Effects of Chemical Additives on Dynamic Capillary Pressure during

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Effects of Chemical Additives on Dynamic Capillary Pressure during Waterflooding in Low Permeability Reservoirs Haitao Li,*,† Ying Li,*,†,‡ Shengnan Chen,‡ Jia Guo,§ Ke Wang,† and Hongwen Luo† †

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary T2N 1N4, Canada § Exploration and Development Institute, PetroChina Huabei Oilfield Company, Renqiu 062552, China ‡

ABSTRACT: It is suggested that the capillary pressure−fluid saturation relationship should be determined as a function of a dynamic coefficient (τ) and the time derivative of fluid saturation (∂Sw/∂t), indicating a dynamic capillary pressure in most cases, which will increase the flowing resistance and injection pressure for oil-wet reservoirs, especially in low permeability formations. To decrease the injection pressure and improve injection, various chemical additives such as surfactants and fluorides have been widely used in the waterflooding process in low permeability reservoirs. Effects and mechanisms of these chemical additives are yet not well-known. In this paper, a series of specially designed waterflooding experiments were conducted to investigate the effects and mechanisms of surfactant additives on the dynamic capillary pressure−fluid saturation relationship in low permeability reservoirs. In the experiment, capillary pressure−fluid saturation relationships in three low permeability core samples were examined during the waterflooding process, as well as the surfactant added waterflooding process. Then, local dynamic coefficients in the core samples were calculated and compared. Results indicate that low permeability reservoirs present a high dynamic coefficient, therefore generating high dynamic capillary pressure, which is the cause of high injection pressure during waterflooding. Furthermore, surfactant additives can reduce the dynamic coefficient and capillary pressure significantly, and the lower permeability core sample shows higher dynamic capillary pressure reduction, indicating that surfactant added waterflooding can significantly reduce injection pressure in low permeability reservoirs. This work provides a method to investigate the interaction among fluids and porous media during waterflooding through the examination of dynamic capillarity. rates.10−12 The difference between dynamic and static capillary pressure can be quantified by a dynamic coefficient (τ) and the

1. INTRODUCTION During the waterflooding process in oil reservoirs, capillary pressure is an important factor to affect injection pressure and oil recovery. The capillary pressure−fluid saturation relationship is commonly used to predict multiphase flow performance in porous media and can be affected by multiple factors such as fluid properties, rock particle size and distribution, interfacial tension, contact angle, etc.1−4 Therefore, the change of these factors can be reflected by a change of capillary pressure. 1.1. Capillary Pressure under Dynamic Conditions. The relationship between capillary pressure (Pc) and wetting phase saturation (Sw) is usually measured under static conditions.5−7 Under such conditions, an equilibrium of various fluids in porous media has been reached, and the saturations of ∂S the fluid phases no longer change (i.e., ∂t = 0). Static capillary pressure can be calculated as follows Pcs = Pnw − Pw = f (Sw )

time derivative of wetting fluid phase saturation follows:

13,14

Pcd = Pnw − Pw = Pcs − τ

∂Sw ∂t

as

(2)

The dynamic coefficient τ in eq 2 is positive. It can be seen that, for water-wet rock, capillary pressure under dynamic conditions is higher than its value under static conditions during the water

water

dSw dt dSw dt

( imbibition (

drainage process

) > 0).

< 0 , whereas the opposite is true for 14

Meanwhile, for oil-wet rocks

during the waterflooding process, eq 2 can be changed to eq 3,15,16 indicating that dynamic capillary pressure is higher than static capillary pressure.

(1)

Pcd = Pwater − Poil = Pcs + τ

where Psc is the static capillary pressure, Pnw represents the average nonwetting fluid phase pressure, Pw stands for average wetting fluid phase pressure, and Sw is the saturation of wetting fluid phase. Pnw and Pw are measured under the same Sw. Opposite to static condition, dynamic condition refers to that the transient multiphase flow will never reach equilibrium during the flowing process.8,9 Capillary pressure under dynamic conditions has been studied to describe the transient multiphase flow in porous media, especially at high flow © XXXX American Chemical Society

∂Sw ∂t

( )

∂Swater ∂t

(3)

The dynamic coefficient τ can be affected by multiple parameters, such as fluid viscosity, fluid saturation, fine-scale heterogeneities, boundary pressures, interfacial tension, dynamReceived: May 29, 2016 Revised: July 28, 2016

A

DOI: 10.1021/acs.energyfuels.6b01272 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Capillary pressure−mercury saturation relationship at different injection rates in different permeability samples (modified from Tian et al.16).

Table 1. Summary of Dynamic Coefficient (τ) Values reference Das et al.33 Camps-Roach et al.34 Fučiḱ et al.35 Bottero et al.18 Hassanizadeh et al.14 O’Carroll et al.17

Tian et al.16

Shu et al.36 Zhang et al.28 Jia and lv37

porosity fraction or grain diameter

permeability (mD)

0.35 8.7 × 105 0.32 3.1 × 105 D50 = 0.42 mm 5.3 × 104 D50 = 0.18 mm 1.47 × 104 0.448 1.63 × 104 D60 = 0.09 mm, D15 = 0.06 mm sand, fine sand, or dune sand (summarized from other studies) 0.311 3.48 0.319 6.48 0.301 6.62 0.12 0.52 0.37 0.2 0.1 0.25 0.1 0.14 0.097−0.14 0.033−0.122

ic contact angle, and wettability.17−21 Early in 1978, Stauffer proposed the following relationship to illustrate what can affect dynamic coefficient (τ)22 τ=

2 αφμw ⎛ P d ⎞ ⎜⎜ ⎟⎟ λk ⎝ ρw g ⎠

dynamic coefficient (Pa·s) 104 to 7 × 105 3 × 104 to 9 × 105 105 to 6.7 × 105 3.7 × 105 to 106 106 to 108 105 to 1.2 × 107 3 × 104 to 5 × 107 3.43 × 107 2.76 × 106 3.74 × 106 2.88 × 106 5.18 × 106 7.92 × 106 105 to 107 1011 to 1013 3.14 × 1011 to 6.1 × 1013

interfacial properties could be rapidly dissipated or eliminated in high/moderate permeability reservoirs.14 This mechanism can also be described by a low dynamic coefficient τ (less than 105 Pa·s) for high and moderate permeability reservoirs, minimizing the effect of dynamic conditions on a multiphase flowing system.14 1.2. Dynamic Capillary Pressure in Low Permeability Reservoirs and Surfactant Additives Effect. Nevertheless, compared with high/moderate permeability reservoirs, low permeability reservoirs are characterized by micro- or even nanopores and throats, and strong reservoir heterogeneity of porous media.24−26 Thus, the value of the dynamic coefficient would increase to as high as 1013 Pa·s.16,27,28 Such a high dynamic coefficient value would significantly affect the capillary pressure.16,23 Figure 1 shows that the difference among capillary pressures in the low permeability core samples (K = 0.2 mD) is dozens times of its value in the high/moderate permeability samples (K = 210 mD). In addition, the effect of mercury injection velocity on capillary pressure in the low permeability

(4)

where α is a dimensionless parameter (defined to be 0.1), ϕ and K are the porosity and intrinsic permeability of the material (isotropic), respectively, uw is the viscosity of the wetting phase (referring to oil in this work), ρw represents the density of the wetting phase, and Pd and λ are parameters from the Brooks− Corey constitutive model,23 and they depend mainly on the pore and particle size distribution of the materials. g is the gravity constant. It is acceptable to neglect the difference between capillary pressures under dynamic and static conditions in high and moderate permeability reservoirs (e.g., reservoir permeability is higher than 100 mD). This is because capillary pressure is a function of interfacial properties, where disturbances to B


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Applications of surfactants during enhanced oil recovery (EOR) processes and their great performance to reduce interfacial tension and change wetting characteristics in porous media were researched early in the 1970s.41,42 During the flooding process for low permeability reservoirs, surfactants are still widely applied to reduce the injection pressure and enhance oil recovery efficiency.43,44 Such an effect is proven to be related to the decrease of capillary pressure during the waterflooding process.45,46 However, previous researches mainly pay attention to the practical effect of surfactant additives during waterflooding (such as improved ease of injection). Therefore, the underlying mechanism of the surfactant additives effect, especially the effect of surfactant additives on dynamic capillary pressure, is still poorly studied. This work is to reveal the impact of surfactant additives upon the dynamic coefficient (τ) and capillary pressure (Pdc and Psc) for low permeability core samples during waterflooding, thus exploring possible mechanisms and potential of surfactant added waterflooding for EOR in low permeability reservoirs. Experiments are specially designed to measure local static and dynamic capillary pressure, as well as local water saturation, for long low permeability core samples. These experiments are separately performed for the process of waterflooding and surfactant added waterflooding to compare the difference between these two processes. Then, local dynamic coefficients and the average capillary pressure−average fluid saturation relationship during waterflooding and surfactant added waterflooding are worked out and compared. Changes of dynamic coefficient and capillary pressure can reflect the change of macro flowing properties and micro interfacial properties in low permeability reservoir rocks caused by surfactant additives. This work may give insight into the underlying mechanism of surfactant added waterflooding in low permeability reservoirs.

core sample is more pronounced compared with that in the relatively high permeability sample.16 Stauffer proposed that the dynamic effect is inversely proportional to the permeability of the porous medium.22 Mirzaei and Das29 examined the impact of porous media permeability on τ in 3D core scale domains in the presence of the gravity effect. They found that the value of τ is higher for low permeability cores. In addition, values of τ change from 105 to 109 Pa·s as reservoir heterogeneity increases through numerical experiments in both 2D and 3D scenarios.29 Bourgeat and Panfilov30 also believed that the heterogeneity in porous media can generate nonequilibrium effects.30 In addition, Hassanizadeh et al. reported that the value of τ would increase if coarse sand was replaced by fine sand in centrifugally accelerated drainage and imbibition experiments.31 Mirzaei and Das also compared the different τ values of coarse sand and fine sand in drainage and imbibition laboratory experiments, showing higher τ values and higher dynamic capillary pressure for fine sand.32 Therefore, the dynamic effect in low permeability reservoirs cannot be ignored when it comes to quantify the capillary pressure−fluid saturation relationship, which will significantly affect the practical production. Table 114,16−18,28,33−37 is a summary of τ values changing along with permeability. It is noted that previous studies obtained their dynamic coefficient values through experiments on different materials, i.e., tubes, sand packed model, and real rock. Different materials have different pore structures and cement. Also, previous studies were conducted under different pressure and temperature. Therefore, these values may be a qualitative reference for the changing trend of τ values with permeability. Another good example is shown in Figure 2; the difference between dynamic and static capillary pressure (Pdc − Psc)

2. MATERIAL AND EXPERIMENTAL METHODS 2.1. Core Samples and Fluids. Three sandstone samples, shown in Table 2, were collected from the outcrop of Shahejie Formation, an

Table 2. Core Samples Used in the Experiments sample no.

length, cm

diameter, cm

Kair, mD

porosity, %

1 2 3

10.900 10.896 10.952

2.504 2.500 2.496

0.97 0.56 0.36

12.9 11.4 11.8

offshore oil reservoir in China. The reservoir temperature is around 75 °C, and the pressure is around 49 MPa. Laboratory measurements show that this is a low permeability reservoir with sample air permeability ranging from 0.02 to 5 mD, a porosity in the range of 5− 15%, and a relatively low clay content, of around 15.3%. The samples are oil-wet with a contact angle of approximate 130° between the water and rock surface. Therefore, the wetting phase in these samples is oil. The crude oil sample and brine sample were taken from the same reservoir. Table 3 shows the properties of the oil, which is characterized by low density, low viscosity, moderate wax content, and moderate content of gum and asphaltene. The properties of formation brine are presented in Table 4. Appropriate surfactant additives should have the capability to reduce interfacial tension or change wettabiliy, and be able to achieve good compatibility, dispersion stability, low injection pressure, permeability improvement, high oil recovery, and little or no formation damage. Good compatibility means that surfactant additives will not cause unexpected deposition, dissolution, or reaction, etc. Representative surfactants, which not only are appropriate but also do not

Figure 2. Difference between dynamic and static capillary pressure (modified from Zhang et al.28).

increases along with the decrease of average throat radius.28 Above all, it is clear that, if the capillary pressure−saturation relationship is still considered to be static in low permeability, errors will occur. Dynamic capillarity in both high/moderate permeability reservoirs38−40,51 and low permeability reservoirs16,28,37 has been investigated in previous studies. However, so far, more experimental examinations are required to estimate the dynamic coefficient and dynamic capillary pressure during waterflooding for such low permeability reservoirs. C


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Energy & Fuels Table 3. Properties of Crude Oil Used in the Experiments properties 75 °C crude oil

density (ρo), g/cm3

viscosity (uo), mPa·s

wax content, %

sulfur content, %

0.651

0.75

21.8

0.12

Table 4. Properties of Brine Used in the Experiments properties 75 °C formation brine

total salinity, mg/L

pH

viscosity (uw), mPa·s

density (ρw), g/cm3

8907

7.1

0.27

1.037

perform like other chemical additives (e.g., polymer to change viscosity), can be selected to study the mechanisms of surfactant additives during our later waterflooding process. Preliminary tests were conducted to get such representative surfactant additives. In this work, a kind of composite surfactant additive was decided as the mixed 0.05 wt % gemini surfactant (GS-L) and 0.3 wt % common surfactant (OPY), which were added in a 6(GS-L):1(OP-Y) weight ratio to the displacing brine. The selected surfactant additives have strong ability to reverse the contact angle (between saturated rock surface and brine used in this work) from 136.5° to 80.5°, which is shown in Figure 3.

Figure 3. Contact angle between rock surface and brine before (a) and after (b) surfactants added (the other phase is air). Also, the composite surfactant additives show excellent ability to reduce interfacial tension between oil and water (σ) from around 30 to 10−3 mN/m (Figure 4), which is the typical function of a surfactant to help with reservoir production. There was nearly no viscosity change in the brine after the surfactant was added.

Figure 4. Interfacial tension reduction with added surfactant. Figure 5. Experimental setup.

2.2. Measurement Apparatus and Methods. The lab experiments were carried out through a specially designed apparatus which is shown in Figure 5. The core sample was held in a horizontal cylindrical core cell to prevent the influence of gravity. In order to get oil and water phase pressure, respectively, an oil-wet semipermeable membrane and a water-wet semipermeable membrane were separately mounted on the two sides of the core at the same altitude. Then, the core wrapped by semipermeable membranes was sealed by a rubber sleeve. Finally, four pairs of pressure transducers (PTs) were plugged

through the rubber case to the surface of the semipermeable membranes. The PTs were installed at different parts of the core sample (with the same distance between each other). The rubber sleeve was tightly sealed around the PTs to ensure that there was no leakage, so the PTs can measure the pressure of the liquid between the semipermeable membrane and the rubber sleeve. Besides, four miniTDR probes were installed at the same level of the core sample with D


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different core parts of the measured parameters. Poj and Pwj are local oil phase and water phase pressures read by PTs, and their corresponding local water saturation was measured by mini-TDR probes at the same core part. As described in the Measurement Apparatus and Methods section of this paper, local water saturation was obtained from mini-TDR probe readings. However, for the average water saturation of the whole ), it was determined from oil outflow (Voi) measured by core (Saverage w the calibrated liquid collector as

the PTs. Every mini-TDR probe has two prongs of 2 cm in length, with a 0.6 cm spacing between the two prongs. Sampling volume is an elliptical cylinder with a 0.6 cm short radius, a 1.2 cm long radius, and a 2 cm height. The probes passing through the rubber sleeve and cell wall were connected to a time domain reflectometer (TDR). The TDR can obtain the dielectric constant so that water saturation of the core sample can be determined by the interpretation software.47 The measurement accuracy of phase saturation is at least 0.02, with a resolution of 0.001. The liquid collector is marked with an accurate volume ruler. Valves shown in Figure 4 were applied to regulate pressure and fluid flowing. A hydraulic pump imposed a set of liquid pressure on the oil or water container. Oil and water pressures were obtained through the pressure transducers, logged by the data logger, and then sent to the computer. Similarly, water saturation was determined through the TDR probe reading, data logger, and then computer. 2.3. Lab Test Theories. 2.3.1. Local Dynamic Coefficient (τ) for a Certain Position at a Specific Saturation. The local dynamic coefficient was quantified in a local part of the core sample. We referred to eq 3 to measure the local parameters. What calls for special attention is that τ values are distinctive at different water saturations.14,33 Therefore, τ should be acquired with all the local parameters being measured at the same water saturation in the local core part, using static local capillary pressure (Psc), local dynamic capillary pressure (Pdc ), and local time derivation of water saturation

Swaverage = Swi +

∂S w ∂t

∂Swater ∂t

(5)

Under the same water saturation in the local core part, local dynamic capillary pressure (Pdc ) and local ∂Sw have a linear relationship, ∂t and the slope of this line is the value of the local dynamic coefficient. Local dynamic capillary pressure can be calculated by the difference between the local oil phase pressure and the water phase pressure obtained from the PTs during dynamic experiments. Likewise, local static capillary pressure can be acquired during quasi-static experiments. Local water saturation at a certain time can be measured through mini-TDR probes.47 Therefore, local time derivation of water saturation

∂S w ∂t

( ) can be derived from

S − Sn ∂Swater = n+1 ∂t tn + 1 − tn

(6)

where Sw is the local water saturation at a certain time, Sn+1 is the local water saturation at time tn+1, and, similarly, Sn is the local water saturation at time tn. 2.3.2. Average Capillary Pressure and Average Water Saturation for the Whole Core Sample. Average dynamic capillary pressure and static capillary pressure are quantified for the entire core sample. Several average approaches (e.g., simple average, simple phase-average, centroid-corrected phase average) which have been thoroughly discussed by Bottero et al.48 were considered to get the average capillary pressure in our study. Considering that the average capillary pressure should be calculated at high water saturation, we applied the following saturation weighted relation for average capillary pressure drawing on the method of Abidoye et al.49 as 8

Poaverage =

∑ j = 1 (1 − Swj)Poj 8

∑ j = 1 (1 − Swj)

(7)

8

Pwaverage = PCaverage

=

∑ j = 1 SwjPwj 8

∑ j = 1 Swj Poaverage

−

Pwaverage

(10)

where Swi shows the initial water saturation, and Vp is the pore volume. 2.4. Experimental Procedure. Experiments are aimed to get the average dynamic and static capillary pressure−average saturation relationship during the process of waterflooding and surfactant added waterflooding. Experimental procedures of waterflooding and surfactant added waterflooding were similar except for the injected liquid. For waterflooding, the injected liquid was brine, and for surfactant added waterflooding, it was composite surfactant added brine. However, dynamic experiments (to obtain the Pdc −Sw relationship) and quasi-static experiments (to achieve the Psc−Sw relationship) were managed differently. Detailed experimental steps were as follows: (1) Preparation of the core samples. Because of the low permeability of the cores, it is difficult and time-consuming to clean the core under the instruction of industry standards. Therefore, we addressed the problem by first drying core samples and placing them under 60 °C for 48 h to avoid minerals change, pore structure damage, as well as electrical property change during the next procedure. Later, the dry core samples were cleaned by being vacuumed and pressurized to 45 MPa with methanol and toluene, then decompressed to let methanol and toluene out. The cleaning process (namely, vacuuming, depressurizing, and decompressing) was repeated to make sure that cores were totally cleaned. We used a silver nitrate solution to titrate the liquid flowing from the pores during the experiment to verify whether there was chloride ions in the liquid. If there was no flocculent precipitate, it was demonstrated that there was not any salt left in samples any more. After being dried in an oven, core samples were vacuumed to remove air and then totally saturated with connate brine (or composite system added connate brine for surfactant added waterflooding test) at reservoir temperature (75 °C). (2) Installation of the experimental system. After being immersed in crude oil (for oil semipermeable membrane) or brine (for water semipermeable membrane) and vacuumed to remove air, semipermeable membranes were mounted on the side of the core. Next, the core sample with the semipermeable membranes was wrapped in a rubber sleeve. Later, the wrapped core sample was put inside the cylindrical core cell. TDRs and PTs were placed through the cell wall and rubber sleeve. Inlet and outlet lines were attached in both ends of the core. Finally, the experimental system was checked for no leakages. (3) Initial water saturation and aging. The temperature of the experimental system was increased to reservoir condition (75 °C), and the confining pressure was raised to 25 MPa. At least 10 PV crude oil was continuously injected into the core sample (initially saturated with connate water at step (1)) by the hydraulic pump. Then, the core was aged in the core cell with crude oil for over 24 h. Brine outflow was recorded to get the initial water saturation (Swi). (4) Brine (or composite surfactant added brine) injection. Prepare TDRs and PTs for the measurement and start to inject brine. For the dynamic experiment processes, we steadily increased the injection pressure at the inlet of the core until it was steady at 10 MPa to get a more typical experimental capillary pressure−saturation observation.50 Moreover, it should be ensured that water invaded the core sample at a constant pressure throughout the experiment.

( ) as Pcd = Pcs + τ

Voi Vp

(8) (9)

and Paverage are the averaged oil and water phase pressures where Paverage o w is the averaged dynamic or static at the same time. In this case, Paverage C capillary pressure under the average fluid saturation. j represents E


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Energy & Fuels For the quasi-static experiments, they were performed through slowly increasing the brine injection pressure at very low rate. For the fluids to reach equilibration, sufficient time was required before further improving the injection pressure. Local static capillary pressure was gained when the injection was going on and outflow was close to 0 through keeping the flow rate close to 0. This process was repeated until water saturation could not rise anymore, which was the highest water saturation during the experiment. Every 30 s, we recorded the oil outflow (Voi), local oil phase pressure of different levels (Poj), local water phase pressure of different levels (Pwj), and local water saturation (Swj). Hence, it was then possible to relate the local capillary pressure and local saturation measured at the same time in the same part of the core sample. On the whole, for the purpose of getting more data of the relationship between capillary pressure (Pdc and Psc) and desaturation rate

3.2. Average Static/Dynamic Capillary Pressure Compared among Different Permeability Samples. The difference among different permeability core samples regarding average static and dynamic capillary pressure is demonstrated in Figure 8. It can be seen that capillary pressure increases along with the increase of water saturation. Moreover, the higher permeability sample presents lower static and dynamic capillary pressure no matter during waterflooding or surfactant added waterflooding. Further, as is exhibited in Table 6, the surfactant additives can reduce the static and dynamic capillary pressure, respectively, for every core sample. It can be seen that the higher permeability sample supplies a greater static capillary pressure reduction rate ((Psc,water − Psc,surfactant)/Psc,water) during surfactant added waterflooding, but the trend is opposite for the d − dynamic capillary pressure reduction rate ((Pc,water Pdc,surfactant)/Pdc,water). 3.3. Comparison between Average Dynamic and Static Capillary Pressure. Relationships between average static and dynamic capillary pressure and water saturation are described in Figure 9. The difference between static and dynamic capillary pressure is compared in Table 7. It can be seen that dynamic capillary pressure is higher than static capillary pressure, and capillary pressure during waterflooding is higher than that during surfactant added waterflooding. Moreover, during waterflooding, the ratio of dynamic to static capillary pressure (Pdc /Psc) generally grows with decreased permeability, which can also been reflected by Figure 9a,c,e, with a small decline from 4.82 of the 0.56 mD core sample to 4.51 of the 0.36 mD core sample (Table 7). However, during surfactant added waterflooding, the ratio of dynamic to static capillary pressure (Pdc /Psc) declines obviously when the sample permeability varies from 0.56 to 0.36 mD, with the value from 4.97 to 3.91 (Table 7).

∂S w ∂t

( ), we repeated the experiment on the same core sample for

several times under the same condition. In addition, we adopted the final steady injection pressure of 10 MPa to get stable driving forces and steady multiphase flow. Since the flow resistance is impacted by permeability, changes in phase saturation under steady injection pressure can better reflect the permeability effect than a constant injection rate.

3. RESULTS 3.1. Local Dynamic Coefficient (τ) during Waterflooding and Surfactant Added Waterflooding. The range of local dynamic coefficient(τ), average reduction rate

(

τwater − τchemical τwater

), and average reduction value (τ

water

− τchemical)

during the waterflooding process as well as the surfactant added waterflooding process are illustrated in Table 5 and Figures 6 Table 5. Local Dynamic Coefficient (τ) Values during Waterflooding and Surfactant Added Waterflooding τ (Pa·s) permeability (mD)

waterflooding

surfactant added waterflooding

0.97 0.56 0.36

3.1 × 107 to 9.9 × 107 8.2 × 107 to 3.0 × 108 1.7 × 108 to 9.3 × 108

7.2 × 106 to 2.4 × 107 2.6 × 107 to 9.6 × 107 6.9 × 107 to 3.6 × 108

4. DISCUSSION 4.1. Influence of Low Permeability on Dynamic Coefficient and Capillary Pressure. There exists an inverse relationship between permeability and dynamic coefficient. When permeability of porous media decreases, the dynamic coefficient (τ) increases obviously (Figure 6). What’s more, dynamic coefficient values in this work are larger than most of the previously reported values of high/moderate permeability porous media, which can be indicated by Tables 1 and 5. Another fact is that the higher permeability core sample provides noticeably lower static and dynamic capillary pressure (Figure 8), which is consistent with the research of Tian et al.16

and 7, respectively. It is clear that values of the dynamic coefficient (τ) in waterflooding are larger than its values in surfactant added waterflooding. Besides, the higher permeability core sample exhibits a larger reduction rate, while the lowest permeability core sample provides the largest reduction value.

Figure 6. Local dynamic coefficient values during waterflooding and surfactant added waterflooding. F


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Figure 7. Reduction rate and reduction value of local dynamic coefficient from waterflooding to surfactant added waterflooding.

Figure 8. Average static and dynamic capillary pressure compared among different permeability samples.

condition will obviously increase the dynamic coefficient and dynamic capillary pressure during waterflooding, which is fairly unfavorable for the production process by increasing injection pressure.45,46 The above results can be accounted for by the properties of low permeability reservoir rocks. Low permeability reservoir rock presents strong heterogeneity of porous media as well as smaller pores and throats compared with high/medium permeability reservoir rock,24,26,52 which will significantly increase dynamic coefficient values by increasing Pd and reducing λ in eq 12.29,34,53 In this work, pore structures of samples were imaged through scanning electron microscopy (SEM) technology and thin section (TS) analyses, which are

Table 6. Reduction Rate of Average Static/Dynamic Capillary Pressure during Waterflooding and Surfactant Added Waterflooding permeability (mD)

(Psc,water − Psc,surfactant)/Psc,water

(Pdc,water − Pdc,surfactant)/Pdc,water

0.97 0.56 0.36

0.596 0.577 0.544

0.552 0.563 0.606

Last, but not least, there is a significant difference between static and dynamic capillary pressure (Figure 9). In general, these results reflect the obvious influence of permeability on the dynamic coefficient and capillary pressure: low permeability G


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Figure 9. Comparison between average dynamic and static capillary pressure during waterflooding and surfactant added waterflooding.

What gives a more detailed explanation is the theory54−56 which suggests that the dynamic coefficient (τ) is related to the finite time required for fluids in the pore structure to rearrange. Using a first-order approximation, the dynamic coefficient can be dependent on a characteristic redistribution time as56

Table 7. Difference between Average Static and Dynamic Capillary Pressure Pdc /Psc sample permeability, mD

waterflooding

surfactant added waterflooding

K = 0.97 K = 0.56 K = 0.36

2.65 4.82 4.51

2.93 4.97 3.91

τ(Sw ) =

dPcs ·TB(Sw ) dSw

(11)

where τ is the dynamic coefficient; TB is the redistribution time, which means the time to achieve static equilibrium of various fluids in porous media. This relationship shows that any properties that increase the redistribution time will increase the magnitude of the dynamic coefficient. Camps-Roach et al.34 presented that a smaller pore structure requires more

presented in Figure 10. It is shown that the experimental samples are characterized by small pore size and strong heterogeneity, causing the high dynamic coefficient and high dynamic capillary pressure. H


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Figure 10. SEM secondary electron image and TS image of the sample.

underlying mechanism is the change in interfacial tension, contact angle, as well as wettability alternation induced by the added composite surfactant. 4.3. The Comprehensive Effect of Surfactant Additives and Permeability on Dynamic Capillarity. While the separate effects of low permeability and surfactant additives are opposite on the production process, the combined influence of these two factors is complex and meaningful. (1) One of the most important findings in this work is that lower permeability provides larger reduction for dynamic capillary pressure as a response to surfactant additives: while the static capillary pressure of higher permeability samples shows more reduction from waterflooding to surfactant added waterflooding, dynamic capillary pressure reacts to surfactant additives diversely (Table 6). This is very obvious in Figure 8d, with nearly the same dynamic capillary pressure between 0.56 and 0.36 mD permeability core samples, indicating the greatest reduction of dynamic capillary pressure of the 0.36 mD permeability core sample from waterflooding to surfactant added waterflooding. What’s more, according to Table 7 and Figure 9, we can discover that, during waterflooding, lower permeability has a larger gap between static and dynamic capillary pressure, but during surfactant added waterflooding, this trend changes. The above finding is resulted from that the magnitude of the reduced τ value (τwater − τchemical) varies with different permeability shown in Figure 7. Compared with K = 0.56, although the 0.36 mD core sample experiences

redistribution time, which causes the increase of dynamic coefficient for low permeability in this work. This is also consistent with the research of Tian et al.16 that lower permeability cores show higher dynamic coefficient values. 4.2. Influence of Surfactant Additives on Dynamic Coefficient and Capillary Pressure during Waterflooding. The surfactant additives in this work have the ability to diminish dynamic capillarity for porous media, which will benefit the production process: the surfactant additives reduce τ values to a certain extent from the waterflooding process to the surfactant added waterflooding process (Table 5 and Figure 6). In addition, both static and dynamic capillary pressure decrease due to the impact of surfactant additives (Table 6 and Figure 9). The reason for the above performance is the capability of surfactant additives to change fluids and rock properties. Some of the factors that may affect capillary pressure include imposed boundary conditions,57 wettability,17 soil properties,22 dynamic contact angle,58 fluid properties,59 air and water entrapment, pore water blockage, air entry value effect,27 etc. Hassanizadeh and Gray60 demonstrated that capillary pressure is a function of the specific area of the fluid−fluid interface per unit volume. Because capillary pressure decreases with decreased interfacial tension, the entrance pressure Pd in eq 4 will be reduced after surfactant additives added. Consequently, from eq 12, we can concluded that surfactant additives will reduce the dynamic coefficient (τ). The expression by Manthey et al.61 shows what can affect the relationship between dynamic capillary pressure and static capillary pressure, which can be modified as

Pcd = where

μc lc

τ μc s Pc Pccφ lc

a lower τ reduction rate

(

τwater − τchemical τwater

), the huge decline

of τ value (τwater − τchemical) contributes to lower dynamic capillary pressure during surfactant added waterflooding referring to eq 3. Because dynamic capillary pressure is the actual factor affecting the production process in low permeability reservoirs, this finding demonstrates the considerable potential of surfactant additives to help with low permeability reservoirs production. (2) In fact, we predicted that the dynamic capillary pressure of the 0.97 mD permeability core sample will decrease

(12)

is the maximum observed desaturation rate, Pcc is

taken as the entry pressure,19 and φ shows porosity. In this work, static capillary pressure is fairly reduced by the changed wettability (contact angle changes from 136.5° to 80.5°) and interfacial tension.62 Therefore, it is clear that dynamic capillary pressure will be decreased significantly as a result of reduction in dynamic coefficient and static capillary pressure. The I


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Figure 11. Final local water saturation at different core parts of the core samples read by mini-TDR probes during waterflooding and surfactant added waterflooding.

Considering capillary number, Manthey et al.61 proposed a dimensionless number named dynamic number (Dy) to quantify the ratio of dynamic capillary to viscous forces as

most profoundly at high water saturation form waterflooding to surfactant added waterflooding. This was deduced referring to eq 3 because higher permeability porous media may experience higher derivation of water saturation

∂Sw ∂t

( )

Dy =

during the flooding process.49 However,

as is compared in Figure 8c,d, the prediction cannot be obviously observed among different permeability core samples, which may be attributed to the relatively small difference of the permeability. Therefore, the effect of surfactant additives on dynamic capillary pressure for a wider range of permeability should be further investigated. (3) In this work, the surfactant additives reduced the surface tension (σ) between oil and water from 28.7 to 2.6 × 10−3 mN/m. Therefore, capillary pressure should also decrease to the same degree of about 1000 times.62 However, in this work, surfactant additives achieve only around 50−60% reduction in both static and dynamic capillary pressure (Table 6). In fact, the reduction rate of the injection pressure from waterflooding to surfactant added waterflooding, which was obtained from our prior research using the same material, can also reflect the distinction: the reduced interfacial tension, contact angle change, and wettability alternation can ideally reduce the injection pressure by at least 1000 times, but the actual reduction rate of the injection pressure is approximately 30%. This divergence above can be attributed to viscous fingering during waterflooding caused by complex pore structure, less continuous porous media, and high heterogeneity of the low permeability core samples utilized in this investigation.24,26,63 Various final local water saturations at different core parts read by mini-TDR probes during both waterflooding and surfactant added waterflooding processes (Figure 11) can reflect such viscous fingering. The macroscopic pattern of the moving interface between fluids is controlled by dynamic properties. Dynamic properties of a system can be described by two parameters, namely, viscosity ratio and capillary number.64 More specifically, in this work, where surfactant additives can arrive is controlled by viscosity ratio and capillary number.

dynamic capillary force Kτ = 2 viscous force μw lc φ

(13)

where μw is viscosity of the wetting phase, i.e., oil viscosity in this work; K is intrinsic permeability; φ is porosity; and lc is the characteristic length (e.g., a distance over which a characteristic pressure drop occurs). From eq 13, we can see that the dominance of dynamic capillary force over the viscous force can be reduced by decreased dynamic coefficient (τ). Since the reduction rate of τ is no more than 75% with nearly no change of fluid viscosity after surfactant additives were applied, viscous force cannot dominate over dynamic capillary force in the whole core, generating a viscous fingering. Therefore, it is difficult for the surfactant added brine to arrive at some position of the core and further decrease in situ dynamic capillary pressure. From eq 12, we can also see that the difference between static and dynamic capillary cannot be very large restricted by the reduction rate of τ, which is consistent with the reduction rate of the average dynamic capillary pressure. In addition, lower permeability achieves a lower reduction rate of τ (Figure 7a), which means that lower permeability can show more serious viscous fingering. Therefore, methods are required to improve the reached and influenced area, as well as to increase viscous ratios when performing surfactant added waterflooding in low permeability reservoirs.

5. CONCLUSIONS In this work, a group of particularly developed waterflooding experiments were performed to investigate the effect of low permeability and surfactant additives on the capillary pressure− fluid saturation relationship, as well as their dynamic effect. During waterflooding and surfactant added waterflooding, the local dynamic coefficient (τ) has been analyzed, the performance of different permeability core samples has been compared, and the difference between dynamic and static capillary pressure has been investigated. The experimental results and mechanisms analyses lead to the following conclusions: J


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(1) Low permeability porous media show a higher dynamic effect on the capillary pressure−saturation relationship than high/moderate permeability porous media, which is caused by the tight pore structure and strong heterogeneity of low permeability porous media. (2) Surfactant additives have great effect on the dynamic coefficient (τ) and capillary pressure in low permeability porous media through changing interfacial tension, contact angle, and wettability. (3) The lower the permeability is, the more obviously the surfactant additives could reduce dynamic capillary pressure. This combined influence of surfactant additives and low permeability condition indicates that surfactant additives have meaningful potential to reduce injection pressure and ease the oil recovery process for low permeability reservoirs.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (H.L.). *E-mail: [email protected], [email protected] (Y.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by The National Science and Technology Major Project of China (No. 2011ZX05022), The China National Offshore Oil Corporation Major Project (No. CNOOC-SY-001), and The China National Offshore Oil Corporation Key Project (No. CCL2012TJPZTS0380).

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NOMENCLATURE τ =dynamic coefficient, M/TL Psc =static capillary pressure, M/(T2L) Pdc =dynamic capillary pressure, M/(T2L) Pnw =nonwetting fluid phase pressure, M/(T2L) Pw =wetting fluid phase pressure, M/(T2L) Pwater =water phase pressure Paverage =volume averaged oil phase pressure o Paverage =volume averaged water phase pressure w Paverage =averaged dynamic or static capillary pressure C Sw =wetting fluid phase saturation, dimensionless Swater =water phase saturation, dimensionless dS =time derivative of fluid phase saturation, T−1 dt α =dimensionless parameter (defined to be 0.1) φ =porosity K =intrinsic permeability (isotropic) uw =viscosity of wetting phase (referring to oil in this work) ρw =density of the wetting phase (referring to oil in this work) g =gravity constant Sn =water saturation at time tn Vp =pore volume TB =redistribution time μc =the maximum observed desaturation rate

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Effects of Chemical Additives on Dynamic Capillary Pressure during

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