The key point in the understanding of these reservoirs is the natural water ...... Xie, X. and Morrow N.: âOil recovery by spontaneous imbibition from weakly ...
SPE 89421 Experimental and Numerical Study of Water-Gas Imbibition Phenomena in Vuggy Carbonates Egermann P., IFP, Institut Français du Pétrole, Laroche C., IFP, Manceau E., IFP, Delamaide E., IFP Technologies Inc, Bourbiaux B., IFP
Copyright 2004, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2004 SPE/DOE Fourteenth Symposium on Improved Oil Recovery held in Tulsa, Oklahoma, U.S.A., 17–21 April 2004. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Tight gas carbonate fields are often faced with early water breakthrough in the presence of fractures connected with an active aquifer. The recovery assessment from such fields requires to take into account the role played by water imbibition of the matrix which, depending on the fracture density and rock properties, can significantly delay water breakthrough. The prediction of such spontaneous imbibition phenomena requires experimental measurements and modeling in the case of rocks of complex porous structure like vuggy carbonates. This paper gives the results of such investigation on samples from a vuggy carbonate field. A thorough petrophysical characterization of the rock was first carried out, followed by water-gas imbibition experiments. Those experiments were finally simulated numerically to check the consistency of the experimental data set and further understand the fluid flow behaviour of those peculiar media. The porous structure of several samples was characterized from capillary pressure and NMR measurements. Spontaneous imbibition was found to be very slow, which required the implementation of a specific accurate measurement device. This slow kinetics was due to the very low mobility of water, which was measured separately as well. To explain this flow behavior, the peculiarity of the porous structure - fairly large vugs dispersed within a tight matrix with very small pore thresholds - is invoked. Simulations on a representative pore network model actually revealed that the flow ability of the water phase is considerably hindered in such type of medium. Finally, the spontaneous imbibition behavior was satisfactorily reproduced with single-porosity and dual-porosity models using the measured petrophysical parameters, thus showing the consistency of the measured data set.
Gas production management from vuggy carbonate reservoirs subjected to water encroachment requires a specific evaluation of matrix imbibition phenomenon as the latter is ruled by unconventional flow parameters linked to the complex two-phase flow interactions between vugs and micropores in such media. Introduction Significant gas reserves are contained in fractured vuggy carbonate reservoirs, which may be faced with early water production leading to well shut-in and low gas recovery. Several of these fractured carbonate gas fields are located in the foothills of the Rocky Mountains with volumes in place 123 exceeding 1 Tcf for the largest ones. , , Reservoirs consist of tight dolomitized carbonates with a permeability generally less than 1 md. Fractures provide the main contribution to well productivities but are responsible for matrix gas bypassing and early water breakthroughs leading to premature well shut-in. Hence, most of these fields have now reached the phase of abandonment with abnormally-low gas recovery factors. The key point in the understanding of these reservoirs is the natural water imbibition of the matrix that occurs with the fracture network invasion by water. This natural imbibition plays a major role in the water breakthrough time prediction at the producers and also in the final gas recovery estimation. This paper is a contribution in the understanding of these mechanisms in vuggy carbonate reservoirs where the complex pore structure (vugs) affects the production kinetics and the recovery from the matrix. The selected approach consists in first performing and analysing laboratory experiments of natural imbibition mechanisms on representative core samples, then in deriving the involved parameters from the numerical simulation of these experiments. Laboratory study Background Spontaneous imbibition has been studied for a long time in the laboratory because this process is of primary importance to assess the hydrocarbon recovery from fractured reservoirs. Most of the published works are related to water/oil system, when water imbibes samples initially at connate water saturation. In this case, the scaling-up of laboratory
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experiments to reservoir conditions has been widely studied and some approaches exist that enable to predict quite well the 456 oil recovery. , , The published results are scarcer for gas/water system. Most papers are mainly focused on the value of residual saturation alone.7,8 Hence, few papers deal with the water imbibition kinetics although the scaling-up problem appears more complicated in this case.9 Three of these papers are entirely focused on the imbibition process of Western Canadian carbonate samples.10,11,12 A petrophysical characterization study of these carbonates is also proposed by Carlson.13 Core selection Sampling One set of cores was collected from a representative fractured vuggy carbonate gas reservoir. The samples are dolomitized carbonates, with intercrystalline porosity and vugs, and are sometime crossed by fractures. The petrophysical data available on neighbour samples shows that the reservoir is not homogeneous. Some parts of the reservoir can reach porosity as high as 12.7%, whereas other parts can be very tight (1.5% porosity). The variability of the reservoir porosity can even be detected visually as some plugs appear rather homogeneously tight whereas others appear highly vuggy. It leads also to a great variability in the permeability of the reservoir as a function of the depth.
to low-density regions (vugs) whereas the white areas correspond to high-density regions (tight matrix). A qualitative comparison of the samples using Figure 1 confirms the heterogeneity of the reservoir. Mainly three categories of samples can be separated from the longitudinal scans: Low-density, homogeneous samples: 3 and 9 Low-density, heterogeneous samples: 0, 1, 5 and 7 High-density and fairly homogeneous samples: 8, 14 and 16 This classification is also confirmed by the cross-section photographs as shown in Figure 2. Sample 3 (left side view) appears as a dark grey medium including uniformlydistributed dark spots, which corresponds to a vuggy porous matrix medium. Sample 5 (middle view) shows a few large black spots, corresponding to large vugs, among a somewhat brighter, i.e. tighter, matrix medium than in Sample 3. Sample 14 (right side view) appears as a uniformly-bright, i.e. very tight, matrix medium, crossed by a white line representing a dense fully-cemented fracture. Sample 3
Sample 5
Sample 14
Figure 2 : Typical CT cross-sections of samples CT screening of the samples Due to the expected low values of the rock porosity, the larger plugs were preferred in order to reduce the experimental uncertainty on saturation values derived from mass balance. The highly heterogeneous or tight samples were also rejected due to a lack of representativity. Hence, the CT screening was only conducted on nine samples: 0, 1, 3, 5, 7, 8, 9, 14 and 16.
Sample 0
Sample 5
Sample 9
Selection Two criteria were followed to select the samples: Good homogeneity to enable the interpretation of measurements at core scale Low density to ensure that the sample porosity is large enough for a sufficient accuracy of laboratory measurements. The first criterion was quantitatively assessed by calculating a heterogeneity index HI . The local value of HI for crosssection k of a given sample is defined as:
HI k =
std k − Min( std k ) Min( std k )
HI =
Sample 1
Sample 7
Sample 14
1 N k HI N k =1
where stdk refers to the standard deviation of the CT attenuation signal within cross-section k; N is the total number of cross-sections.
Sample 3
Sample 8
Sample 16
Figure 1 : Longitudinal CT-scans of the samples The nine samples were CT-scanned longitudinally and transversely (cross-section) every 5 mm. Longitudinal scans of all samples are shown in Figure 1. The dark areas correspond
When all the cross-sections have the same order of standard deviation, HI decreases, which means that the sample is very homogeneous, whereas HI increases when variations of the standard deviation exist due to petrophysical contrasts along sample axis. Two examples of HI profiles can be compared in Figure 3. Sample 3 is clearly more homogeneous than sample
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1. The second criterion is directly related to the CT attenuation amplitude. The higher the attenuation, the higher the density and the lower the porosity. Figure 4 plots the CT attenuation as a function of the heterogeneity index for the nine samples. The right part of the figure corresponds to the most heterogeneous samples, whereas the upper part corresponds to the least porous samples. When a 25% cut-off is considered for HI and 2300 for the CT attenuation, it can be seen from Figure 4 that four samples can be easily selected (3, 5, 7 and 9) using the two criteria.
Figure 5 : longitudinal slice of sample 3 Core preparation and characterization Coring The four best samples (3, 5, 7 and 9) were carefully plugged in order to have some spare cores rapidly available in case of rock damage during the study. In each case, it was possible to extract one 4 cm diameter core with a length around 5 cm. For each sample, the best part of the end cut was also recovered in order to perform Mercury injection analysis.
120% Sample 3: average HI = 10.3%
100% Sample 1: average HI = 38.55%
80%
HI (%)
homogeneous from the CT-scanner analysis at the sample scale according to HI values but this is no longer valid at a centimetric to millimetric scale.
60% 40%
Cleaning Both cores and end cuts were cleaned using a Soxhlet device. Toluene was used as the cleaning solvent. The cleaning procedure was applied continuously for 1 week. The colour of the Toluene remained very clear during all the cleaning process showing that the cores were already very clean naturally.
20% 0% 0
10
20
30
40
50
60
70
Length (mm)
Figure 3 : Two examples of heterogeneity index profiles Sample samples selection Selected 2600
CT attenuation
Sample 0 Sample 1
Tight samples
2500 2400
Sample 3
2300
Sample 5 Sample 7 Sample 8
2200
Sample 9
2100
Sample 14 Sample 16
Heterogeneous samples
2000 0%
10%
20%
30%
40%
50%
Heterogeneity Index
Figure 4 : Selection of the 4 best samples Finally, samples 3 and 9 were selected for the laboratory study because they reach the best compromise between homogeneity and density. Although sample 3 is the best candidate for laboratory work among the nine samples, it can be seen from Figure 5 that the rock texture is not conventional. Dark spots that can be around 1 mm in diameter exist and are distributed within the matrix very homogeneously. Hence, such a sample appears very
Porosity and permeability measurements Results The cores and end cuts were then dried in the oven at 60°C for three days. Then, the cores were weighed and the air permeability was measured. The cores were then put under vacuum and saturated using a synthetic 30 g/l brine as the water phase. The cores were weighed and the water permeability was measured. The weight difference between the dry state and the saturated state gave us a first evaluation of the porosity. The brine saturated cores were then placed in a low field NMR tool (Maran) in order to evaluate directly the volume of water contained in the core. This measurement gave us a second evaluation of the porosity. All the core properties measured during the above phase are gathered in Table 1. The porosity measurements using the weighing technique or the NMR technique are very consistent. It can be noticed that the NMR porosity is always higher than the porosity obtained by weighing. We suspected some solvent was not removed by the drying in the oven due to the existence of very small pores. This possible problem has no incidence on the rest of the program since all the cores were subsequently flushed with a large volume of brine (10 pore volumes), which ensure the remaining solvent was displaced by miscibility. As expected by the CT-screening, MP3 is the more porous and permeable sample (13.16% - 3.26 md),
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which confirms this is our best candidate for the laboratory work. Comparison with published results A permeability / porosity cross plot can be found in Figure 6. As the porosity is of the same order for all the samples (between 8% and 13%), we added some data about samples used for imbibition experiments in the same type of rock. The extreme dispersion of the data points tells us it is difficult to draw a simple correlation between the permeability and the porosity. 100
1
The T2 distributions of our samples differ largely from the conventional form: Several separate peaks can be distinguished, which indicates at least a bimodal pore size distribution.
0.1 Our Data Kantzas Ding Pow Bounding curve: Carlson Bounding curve: this study
0.01
0.001 1%
10%
Most of the volume is contained in the largest pores 100%
The peak corresponding to the largest pores is centered around a T2 value of 2 seconds. This value is extremely high because it is practically the value of the relaxation time of water in bulk. This means that the largest pores, which account for most of the pore volume, have a very large size. This result is in good qualitative agreement with the CT-scanner analysis.
Phi (%)
Figure 6 : Permeability / Porosity plot
Figure 6 shows that our data are in line with the envelop matrix curve proposed by Carlson. Hence, our samples are representative of the matrix so that the imbibition tests will not be affected by the presence of fractures. Figure 6 would also suggest that the samples studied by Kantzas et al. (1997) and Ding et al. (2002) may not be really representative of the matrix medium. This could explain why Kantzas (1997) could not scale up its imbibition tests using a dimensionless time. When fractures exist, the characteristic imbibition length decreases, which leads to a strong decrease of the dimensionless imbibition time, as will be discussed later on in this paper. Moreover, it seems from our data and some data from Ding (2002) that the bounding curve could be slightly translated towards the high porosity values (Figure 6). The following Kφ empirical law was derived from our data:
φ = 0.01722 × Ln (K ) + 0.010418 where φ is in fraction and K in md
16
40
14
35
12
30 100% Water
10
Signal
This result is in good agreement with the study from Carlson (1999) on the petrophysical characterization of fractured Western Canada reservoirs, provided some precaution in the analysis of results. Actually, he found that the K-Phi log-log plot often presents a triangular shape due to the existence of fractures inside the samples. The lower the porosity, the higher the probability to have fractured samples. Hence, for a given porosity, only the lowest permeability data points of Carlson’s permeability-porosity graph have to be considered to establish a K-φ correlation representative of the matrix.
100% Water
25
Signal
k (md)
10
Porous medium characterization Pore size distribution A qualitative idea of the pore size distribution is given by the NMR tool with the T2 distribution. The higher the T2, the larger the relaxation and the larger the pore size. The amplitude of the signal is directly proportional to the volume of fluid. 1 S 1 = ρ2 ∝ T2 V r where ρ2 is the surface relaxation parameter, S/V the characteristic ratio of pore surface to pore volume and r the equivalent pore radius. Figure 7 shows the T2 distribution for MP3 and a classical homogeneous Vosges sandstone.
8
20
6
15
4
10
2
5
0
0 0.1
1
10
100 T2 (m s)
1000
10000
0.1
1
10
100
1000
10000
T2 (m s)
Figure 7 : T2 distribution for MP3 and a Vosges sandstone Pore-throat size distribution Mercury porosimetry analysis was carried out on each end-cut of the cores to assess the pore-throat size distribution. The raw data are plotted in Figure 8. Most of the curves are looking as if the porous medium is very homogeneous (throat size distribution centered around 2 µm).
By combining the results of the CT-scanner, the NMR and the Mercury porosimetry, we can then confirm that the porous medium to study is very particular as the main pore volume corresponds to large vugs (around 1 mm) that are disconnected and homogeneously distributed in a tight porous matrix (with an average pore-throat radius around 2 µm) which completely controls the access to these vugs.
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0
1 - S Hg (fraction) 40 60
20
80
100
1000 MP3
MP5
MP7
MP9
A very strong relationship exists between the maximum gas relative permeability at Swi and the Swi value as shown by Figure 10. A small increase of initial water saturation leads to a significant decrease in the gas relative permeability.
Pc Hg (bar)
100
10
krg M
1
0
Figure 8 : Mercury porosimetry curves Swi establishment and 1st drainage Pc curves Procedure The irreducible water saturation was set using the centrifuge technique. A multi-step experiment was conducted in order to determine some intermediate points of capillary pressure. Six rotation speeds were used from 500 to 3000 RPM. This last speed corresponds to a capillary pressure around 11 bar at the inlet of the core. The duration of each step was two days to make sure that water production was stabilized. The saturation was calculated by weighing the plug at the end of each step. The saturation value was also checked by NMR measurements at the end of the 1200 and 3000 RPM phases. Results Average Swi values ranging from 15% to 25% were obtained using the centrifuge technique. Then, the samples were mounted again in a core holder and the air permeability (kg) was measured at Swi. Table 2 gathers the petrophysical properties at the end of the Swi establishment step. (b) corrected curves with J-function
Pc air/eau (mbar)
12000 10000
MP3 MP5 mod
8000
MP7 mod MP9 mod
6000
1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5
y = -2.1297x + 1.2684 2
R = 0.9994
krgM Linéaire (krgM)
0
0.05
0.1
0.15
0.2
0.25
0.3
Swi (fraction)
Figure 10 : KrgM / Swi cross plot Spontaneous imbibition experiments Apparatus and procedure As we work on low-porosity and low-permeability samples, the measurement of reliable and accurate imbibition data required a specific experimental procedure enabling us: to operate over a long period of time: this is of primary importance since we anticipate extremely-low imbibition rates.
to obtain the saturation evolution as a function of time with a good accuracy: this is also an important issue as the sample pore volumes are very small. Practically, this was achieved by performing preliminary imbibition tests on companion plugs in order to validate the whole experimental approach. The experimental apparatus is shown in Figure 11. It is mainly composed of an accurate weighing system (within 0.001 g) that is connected to a computer for automatic data recording. Data acquisition
4000 2000
Brine
Oil film
0 0
0.2
0.4
0.6
0.8
1
1.2
Sw (fraction)
Figure 9 : Air/water capillary pressure curves
All the capillary pressure curves obtained by the centrifuge technique were plotted by reference with our best sample MP3 after a renormalization based on Leverett’s J-function to take into account porosity and permeability differences from one sample to another. Figure 9 shows that the application of the Jfunction enables to lump the Pc curves of the 4 samples into a unique curve. This result demonstrates that the samples used within the study are very similar in their structure and belong to the same “rock type”.
Sample
Digital balance
Figure 11 : Experimental apparatus for imbibition tests The sample, set in a horizontal position, is suspended by a thread into a container filled with brine and a thin oil film floating to the top. The weight of the container is recorded as a function of time and converted to saturation values.
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Initiating a spontaneous imbibition test involves the following steps: The sample at Swi is tied to a support by a thread and placed in a horizontal position just above the bottom of an empty container, which weight is initialized at zero value;
This second container is used to rapidly immerse the sample into brine, with the air/water interface located 2 centimeters above the upper part of the sample. The brine container is weighed back again on the other balance, which gives the weight of brine added (Wa). The recorded weight of the sample container increases from its initial zero value to a certain value that corresponds to the weight of the added water minus the Archimede force due to the presence of the immersed sample hanging to the thread. This initial weight is measured directly and checked analytically. Gas is expelled progressively from the sample and replaced by water, which leads to a slow decrease of the the recorded weight. A thin film of mineral oil is then added at the air/water interface a few minutes after the beginning of the experiment. This oil film prevents the water evaporation, which would also lead to a weight decrease. Results Kinetics The increase of water saturation as a function of time for MP3 is plotted in Figure 12. For our best candidate MP3, it took approximately 24 days to obtain a stabilization of the saturation. We obtain a S shape curve in semi-log, which is very typical of a spontaneous imbibition process. MP3 0.25
0.3 0.25 0.2 0.15 0.1 0.05 0 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Time (s)
Figure 13 : Increase of Sw during the spontaneous imbibition process MP7
The stabilization was reached after 35 days of imbibition for MP7. The difference of stabilization kinetics between MP3 and MP7 is related to the value of their respective permeability: 1.92 md for MP3 and 0.97 md for MP7. Actually, the imbibition kinetics can be scaled by the square root of the permeability. Hence, if the imbibition of MP3 lasts for 24 days, we expect MP7 imbibition to last for 33.8 days (24 days times 1.92 ), which is in good agreement with the 0.97
experimental measurement. Whatever the sample tested, the water imbibition is a very slow process. As it will be confirmed in a subsequent section, we can already suspect that the water mobility is very low during the imbibition process. Residual gas saturation The second important information that is derived from the imbibition tests is the residual gas saturation Sgr. The values obtained are ranging from 26.6 % to 61.9 % (Table 3) and seem to be well correlated with the initial gas saturation Sgi as shown in Figure 14. The higher Sgi, the higher Sgr.
0.15
0.7 0.6
0.1
Sgr (fraction)
dSw (fraction)
0.2
0.35
dSw (fraction)
Another container filled with brine is weighed on another balance.
MP7
0.4
0.05
0 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Temps (s)
Time (s)
0.5 0.4 0.3 0.2 0.1 0 0.70
Figure 12 : Increase of Sw during the spontaneous imbibition process (MP3)
0.75
0.80
0.85
0.90
Sgi (fraction)
Figure 14 : residual gas saturation as function of initial gas saturation
From these results, the trapping of the gas phase can be quite significant in spite of the water wettability of the porous medium. In this case, the trapping process is dominated by the
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pore structure, which favors a lot the by-passing of the nonwetting phase mainly located in the large disconnected vugs. The saturation state of the samples was also checked by NMR technique at the end of the imbibition tests. The results are in good agreement with those obtained by continuous weighing. Another interesting output of the NMR tool is the T2 distribution as a function of the saturation state. The Figure 15 shows the T2 distribution when the samples are fully saturated with brine, at irreducible water saturation and at the end of the imbibition. It can be observed that only a minor part of the vugs has been imbibed by water due to severe trapping during the imbibition process.
The corresponding kw value were found extremely low, from 0.0038 md for MP7 down to 0.00043 md for MP3 (Table 4). From these two measurements, kw seems to be strongly correlated with the residual gas saturation. The higher Sgr, the lower kw. Brine vessel
h
MP3 16
Core holder
14 100% Water
10
Swi
8
Sgr
Figure 16 : Water permeability measurement apparatus
6 4 2 0 0.1
1
10 100 T2 (ms)
1000
10000
Figure 15 : T2 distribution at various saturation states (MP3) Direct measurement of kw at the end of the imbibition As the experimental results showed that the imbibition rates are extremely low, two samples were mounted back in a core holder after spontaneous imbibition, in order to check the water permeability, kw, in the presence of trapped gas, Sgr. The constant injection flowrate technique was discarded because the low permeability would drive to high pressure at the inlet even with the lowest rate available (0.1 cm3/hour). Because of compressibility effects, high pressures can change dramatically the effective value of Sgr and the corresponding value of kw measured under injection. Hence, a specific approach was followed to derive a representative value of kw.
The apparatus is described in Figure 16. The inlet of the core holder is connected to a vessel filled with brine that can be moved to an adjustable height h. The outlet of the core is connected to a small diameter tubing (1/16’’) placed horizontally. Tracking the position of air/water meniscus in this tubing (initially full of air) enables to measure very small volumes of produced brine. If meniscus position accuracy is in the order of one millimeter, we can detect a volume variation in the order of 10-4 cm3. The pressure vessel was placed at a maximum height of 1.25 meter, in order to set a low inlet pressure, equal to 125 mbar (relatively to atmospheric pressure). The evolution of the meniscus into the 1/16’’ tubing was then recorded as a function of time. The injection was continued until the instantaneous flowrate was stabilized (after typically 2 days).
Remark about compressibility effects Kw has been measured with an inlet pressure around 100 mbar. If we assume the pressure profile is linear, we can consider the average pressure is around 50 mbar. Using the perfect gas law, we can then derive the average gas saturation change into the core: P S grflow = atm × S gr = 0.953 × S gr Pflow This means that for an average residual gas saturation equal to 50%, the saturation decrease due to the measurement technique is only 2.5 %. Indirect evaluation of kw at the end of the imbibition A pore network model was also used to assess the value of kw in presence of trapped gas at the end of spontaneous imbibition14. As the vugs are not connected and homogeneously distributed in the rock, the porous medium was modelled as if it was homogeneous. The pore network model was parametrized in order to reproduce the throat size distribution derived from the Mercury porosimetry curve. The pore size was assumed uniform, i.e. independent of the throat size, to take into account the pore volume associated with the disconnected vugs. 1.E+00 1.E-01 1.E-02 1.E-03
Kr
Signal
1/16’’ tubing 12
Krg
1.E-04
Krw
1.E-05 1.E-06 1.E-07 1.E-08 0
0.2
0.4
0.6
0.8
1
Sw
Figure 17 : kr curves predicted by the pore network model
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The first drainage gas/water relative permeability curves for MP3 are plotted in Figure 17. It is generally admitted that the wetting phase relative permeability (water phase) is not affected a lot by hysteresis effects during imbibition. Hence, in first approximation, this first drainage krw curve provides a reasonable order of magnitude of the water mobility in the presence of trapped gas. In the case of MP3, where the final water saturation was 38%, it gives a krw value around 0.0003, which is in good agreement with the direct measurement value, 0.00022. Interpretation of the imbibition tests Analysis Comparison with published results Two published references on the kinetics of imbibition in vuggy carbonates samples are found in Kantzas et al. (1997) and Pow et al. (1997) for Western Canada fields. Results are compared to ours by plotting all the curves as a function of the dimensionless time td proposed by Mattax et Kyte 15 and Ma et 16 al. :
td =
k σ 1 φ µ m L2c
with µ m = µ w µ g and Lc is a characteristic length for imbibition The imbibition tests published by Kantzas et al. are systematically faster than the others (SPP07,18,19,32). This particular behavior has to be related to the general trend we observe on the k-φ plot referring to Kantzas’ samples. This plot suggests the samples used by Kantzas were probably fractured. The imbibition tests tend to confirm this behavior for two reasons: it is difficult to reconcile the tests of Kantzas all together most probably because the characteristic imbibition length varies from one sample to another depending on the fracture density; the kinetics of imbibition of Kantzas samples is very fast. 1 0.9
Normalized recovery
0.8 0.7
Pow et al.
Matrix gas recovery factor Pow et al. used the following simplified formulation of the gas recovery by the water imbibition: R = (1 − e −λt ) R∞
λ = C
where
k σ 1 φ µ gm L2c
and Lc expressed versus the dimensions a,b,c of a parallelepipedic block as : Lc =
abc 2 a b + a 2 c 2 + b 2c 2 2 2
The constant involved in λ, C, has to be calibrated from laboratory experiments of spontaneous imbibition. Using our tests results, we obtain a C value equal to 2.1 E-7 min-1, which is in the same order of magnitude as the value obtained by Pow et al. (4.55 E-7 min-1). This was expected since the dimensionless representation of imbibition kinetics of Figure 18 showed that our imbibition results and Pow’s results were fairly close. Using this calibrated exponential function with our experimental data, we calculated the matrix gas recoveries (Table 5) for various petrophysical properties rocks yielding the same imbibition behaviour (i.e. C remains the same) and several block sizes. A production time of three years was considered as representative of the single-phase gas flow production time before the water breakthrough at the production wells in such reservoirs. We also assumed full reservoir pressure maintenance thanks to a strong aquifer drive. The results demonstrates that depending on the local properties of the rock and the local density of the fracture network, only part of the matrix gas can be recovered by water imbibition before the water breakthrough at the production wells.
MP3 SPP19
In addition to high Sgr values, the slow imbibition of water in these vuggy carbonates is probably another reason that explains why low recovery factors are often obtained in such fields in the presence of an active aquifer.
SPP32
0.6
SPP18
0.5
SPP07
0.4 0.3
History matching of the imbibition tests
0.2 0.1 0 1.E+00
The imbibition kinetics of MP3 is in line with the experimental results published by Pow et al. (1997). Pow’s experiment is probably more reliable as it was conducted on a full size sample, which is less prone to fracturing. Hence, this comparison of our experimental data with other published results tends to confirm that our imbibition tests are representative of the process of imbibition into the matrix.
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
Dimensionless td (min)
Figure 18 : Comparison of different imbibition tests (MP3, Kantzas and Pow)
Single porosity numerical model Gridding We used ATHOS (the IFP Group reservoir simulation software) to simulate the spontaneous imbibition tests. Only 1/8 of the sample was simulated due to the existence of several symmetry axis (Figure 19). Gravity forces have actually a negligible impact on imbibition. The presence of the free brine at the boundary of the sample was simulated using
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surrounding high-permeability, high-porosity cells with no capillary pressure. This enables to feed the rock matrix with brine unrestrictedly during the whole simulation. Simulations were carried out using a parallelepiped geometry equivalent to the core (cylinder) in terms of volume and length. Initial time
Fracture
The experiment was also simulated with a dual-porosity model because this model will be used for the reservoir evaluation study. However, it is necessary to validate the dualporosity model prediction of water-gas matrix-fracture transfer by comparison with the fine-grid single-porosity model prediction. Actually, the dual-porosity model adopts an upscaled formulation of transfer which averages the localscale process occurring within matrix blocks. MP3 0.25
Matrix
Beginning of the water imbibition
Sensitivity study on the kr curves The set of kr curves was parameterized with Corey functions and a short sensitivity study was conducted to evaluate the ones that really control the imbibition kinetics.
The krg curve does not impact the imbibition kinetics because of the low viscosity ratio between the gas phase and the water phase. Figure 20 shows that the kinetics is mainly affected by the maximum value of krw rather than by the shape of the curve itself. This kr sensitivity supports the existence of a piston-like displacement of moveable gas by water, which drives the water saturation from Swi up to 1-Sgr behind the imbibition front. krw shape
krg shape 0.3
0.3
0.25
ng=2;nw=4
0.2
0.15
dSw
dSw
0.2
ng=4;nw=4 ng=4;nw=2
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Dual porosity 0.15
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dSw
Figure 19: Grid system used for the single porosity model (horizontal cross-section)
Experiment
0.2
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Figure 21 : History matching MP3 spontaneous imbibition test using single- and dual-porosity numerical models
For this dual-porosity simulation, the sample was simply modelled as a single matrix cell. The input set of petrophysical parameters was the same as for the single porosity model.The simulation was performed using an improved formulation of matrix-fracture capillary transfers available in the dualporosity version of ATHOS 17. Due to high capillary forces and the small size (height) of plugs, gravity forces play a negligible role in the imbibition process. As expected, Figure 21 shows that the dual-porosity model results are nearly superimposed on those obtained with the single-porosity model.
Time (s)
To conclude, the numerical simulation of imbibition tests with a fine-grid single-porosity model confirm the consistency of our experimental data set and validate its use to model water-gas spontaneous imbibition phenomena. Furthermore, a dual-porosity model can be used for reservoir-scale simulation studies, without any significant loss of prediction accuracy.
k rw e nd p o int 0 .3
ng= 4 ;nw = 4 ; k rw M = 0 .0 0 0 1
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ng= 4 ;nw = 4 ; k rw M = 0 .0 0 1
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Figure 20 : Sensitivity of imbibition to krg and krw History matching Figure 21 indicates that MP3 imbibition can be reproduced with a krwM value equal to 0.0001. This result is in agreement with what was found by direct measurement of krw. Dual porosity numerical model
Conclusions Assessment of gas production and recovery from fractured vuggy carbonate reservoirs requires special consideration be awarded to water-oil spontaneous imbibition phenomena. Actually, water imbibition into vuggy carbonates involves an important gas trapping and the imbibition kinetics can change considerably depending on matrix block size and permeability. Thanks to a specific experimental procedure adapted to tight and low-porosity rock samples, the present study provides a representative experimental data set and a better understanding of the physical process of imbibition in those media: - tight and vuggy carbonates imbibe water but very slowly,
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SPE 89421
due to a very low relative permeability to water ; this behavior stems from the peculiarity of the porous structure - fairly large vugs dispersed within a tight matrix with very small pore thresholds ; such a porous structure explains the high residual gas saturation obtained at the end of imbibition: the aqueous phase imbibes the small pore network and bypasses numerous gas-filled vugs ; single-porosity and dual-porosity simulation models incorporating the measured petrophysical parameters are able to reproduce this imbibition behavior very satisfactorily, and thus demonstrate the consistency of the measured data set.
7
Kantzas, A., Ding, M. and Lee, J.: ”Residual gas saturation revisited”, SPE Reservoir Evaluation and Engineering, December 2001. 8
Hamon, G., Suzanne, K., Billiotte, J. and Trocme, V.: ”Fieldwide variations of trapped gas saturation in heterogeneous sandstone reservoirs”, SPE 71524, presented at the ATCE, 30 September-3 October, 2001. 9
Li, K and Horne, R.: ”Scaling of spontaneous imbibition in gas-liquid-rock systems”, SPE 75167, presented at the SPE/DOE Improved Oil recovery Symposium, April 13-17, 2002.
The experimental results obtained in the present study can then be used as reference data for assessing the production behaviour of analogous fractured carbonate reservoirs.
10
Acknowledgements The authors wish to thank G. Thibault, A. Templier, C. Schlitter, N. Blin and J. Behot for their major contribution in the development of the experimental apparatus and the realization of the different tests. A special acknowledgement is also adressed to M. Fleury, F. Deflandre and A. Samouillet for their contribution in NMR and the centrifuge experiments.
11
References
13
Kantzas A., Pow M., Allsopp K. and Marentette D.: ”Cocurrent and counter-current imbibition analysis for tight fractured reservoirs”, CIM 97-181, October 19-22, Regina. Pow M., Allan V., Mallmes R. and Kantzas A.: ”Production of gas from tight naturally-fractured reservoirs with active water”, CIM 97-03, October 19-22, Regina. 12
Ding M., Kantzas A.: ”Residual gas saturation investigation of a carbonate reservoir from Western Canada”, SPE 75722, presented at the Gas Technology Symposium at Calgary, 30 April – 2 May, 2002. Carlson M.R.: ”Reservoir characterization of fractured reservoirs in Western Canada”, JCPT, Volume 38, n°7, 1999.
14 1
Hnatiuk, J. : "Lateral Water Encroachment in the Pincher Creek Field", JCPT, April-June 1970, 85-91.
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Davidson, D.A. and Snowdon, D.M.: "Beaver River Middle Devonian Carbonate: Performance Review of a High-Relief, Fractured Gas Reservoir With Water Influx," JPT, Dec. 1978, 1672-78. 3
Thomas, M.B., Nutakki, R., Baker, R.O., Gegunde, G ., Geppert, J. and Gould, B.: "A New Interpretation of Fracture Distribution in Waterton Sheet III : An Integrated Reservoir Characterization Study," SPE 35605 presented at the Gas Tech. Conf., Calgary, May 1996. 4
Cuiec, L.E., Bourbiaux, B. and Kalaydjian, F.: ”Imbibition in low-permeability porous media: understanding and improvement of oil recovery”, SPE/DOE 20259, presented at the 7th Symposium on Enhanced Oil recovery, Tulsa, April 2225 1990. 5
Xie, X. and Morrow N.: ”Oil recovery by spontaneous imbibition from weakly water-wet rockes”, SCA, Abu-Dhabi, October 22-25 2000. 6
Hamon, G. and Vidal, J.: ”Scaling up the capillary imbibition process from laboratory experiments on homogeneous and heterogeneous samples”, SPE 15852, presented at the European Petroleum Conference, London, October 20-22, 1988.
Laroche, C., Vizika, O., Kalaydjian, F: ”Network modeling as a tool to predict three-phase gas injection in heterogeneous wettability porous media”, Journal of Petroleum Science and Engineering, (1999) 24 , 155-168. 15
Mattax, C. and Kyte, J. : "Imbibition Oil Recovery from Fractured , Water-drive Reservoirs", SPE Journal, June 1962.
16
Ma, S., Morrow, N. and Zhang, X.: ''Generalized Scaling of Spontaneous Imbibition Data for Strongly Water-Wet Systems'', Paper 95-138, CIM, Regina, October 1995.
17
Sabathier, J.C., Bourbiaux, B., Cacas, M.C., and Sarda, S.: "A New Approach of Fractured Reservoirs," SPE 39825, presented at the SPE Int. Pet. Conf. & Exh., Villahermosa, Mexico, March 3-5, 1998.
SPE 89421
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Core name MP3 MP5 MP7 MP9
Length, mm Diameter, mm φ (weighing) 48.88 37.96 12.20 % 50.44 37.96 7.14 % 50.06 37.96 8.02 % 50.08 37.96 7.73 %
φ (NMR) 13.16 % 7.86 % 8.96 % 8.18 %
Kg, md 3.26 0.46 1.94 1.00
Kw, md 1.92 0.19 0.97 0.42
Table 1 : Petrophysical core properties Core name φ (NMR) VP, cm3 Kw, md Kg, md MP3 13.16 % 7.28 1.92 3.26 MP5 7.86 % 4.48 0.19 0.46 MP7 8.96 % 5.07 0.97 1.94 MP9 8.18 % 4.64 0.42 1.00
Swi 15.75 % 24.89 % 18.82 % 23.65 %
Kg at Swi, md 0.935 0.739 0.864 0.765
Table 2 : Swi state Core name φ (NMR) VP, cm3 Kw, md MP3 13.16 % 7.28 1.92 MP5 7.86 % 4.48 0.19 MP7 8.96 % 5.07 0.97 MP9 8.18 % 4.64 0.42
Sgi 84.2 % 75.1 % 81.2 % 76.3 %
Sgr 61.9 % 26.6 % 49.7 % 42.6 %
Sgi -Sgr 22.3 % 48.5 % 31.5 % 33.7 %
Sgr (NMR) 66 % 32 % 51 % 49 %
Table 3 : residual gas saturation Core name MP3 MP7
φ (NMR) 13.16 % 8.96 %
PV, cm3 Kw, md 7.28 1.92 5.07 0.97
Sgr 61.9 % 49.7 %
Kw at Sgr, md 0.00043 0.0038
Krw at Sgr 0.00022 0.0039
Table 4 : Direct kw measurement after imbibition
Rock type 1 Rock type 2 Rock type 3
k, md 1.92 0.42 0.01
φ, fraction 0.13 0.08 0.04
block size= 10 cm 1 1 0.9999
block size= 100 cm 0.524 0.358 0.092
block size= 1000 cm 0.0074 0.0044 0.0009
Table 5: gas recovery from the matrix after 3 years of production as a function of the rock properties and the block size
