Screening and optimization of polymer flooding projects using artificial-neural-network (ANN) based proxies

Journal Pre-proof Screening and optimization of polymer flooding projects using artificial-neural-network (ANN) based proxies Qian Sun, Turgay Ertekin PII:

S0920-4105(19)31038-1

DOI:

https://doi.org/10.1016/j.petrol.2019.106617

Reference:

PETROL 106617

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 27 March 2019 Revised Date:

14 August 2019

Accepted Date: 25 October 2019

Please cite this article as: Sun, Q., Ertekin, T., Screening and optimization of polymer flooding projects using artificial-neural-network (ANN) based proxies, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/j.petrol.2019.106617. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Screening and Optimization of Polymer Flooding Projects Using Artificial-neuralnetwork (ANN) Based Proxies Qian Sun, Petroleum Recovery Research Center, and Turgay Ertekin, the Pennsylvania State University

Abstract Polymer flooding is one of the most broadly implemented chemical EOR processes due to its low injection cost and successes in oil production increments. This work develops artificial-neural-network based proxies by utilizing synthetic production histories generated from a high-fidelity numerical simulation model. Injection-pattern-based reservoir models are structured to establish the knowledgebase to train the proxies. A forward and an inverse-looking ANN models are structured in this study. The forward-looking expert system are employed as a forecasting and screening tool that is capable to predict time-based project responses. And the inverse-looking ANN predicts the project design schemes that fulfill the expected oil recoveries. The proxies are generalized considering reservoir rock and fluid properties and project design parameters. In this paper, we present results of extensive blind testing applications to confirm the validates of the proxy models. Afterwards, various applications of the expert systems are discussed. A project screening protocol that couples the expert system and particle swarm optimization (PSO) methodology is presented to maximize the polymer injection projects’ net present value (NPV). Moreover, we propose a robust computational workflow that coupled utilize the inverse and forward-looking proxies to find various polymer injection schemes to fulfill the expected oil production profile, which effectively addresses the issue associated with the existence of non-unique solutions in the inverse design problems. The expert ANN systems and the associated project design workflows provide versatile approaches for the field engineers to obtain quick techno-economical assessments of polymer injection projects. Key words: Artificial neural network, polymer injection, optimization, EOR screening, EOR project design

1

Screening and Optimization of Polymer Flooding Projects Using Artificialneural-network (ANN) Based Proxies Qian Sun, Petroleum Recovery Research Center, and Turgay Ertekin, the Pennsylvania State University

Introduction Polymer injection is one of the more attractive chemical enhanced oil recovery (EOR) processes which is typically implemented after waterflooding. A prescribed amount of polymer slug, typically measured by portion of pore volume (PV), is injected to the reservoir to reduce the mobility of the aqueous phase, and therefore improve the sweep efficacy. Field applications indicate that polymer injection is more practical than other chemical EOR processes due to the low injection fluid cost and prolific production increments (Wang et al. 2003, Sheng et al 2015). Typically, synthetic polymers such as HPAM and xanthan type biopolymers are widely utilized as mobility control agents in chemical EOR projects (for example, Wang et al. 2019). Experimental investigations and field experiences show that HPAM is more competent than xanthan for large scale projects due to its low price and better viscoelasticity (Yang et al. 2004, Wang et al. 2009 and Sheng 2013). Statistical data shows that average incremental oil production for polymer injection project is 2.91% of OOIP with 125 ppm-PV to 240 ppm-PV of polymer injected in U.S. field projects (Manning et al. 1983 and Sheng 2013). Extensive polymer injection projects are also carried in Daqing Oil field, China. From a survey of 55 polymer injection projects in Daqing Oil field, incremental oil production quantities ranging from 1.9% to 19.5% OOIP are reported (Zhang et al. 2016). However, the projects in China inject a much higher polymer amounts of 400-500 ppm-PV ranges as average. Moreover, literature indicates that 5-spot pattern is the most widely used design to align the injection and production wells for chemical EOR projects (Talash and Strange, 1982, Li et al. 2004, Zhang et al. 2016). Machine-learning (ML) based proxy models have exhibit their strength in terms of computational efficacy and generalization capability by successfully solving a large spectrum of reservoir

2 engineering problems (for example, Kamari et al. 2016, Amirian and Chen, 2017). Artificialneural-network (ANN) is one of the most popular employed ML algorithm in petroleum industry. Research works have been conducted to structure ANN models in the areas of reservoir characteristics, infill drilling location selection, virtual well testing analysis, optimization of field development strategies, EOR field implementation, etc. (for instance, Mohaghegh and Ameri 1995, Deng et al. 2000, Bansal et al. 2013, Ibrahim 2015, Abdullah et al. 2019). In such reservoir engineering applications, expert ANN systems act as multi-dimensional regression and classification tools to learn a given data structure. Training an expert system could be challenging especially for problems with large dimensions and voluminous data. A relevant review of literature shows that an ANN architecture optimization workflow can be employed to determine the most adaptive neural network topology (number of hidden layers, number of hidden neurons and transfer functions) in an effective way (Ketineni et al. 2015, Sun and Ertekin, 2015). In general, ANN systems are trained to solve the following three types of reservoir engineering problems (Ertekin and Sun, 2017): 1) Forward-looking problems: ANN utilizes reservoir properties and engineering design parameters as input to predict the project response surface. Forward-looking ANN models typically serve as forecasting proxies to predict the fluid productions and pressure responses. 2) Inverse project design problems: ANN predicts the required project design parameters to achieve a desired project outcome. The project design ANN models utilize the hydrocarbon recovery and the reservoir rock and fluid properties as input, and predict the project design parameters. 3) Inverse history-matching problems: ANN utilizes field production and pressure data as input and predict the suitable reservoir rock and fluid properties that can be used by a numerical simulation model to generate flow rate and pressure predictions to fit the field measurements.

3 This discussion of this article focuses on the forward-looking and inverse project design problems. It is worth to emphasize that solutions of both the two inverse problems (project design and history matching) always exhibit strong multiplicity characterization. One of the primary goals of the research work is to explore effective methodologies to address the issues related to nonunique solutions employing the ANN proxies. Research works have been conducted to couple ML-based proxies with computational protocols that require large volume of simulation runs, such as project uncertainty analysis (for example, Dai et al. 2016) and optimization studies (for example, Dai et al. 2014 and Amphoma et al. 2017). These studies demonstrate the importance of the proxy models by enabling the reservoir engineering analysis with prohibitive intensive computational overheads. Particle swarm optimization (PSO) is an increasingly popular optimization technique utilized in many applications in reservoir engineering. It is a more robust optimization algorithm as compared to more classical methods such as genetic algorithm (GA) for its better computational efficiency (for example, Duan et al. 2009, Chui et al. 2012, Tayebi et al. 2014). Onwunalu and Durlofsky (2011) propose a novel procedure to optimize well pattern design for a waterflooding project using PSO to maximize the net present value (NPV). Wang et al (2012) developed a retrospective workflow to optimize well placement scheme under uncertainty using PSO. Aliyev and Durlofsky (2016) utilizes PSO to optimize a field development strategy using an upscaled reservoir model to evaluate the fitness. Taking advantages of the fast-computational speed of the expert ANN system to evaluate the fitness of the particles, it is quite interesting to couple expert ANN systems with PSO in a hybrid optimization procedure. Published research works have established significant insights in utilizing expert ANN systems to study polymer flooding. Al-Dousari and Garrouch (2013) developed an ANN model to predict oil recovery versus injection volume of polymer/surfactant slug of a coreflooding process. Alghazal (2015) developed forward and inverse-looking ANN models to study polymer injection projects

4 in naturally fractured reservoirs. The ANN models consider the variation of spatial reservoir properties, but the properties of reservoir fluid and chemical additives are fixed. Norouzi et al. (2017) developed ANN models for a synthetic reservoir to design Disproportionate Permeability Reduction (DPR) polymer gel injection projects. In this work, ANN model predicts cumulative oil and water production at 600 days of continuous polymer injection. Ololo and Chon (2017) trained ANN expert systems that predict the oil recovery by implementing polymer injection in a synthetic reservoir. In their paper, the discussion focuses on the development of universal expert (ANN) systems to study pattern-based polymer injection projects. One forward-looking and one inverse design ANNs are successfully trained. The expert systems are generalized to be implemented with polymer injection projects with various reservoir rock and fluid properties and project design parameters. In this article, we present the developments of forward-looking and inverse project design ANN proxies for polymer injection projects. An in-house multi-layer neural network (MLNN) training module using scaled conjugate gradient training algorithm and a neural network topology design workflow are employed to train and optimize the prediction performance of the proxy models. To demonstrate the practicability and robustness of the proxy models, the forward-looking ANN model is coupled with the PSO algorithm to optimize the NPV of a polymer injection project. More importantly, we structure a versatile computational workflow composed of the ANN models to solve the inverse project design problem exhibiting strong solution multiplicity characterization.

Reservoir Modeling Structuring numerical simulation model In this study, we employ a commercial chemical EOR simulator, CMG-STARS®, to generate the synthetic field histories to serve as knowledgebase for ANN training. As shown in Figure 1, a two-dimensional model with dimensions of 67 × 67 is structured to simulate one-eighth of a 5-

5 spot injection pattern. All the external boundaries are completely sealed. Spatial reservoir properties exhibit homogeneous distributions and isotropic permeability characteristics. The impacts of the gravitational forces and capillary pressure are assumed to be negligible. The reservoir fluid model is structured with four components including water, polymer, dead oil and total dissolved solid. nx=67

I nj ector

ny=67

Injector

y Producer

x Producer

Figure 1. Illustration of the reservoir model of 1/8 of a 5-spot injection pattern

Injection and production specifications The simulation starts from continuous water injection and once the water cut increases to a certain level, the polymer slug injection starts. The water cut to switch from water flooding to polymer slug injection is considered as one of the project design parameters (WCswitch) in the development. Once the prescribed slug amount is injected, the injection fluid switches to water until the end of the project. Figure 2 illustrates the injection timeline for the polymer injection process.

6

Polymer slug injection starts Polyme r slug injection ends

Injection fluid composition: Wate r

Chasing water

Polymer slug

Figure 2. Injection timeline of the polymer flooding process

The simulation model specifies a constant injection rate for the injector, while the production well produces at a specified bottomhole pressure (PBHP). For the convenience of data preparation, the PBHP are normalized as portions of the initial reservoir pressure (pi). Rock and Fluid properties In this section, we introduce a critical formalism that would generalize the reservoir model in term of polymer rheology properties, rock and fluid interaction mechanisms with certain delineative coefficients. Aqueous phase viscosity In this work, a nonlinear mixing rule is implemented to calculate the aqueous phase viscosity. The viscosity of the aqueous phase changes as a function of polymer concentration according to the following [Equation (1)]:

7

( )

fa xp =

ln µ p − ln µw ln µ p max − ln µ w

(1)

In Equation (1), xp is the polymer concentration (by weight), in ppm, µp is the aqueous phase viscosity in cp, µw is the viscosity of water, µpmax is the viscosity of the saturated polymer solution. In order to implement the nonlinear mixing rule in the numerical simulation model, one needs to generate a table which provides a one-to-one relationship between polymer weight concentration against fa. Also, the viscosity of the polymer solution should satisfy Equation (2) as given below:

µ p ( c p ) = µ w (1 + 10c p + 10 2 c p 2 + 103 c p 3 )

(2)

Thus, the following algorithm can be implemented to generate the tabulated data for a specific type of polymer solution (Computer Modeling Group, 2012): 1. Calculate the solubility of the polymer in terms of weight concentration, cpmax by solving the cubic equation:

µ p max = µ w (1 + 10c p max + 10 2 c p max 2 + 103 c p max 3 ) 2. Generate a polymer weight concentration vector from 0 to cpmax using ten intervals and calculate aqueous phase viscosity µp for each polymer weight concentration. 3. Calculate the nonlinear mixing parameter fa from the values of µw, µp and µpmax. The advantage of using this approach to capture the aqueous phase viscosity is that once µpmax is specified, the nonlinear mixing parameters can be simultaneously generated. In other words, no additional input parameter is required to capture these fluid properties, which potentially simplifies the problem in terms of neural network training. Non-Newtonian behavior is considered as a modification of the apparent viscosity of polymer solution. In this work, the polymer solution is considered as power-law fluid and the apparent viscosity can be calculated from Equation (3) as shown below:

8

µapp

 v  = µp  l   vlow 

n −1

(3)

In Equation (3), n is the flow behavior index (dimensionless). vlow term is the fluid velocity at saturated polymer solution which can be calculated using Equation (4) (Cannella et al. 1998):

µsat

 3n + 1  = K   4n 

n

 Cv low   kk φ S rl l 

   

n −1

(4)

In the above equation, µsat is the viscosity of the saturated polymer solution, K is flow consistency index in cp-secn-1, n is flow behavior index (dimensionless). C is a constant which is equal to 0.6, v is the velocity in ft-s-1, k (in md) and krl (dimensionless) is the absolute and relative permeability values, ϕ is porosity (fraction). For a non-Newtonian fluid, n ranges from 0.5 to 1 and as n approaching to 1, the fluid behavior becomes more like the Newtonian fluid. This work considered the effect of salinity on the viscosity of the aqueous phase. The viscosity of the aqueous phase can be calculated by Equation (5):

x  µ p = µ p ,0  salt   xmin 

sp

(5)

In Equation 5, µp0 is the viscosity without any salinity effect in cp, and xsalt is the salinity of the solution in ppm. xmin is the minimum salinity which causes observable viscosity of the polymer solution to change. The value of xmin is 585 ppm. The superscript “sp” is a positive coefficient which is less than 1. By applying this correlation, it is seen that the higher the salinity of the polymer solution, the lower the viscosity will be. In this work, we assume that the injected and insitu water salinities are identical.

9 Polymer Adsorption Adsorption is considered as the major mechanism for polymer loss. In this work, a Langmuirisotherm type model is employed to model the adsorption effect. Polymer adsorption to porous media can be expressed as Equation (6):  lbmole  Az Ads  3 =  ft PV  1 + Bz

(6)

where, A is in lbmole/ft3 and B is dimensionless. z is the polymer mole fraction of the solution. In reality, it is difficult to obtain A and B directly by experimental means. The experimental tests provide adsorption data in polymer adsorbed per unit rock in terms of mass. In this work, the Langmuir isotherm coefficients are calculated using the following method: 1. Two input parameters are required: Admax, in µg/g rock is the maximum amount of polymer that could be adsorbed by the formation rock and CpAdsmax, in ppm is the polymer weight concentration when the maximum adsorption occurs. 2. Convert Admax to lbmole adsorbed polymer of unit weight of formation rock according to Equation (7):

1 cm3 −5 0.0022lbm 1 −6 3.53 × 10 ×10 Ad max × × g MWp ft 3 1−φ Adc = × 1 φ

(7)

ρrock

3. Convert CpAdsmax to mole fraction zAdmax. 4. Calculate coefficients A and B:

B=

10 z Admax

; A = B × Ad c

The adsorption effect can be captured once Admax, Cpmax are specified. This method brings a considerable convenience for establishing a library of adsorption data to train the ANN model

10 because the range of Admax and Cpmax can be obtained from available experimental studies (for example, Broseta et al. 1995, Zheng et al. 2000, Sheng 2010). This protocol eliminates the possibility that the randomly generated adsorption data in the library is unrealistic. The adsorption of surfactant and alkali is modeled employing this protocol. Relative permeability To generalize the model in terms of relative permeability curves, we employ Corey’s two-phase relative permeability model as expressed in Equation (8) and Equation (9): n

 1 − Sw − Sorw  ow krow = kroiw    1 − Siw − Sorw   Sw − Siw  krw = krwro    1 − Siw − Sorw 

(8)

nw

(9)

In this case, the relative permeability curve of a two-phase system can be characterized by coefficients krwro, kroiw, Siw, Sorw, nw, now introduced by Equation (8) and Equation (9). This work utilizes residual resistant factor (RRF) to calculate the mobility alternative of the aqueous phase associated with adsorption. A modification parameter RKW can be calculated as described by Equation (10):

RKW = 1 + ( RRF − 1)

Ad adsorp Ad max

(10)

Adadsorp is the amount of polymer adsorbed by the rock. Admax is the maximum amount polymer that can be adsorbed. The mobility change can be evaluated by dividing the water phase relative permeability by RKW. RRF can be tested via experimental studies and is always larger than 1.

11

ANN Model Development I/O Setup and Data Pretreatment

Training of the ANN models utilizes the synthetic production data generated using the constructed reservoir model. Critical parameters involved in the development are categorized as spatial reservoir rock properties, initial conditions, crude properties, relative permeability coefficients, polymer properties, project design parameters and project response data. Employing the highfidelity simulation model, synthetic production data are generated from batch runs using parameters with uniformly distributed by pseudo-random numbers. In Table 1, we summarize the input parameters and their corresponding ranges utilized to train the ANN model. Table 1. Reservoir properties and the corresponding ranges of polymer augmented water flooding model Category Reservoir Rock Properties Initial Conditions Fluid Properties

Polymer Properties

Relative Permeability Coefficients

Engineering Design Parameters

Parameter ϕ k h Swi pi µo Salinity µp

Unit fraction md ft fraction psi cp ppm cp

Min 0.1 200 10 0.1 500 5 5,000 10

Max 0.3 2,000 100 0.4 1500 20 50,000 50

Polymer adsorption

ug/g

10

120

5 0.5 -0.3 1 0.3 0.8 0.1 0.1 2 2 500 0.2 5 0.1

50 0.9 0 15 0.8 1 0.3 0.3 4 4 2,000 0.8 20 0.3

ppm

800

2,500

fraction

0.85

0.95

Kp np Salinity coefficient RRF krwro kroiw Siw Sorw nw now Injection rate Slug Size Pattern Size PBHP Polymer concentration (Cpolymer) WCswitch

(n-1)

cp·sec fraction fraction fraction fraction fraction fraction fraction bbl/day %PV Acres portion of pi

12 One forward-looking and one inverse design ANN models are trained in this work. The involved project response data are water (qw vs. t) and oil (qo vs. t) production rates and injection sandface pressure profile (pwf vs. t). Table 2 displays the input/output lineup of the two ANN models. Table 2. Input and output of ANN models Components/ Model IO Reservoir rock properties Initial conditions Fluid properties Polymer properties

Forward-looking Input Input Input Input

Inverse design Input Input Input Input

Relative permeability coefficients

Input

Input

Engineering design parameters qw vs. t qo vs. t Injection well pwf vs. t

Input Output Output Output

Output Output Input Output

The project response data presents a strong nonlinearity due to the complex nature of the injection scheme, which creates significant challenge for ANN training. Therefore, we decompose the production response data profile along the injection timeline utilizing critical time nodes. As shown in Figure 3, we use 4 temporal nodes to represent the critical events along the injection timeline: •

t1, the end of the plateau period of the waterflooding stage

•

t2, time to start the slug injection

•

t3, time when qo vs. t start to response to the slug injection

•

t4, time when qo reaches the peak rate after t3

•

tp, time to terminate the project, (which is set as 7,650 days).

A total of 40 discretized production data are extracted following the time line of t = [1, t1, t3, t4, tp] for qo and qw vs. t profile and 50 data points are extracted for pwf vs. t profile based on the timeline of t = [1, t1, t2, t3, t4, tp].

13 Amongst the data patterns, the production response data within the interval of the critical time nodes presents similar structure, which reduces the complexity of the data and help the ANN model to learn it more effectively.

t1

t2

t3 t4

Figure 3. Critical temporal nodes on production profiles

ANN Topologies

Results generated from 1,200 batch simulation runs are utilized in training the expert systems. An in-house multilayer neural network training module employing scaled conjugate gradient algorithm is utilized in developing the ANN models. During the training stage, 1,000 sets of data are used for training and 100 sets of data are utilized for validation and blind testing applications, respectively. In order to structure ANN models with promising generalization performance, an ANN architecture optimization workflow (Sun and Ertekin, 2015) is employed to design topologies that yield desirable testing error margins. When a certain ANN architecture is being evaluated, the model is retrained for multiple times by shuffling the training/validation/blind testing data then we use the overall blind testing performance to assess the robustness of the ANN architecture (Sun and Ertekin, 2015). As shown in Figure 4 and Figure 5, two one-layer feedforward ANN models are trained with 60 and 75 hidden neurons for the forward-looking and inverse design applications, accordingly.

14

Hidden layer (60 Neurons) Input layer (25 Neurons) (1). Spatial reservoir properties

Output layer (147 Neurons)

(a). Oil production history

(2). Initial conditions (3). Oil properties

(b). Water production history

(4). Polymer properties (5). Relative permeability coefficients

(c). Injection sandface pressure data

(6). Design parameters

Logistic sigmoid

Figure 4. Topology of the forward-looking ANN

Hidden layer (75 Neurons)

Input layer (63 Neurons) (1). Expected oil recovery (qo versus t)

Output layer (109 Neurons) (a). Engineering design parameters

(2). Spatial reservoir properties

(b). qw versus t

(5). Initial conditions (3). Oil properties

(c). Injection well pwf versus t

(4). Polymer properties

Logistic sigmoid

Figure 5. Topology of the inverse design ANN

Blind Testing Applications

Forward-looking ANN model for project response The forward-looking ANN model is tested using 200 blind testing applications and the observed error distributions are presented in Figure 6. Noticeably, 89% of the blind testing applications yield less than 10% of relative error. Amongst the 200 blind testing applications, the largest relative error is 13.37% and the mean is 5.83%. The statistical data for solution error indicates

15 that the forward-looking ANN models are quite successfully trained. Moreover, we present the matches between the project response functions predicted by the ANN models against the data generated from the high-fidelity model. In Figure 7, we present a best, an average quality and a worst case to demonstrate accuracy levels encountered during the blind testing applications. The blind testing applications show quite satisfactory matches, even for the worst cases, during the water flooding stage of the project in terms of qo, qw and pwf vs. t. We can state that the data structure during the waterflooding stage as simpler because many of the non-linearities such as polymer rheology properties, slug size and polymer concentration have no impact on the project response surface. The ANN models are found to be competent in predicting the slug response time along the project timeline, which presents itself as an oil production rate incremental on the qo vs. t profile and a water production reduction on the qw vs. t profile. The best and average quality cases show excellent matches when compared against the results generated by the high-fidelity model. Deviations are mostly observed, especially in the worst cases, as the errors in the peak oil/low water production rates (shifting the slug response time along the project timeline). Also, mismatches of pwf vs. t profile are also observed in the worst cases. This observation is linked to the polymer slug injection that introduces most of the nonlinearities of the problem. However, the probability of the presence of cases with high relative error is very low. At this stage, we can conclude that the forward-looking ANN model is successfully developed and can be employed to generate qo, qw and pwf vs. t data for polymer flooding processes.

16 Blind testing error distribution, forward-looking ANN model

0.25 0.2 0.15 0.1 0.05 0 0.02

0.04

0.06

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0.1

0.12

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Relative Error, fraction

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Best case (Error~2.78%)

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17 Inverse project design ANN Model The inverse design ANN model is trained to calculate the project design parameters to achieve a desired project performance. Meanwhile, during this application, water production and injection sandface pressure profiles are also predicted. Figure 8 illustrates the overall relative errors of the predicted design parameters presented in the

blind testing applications for the inverse design ANN model. The analysis of the statistical distribution of error explicitly shows relatively poor forecasting of design parameters such as production well sandface pressure, polymer concentration and slug size. Only the design parameters such as injection rate, pattern size and water saturation to start the slug injection display errors within promising margins. It is decided to further investigate the impact of the high error margins on the project response using a ‘back-check’ protocol. We employ the forward-looking ANN model to predict the project response using the predicted design parameters from the inverse ANN model. For the backchecking purposes, we compare the qo vs. t profile predicted by the forward-looking ANN against the expected oil production profile which is part of the input of the inverse design ANN. Also, we compare the qw and pwf vs. t data predicted by the forward-looking ANN model amongst the data generated from the high-fidelity and the data predicted by the inverse design model (recall that qw and pwf vs. t profiles are parts of the inverse design ANN output.). We have selected a best, an average and a worst case in terms of the design parameters prediction errors in the back-checking process. Table 3 shows the detailed data of these three representative cases (best case, average quality case and worst case), and the corresponding matching results are plotted in Figure 9. The following critical observations are made: •

Excellent matches of qo and qw vs. t profiles are presented in the best and average quality cases. Even for the worst cases, the qo and qw vs. t matches are still found to be reasonable.

18 •

Regardless of the inverse design ANN prediction error, the pwf vs. t profiles always exhibit relatively poor matches. Using the average quality case as an example, we see that the three pwf vs. t profiles are displayed in a parallel manner with different shifts in magnitude.

These observations indicate that the poor prediction capabilities of the inverse design ANN model are caused by the multiple solutions (non-unique) nature of the problem. In a polymer injection project, injection scheme with the same product of the slug size and polymer concentration would yield similar effect on the mobility control of the aquifer phase. In other words, there are infinite number of slug size and polymer concentration combinations that can obtain similar oil recoveries. This implies that prediction from the inverse ANN model simply suggests one of the solutions that is capable of achieving the expected oil recovery. Therefore; it is quite difficult for the inverse design ANN model to predict a pwf vs. t profile that matches the original data using only qo vs. t profile as input.

Inverse Design ANN Model Performance 30%

Relative Error, %

25%

20%

15%

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5%

0% Injection Rate 3.37%

Production PBHP 26.79%

Pattern Size 10.90%

Polymer Slug Size 24.86%

Polymer Concentration 17.49%

Switching Water-cut 1.19%

Figure 8. Blind testing error statistics of the inverse design ANN

19 Table 3. Back-check cases Unit Injection Rates PBHP Pattern Size Cploymer Slug size WCswitch mean

STB/day psi Acres %PV ppm fraction

Target 1433.679 132 13.590 1454.920 0.541 0.879

Best Cases Prediction 1442.927 165.8 13.475 1416.843 0.595 0.883

Best Case (Error~5.48%)

Average Quality Cases Target Prediction Error 1006.252 1048.105 10.99% 76.5 95 5.24% 8.776 9.610 0.35% 1519.358 1708.033 19.07% 0.400 0.296 21.10% 0.874 0.876 31.99% 14.79%

Target 602.459 104.8 8.471 1100.174 0.207 0.901

Average Case (Error~14.79%)

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Worst Cases Prediction 631.308 153.6 8.656 1488.780 0.336 0.890

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20 To further investigate the robustness of the inverse design ANN model, and confirm the existence of non-unique solutions to the problem, we present additional cases employing the oil production profiles of the forward-looking ANN blind testing applications. Figure 10. (a), (b) and (c) displays the oil production profiles of the best, average and worst testing cases of the forwardlooking ANN applications, respectively. Using these oil production profiles as input (expected oil recovery) to the inverse project design model, the predictions of the polymer flooding design parameters are shown in Table 4. One can observe that average prediction errors of the three cases are within reasonable error margins of 11.29%, 15.11% and 13.15%, respectively. However, there are design parameters that yield large disparities between the prediction from the inverse ANN and the original values. For instance, the polymer slug size and polymer concentration values of Case (b) exhibit relative errors of larger than 30%. Afterwards, the forward-looking model is employed to forecast project responses using the predicted design schemes. As illustrated in Figure 11, although large prediction errors occur in some design parameters, the oil and water productions show good agreements with the expected fluid recovery profiles. However, mismatches are observed between the injection well sandface pressure comparisons. This is due to different pressure constraints that need to be imposed to satisfy the expected oil recovery for those non-unique polymer flooding schemes. The observations obtained from the blind testing applications of the inverse design ANN model highlight that there exist more than one set of project design parameters that could achieve the same expected oil recovery. Nonetheless, the inverse design ANN is trained to adapt to the one-toone relationship between the inputs and outputs. Therefore, the prediction from the inverse ANN cannot cover all the possible solutions. In the discussion of the next section, we will propose a workflow to utilize the inverse design ANN and the forward-looking ANN to find a catalogue of possible solutions for the design problem.

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Table 4. Prediction performance of the design parameters Unit Injection Rates PBHP Pattern Size Cploymer Slug size WCswitch mean

STB/day psi Acres %PV ppm fraction

Case (a) Prediction 1126.53 190 11.70 1152.60 0.59 0.92

Target 1113.57 256.5 11.69 864.54 0.57 0.91

Error 1.16% 28.81% 0.08% 33.32% 3.72% 0.65% 11.29%

Case (a)

Target 1096.20 161.5 15.51 2363.35 0.76 0.93

Case (b) Prediction 1104.07 181.0 15.42 1431.68 0.48 0.93

Error 0.72% 13.31% 0.57% 39.42% 36.09% 0.53% 15.11%

Target 1905.11 123.5 5.26 1487.47 0.96 0.94

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Expected Oil Production Oil Production w Predicted Design Scheme

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Applications of ANN models In this section, we will present the applications of the forward and inverse-looking of the ANN models using three case studies in terms of parametric study, project NPV optimization and inverse project design implementations. Case 1: Parametric study of polymer flooding projects

The developed ANN model can be employed to carry parametric studies of polymer flooding projects. In this section, we display the sensitivity of various parameters to the oil and water recovery using the results generated by the forward-looking ANN model. The same sensitivity analysis is conducted by running the high-fidelity numerical simulator.

kh= 15 D-ft:

o

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* □

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Figure 12. Sensitivity to permeability-thickness product

□

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23 Figure 12 shows the sensitivity of the fluid recovery profiles to the permeability-thickness

product, which is a critical parameter in scaling transmissivity of the system (since the viscosity of the fluid is not changing). The oil production rates are the same during the water flooding stages for the reservoirs with various kh values. However, reservoir systems with lower kh exhibit earlier water breakthrough time, and lower production increments from the polymer slug injection. Notably, the ANN model is competent to identify cases with different kh values and the fluid

Relative Permeability

recovery prediction exhibit good agreement with the numerical simulation model.

Set 1:

o

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Figure 13. Relative permeability data Table 5. Corey’s coefficients

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Figure 14. Sensitivity to relative permeability curve

Another set of sensitivity analysis is carried to observe the impact of relative permeability curves to the fluid recovery. In this experiment, three sets of relative permeability data are prepared as shown in Figure 13, with the corresponding Corey’s coefficient listed in Table 5. The relative permeability data Sets 1 through 3 characterize increasing oleic phase mobilities and decreasing aqueous phase mobilities. Thus, the results of the sensitivity run (Figure 14) shows that reservoir with relative permeability Data Set 1 yields earliest water breakthrough time and polymer slug response time. Again, the fluid recovery profiles obtained using the ANN models and numerical simulator agree with each other within acceptable margins. Moreover, Figure 15 and Figure 16 illustrate the parametric study results of the injection rate and pattern size, respectively. In Figure 15, one can see that the higher the injection rate, the higher the production rate would be obtained during the waterflooding stage. However, the water breakthrough would occur earlier. As displayed in Figure 16., the cases with larger pattern sizes show delayed water breakthrough time, as well as the production increment response time due to the polymer slug injection. Also, satisfactory matches are observed comparing the oil and water productions generated using the ANN models and high-fidelity numerical model.

ANN

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Figure 15. Sensitivity to injection rate

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These parametric studies highlight the versatile generalization capability of the ANN model to adapt to variation of reservoir properties and project design parameters. More importantly, the use of ANN models would considerably reduce the typical computational overhead encountered of during the parametric studies. When experimenting on this facet of our study, we have observed that running one of the parametric cases with the high-fidelity model would take three to five minutes of CPU time depending on the project abandonment time while the ANN model could generate its predictions only within a fraction of a second.

26 Case 2: Project NPV Optimization

This case study employs the forward-looking ANN to act as a proxy of the high-fidelity model in an optimization process of a polymer flooding projects. Coupling with a robust global optimization protocol, particle swarm optimization (PSO), the polymer flooding project net present value (NPV) is maximized which is defined in Equation (11):

NPV = CAPEX +

N

Rt

∑ (1 + i) t =1

(11)

t

CAPEX is the capital expenditure of the project, which in our case is the drilling and completion cost of a project. Rt is the net cash flow of a time interval calculated using Equation (12): Rt = (Gross income) – (Operational cost)

(12)

In Equation (12) “i” is the discount rate. Table 6 shows the cost and price data used in the optimization problem. Table 6.Cost and price data used in calculating the NPV of the project CAPEX Daily cost

Injector Producer Polymer cost Water injection cost Discount rate Oil price

944,000.00 1,262,600.00 1.5 0.548

USD USD USD/lbm USD/bbl

10% 55

USD/bbl

In this case, the target is to optimize the design of polymer slug that maximizes the project NPV, which are the slug size and the polymer concentration of the injection fluid. As shown in Figure 17, we introduce a hypothetical field case with reservoir properties listed in Table 7.

27

Producer Injector

Figure 17. A hypothetical field undergoing polymer flooding

The overall project would terminate when the water cut increases back to 99% after the polymer slug injection. We employ PSO to optimize the NPV of the project in terms of variables of slug size and polymer concentration. The forward-looking ANN model for polymer injection processes is employed as a proxy model of the high-fidelity simulation model in calculating the oil recovery (which serves as a critical input of the NPV calculation). For comparison and validation purposes, we optimize the same problem using genetic algorithm (GA) and random search protocol. The searching domains for the optimizing parameters are within the polymer concentrations of 1,000 to 2,500 ppm and slug sizes of 0.3 to 1 of PV. Each optimization iteration calls the forwardlooking ANN model to compute the oil recovery and the NPVs for 100 particles (individuals) for PSO and GA algorithms. The blind searching protocol employs forward-looking ANN model for 10,000 times using randomly distributed polymer concentrations and slug size data within the margins of the search domain.

28 Table 7. Input and optimizing parameters of the case study Category Reservoir Rock Properties

Initial Conditions

Polymer Properties

Relative Permeability Coefficients

Engineering Design Parameters

Parameter ϕ k h Swi pi µo Salinity µp Polymer adsorption Kp np Salinity coefficient RRF Krwro Kroiw Siw Sorw nw now Injection rate Slug Size Pattern Size PBHP Cpolymer WCswitch

Unit fraction md ft fraction psi cp ppm cp

Value 0.25 1000 50 0.2 800 10 20,000 30

ug/g

80

cp·sec -

(n-1)

35 0.7

-

-0.1

fraction fraction fraction fraction fraction fraction fraction bbl/day %PV Acres psi ppm fraction

8.0 0.5 0.95 0.15 0.15 2.5 2.5 1000 TBD 10 160 TBD 0.9

Table 8 summarizes the optimization results using various algorithms. Noticeably, the NPV

calculated using the design parameters optimized by PSO is larger than that of the GA and random search protocols, which indicates that the solution determined by PSO is closer to the global minimum of the objective function surface. Table 8. Optimization results using different algorithms. Algorithm PSO GA Random search

Polymer concentration, ppm 2254.8329 2275.2737 2248.8384

Slug size, PV 0.87499 0.87602 0.86758

NPV, MM$ 20.08811 20.08719 20.08661

We compare the iteration logs of the evolutional processes using PSO and GA algorithms. It can be observed from Figure 18 that the optimum solution found by PSO getting stabilized as the plateau at the 15th iteration, while GA took 34 iterations to find the solution at a same level of

29 fitness. The CPU time takes to finish the optimization process for GA is 105.6 second, which is two times longer than that of PSO algorithm (49.6 seconds). Optimization evolution process 20.2 20

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Moreover, we plot the heat map of the NPV values generated using the 10,000 calculation results of the blind searching protocol as shown in Figure 19. The heat map illustrates location of the optimum solution in the dimensions of polymer concentration and slug size.

Figure 19. Surface map of the NPV value as a function of slug size and polymer concentration

Finally, we investigate the project response function implemented generated by the polymer concentration and slug size as determined by the PSO algorithm. Figure 20 (a), (b) and (c) show the qo vs. t, qw vs. t and pwf vs. t profiles. The injection project terminates at 2250 days with a water-cut of 99%. The pwf vs. t profile shown in Figure 20 (c) is a critical consideration to apply the design parameter because the injection must ensure that the sandface pressure (maximum

30 2829.92 psi) reached at the injector would not damage the formation and the surface pump is capable to operate at such injection pressures to sustain the specified injection rate. Water production rate profile

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Case 3: Inverse Design Implementation

In this case study, a robust workflow is executed to construct a repository containing multiple design schemes to achieve a desirable oil recovery, which adapts to the non-unique nature of the solution for the inverse design problem. The proposed workflow that collectively utilizes the inverse design ANN, the forward-looking ANN and the original project response data is summarized in the Steps 1 to 5 below: 1. For a certain reservoir system, employ the inverse design ANN model to predict a design parameter scheme.

31 2. Use the predicted design scheme as a base case, generate n random design schemes by varying all the design parameters but the injection rate and the water saturation to start slug injection. The random design parameters follow uniform distributions. Noticeably, we use the blind testing error margins of the inverse design ANN models to set the upper and lower limits in generating the pseudo random numbers. 3. Employ the forward-looking ANN model to predict the project response data for all the design schemes generated in Step 2 and compare the qo vs. t data against the expected oil production as the input of the inverse ANN. 4. If the predicted qo vs. t profile presents satisfactory matches with the expected oil production, save the design scheme to the solution repository. The corresponding qw and pwf vs. t profiles are the simultaneous output of the design scheme. 5. Repeat Step 1 to Step 4 until all the n schemes are examined. It is worth to mention that we have examined 10,000 random design schemes to construct a solution library for each design scheme (n = 10,000 in Step 2). It should be stressed that a design scheme will become a candidate to be selected to the solution library when the average disparity of the oil production is less than a prescribed error margin with the expected oil recovery. We use 5% as a cutoff to control both the size of the repository and the match quality against the expected oil recovery. The proposed workflow is visualized in Figure 21. Furthermore, we test the workflow to find the design schemes that can better match the expected oil recoveries for the worst case presented in the blind testing application of the inverse design ANN, with the input parameters listed in Table 7. The proposed work flow establishes solution libraries containing 155 design schemes that can match the expected oil recovery profile as shown in Figure 22. Table 8 gives the upper and lower limits of the search ranges for design parameters such as producer bottomhole pressure, pattern size, polymer concentration, and slug size.

32 Table 11 lists the three representative design schemes included in the repository, and Figure 23

illustrates the project response matches using the improved design schemes. Noticeably, the predicted qo vs. t profiles show much better agreement with the expected oil recovery by using the design schemes found by the proposed workflow, so do the qw vs. t profiles. Also, it is not surprising to observe that each design scheme yields a different slug size, polymer concentration, production well bottomhole pressure and injection well pwf vs. t profile. At this stage, we have successfully solved the inverse design problem of the polymer injection projects exhibiting strong non-uniqueness utilizing the workflow proposed earlier. The proposed workflow takes the advantages of the forward-looking ANN models to carry 10,000 simulations within short period of time to construct a comprehensive design scheme library. Accordingly, we can state that the solution repository established by the proposed workflow provides the field engineers opportunities to select the most practical polymer injection scheme considering other operational constraints such as availability of the polymer, surface water treatment limitation, injection pump capacity, etc. Start of the workflow

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33 Figure 21. Schematic workflow of the inverse design process

Category Reservoir Rock Properties Initial Conditions Fluid Properties

Polymer Properties

Relative Permeability Coefficients

Parameter ϕ k h Swi pi µo Salinity µp Polymer adsorption Kp np Salinity coefficient RRF krwro kroiw Siw Sorw nw now

Unit fraction md ft fraction psi cp ppm cp

0.148 867.432 95.024 0.296 605.604 6.997 40925.879 49.038

ug/g

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13.6 0.785 0.818 0.281 0.281 2.208 2.092

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Table 9. Input parameters used in the design case study

Figure 22. Expected oil recovery profile

Table 10. Search ranges used in the design process

Upper limit Lower limit

Production PBHP, fraction of pi 0.244 0.141

Pattern Size, Acres 9.600 7.713

Polymer Concentration, ppm 1749.167 1228.392

Slug Size, %PV

Table 11. Representative design schemes Design parameter Injection Rate Production PBHP Pattern Size Slug size Cpolymer WCswitch

Unit STB/day psi Acres %PV ppm fraction

Case 1 631.308 86.60 9.056 0.294 1381.75 0.890

Case 2 631.308 110.22 8.548 0.260 1402.48 0.890

Case 3 631.308 141.71 7.852 0.371 1697.95 0.890

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Concluding Remarks In this paper, we describe the development of a forward-looking and an inverse design expert ANN system to be used as screening and optimized design tools for polymer injection projects. The expert systems are trained as universal models so that they can be implemented in projects with varying design parameters and reservoir properties. This paper presents case studies that highlight the elevated prediction accuracies and fast computational speeds of the expert systems in conducting parametric studies, optimizing the project NPV and in determining the required

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35 engineering design parameters for a desired oil recovery profile. The following conclusive statement can be drawn from this study: •

The forward-looking ANN models are trained to interpret the project response data based on temporal nodes indicating critical physical events along the project timeline, such as water breakthrough, slug response, and occurrence of peak oil rate. The expert systems are trained to identify these critical data features. Consequentially, the ANN models can adapt to the data structure more effectively because the production and pressure responses between two of the temporal points present similar trends. This observation highlights the importance of using physical features to develop ML models. More importantly, such approach can be applied to develop other ML models with improved generalization capabilities.

•

The forward-looking expert system is competent to predict time-series data including oil and water production and injector sandface pressure, which all provide project related feasibility guidelines for engineers involved in designing polymer injection projects in consideration of various techno-eco and techno-economical constrains. In this article, we present a successful protocol that couples the forward-looking proxy with PSO algorithm to optimize the project NPV. Notably, with the help of the proposed expert system, the engineers can consider different optimization scenarios by varying the project economic parameters such as capital cost, oil price, injectant cost, etc. in a time-effective manner.

•

The inverse design problem of the polymer injection process may inherently exhibit nonunique solutions since there are more than one injection schemes that could achieve a similar mobility control effect. The inverse design ANN model is developed to find one of those solutions because the model is trained to learn one-to-one relationship between the input and output parameters. One of the major contributions of this paper is to propose a robust workflow that can find various project development strategies to achieve the

36 expected oil recovery profile employing the forward and inverse-looking ANN models. Field engineers can make decisions to select and adapt the most practical injection scheme from the repository by giving due consideration to other operational constraints. •

In the future work, we would suggest enhancing the generalization capability of the ANN models by considering the reservoir structure, capillary pressure data and heterogeneities and anisotropies of permeability. Moreover, similar proxy models can be developed employing different types of injection patterns including 7-spot, 9-spot and line-drive, which will enable the optimization process to consider various potential field development strategies.

Nomenclature A API B Cpolymer fa k kroiw krwro K n ng nog now nw pi Siw Sorw RKW RRF sp tp xp xsalt xmin vlow v

= Langmuir isotherm coefficient A, lbmole/ft3 = API gravity of crude oil, degrees of API = Langmuir isotherm coefficient B, dimensionless = Polymer concentration, ppm = nonlinear mixing rule coefficients = absolute permeability, md; = oleic phase relative permeability at irreducible water saturation, dimensionless = aqueous phase relative permeability at residual oil saturation, dimensionless = flow consistency index, cp-secn-1 = Non-Newtonian fluid exponent, dimensionless = gaseous phase relative permeability exponent = oleic phase relative permeability exponent in gas-liquid table = oleic phase relative permeability exponent in water-oil table = aqueous phase relative permeability exponent = initial pressure of the system, psi = irreducible water saturation, fraction = residual oil saturation in oil-water relative permeability table, fraction = relative permeability modification parameter = residual resistant factor, dimensionless = salinity-viscosity exponent = production life of a project = polymer weight concentration, ppm = salinity of the solution, ppm = the minimum salinity which causes observable viscosity change on the polymer solutions, ppm = fluid velocity at saturated polymer solution, ft/s = the velocity of the fluid, ft/s

Greek ϕ = porosity of the porous media, fraction

37 µ µp µw

= viscosity, cp; = polymer solution viscosity, cp = viscosity of water, cp

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Screening and Optimization of Polymer Flooding Projects Using Artificial-neuralnetwork (ANN) Based Proxies Qian Sun, Petroleum Recovery Research Center, and Turgay Ertekin, the Pennsylvania State University Highlight • • • •

Forward-looking proxy accurately predicts fluid productions and pressure responses Design proxy predicts the design schemes to achieve a desired project outcome PSO can collaborate with proxy models to optimize project NPV Proxy models are employed to effectively solve the inverse design problems