Numerical and ANFIS modeling of the effect of fracture parameters on the performance of VAPEX process

Journal of Petroleum Science and Engineering 143 (2016) 128–140

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Numerical and ANFIS modeling of the effect of fracture parameters on the performance of VAPEX process Heydar Pendar a, Mehdi Mohammad Salehi b,n, Riyaz Kharrat a, Saeed Zarezadeh c a

Petroleum University of Technology, Ahwaz, Iran Chemical Engineering Department, Sahand University of Technology, Tabriz, Iran c Iranian Offshore Oil Company, Iran b

art ic l e i nf o

a b s t r a c t

Article history: Received 24 July 2014 Received in revised form 3 November 2015 Accepted 23 February 2016 Available online 24 February 2016

The Vapor Assisted Petroleum Extraction (VAPEX) process, a newly developed enhanced heavy oil recovery process, is a promising EOR method for certain conventional non-fractured heavy oil sandstone reservoirs such as reservoirs located in Canada, but its applicability on low permeable naturally fractured reservoirs like Persian Gulf reservoirs is controversial. Previous studies show that the foremost concern for VAPEX application in naturally fractured reservoirs is the low non-economical production rates. The aim of the present work is studying the effect of fracture geometrical properties such as orientation, length, intensity, discontinuity, and position of fractures on the performance of the VAPEX process in a fractured model. Then an intelligent model is proposed for predicting the recovery of the process. To do so, first, a non-fractured, two-dimensional numerical model, i.e. a conventional model is constructed to simulate the VAPEX process. Then, different fracture patterns are applied in the model and the simulation results are analyzed. The qualitative analysis of the simulation results demonstrates that the presence of the fractures enhances the recovery of the VAPEX process. In order to quantify and model the effects of these geometric fracture parameters on the performance of VAPEX process, an intelligent modeling tool, Adaptive Neural Fuzzy Inference System (ANFIS) is employed. For the model results to be generalized, dimensionless forms of geometrical parameters are utilized. In fact, this model employs an image of the fracture pattern which determines the geometrical parameters of the fractures. Considering a constant Pressure-Volume-Temperature (PVT), relevant rock properties and operational condition, the recovery of the pattern can be determined fairly well. The results of this study show that the presence of both vertical and horizontal fractures improve VAPEX recovery, but the effect of vertical fracture are more than horizontal fractures on the VAPEX recovery. Fracture length is an important parameter on the performance of VAPEX as higher production rates achieved in the case of larger length. In addition, discontinuity in the fractures decreases the oil production rate in the VAPEX period. Finally, the effect of position of the fractures on the recovery are very complicated. As the distance of the fractures from the hypothetical line increases, the oil production rate in the VAPEX period increases. Weight in on ANFIS as an intelligent tool by combining fuzzy logic and neural networks can predict an output according to the input parameters. This ability helps quantify the complicated effect of different parameters on the recovery of the VAPEX process. & 2016 Elsevier B.V. All rights reserved.

Keywords: VAPEX Fractured reservoir Dimensionless fracture parameters ANFIS modeling

1. Introduction Proven reserves of the world for heavy and extra heavy oil are approximately 8 trillion barrels, approximately three times more

Abbreviations: VAPEX, Vapor Extraction; PVT, Pressure Volume Temperature; CSS, Cyclic Steam Stimulation; SAGD, Steam Assisted Gravity Drainage; ISC, In Situ Combustion; NFR, Naturally Fractured Reservoirs; EOR, Enhanced Oil Recovery n Corresponding author. E-mail addresses: [email protected] (H. Pendar), [email protected] (M.M. Salehi), [email protected] (R. Kharrat). http://dx.doi.org/10.1016/j.petrol.2016.02.029 0920-4105/& 2016 Elsevier B.V. All rights reserved.

than the world's reserves of light oil, but only 13% of the world's crude oil production is from heavy oil reservoirs. Heavy oil and bitumen are characterized by their high viscosities and low API gravities. High capital investment and high operational cost of heavy oil recovery are the reasons which make the heavy oil as a possible future potential source of energy. Among these reservoirs, carbonate reservoirs which are mostly fractured, contain one-third of the total heavy oil worldwide and have estimated reserve of 1.6 trillion barrels. Many of fractured reservoirs in the Middle East are candidates for heavy oil recovery methods (Dusseault, 2006;

H. Pendar et al. / Journal of Petroleum Science and Engineering 143 (2016) 128–140

Pooladi et al., 1995; Briggs et al., 1998). There are numbers of processes for exploiting heavy oil from the reservoirs, including cold production (primary production), Cyclic Steam Stimulation (CSS), Steam Assisted Gravity Drainage (SAGD), In-situ Combustion (ISC) and Vapor Extraction (VAPEX). The VAPEX of heavy oil by solvents is considered to be one of the most energy efficient, economically attractive and pollutionfree alternatives to thermal extraction methods (Abukhalifeh et al., 2012; Alkindi and Al-Wahaibi, 2008; Abdullah, 2009). VAPEX is suitable for thin, shallow, low permeability reservoirs, or those underlain by aquifers, since these can result in excessive heat loss and thus poor recovery efficiency for thermal Enhanced Oil Recovery (EOR) methods (Das, 1998; Frauenfeld et al., 2006). CO2-based solvents have been shown experimentally to be more productive than methane and ethane-based solvents in VAPEX process (Dunn et al., 1989; Talbi and Maini, 2003). VAPEX may therefore be a way of improving oil recovery whilst simultaneously storing excess CO2 in the subsurface and thus reducing greenhouse gas emissions. VAPEX mechanism was first proposed by Butler and Mokrys as an analogue of Steam Assisted Gravity Drainage (SAGD) in that diffusion driven mass transfer between the solvent-heavy oil reduces oil viscosity in a similar way to the heat diffusion between the steam and oil. Two long horizontal wells are drilled parallel to each other (as in SAGD) in order to maximize the exposure to the reservoir. Solvent is then injected into the upper well while the diluted oil from the solvent-oil diffusion layer drains under gravity effect to the lower well (Butler and Mokrys, 1991). Unlike thermal processes, the VAPEX process can be operated at a reservoir temperature with no heat loss. Hence, it is an efficient method for producing heavy oil as it consumes less energy for production the same amount of the oil. Therefore, VAPEX can be used as an alternative method to recover the heavy oil and bitumen where thermal processes are not operationally and/or economically applicable. These reservoirs include thin reservoirs, low permeability reservoirs with vertical fracture, low porosity and low thermal conductivity reservoirs where the heat capacity per unit of volume of contained oil is high, and reservoirs with aquifers and/or gas caps. Hence, low energy consumption, low environmental pollution, in-situ upgrading, and lower capital costs compared to thermal processes are all the attributes which make the VAPEX process an attractive method instead of conventional thermal processes. The main uncertainty limiting the field application of this process is the oil drainage rate and the effect of reservoir heterogeneity on the rate. Oil drainage rates of VAPEX are much lower than SAGD because the oil viscosity is reduced via mass diffusion and dispersion rather thermal diffusion. So, it is unclear whether these low rates will be economic or not. It is very inefficient to perform accurate numerical simulations of the process due to the levels of grid refinement needed to solve the diffusion and drainage processes occurring at the solvent-oil interface. To circumvent this issue Butler and Mokrys (1991) derived a semi-analytical equation for estimating oil drainage rate without simulation. A further uncertainty in the field scale application of VAPEX is the impact of geological heterogeneity. Small (mm to cm) scale heterogeneities may be expected to increase dispersive mixing and thus the oil drainage rate. Larger scale heterogeneities (greater than 10 m) can alter the shape of the solvent cone and thus either improve or, more likely, reduce the oil drainage rate, depending on the nature of the heterogeneity (Jimenez, 2008). Previous theoretical and experimental studies on the fractured system showed that in a fractured system, due to differences in matrix and fracture permeabilities, the solvent first spreads through the fractures and then starts diffusing into the matrix and the cross flow enhances in the system. Thus, the solvent surrounds

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the oil bank and an oil chamber, rather than the solvent chamber is formed and shrinks as the process proceeds. Even for the side fractures being far apart from the bottom fracture, the solvent distribution differs significantly from no-fracture model. When the matrix is surrounded by four connected fractures, combination of diffusion phenomenon and gravity segregation was observed to be the effective mechanism of the VAPEX process in all the systems studied. Also, increase of fracture-matrix contact directly improves the solvent- heavy oil contacts and results in higher oil recovery by VAPEX process, as the fractures are likely to enhance the VAPEX process by increasing the overall vertical permeability in the system, improving counter current flow of solvent and heavy oil, and providing more area for solvent diffusion (Azin, 2007; Azin et al., 2005a, 2005b, 2008a, 2008b; Rostami et al., 2005; Marzbanfard et al., 2005). Based on the experimental results, analytical models have been developing to scale up oil production rates in experiments to field prediction. Butler and Mokrys (1989) derived an analytical model to predict oil-drainage rates during VAPEX in a vertical hele-shaw cell. This model was further modified by Das and Butler (1998) to evaluate the oil-drainage rates by using an apparent diffusivity term. Some researchers integrated dispersion effects into mass transfer models and proposed the effective diffusivities, which are two to five orders of magnitudes higher than the molecular diffusivities (Boustani and Maini, 2001; Karmaker and Maini, 2003). Yazdani and Maini (2005) suggested that the increased drainage rates caused different dependency on reservoir thickness, and a function of drainage height to the power of 1.1–1.3. Nenniger and Dunn (2008) developed a new correlation to predict the oil production rate based on the 60 experimental data sets. Their results indicated some contradictions in Butler's model. Despite the great efforts to improve the techniques for prediction of VAPEX performance, it needs to be developed further. In a different study performed using numerical simulations to evaluate the impact of reservoir permeability distributions on VAPEX, Zeng et al. (2008) concluded that a random permeability distribution had a very minor effect on overall VAPEX performance compared to homogeneous cases. It was also noted that the highest oil drainage rates were obtained for models with a high permeability layer close to the producer. Frauenfeld et al. (2006) meanwhile, tested the impact of sand lenses and layering, as well as bottom aquifers. Their physical model was constructed from a field scale reservoir model applying Pujol and Boberg's gravity and diffusion scaling criteria (Pujol and Boberg, 1972). The model simulated a 30 m thick reservoir underlain by a 10 m thick aquifer with a geometric ratio of 100:1 (i.e. 30 cm reservoir thickness, 10 cm bottom water zone and 25 cm horizontal well offset). In these experiments, Kerrobert oil (50,000 mPa s) was used with butane as the solvent. It was observed that oil drainage rates were lower in layered systems compared to homogeneous models with uniform permeabilities, and the layering resulted in the formation of mini-vapor chambers above the injectors. Interestingly, it was noticed that low permeability lenses did not severely inhibit the oil rate as the solvent was diverted sideways and around these features. In order to quantify and model the effects of these geometric fracture parameters on the performance of VAPEX process, an intelligent modeling tool, Adaptive Neural Fuzzy Inference System (ANFIS) is employed. For the model results to be generalized, dimensionless forms of geometrical parameters are utilized. In fact, this model employs an image of the fracture pattern which determines the geometrical parameters of the fractures. Considering a constant Pressure-Volume-Temperature (PVT), relevant rock properties and operational condition, the recovery of the pattern can be determined fairly well.

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2. Methodology

Table 1 The properties of conventional model.

In this paper, first, a non-fractured, two-dimensional numerical model, i.e. a conventional model is constructed to simulate the VAPEX process. Then, in order to investigate the effect of different fracture parameters on the performance of the VAPEX process, different fracture patterns are applied to the model and the simulation results are analyzed. By preliminary analysis of the results, the effect of the parameters is qualitatively described. In order to quantify the results, it is necessary to properly model the effect of all variables. To achieve the ends, the images of different fracture patterns are used as input of MATLAB (R20133a) Image Processing Toolbox and output of Image Processing are used as dimensionless parameters of input of an ANFIS model. By training this model, predictive tool for forecasting the recovery of the VAPEX process is developed. 2.1. Simulation of VAPEX presses To study the VAPEX recovery mechanism in Naturally Fractured Reservoirs (NFRs) and the effect of different fracture parameters, a conventional model is created and modified. Hence, to import different fractured patterns, very thin high permeable layers have been inserted into the conventional model to represent the fracture. 2.1.1. Description of the conventional model In order to simulate the VAPEX process at certain pressure conditions in the conventional system, a rectangular model was considered. The simulator is used in this study is CMG. So, first, a two-dimensional numerical model was created by CMG's GEM module to simulate the VAPEX process. Fig. 1 depicts the schematic of the rectangular conventional model which is used in the simulation studies of the VAPEX process. The model properties are summarized in Table 1. All of the dimensions of the base case model are equal to 1 ft (30.48 cm). The matrix model has 21
21
1 (441) grid blocks with length of 1.45 cm. The fracture models are based on developing the dual porosity model by using the single porosity pattern to minimize the error of the dual porosity model, and also for better

1 ft

Injection well

1 ft

Fig. 1. Schematic of the rectangular conventional model.

Length in X, Y and Z direction (ft)

1, 0.1 and 1

Porosity Permeability (md) Initial pressure (psia) Temperature (°F) EOS Number of pseudo component Initial dead oil viscosity (cp) Injection solvent Number of injection well Number of production well

0.3 100 1000 70 PR (1979) 8 500 0.25C3 þ 0.75 C1 1 1

visualization of the performance of the process in the model. Therefore, the properties of the fracture must be assigned to these very thin layers. Since porosity, permeability, thickness and relative permeability curves are different for the fracture grids, the fracture porosity and permeability should have an acceptable value and must be different from matrix porosity and permeability. To approach to a realistic model, the actual set of relative permeability data from one of Iranian carbonate reservoir are used in the model. The relative permeability curve is shown in Fig. 2. The average porosity and permeability are set to 0.3 and 100 md, respectively. One injector is located at top center of the model and one producer is employed right below it at the bottom of the model. The system pressure and temperature are set at 1000 psia and 21 °C, respectively. The properties of heavy crude oil which are used in simulations are taken from the Soroosh oil field, for which the rock and fluid data are available. The oil has a viscosity of 500 cP at atmospheric condition and its dead oil API gravity of 19. The Equation of State (EOS)-based compositional simulator is used in this study which is enhanced to include the effect of molecular diffusion and convective dispersion. The compositional model is a subset of the general flow equations which includes multi-component and multiphase flow, mass transfer, and continuity equations. The lumped oil system which is used in the simulations is shown in Table 2. Thermodynamic and phase behavior data, as well as equation of state tuning are done by the Win Prop module of CMG. Also, the compositional simulations in this study are performed using GEM module 2006.1, which is the CMG's advanced general equation of state compositional simulator. CMG is a finite difference simulator that solves the mathematical models for flow, diffusion–convection, and continuity equations simultaneously. This simulator have been successfully applied to the VAPEX process by other investigators such as Nghiem et al. (2001), and Dauba et al. (2002). The Peng–Robinson Equation of State (PREOS) (Peng and Robinson, 1976) is used in the simulations. PVT data for the oil, such as oil formation volume factor, relative volume, oil specific gravity, oil viscosity, gas compressibility, and gas–oil ratio are used to tune the EOS. The vapor pressure of the oil is 3000 kPa (433 psia). So, there is no free gas in the model according to the constant operating conditions at all stages of the process, since the operating condition is located above the bubble point at all times during the simulation. Thus, the model can be regarded as an under-saturated reservoir. The criterion that should be met in selecting the solvent system is that it should be injected in saturated vapor (dew point) conditions without any liquefaction before it dissolves in to heavy oil (Butler et al., 1995). As the vapor pressure of solvents (Propane or Butane) are very low at the specified reservoir conditions, liquefaction of the solvent in the high pressure reservoir is inevitable. To avoid this, the solvent should be mixed with a suitable noncondensable gas such as methane in order to reach the dew-point

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krog

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SI Fig. 2. Relative permeability curves for matrix blocks.

11*11

Table 2 Oil composition for the 8-component EOS. Component Composition (mole fraction)

43*43

25

0.00187 0.09471 0.05465 0.01055 0.02506 0.04973 0.6945

Recovery (%)

N2 C1 CO2 to C2 IC4 NC4 NC5 to C6 C7 to C33 þ

21*21

30

20 15 10 5 0 0

75% C1 25% C3

1600

1

2

3 Time (Day)

4

5

6

Fig. 4. Oil recovery comparison for different mesh refinement patterns.

1400

Pressure (psia)

1200 1000 800 600 400 200 0 -150

-100

-50 0 Temperature (deg F)

2-Phase boundary

Critical

50

100

To study the effect of numerical dispersion on the simulation results, sensitivity analysis has been performed on three mesh refinement patterns of 11
11, 21
21 and 43
43 grid size and the results of the oil recovery factor and solvent chamber propagation of them are compared with each other. Figs. 4 and 5 show this comparison. Another criteria for selecting the grid size is computation time of each mesh refinement pattern which also given in Table 3. It is acceptable to claim that the 21
21 mesh refinement is fair because it has a better accuracy than coarser mesh refinement pattern and by more refining, accuracy did not change considerably. In addition, it is not too computationally expensive as finer one. Therefore, the simulation studies are done with this grid model.

Reservoir Condition

Fig. 3. Phase envelope diagram for solvent mixture of 75% C1 and 25% C3.

state under reservoir conditions. Different solvent mixtures were tested to find the best system which meets a fore mentioned criterion. Fig. 3 depicts the P–T diagram for this system, which have a composition of 75 percent C1 and 25 percent C3. It is clear from this figure that reservoir conditions fall on the dew point curve, which meets the required criterion. Any changes in the composition of solvent makes the operation conditions to be deviated from saturation conditions and falling through two-phase or super-heated regions. If the operation conditions fall within these regions, liquid solvent will be injected into reservoir, which is undesirable.

2.1.2. Description of the fractured model According to Golf-Rakht (Van Golf, 1982), in a non-conventional fractured reservoir two types of reservoirs may be distinguished: fractured reservoirs of single porosity; and fractured reservoirs of double porosity. In this case, single porosity model are used to develop dual porosity fractured model in order to minimize the error of the dual porosity model, and also for better visualization of the performance of the process in the model. The fractured layers are modeled with very thin layers between the blocks. So, the properties of the fracture must be assigned to these very thin layers. Since porosity, permeability, thickness and relative permeability curves are

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Fig. 5. Propagation of solvent chamber for different mesh refinement patterns (viscosity profile).

Table 3 Computation time of different mesh refinement patterns. Mesh refinement pattern CPU time used 11*11 21*21 43*43

435 852 1842

different for the fracture grids, the fracture porosity and permeability should have an acceptable value and must be different from matrix porosity and permeability. The other sensitive parameter is relative permeability curve for the fractures that should form two straight lines crossing each other at the center with 45° angles. Fig. 6 shows the relative permeability curve of the matrix. The matrix dimensions, system pressure and temperature, and oil sample are set similar to its values in the simulation of the conventional reservoir. One injection well was located at the top center of the model in the fracture layer and one production well at the bottom fracture layer exactly below the injection. Other model parameters are summarized in Table 3. The oil system and lumping method applied in the fractured system were similar to those which are used in the conventional system. Also, the solvent system same as that used in the conventional system is applied in studying the fractured system (Table 4).

2.1.3. Developing VAPEX model by ANFIS 2.1.3.1. ANFIS. ANFIS stands for Adaptive Neural Fuzzy Inference System that applies a given input/output data set. ANFIS training uses learning algorithms of the neural network. ANFIS is based on Takagi–Sugeno inference model (Takagi and Sugeno, 1985). It uses a hybrid learning algorithm to identify consequent parameters of Sugeno-type fuzzy inference systems. ANFIS is employed to model nonlinear or fuzzy input and output data, and to predict output according to the input. It applies a combination of the least squares method and the back-propagation gradient descent method to train the fuzzy inference system membership function parameters formulating a given training data set. Functionally, it is equivalent to the combination of the neural network and the fuzzy inference system (Soltani et al., 2010). ANFIS, as shown in Fig. 7, consists of 5 layers of nodes. The nodes in the first layer compute the membership degree of the inputs in the antecedent fuzzy sets. The nodes in the second layer are fixed and play the role of a simple multiplier. The outputs of these nodes give the so called firing strengths of the rules denoted by w's. The nodes in the 3rd layer calculate the ratio of the ith rule's firing strength to the sum of all the rules firing strengths and its output denoted by w's (also called normalized firing strength). The 4th layer contains the adaptive nodes and the output of each node in this layer is simply the product of the outputs from the third layer with a linear based model. The final 5th layer produces the overall output of the ANFIS model by computing the summation of all incoming signals. In this work, for developing a model which can predict the recovery curve

H. Pendar et al. / Journal of Petroleum Science and Engineering 143 (2016) 128–140

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Sl Fig. 6. Relative permeability curves for fractured blocks.

Table 4 Fractured models properties. Length in X, Y and Z direction (ft)

1, 0.1 and 1

Matrix porosity Matrix permeability (md) Fracture porosity Fracture permeability (md) Fracture thickness (ft) Initial pressure (psia) Temperature (°F) EOS Number of pseudo component Initial dead oil viscosity (cp) Injection solvent Number of injection well Number of production well

0.3 100 0.99 100,000 0.005 1000 70 PR (1979) 8 500 0.25C3 þ 0.75 C1 1 1

Fig. 7. Basic flow diagram of computations in ANFIS.

of various fractured pattern an ANFIS model is used. 2.1.3.2. Modeling. There is a wealth of observational data on the VAPEX process in the simulation of the fractured systems. Hence, experimental data in this case are not reached, but they validate the simulation studies Rahnema et al. (2008) and Pourabdollah et al. (2011). Some of the works provide qualitative and descriptive information about role of the fracture geometrical characteristics on the VAPEX process. Moreover, simulation works that are mentioned in this paper, give a fair amount of quantitative and qualitative information (e.g. the behavior of the oil recovery relative to increase of the fracture length, number of the fractures,

change of the fracture orientations etc.). Examples of the qualitative information would be “By increasing the fracture length, the oil recovery value will increase”, or “Increase in fractures numbers, leads to more recovery values”. Such statements carry information, but are not easily quantified. Indeed, these types of qualitative information are commonly the exact kind of information that is obtained through the studies. To model the recovery of the VAPEX process in the fractured reservoirs, the fractures parameters should be included in the model. These parameters must be also imported in a form which can be used in any scale. Hence, dimensionless parameter seems to be good choices. Parameters that are used in this case are geometrical parameters such as length, orientation, intensity, and parameters which describe location of the fractures such as the center of fractures. The other parameters of the model which depend on the reservoir fluid and the injection fluid properties, the operating condition, and the rock properties, remain constant and the only concern is about the fracture parameters. 2.1.3.3. Model parameters. To obtain the required information from the studied patterns, an image processing scheme is used. To do so, the images of all the patterns are applied. Then, some codes for processing the image under MATLAB software are developed and the program processes the images and provides the required information. 2.1.3.3.1. Dimensionless coordinate of fractures center (XD and YD). In order to handle the location of the fractures in different patterns, the center coordinate of the fractures are specified (in Cartesian coordinate, X and Y, with respect to the lower center of the model, is the location of the production well as a reference). Then, coordinate of the point is transformed to a dimensionless form. X and Y are divided by dimension of the model and a dimensionless abscissa and the ordinate of the fractures center point, XD and YD, are obtained. In the patterns which have several fractures or for the patterns with discontinuous fractures, an equivalent XD and YD are determined using a weighted average of all XDs and YDs and therefore, each pattern is specified by an equivalent dimensionless abscissa and a dimensionless ordinate of all the fractures center points in that pattern. The weight used in this average scheme is the fracture length. 2.1.3.3.2. Dimensionless standard deviation of fracture centers (XDSTD and YDSTD). XD and YD may not be the good

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representative parameters of the location and distribution of the fractures. It is required to have parameters that can represent the distribution of the fractures in the patterns. Therefore, standard deviation of all XDs and also YDs of the fractures determined. The standard deviation gives an idea of how close the entire set of the data is to the average value. In this case, it provides an idea of the distance and the distribution of the fractures to the equivalent or average XD and YD. A pattern with a small standard deviation has concentrated fractures and the patterns with large standard deviations have more dispersed fractures. 2.1.3.3.3. Dimensionless fracture length (LD). The fracture length is a parameter that affects the performance of the VAPEX process. This parameter also was used in the form of a dimensionless length (LD). This parameter is obtained by dividing of equivalent fracture length by the length of the diagonal of the model. The equivalent fracture length used is the average length of all the fractures in the pattern. 2.1.3.3.4. Dimensionless standard deviation of fracture lengths (LDSTD). In a similar method, the standard deviation of all the fracture lengths in a pattern is used to represent the difference in the length of the fractures to the equivalent fracture length. The dimensionless form of the parameter is made same as the dimensionless fracture length. 2.1.3.3.5. Fracture orientations. In addition to the mentioned data, the fracture orientations information is also required. Hence, the parameter is imported to model in a form of equivalent orientation of all the fractures presented in a pattern. For this purpose, the orientation of 90° and 0° assigned to a vertical and a horizontal fracture, respectively, and in the case of networks and a combination of vertical and horizontal fractures, an equivalent orientation by using length weighted average is assigned to a pattern. The average relation used in this case is as follows: n

Orientation =

∑i = 1 (length × orientation)i n

∑i = 1 (length)i

where n is the total number of fractures in the pattern. 2.1.3.3.6. Fracture intensity. In order to include the degree of fracturing of various patterns in the model, the intensity was defined as the ratio of the total surface of the fractures to the surface of the pattern. It is noteworthy that this parameter will be calculated by the image processing. An image Processing program developed in MATLAB distinguishes the fractures and the matrix area from each other and then the fracture intensity is calculated from their ratio.

3. Results and discussion 3.1. Comparison of simulation of fractured model with model Different fracture patterns were designed and the effect of the fracture parameters in terms of orientation, length, intensity, discontinuity and position of fractures were investigated. All the patterns, which the simulation was run for investigating the effect of the parameters or for developing the model, were 90 different patterns as are ference. Some of these patterns are shown in Fig. 8a, b, c, and d. 3.1.1. Effect of fracture orientations To study the effect of fracture orientations on VAPEX process recovery, vertical fractures and horizontal fractures (black strips2v1 and 2h1 in Fig. 8) have been added to the previous sections, conventional model. Simulation result of different fracture orientations and conventional model comparison shows that fractures enhance the VAPEX process by improving the contact

between solvent and oil in both cases of horizontal and vertical fractures (Fig. 9). Vertical fractures had a better performance than horizontal ones because extension of these fractures is in the direction of oil flow and this provides a high permeability flow path for oil and solvent. Hence, vertical fractures enhance the process by increasing the contact between solvent and oil and in addition by increasing overall vertical permeability of the system. In fact, these fractures enhance both mass transfer and gravity drainage mechanisms in VAPEX. Horizontal fractures also enhance the VAPEX process, but they are not as effective as vertical fractures. In fact, horizontal fractures same as vertical fractures, provide high permeability mediums in the model and increase solvent oil contact which accelerates the dilution process, but they do not enhance the gravity drainage by increasing vertical permeability. Horizontal fractures cause lateral expansion of the solvent chamber. Also, the simulation results of different fractures orientation and conventional model which is compared with the case of chamber development are shown in Fig. 10. 3.1.2. Effect of fracture length Patterns 2v1, 2v4, and 2v13 have been studied. As Fig. 11 shows that in the case of a longer fracture (2v1), the oil production rate increases. Actually, mass transfer and dilution process accelerate due to more diffusion and the oil rate increases consequently. This increase in the oil production rate can be seen in VAPEX or pseudo steady state period which in turn, causes more recovery (Fig. 12). The longer vertical fractures may establish strong connection between the injection and the production wells and therefore, shorten the displacement period. More extension of horizontal fractures as well as the vertical ones enhance the effectiveness of the process, but it has no significant effect on the duration of the displacement period. As the length of vertical fracture increases, the production time due to displacement mechanism decreases. It means that the VAPEX production period starts after breakthrough of injected gas in production well. After that, the oil which had mass transfer with injected gas will be produced which is favorable oil in this case. Although the rate of production in displacement process is maximum and more oil will be produced by time, the high viscosity of oil makes this process inappropriate. Of course it should be noted that the studied fracture parameter are not thoroughly independent and some parameters like fracture position have a complex effect on the process and its effects on other parameters like length and continuity cannot be fully recognized. 3.1.3. Effect of fracture intensity In order to study the effect of fracture intensity in both vertical and horizontal ones, patterns 2v2, 4v3 and 6v1 for vertical and 2h4, 4h0 and 6h1for horizontal have been compared. The simulation analysis shows that increase of fracture intensity improves the oil recovery. This effect can be noticed in Figs. 13 and 14. The relation between the oil recovery and fracture intensity can describe this fact that the higher intensity provides more contact area between the solvent and the oil and result in enhancement of the diffusion effect. 3.1.4. Effect of fracture position Patterns 2v4, 2v7 and 2v10 have been studied for effect of vertical and patterns 2h1, 2h2 and 2h3 have been studied for effect of horizontal fractures. Considering the simulation results, it can be concluded that the oil recovery increases as the distance between the fractures and the injection well decreases. This effect can be seen both for the horizontal and vertical fractures. Fractures located at the top of the models provide a path for propagating of the solvent in the upper part of the model and it dilutes the oil in

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a)

2h1

2h6

2h2

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2h3

2h9

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6h1

b)

2v1

2v2

2v3

2v10

2v13

3v14

2v4

4v3

2v7

6v1

c)

Combination 1

Combination 1

Combination 3

Combination 4

Combination 5

d)

Network 1

Network 1

Network 3

Network 4

Network 5

Fig. 8. Some of the patterns used in modeling: (a) Horizontal fractures patterns; (b) Vertical fractures patterns; (c) Combination of vertical and horizontal; and (d) Fractured network patterns.

the region and causes the oil to drain by the gravity. It is noteworthy that the gravity effect on the dilute oil at the upper part of the model is more than the lower part of the model and it leads to

a better oil production rate in the VAPEX period. These effects are shown in Figs. 15 and 16. In addition, Fig. 17 shows the fractures, which located at a long distance from the hypothetical line

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conventional

2v1

2v1

2h1

2v4

2v13

10

60

9 8 Oil Rate (cc/hr)

Oil Recovery %

50 40 30 20

7 6 5 4 3 2 1

10

0 0

1

2

3 Time (Day)

0 0

1

2

3 PV Injected

4

5

6

4

5

6

Fig. 11. Effect of vertical fracture length on production oil rate.

Fig. 9. Oil recovery as a function of time in the case of patterns 2v1, 2h1 and conventional base case model, showing higher ultimate oil recovery achievable in the case of presence of vertical fractures.

2v1

2v4

2v13

60

3.1.5. Effect of fracture discontinuity 3.1.5.1. Effect of vertical fractures discontinuity. Inducing discontinuity in vertical fractures means less contact area between fissures and matrices which reduce the solvent vapor diffusion from fissure into matrix and vice versa. Hence, in the case of continues fracture, more recovery factor expected. However, this increase in recovery factor depends on position of fractures and fractures orientation. To study the parameter mentioned a few patterns include 2v13 and 2v14, have been selected. Results show that continuity and discontinuity have more significant effect in the case of vertical fracture and this is because of the role of this type of fracture orientation in oil recovery at displacement or transient stage. Results of inducing discontinuity in vertical fracture are shown in Fig. 18. 3.1.5.2. Effect of horizontal fractures discontinuity. For studying continuity of horizontal fractured two patterns have been considered and shown in Fig. 19. Patterns 2h6 and 2h9 have been compared. These patterns have the same extension and location of horizontal fractures but pattern 2h9 includes discrete fissures. Solvent vapor could diffuse further into upper fissures areas of reservoir appreciating matrix parts between these fractures. As a result the process performance will be enhanced in comparison with pattern 2h9.

Conventional

Oil Recovery (%)

50 40 30 20 10 0 0

1

2

3

4

5

6

7

6

7

PV Injected Fig. 12. Effect of vertical fracture length on oil recovery.

2v2

4v3

6v1

60 50 Oil Recovery (%)

between two wells (or from the center of the model), in the case of pattern (2v3) fractures cause the solvent chamber to spread laterally into the more areas of the model and, in turn, the oil produces at more rates in the VAPEX period. Hence, after a period of time it results in more recovery of the oil.

Vertical (2v1)

40 30 20 10 0 0

1

2

3 4 PV Injected

5

Fig. 13. Effect of vertical fractures intensity on oil recovery.

Horizontal

(2h1)

Fig. 10. Viscosity map or profile due to propagation of solvent chamber for conventional and different fracture orientations after 48 h.

H. Pendar et al. / Journal of Petroleum Science and Engineering 143 (2016) 128–140

4h0

2h4

6h1

2v13

50

Oil Recover (%)

40

40 30 20

30 20 10

10 0 0

1

2

3

4

5

6

0

7

0

1

2

PV Injected Fig. 14. Effect of horizontal fracture intensity on oil recovery.

2v4

2v7

3 4 PV Injected

5

6

7

Fig. 18. Effect of vertical fracture discontinuity on oil recovery.

2h6

2v10

60

2h9

50

50

40 Oil Recovery (%)

Oil Recovery (%)

2v14

50

60

Oil Recovery (%)

137

40 30 20

30 20 10

10

0

0 0

1

2

3 4 PV Injected

5

6

7

Fig. 15. Effect of vertical fracture position (in term of distance to wells) on oil recovery.

0

1

2

3 4 PV Injected

5

6

7

Fig. 19. Effect of horizontal fracture discontinuity on oil recovery.

3.2. Simulation by ANFIS model

2h2

2h3

2h4

50

Oil Recovery (%)

40 30 20 10 0 0

1

2

3

4

5

6

7

PV Injected Fig. 16. Effect of horizontal fracture position (in term of distance to wells) on oil recovery.

2v1

2v2

2v3

70

Oil Recovery (%)

60 50 40 30 20 10 0 0

1

2

3

4

5

6

7

PV Injected Fig. 17. Effect of vertical fractures position (in term of distance to connecting line of wells) on oil recovery.

After extracting the data from all the patterns and classifying them, a nine input ANFIS model is developed. In this model XD, YD, XDSTD, YDSTD, LD, LDSTD, orientations, intensity, and PV (pore volume) are the inputs and the only output is the recovery. About two-thirds of the entire patterns data are used for the model training and one-third for checking and testing the model. Therefore, for each pattern, the parameters and a data set of the number of pore volume of injected fluid versus the oil recovery are present. As an example in the case of pattern 2v1 the data as shown in Table 5 are available. The ANFIS modeling steps have been performed by means of MATLAB Toolbox that incorporates a user-friendly environment. The procedure involves a few basic steps, i.e. loading the data sets, generating the fuzzy inference systems, training, and validating of the model. To generate the fuzzy interface system, hybrid method as an optimum method is used with the error tolerance of 0. After generating the model with a minimum error, training data which is used to develop the model and the ANFIS outputs for the same data are evaluated to analyze the precision and validation of the model. This comparison also should be repeated to check and test the data, but in the case of these two data sets, it should be noticed that they are not used in the modeling and the training. So, if the ANFIS outputs for these sets are appropriate, the model is acceptable. These comparisons are shown in Figs. 20–22. In addition, cross plot of initial data (simulation data) and ANFIS outputs are presented in Figs. 23–25. The recovery curve that is predicted for a random selected pattern is shown in Figs. 26 and 27. As can be seen in these figures, this model can predict the recovery curve fairly. The prediction is also performed for all the patterns, and its corresponding coefficient of determination, R2, is established. Average R2 is 0.9765, which indicates that the model is a precise.

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Table 5 Data set of pattern 2v1 for ANFIS modeling. XD

YD

XDSTD

YDSTD

LD

LDSTD

Orientation

Intensity

PV

Rec %

0.1687 0.1687 0.1687 0.1687 0.1687 0.1687 0.1687 0.1687 0.1687

0.5036 0.5036 0.5036 0.5036 0.5036 0.5036 0.5036 0.5036 0.5036

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0.5643 0.5643 0.5643 0.5643 0.5643 0.5643 0.5643 0.5643 0.5643

0 0 0 0 0 0 0 0 0

90 90 90 90 90 90 90 90 90

0.0078 0.0078 0.0078 0.0078 0.0078 0.0078 0.0078 0.0078 0.0078

0 0.1792 0.3506 0.5181 1.3148 3.1361 4.8404 5.5806 6.0384

0 5.9215 8.9602 11.4924 19.4786 33.0162 43.3399 46.9434 49.0861

ANFIS Model Output (% Recovery)

70

Fig. 20. Comparison between training data and ANFIS model prediction.

60 50

2

R = 0.9924

40 30 20 10 0 0

10

20

30

40

50

60

70

Simulation Data (% Recovery)

Fig. 21. Comparison between checking data and ANFIS model prediction.

ANFIS Model Output (% Recovery)

Fig. 23. Cross plot of training data and ANFIS model prediction.

70 60 50

2

R = 0.9932

40 30 20 10 0 0

10

20

30

40

50

60

70

Simulation Data (% Recovery)

Fig. 24. Cross plot of training data and ANFIS model prediction.

Fig. 22. Comparison between testing data and ANFIS model prediction.

4. Conclusions

ANFIS Model Output (% Recovery)

70 60 50 2

R = 0.9919

40 30 20 10 0

The results of this study reveals the following conclusions:

0

10

20

30

40

50

60

70

Simulation Data (% Recovery)

1. The vertical fractures have high effect on the performance of VAPEX process, because the extension of the fractures is in the direction of the oil flow; hence, they provide a high permeability flow path for the oil and solvent. 2. The horizontal fractures cause lateral expansion of the solvent chamber and enhance the VAPEX process, but they are not as effective as the vertical fractures.

Fig. 25. Cross plot of testing data and ANFIS model prediction.

3. Longer vertical fractures may make good connections between the injection and the production wells and therefore shorten the displacement period, but the extension of the horizontal fractures has no effect on the duration of the displacement period.

H. Pendar et al. / Journal of Petroleum Science and Engineering 143 (2016) 128–140

6V3

60

Anfis Model Simulation Model

Recovery%

50 40 30 20 10 0

0

1

2

3

4

5

6

40

50

60

PV

(a) Cross Plot R = 0.98887

60

Data y=mx and m=1

50

Model

40 30 20 10 0

0

10

20

30

Simulation

(b) Fig. 26. Recovery curve prediction for pattern 6v3 (a) and comparison with simulation data (b).

4. As the number of the fractures increase, the oil recovery factor increases. 5. The fractures at the top of the models cause propagation of the solvent and dilution of the oil in that region. It is obvious that the effect of gravity on the diluted oil of the upper part of the model is more significant and the gravity effect increases the oil production rate in the VAPEX period. 6. As the distance of the fractures from the hypothetical line increases, the oil production rate in the VAPEX period increases. This is due to more lateral spreading of the solvent chamber. In general, the effect of position of the fractures on the recovery is very complicated. 7. Inducing discontinuity between the fractures causes less contact area between the fractures and the matrix. Hence, in the case of continuous fracture more oil recovery factor is expected. 8. By using the results of the simulation or experimental data, the effects of geometrical parameters on the performance of the process can be just studied in a qualitative manner. To quantify these effects, an intelligent tool like fuzzy logic should be used. 9. ANFIS as an intelligent tool by combining fuzzy logic and neural networks can predict an output according to the input parameters. This ability can help quantify the complicated effects of different parameters on the recovery of the VAPEX process.

Acknowledgment We would like to extend our appreciation to our friend Abolfazl Dehghanmonfared for his friendship, help and encouragement during this work. References Abdullah, A., 2009. Experimental investigation of the vapor extraction (VAPEX) process for heavy oil recovery (Ph.D Thesis). Imperial College London.

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Abukhalifeh, H., Upreti, S.R., Lohi, A., 2012. Effect of drainage height on concentration dependent propane dispersion in VAPEX. Can. J. Chem. Eng. 90 (2), 336–341. Alkindi, M.A., Al-Wahaibi, Y., 2008. Physical properties (density, excess molar volume, viscosity, surface tension, and refractive index) of ethanol þglycerol. J. Chem. Eng. Data (12), 2793–2796. Azin, R., 2007. Investigation of the VAPEX process in fractured carbonate reservoirs (Ph.D Thesis). Sharif University of Technology. Azin, R., Kharrat, R., Ghotbi, C., Vossoughi, S., 2005a. Applicability of the VAPEX process to Iranian heavy oil reservoirs. SPE 92720, Presented At The 14th SPE Middle East Oil And Gas Show and Conference, Bahrain, 12–15 March. Azin, R., Kharrat, R., Ghotbi, C., Vossoughi, S., 2008a. Improved heavy oil recovery by VAPEX process in the presence of vertical and horizontal fractures. J. Jpn. Pet. Inst. (JPI) 50 (6), 340–348. Azin, R., Kharrat, R., Rostami, B., 2005b. Effect of solubility and diffusivity of solvent in heavy oil on the performance of the VAPEX process as an enhanced oil recovery process. Presented at 10th Iranian National Chemical Engineering Congress (Inchec), Iran, 15–17 November. Azin, R., Kharrat, R., Vossoughi, S., Ghotbi, C., 2008b. Study of the VAPEX process in fractured physical systems using different solvent mixtures. Oil Gas. Sci. Technol. – Rev. IFP 63 (2), 219–227. Boustani, A., Maini, B.B., 2001. The role of diffusion and convective dispersion in vapor extraction process. J. Cryst. Process Technol. 40 (4), 68. Briggs, P.J., Baron, R.P., Fulleylove, R.J., Wright, M.S., 1998. Develop of heavy oil reservoirs. J Pet. Technol. Butler, R.M., Mokrys, I.J., Das, S.K., 1995. The solvent requirements for VAPEX recovery, SPE 30293, Presented at the International Heavy oil Symposium held in Calgary, Alberta, Canada, June 19–21. Butler, R.M., Mokrys, I.J., 1989. Solvent analog model of steam-assisted gravity drainage. AOSTRA J. Res. 5 (1), 17. Butler, R.M., Mokrys, I.J., 1991. A new process (VAPEX) for recovering heavy oils using hot water and hydrocarbon vapor. J. Cryst. Process Technol. 30 (1), 97–106. Das, S.K., 1998. VAPEX: an efficient process for the recovery of heavy oil and bitumen. SPE J. 3 (3), 232–237. Das, S.K., Butler, R.M., 1998. VAPEX: an efficient process for the recovery of heavy oil and bitumen. SPE J., 232–237. Dauba, C., Quettier, L., Christensen, J., Le Goff, C., Cordelier, P., 2002. An integrated experimental and numerical approach to assess the performance of solvent injection into heavy oil. SPE77459, Presented at the SPE Annual Conference and Exhibition Held in San Antonio, Texas, 29 September–2 October. Dunn, S., Nenniger, E., Rajan, V., 1989. A study of bitumen recovery by gravity drainage using low temperature soluble gas injection. Can. J Chem. Eng. 67 (6), 978–991. Dusseault, M.B., 2006. Future trends in oil and gas industry, Canadian heavy oil resources and new production technologies. GEOMEC Oil Fields Geomechanics International. Frauenfeld, T., Jossy, C., Rispler, K., Kissel, G., 2006. Evaluation of the bottom water reservoir VAPEX process. J. Can. Pet. Technol. 45 (9), 29–35. Jimenez, J., 2008. The field performance of SAGD projects in Canada. In: International Petroleum Technology Conference. Karmaker, K., Maini, B.B., 2003. Applicability of vapor extraction process to problematic viscous oil reservoirs, SPE 84034, Presented at the SPE Annual Technical Conference, Denver, Colorado, 5–8 October. Marzbanfard, E., Kharrat, R., Azin, R., 2005. Experimental study of vapor extraction (VAPEX) in fractured reservoirs. 10th Iranian National Chemical Engineering Congress, Iran, 15–17 November (Original Paper in Persian). Nenniger, J., Dunn, S., 2008. Situ extraction process for the recovery of hydrocarbons. Nghiem, L.X., Kohse, B.F., Sammon, P.H., 2001. Compositional simulation of the VAPEX process. J. Can. Pet. Technol. 40 (8), 54–61. Peng, D.Y., Robinson, D.B., 1976. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15, 59–64. Pooladi, D.M., Farouq, A., Tortike W.S., 1995. Behavior of gravity drainage in heavy oil fractured reservoirs under steam injection. Presented in UNITAR International Conference on Heavy Crude and Tar Sands in Houston, Texas, February 12–17. Pourabdollah, K., Zarringhalam, M.A., Kharrat, R., Mokhtari, B., 2011. Improvement of heavy oil recovery in the VAPEX process using montmorillonite nanoclays. Oil Gas. Sci. Technol. – Rev. IFP 68 (3), 507–519. Pujol, L., Boberg, T., 1972. Scaling accuracy of laboratory steam flooding models. In: SPE California Regional Meeting. Rahnema, H., Kharrat, R., Rostami B., 2008. Experimental and numerical study of vapor extraction process (VAPEX) in heavy oil fractured reservoir. Presented at Canadian International Petroleum Conference (The Petroleum Society's 59th Annual Technical Meeting), Calgary, Canada, 17–19 June. Rostami, B., Azin, R., Kharrat, R., 2005. Investigation of the VAPEX process in high pressure fractured heavy oil reservoir. SPE 97766, Presented at the International Thermal Operations and Heavy Oil Symposium, Calgary, Canada. Soltani, F., Kerachian, R., Shirangi, E., 2010. Developing operating rules for reservoirs considering the water quality issues: application of ANFIS-based surrogate models. Expert Syst. Appl. 37 (9), 6639–6645. Takagi, T., Sugeno, H., 1985. Fuzzy identification of systems and its application for modeling and control. IEEE Trans. Syst. Man Cybern.

140

H. Pendar et al. / Journal of Petroleum Science and Engineering 143 (2016) 128–140

Talbi, K., Maini, B., 2003. Evaluation of CO2 based VAPEX process for the recovery of bitumen from tar sand reservoirs. In: SPE international Improved Oil Recovery Conference in Asia Pacific. Van Golf, T.D., 1982. Fundamentals of fractured reservoir engineering. Elsevier Scientific Publishing Company Amsterdam, Oxford, New York. Yazdani, A.J., Maini, B.B., 2005. Effect of drainage height and grain size on

production rates in the VAPEX process: experimental study. SPE Reserv. Eval. Eng. Journal., 205–213. Zeng, F., Knorr, K., Wilton, R., 2008. Post-cold production solvent vapor extraction (SVX) process performance evaluation by numerical simulation. In: Canadian International Petroleum Conference.