)-(6) into equation (1) we can get 2
qth qth h ⎛ qth ⎞ + + aρw λ (7) ⎜ ⎟ + bρ w gh Iw Jw 2d ⎝ A0 ⎠ The threshold pressure of dump flooding can be computed by equation (7). The reservoir can be developed at the designed production rate by dump flooding technology only if the water layer pressure is above the threshold pressure. pth = poi +
1.2.
sure and the differential pressure between water layer and oil layer will decrease constantly, based on equation (9), the water injection rate will decrease too. When water injection rate is lower than oil production rate, the oil layer pressure also begins to decrease. When the oil layer pressure decreases to a critical pressure that can’t maintain the stable liquid production, the production will turn to produce at a stable bottom hole pressure, at this point, the liquid production rate can be expressed as qL = qo + qw = J L ( po − pw f ) (16)
Calculation of dump flooding
During dump flooding, the water injection rate is controlled by the water layer pressure and oil layer pressure, conversely, the water injection rate affects the water layer pressure and oil layer pressure, and the production plateau and recovery, so the calculation of water injection rate is very important. Assuming at a time t, water injection rate is qiw, oil production rate in the oil layer is qo, water production rate is qw, water layer pressure is pw, oil layer pressure is po, based on pressure relationship we can get pw = po + pob + pf + pwb + ph (8)
(17)
Before water breakthrough, qw=0, Wp=0, qL=qo, the production index is constant. Based on equations (9)-(13), (15) or (16) we can get the 6 unknown parameters: qiw, Wiw, qo, Np, po, pw, the computing process is shown in Fig. 1. At the point of water breakthrough, based on Buckley-Leverett theory[14] we can get f ′( S ) T L = w wf ∫ qi w dt (18) 0 φA The cumulative water injection at the point of water breakthrough is T φ AL Wiw(T ) = ∫ qiw dt = (19) 0 f w ′( S wf ) Based on oil-water relative permeability curve we can get
With the same derivation as equations (2)-(7), we can get 2
h ⎛ qiw ⎞ q q pw = po + iw + iw + a ρ w λ (9) ⎜ ⎟ + bρ w gh Iw Jw 2d ⎝ A0 ⎠ The cumulative water injection, cumulative oil production and cumulative water production at time t are t
Wiw = ∫ qiw dt 0
t
N p = ∫ qo dt 0 t
Wp = ∫ qw dt 0
(10) (11) (12) [13]
For the oil layer, based on material balance equation we can get Wi w − N p Bo − Wp = N o BoiCto ( po − poi ) (13)
For the water layer, based on material balance equation we can get Wiw = N w Bw Ctw ( pwi − pw ) (14) If the oil layer is producing at constant liquid production rate, then qL = qo + qw = qc (15) With the ongoing of dump flooding, the water layer pres− 692 −
Fig. 1.
Schematic of dump flooding computing program.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
the relationship fw-Sw and fw′-Sw, and then the fw′(Swf) value can be worked out, finally the Wiw(T) value is obtained based on equation (19). Based on the Wiw(T) value we can get the water breakthrough time. After water breakthrough, equation (18) can be written as f ′( S ) t L = w wo ∫ qiw dt (20) 0 φA So we can get f w ′( S wo ) =
φ AL t
∫q 0
iw
dt
=
φ AL
(21)
Wiw
Based on oil-water relative permeability curve we can get the relationship fw-Sw and fw′-Sw, in combination with fw′(Swo) value from equation (21) we can get the water cut at exit end fw(Swo), so the water production rate and oil production rate at a point after water breakthrough are qw = q L f w (22) qo = qL (1 − f w )
(23)
After water breakthrough, the production index JL changes with the water cut. According to the document [15], the ratio of production index at a point after water breakthrough to production index at the point with water cut of 0 is J L K ro ( S w ) K rw ( S w ) μo = + (24) J L0 K ro ( S wi ) K ro ( S wi ) μ w The production index at different water cut after water breakthrough can be calculated based on equation (24). After water breakthrough, based on the 11 equations (9)-(15)(or (16)), (21)—(24) and permeability curve we can get the 11 unknown parameters: qiw, Wiw, JL, qL, fw, qo, Np, qw, Wp, pw, po, the computing process is shown in Fig. 1. From the process of computing the dump flooding parameters, we can find that the difference between artificial water flooding and dump flooding is embodied in equation (9), that is the water injection rate in dump flooding is controlled by the water layer pressure and oil layer pressure. Equation (9) is a nonlinear equation about qiw which can be solved by Newton iterative method [16]. Let F (qiw) be the function of qiw: F ( qiw ) = po − pw +
pressure, oil layer pressure, cumulative water injection, cumulative water and oil production at any time during dump flooding.
2. Application of dump flooding computing method 2.1.
A case study
The N reservoir in the Middle East is in a desert with scarce ground water. There is an M water layer 1478 m above the N reservoir (shown in Fig. 2). The N reservoir consisting of quartz sandstone of weak heterogeneity, has a porosity of 18%−21%, permeability of about 500−700×10−3 μm2, initial reservoir pressure of 39.34 MPa, saturation pressure of 19.24 MPa, thickness of 15 m, the injectivity index of 116.74 m3/(d·MPa), and production index of 104.87 m3/(d·MPa). The M water layer has water reserves 15 times of the oil reserves in N reservoir, a porosity of about 22.4%, permeability of 600×10−3 μm2, initial formation pressure of 25.48 MPa;, and the injectivity index of 137.16 m3/(d·MPa). The fluid properties are as follows: the oil volume factor at initial reservoir pressure is 1.49, formation water viscosity is 0.68 mPa·s, oil viscosity is 0.90 mPa·s, compressibility coefficient of oil is 24.5×10−4 MPa−1, compressibility coefficient of formation water is 5.66×10−4 MPa−1, and compressibility coefficient of rock is 8.73×10−4 MPa−1. The well pattern is row pattern, with well spacing of 500 m, row spacing of 500 m, and the wellbore diameter is 0.1778 m. The minimum pressure during reservoir development must be higher than saturation pressure, so the minimum bottom hole pressure pwf is set to be 20 MPa. From the above reservoir conditions, it can be seen the N reservoir and the M water layer have high porosity, high permeability, weak anisotropy, high production index and high injectivity index, and the oil viscosity is low, so the N reservoir is suitable for dump flooding (Fig. 3). 2.1.1.
Calculation of dump flooding threshold pressure
The initial pressure of N reservoir was 39.34 MPa which is
2
qiw qiw h ⎛ qiw ⎞ + + aρw λ ⎜ ⎟ + bρ w gh (25) I w Jw 2d ⎝ A ⎠ 2
h h ⎛ qiw ⎞ 1 1 + + a ρ w λ 2 qiw + a ρ w ⎜ ⎟ λ ′(qiw ) I w Jw dA 2d ⎝ A ⎠ (26) Give equation F(qiw)=0 an initial solution qiw(n=0), then
F ′ ( qiw ) =
qiw ( n +1) = qiw ( n ) −
F ⎡⎣ qiw ( n ) ⎤⎦ F ′ ⎡⎣ qiw ( n ) ⎤⎦
(n=0, 1, …, N)
Fig. 2.
Profile of N reservoir and M water layer.
(27)
Set an error bond ε, if |qiw(n+1)−qiw(n)|≤ε, then qiw(n+1) is the solution of F(qiw)=0, that’s the solution of equation (9). Finally, we get the water injection rate at any time. A computing program of dump flooding has been made based on the above mechanism, the program can compute water injection rate, oil and water producing rate, water layer − 693 −
Fig. 3.
Schematic of dump flooding in N reservoir.
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
much higher than saturation pressure of 19.24 MPa and initial water layer pressure of 25.48 MPa, so firstly an expansion drive was taken for the reservoir to decrease the reservoir pressure and build a differential pressure between N reservoir and M water layer, then dump flooding was taken. In this case, the development mode was converted from expansion drive to dump flooding when the N reservoir pressure decreased to the critical pressure that can’t maintain the stable liquid production, from equation (17) we can get the critical pressure is 23.79 MPa, this is also the pressure poi at the beginning of dump flooding. The plateau production was 397.5 m3/d. Based on the definition of dump flooding, to satisfy injection and production balance under designed production rate during dump flooding, the injection and production rate should be 592 m3/d. Other parameters needed are as follows: reservoir injectivity index of 116.74 m3/(d·MPa), differential pressure between N reservoir and wellbore of 5.07 MPa, production index of M water layer of 137.16 m3/(d·MPa), differential pressure between wellbore and M water layer of 4.31 MPa, wellbore length between M water layer and reservoir of 1 478.9 m, friction pressure loss in wellbore of 0.01 MPa, water column pressure in wellbore of 14.48 MPa. Based on equation (7) and the above parameters, the calculated threshold pressure of dump flooding for the N reservoir is 18.69 MPa, much lower than the M water layer pressure of 25.48 MPa, so N reservoir can be developed by dump flooding. 2.1.2.
Calculation of dump flooding parameters
The dump flooding parameters of N reservoir were calculated based on the dump flooding computing program to evaluate the development effect of dump flooding in the N reservoir. The changes of water injection rate, oil production rate, oil layer pressure, water layer pressure with time were computed and compared with the results computed by Eclipse software (Figs. 4 and 5) . The friction pressure loss in wellbore was computed by multiple well model in Eclipse model:
Fig. 5. Curve of injection rate, production rate with time during dump flooding.
h ρwv2 (28) d The calculation method of friction pressure loss used in equation (28) is a little different from that used in equation (4), but the friction pressure loss in the wellbore is very small, so the difference of these two methods had little effect on the computing results. The result computed by the model in this paper and that computed by Eclipse software are nearly the same, indicating the computing method in this paper is reliable. Dump flooding was started in N reservoir when the reservoir pressure decreased to 23.79 MPa. In the initial phase, the differential pressure between oil layer and water layer was high, so the dump flooding rate was large and the oil layer pressure increased a little; then as the dump flooding rate decreased constantly and the production rate of the oil layer stayed the same, the oil layer pressure decreased slowly. The oil layer pressure had been kept above 60% of initial pressure for 2.92 years and the water layer pressure continuously decreased (Fig. 4). The dump flooding rate was 1 005.77 m3 at maximum in the beginning, and then it gradually decreased as the differential pressure between oil layer and water layer decreased. Water broke through 1.78 years after the dump flooding, then water cut increased and oil production decreased rapidly (Fig. 5). Five years after the dump flooding started, the cumulative oil production was 438 891 m3, cumulative water production was 167 759 m3. The production plateau would only last for 0.6 years if the reservoir was developed by expansion drive. Dump flooding make the production plateau 1.78 years longer and the recovery 6.37% higher (Fig. 6). The calculation results show that, the dump flooding in N reservoir was good at keeping reservoir pressure, maintaining production plateau and improving oil recovery. pf = 2 f
2.2. Fig. 4. Curve of reservoir pressure, water layer pressure with time during dump flooding.
2.2.1.
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Factors affecting dump flooding Water-oil reserve ratio
In the above case, water reserves is 15 times the oil reserves,
SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
Fig. 6. drive.
Oil production curve of dump flooding and expansion Fig. 8. Effect of dump flooding timing on production plateau and recovery.
Fig. 7. Effect of water-oil reserve ratio on dump flooding production plateau and recovery.
assuming the water-oil reserve ratio is 1, 15, 30, 45, 60, 75, 90, 105, 120 respectively, the effect of different water-oil reserve ratio on dump flooding development is investigated (Fig. 7). To find out the effect of different water-oil reserve ratio on production plateau, the program was changed to produce at a constant oil rate. The results show that when water-oil reserve ratio is less than 60, production plateau extends with the increase of water-oil reserve ratio, when water-oil ratio is more than 60, its effect is negligible. The longest production plateau is about 5.46 years. Then the effect of different water-oil reserve ratio on recovery was studied. The results show that when water-oil reserve ratio is less than 60, oil recovery increases with the increase of water-oil reserve ratio, when water-oil ratio is more than 60, its effect is also negligible. The highest recovery of dump flooding is 19.08%. 2.2.2.
Timing of dump flooding
In the above case, the N reservoir was developed by expansion drive firstly, when the reservoir pressure decreased to the critical pressure that couldn’t maintain the production plateau (60% of the initial reservoir pressure), it was converted to dump flooding. At the water-oil reserve ratio of 15, assuming the development mode was converted from expansion drive to dump flooding when the reservoir pressure decreased to 100%,
90%, 80%, 70%, 60% of the initial reservoir pressure respectively, the effect of dump flooding conversion timing on development result was studied (Fig. 8). The program was improved to consider the two phases of expansion drive and dump flooding. The results show that the later the timing of dump flooding conversion, the longer the production plateau and the higher the recovery of expansion drive + dump flooding, that’s because the formation energy is more fully used. Therefore, the later the timing of dump flooding conversion will be better. But the time shall not be too late because the dissolved gas will release and have an adverse effect on the development. So the best timing of dump flooding conversion should be before the reservoir pressure decreases to the saturation pressure.
3.
Conclusions
Dump flooding needs enough differential pressure between water layer and oil layer to overcome differential pressure between water layer and wellbore, friction pressure loss in wellbore, water column pressure in wellbore and water injection differential pressure between wellbore and oil layer. That is to say the water layer pressure should be higher than the threshold pressure of dump flooding. Based on fundamental of fluid mechanics and reservoir engineering, the expression of dump flooding threshold pressure was built, the computing method of water injection rate, oil and water producing rate, water layer pressure, oil layer pressure, cumulative water injection, cumulative water and oil production during dump flooding have been proposed, and the computing program was compiled by VB. A case study of the dump flooding computing method show that the method simple in principle, reasonable and reliable in calculation results, is suitable for calculating dump flooding parameters. The factors affecting dump flooding were analyzed by using the computing program. The results show that when water-oil reserve ratio is less than 60, production plateau extends and oil recovery increases with the increase of water-oil reserve ratio, when water-oil reserve ratio is more than 60, its effect is negligible; the timing of dump flooding conversion
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SU Haiyang et al. / Petroleum Exploration and Development, 2015, 42(5): 691–696
has a significant effect on production plateau and oil recovery, the later the timing of dump flooding conversion, the longer the production plateau and the higher the recovery of the reservoir will be.
T—water breakthrough time, d; v —flow velocity of water in wellbore, m/s; Wiw—cumulative water injection, m3; Wiw(T)—cumulative water injection when water breaks through, m3; Wp—cumulative water production, m3; λ—hydraulic friction coefficient, f; μo—oil viscosity, mPa·s; μw—water viscosity, mPa·s; ρw—formation water density, kg/m3; φ —porosity of oil layer, %.
Nomenclature A—sectional area of the flow region, m2; A0—sectional area of the wellbore, m2; a, b—unit conversion factor, a is 2.296 68×10−15, b is ±1×10−6, b is negative when the water layer is above the oil layer, b is positive when water layer is below the oil layer; Bo—volume factor of oil, m3/m3; Boi—initial volume factor of oil, m3/m3; Bw—volume factor of water, m3/m3; Cto—total compressibility of the oil layer, MPa−1; Ctw—total compressibility of the water layer, MPa−1; d—wellbore diameter, m; f—Fanning factor; fw—water cut; fw′—derivate of water cut; g —acceleration of gravity, m/s2; h—the length of the wellbore between water layer and oil layer, m; Iw—injectivity index of the oil layer, m3/(d·MPa); JL—production index of the oil layer, m3/(d·MPa); JL0—production index when water cut is 0, m3/(d·MPa); Jw—production index of the water layer, m3/(d·MPa); Kro—relative permeability of oil phase; Krw—relative permeability of water phase; L—well spacing between injection and production well, m; n—number of iterations; N—end number of iterations; No—reserves of the oil layer, m3; Np—cumulative oil production, m3; Nw—reserves of the water layer, m3; pc—critical pressure, MPa; pf —friction pressure loss in wellbore, MPa; ph—water column pressure in wellbore, MPa; po—oil layer pressure, MPa; pob—differential pressure between wellbore and oil layer, MPa; poi—initial oil layer pressure at the beginning of dump flooding, MPa; pth—threshold pressure of dump flooding, MPa; pw—water layer pressure, MPa; pwb—differential pressure between water layer and wellbore, MPa; pwf —minimum bottom hole pressure, MPa; pwi—initial water layer pressure, MPa; qc—stable liquid production rate of the oil layer, m3/d; qiw—water injection rate of dump flooding, m3/d; qL—liquid production, m3/d; qo—oil production, m3/d; qth—threshold water injection rate of dump flooding, also threshold water production rate of water layer, m3/d; qw—water production rate of water layer, m3/d; Re—Reynolds number; Sw—water saturation, f; Swf —frontal water saturation of water flooding, f; Swi—initial water saturation, f; Swo—water saturation at exit end, f; t —water injection time, d;
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