Intelligent design and selection of natural gas two-phase separators

Journal of Natural Gas Science and Engineering 1 (2009) 84–94

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Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse

Intelligent design and selection of natural gas two-phase separators Luis F. Ayala H.*, Doruk Alp, Mohamad Al-Timimy Department of Energy and Mineral Engineering, The Pennsylvania State University, 121 Hosler Building, University Park, PA, United States of America

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 March 2009 Received in revised form 3 June 2009 Accepted 30 June 2009 Available online 28 July 2009

Proper design of separators for surface production facilities is essential in order to maintain the quality and quantity of produced hydrocarbon fluids and avoid major operational problems in downstream equipment. Separators that are not properly sized or built will invariably be involved in operational mishaps encountered in natural gas surface operations and processing. This study addresses the basis of two-phase separator design and selection and explores the applicability of Artificial Intelligence techniques, such as Artificial Neural Networks (ANNs), for the creation of intelligent systems capable of predicting proper two-phase separator dimensions which can guide their selection. The expert system is able to unveil the most accurate mapping among input parameters and output sizing parameters and greatly facilitates identifying which parameters have the most influence and/or govern separator design and selection, while quantifying their relative influence. The proposed system is robust, fast, dependable, and unambiguously quantifies the relevance and impact that each fluid property and process conditions has on the correct selection of separation devices needed for natural gas processing applications. Ó 2009 Elsevier B.V. All rights reserved.

Keywords: Neural network Natural gas Two-phase separator

1. Introduction Based on fluid composition and reservoir conditions, hydrocarbon (HC) fluids may be in gas or liquid phase or both phases may coexist in the pore space as prescribed by the prevailing thermodynamic equilibrium conditions. In natural gas reservoirs, for example, initial reservoir conditions are found in the single-phase region, as indicated by Fig. 1. Whenever reservoir fluids are brought to surface, to conditions of relatively lower pressures and temperatures compared to that of reservoir, phase equilibrium shifts to a new point in the mixture phase envelope (Fig. 1). Heavier components in the gas phase condense, and in the case of oil flows, lighter components would abandon the oil phase. Rich natural gases can yield considerable amounts of condensate at surface separation conditions, with typical yield values of 50–250 bbl/ MMscf for wet gases and 200–400 bbl/MMscf for retrograde natural gases, depending on condensate content and surface separation conditions. Surface facilities utilize liquid–vapor separators to collect the readily condensable hydrocarbon phase as the first step prior to further processing. Liquid–vapor separators are one of the most common types of process equipment in the natural gas processing industry (Chin, 2007; Guo et al., 2007; Kidnay and Parrish, 2006; Guo and

* Corresponding author. Tel.: þ1 814 8654053; fax: þ1 814 8653248. E-mail address: [email protected] (L.F. Ayala H.). 1875-5100/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jngse.2009.06.001

Ghalambor, 2005; GPSA, 2004; Abdel-Aal et al., 2003; Arnold and Steward, 1999; Campbell, 1994; Manning and Thompson, 1991; Kumar, 1987). Separation of the condensate and gas phase enables the independent handling, metering, processing, and marketing of each phase. Separation vessels provide the incoming natural gas mixture with necessary conditions of time and space needed to achieve adequate mechanical separation of phases at the prescribed thermodynamic operating conditions. Poor separation can result in high costs, poor quality products, and even damage to downstream equipment. A successful separation process ensues in higher quality and quantity of both phases. Therefore, proper design of separators is essential for getting the maximum yield (thus profit) and meeting contractual specifications for the delivered fluids. No design project begins with detailed engineering computations right off the start. Design of surface production facilities is not the exception, and it typically entails an iterative procedure completed in stages which increase in detail and precisiondas in the case of most process plant designs. Establishment of a design basis is followed by a preliminary (quick estimate) design stage which is usually based on approximate methods to explore several design options quickly (Peters and Timmerhaus, 1991). At this basic engineering stage, generation of as many viable solutions as possible is advantageous to the design process while alternatives are screened according to rough cost estimates. Typically, computers are utilized in the solution of equations governing the design. However, time available for completion of the preliminary design stage limits the number of alternative designs that could be sought with

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Nomenclature

v vT

Drag coefficient [–] Vessel diameter [ft] Target droplet diameter [ft] Fraction of cross sectional area [–] Fraction of vessel height [–] Gravitational acceleration [ft/s2] Gas oil ratio (scf/bbl) Vessel height [ft] Height of liquid column [ft] Vessel length [ft] Flow rate at operating conditions [ft3/s] Slenderness ratio [–] Retention time [s]

CD d dp fA fH g GOR h hlc L q rS tR

Phase velocity [ft/s] Droplet terminal velocity [ft/s]

Greek Density at operating conditions [lbm/ft3] Viscosity at operating conditions [lbm/ft/s]

r m

Subscripts d Droplet g Gas phase H Horizontal separator l Liquid (oil) phase t Total V Vertical separator

economical evaluation as well (Towler and Sinnott, 2008). In this work, the applicability of advanced intelligence technology is explored as a robust alternative to successfully undertake preliminary design calculations where the evaluation of multiple design solutions is essential. Speed and accuracy that has been achieved with ANNs in other engineering applications assert ANNs as a candidate to replace conventional analysis methods at this preliminary design stage. In particular, this study explores the applicability of Artificial Neural Networks (ANNs) for the prediction of proper separator dimensions. Our ultimate goal is to develop an ANN capable of providing the user with appropriate separator dimensions once the parameters that govern the design, such as operating pressure, fluid flow rates and densities, are provided as an input. In the last decades, ANN models have been successfully utilized in several oil and gas industry applications, where there has been a continued interest in their application for the study of long-standing problems (Mohaghegh, 2000). Several expert systems have been presented in the literature myriad applications in petroleum and natural gas engineering; a very recent presentation of which has been compiled by Gharbi and Mansoori (2005). Some other applications include, for example, the work of Ayala et al. (2007) and Ayala and Ertekin (2007), where ANN technology was employed for the analysis of cycling operations in retrograde gas condensate reservoirs. Al-Farhan and Ayala (2006) also used artificial intelligence technology for the prediction of the optimal middle stage surface separation pressure as a function of hydrocarbon composition and associated surface design parameters. Mann and Ayala (2009)

Critical Point Reservoir Conditions

Liquid

85

recently developed, tested, and validated a reliable ANN tool capable of predicting the optimal design of facilities dedicated to natural gas storage operations. In general, ANNs can prove to exhibit superior performance to conventional approaches for oil and gas applications (Mohaghegh, 2000). 2. Artificial Neural Networks An Artificial Neural Network (ANN) could be defined as a tool which takes in a set of input data (stimuli) and transmits it over a web of neurons that manufacture the response or set of outputs associated with the current stimuli. In such visualization, ANNs resemble the actual neuron connections of living organisms which transmit signals within the body of organisms to induce its function. Likewise, these tools can be used to learn patterns and make predictions when particular inputs lead to specific targets. During this learning process, network structure is properly adjusted, as illustrated in Fig. 2. ANN tools have been successfully utilized to recognize patterns, capture otherwise unrecognized input–output relations, and match and filter data where other traditional methods have not been successful. As in the case of a brain, before ANNs can make accurate predictions it has to ‘‘understand’’ the relation between the input and the desired output. ANNs learn these relations through the training process where network is continuously fed with the same sets of input and target data (covering the extremes of data for desired ANN function) which allows the network to adjust weights and biases to match ANN output to the target values. Any input that is fed to the network and the targets used in the training process should be pre-processed, which involves data normalization. The normalization procedure evenly distributes and scales the data to ensure that data of all the parameters fall within a certain range, such as [1, 1]. This prevents the parameters with large scales from dominating the network structure and influencing the output. The

Pressure

Target

Surface Conditions Gas

5%

10

Input

Output ANN

2-Phase

70

80

90

Temperature Fig. 1. Phase envelope of a natural gas fluid.

compare

No Match

100 Adjust ANN Fig. 2. How ANNs learn.

Match

ANN Ready

86

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qg Incoming Data [P]

x Weight [w]

f(wP+b)

Output [a]

+ Bias [b]

hME Fig. 3. How Neurons work.

measure for good training is the magnitude of associated training errors. Training error is defined as the difference between target and output values. There are several training algorithms available which aim to provide better training for the ANN in shorter periods of time. The fundamental element of ANNs is the neuron. Neurons could be viewed as black boxes where incoming scalar data is initially amplified or attenuated based on the weight associated with the data type (or data origin). Altered incoming data could be further modified prior to main process in the box by adding a scalar value called bias. This final form of the data is then transformed according to a certain mathematical function, called transfer function, assigned to the box. Transfer functions map neurons to each other through adjacent layers. Common transfer functions are the log-sigmoid, hyperbolic tangent sigmoid, and the linear functions. This process is illustrated in Fig. 3. Neurons can be arranged to work both in parallel and in series to each other, hence they construct the Artificial Neural Network. A group of neurons working in a parallel arrangement is called a layer. Layers can be arranged in series in an ANN. The number of neurons in an output layer, which is the last layer of a network, is typically equal to the number of different types of output desired because each neuron produces only a single output. Again typically, but not necessarily, the number of neurons in an input layer, which is the first layer of a network, is equal to the number of input parameters. Generally, there are additional layers between input and output layers in an ANN, each called a hidden layer. Usually, same transfer function is assigned for all the neurons in a layer. Nevertheless, it is fairly common to have neurons with different transfer functions in the same layer. While number of input parameters and the number of neurons in the output layer are typically governed by the problem to be solved, the number and size of all the other layers, including the input layer, are determined by the user. Fig. 4 depicts a typical ANN architecture with 2 hidden layers, 3 input neurons, and 2 output neurons. 3. Separator modeling and design The essence of separator design relies on the manipulation of flow velocity or fluid inertia in order to allow gravity to mechanically separate the liquid and gas phases. In addition, the separator must allow for sufficient residence time for separation to take place and enough space for liquid collection. The final aim of the design is to assure this adequate split of oil and gas while using minimum amount of material for the construction of the vessel. In this section, a brief overview of separation design theory is presented and discussed while additional details can be found elsewhere (Chin, 2007;

dV hVD

qt

hli

hlc

oil ql

Fig. 5. Vertical two-phase separator schematics.

Guo and Ghalambor, 2005; GPSA, 2004; Abdel-Aal et al., 2003; Arnold and Steward, 1999; Campbell, 1994; Manning and Thompson, 1991; Kumar, 1987). For adequate separation, separation vessel dimensions are required to satisfy two restrictions: 1) Gas Capacity Constraint: Gas flow in the separator should be slow enough to let oil droplets return to the oil phase under gravity, without being dragged away with the gas phase. 2) Liquid Capacity Constraint: Vessel should provide enough liquid residence time in order to guarantee adequate mass transfer between the phases (and thus the most efficient separation) and enough room for liquid level control capabilities. The most common geometrical configurations available for separator construction are (1) vertical, as depicted in Fig. 5; and (2) horizontal, as depicted in Fig. 6. Although the basis of design and design constraints are the same for both types of separators, calculation procedures differ due to orientation of flow in the vessels. The selection of the horizontal or vertical configuration is usually

qt

qg

hg Input Layer (3 Neurons)

Hidden Layer (6 Neurons)

Hidden Layer (4 Neurons)

dH Output Layer (2 Neurons)

Input type 1

hl

oil

Output type 1

Input type 2

Output type 2

Input type 3

L Fig. 4. Structure of a typical ANN of 4 layers.

Fig. 6. Horizontal two-phase separator schematics.

ql

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Hidden Layer (30 Neurons) γo

Table 2 Input parameters and range.

Hidden Layer (30 Neurons)

− γg GOR

dV

qg

hV

γo

Unit

Min.

Max.

GOR (gas oil ratio) Gas flow rate Gas gravity Oil gravity Pressure

scf/bbl MscfD – – psi

1500 5000 0.56 1.00 200

8000 30,000 1.20 0.702 800

LG

P

Table 3 Targets and range (training sets).

Fig. 7. Proposed ANN architecture.

a matter of economics. When the two designs fully satisfy the constraints listed above, the surface area or volume of the vessels can be compared to determine which one would require less material. Minimization of surface area or separator volume implies that less steel would be needed for construction. The basic theory behind separation design relies on a force balance around a liquid droplet that is suspended in a vapor stream and which tends to fall due to the force of gravity but needs to overcome the dragging force that tends to carry the liquid droplet out of the vessel with the gas phase. This force balance leads to the following definition for the droplet terminal velocity (see, for example, Chin, 2007 and Abdel-Aal et al., 2003):

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 g$dp rl  rg vT ¼ rl 3 CD

(1)

In vertical design, gas velocities can be directly constrained using the vt-terminal velocity as the reference for maximum allowable gas speed. Since gas occupies the entire cross sectional area of the gravity settling section, the diameter of the vessel can be readily related to maximum allowable gas velocity using the equation:

sffiffiffiffiffiffiffiffiffiffi 4$qg p$vg

(2)

Equation (2) is the design equation that satisfies the gas capacity constraint for vertical vessels. Once separator diameter is determined, total vessel height (ht) is calculated adding up individual heights of liquid column, inlet-to-liquid, vapor disengagement and mist extractor sections. The height of the liquid column is computed based on the liquid capacity constraint of the vessel, given by:

hlc ¼

Input parameter

dH

γg

dV ¼

87

ql $tR p$d2V

¼

4

4$ql $tR p$d2V

(3)

The vertical design is concluded by ensuring that projected dimensions yield a reasonable structure and shape (neither too tall

Target (training)

Unit

Min.

Max.

Vertical separator diameter Vertical separator height Horizontal separator diameter Horizontal separator length

ft ft ft ft

1.78 6.89 1.19 4.20

8.46 28.85 7.00 21.20

and thin nor too wide and short) by ensuring that the slenderness ratio for the vessel is found between the typical range of 3–4. Slenderness ratio, rS, is defined as:

rS ¼

hV dV

(4)

For horizontal design, gas velocities can be larger than droplet terminal velocity (Svrcek and Monnery, 1993) and vt-values cannot be used to directly constrain gas flow. In these cases, the design has to guarantee sufficient gas residence time for the liquid droplets to be able to travel the distance hg between the top of the vessel and the liquid interface (see Fig. 6). Incorporating the appropriate geometrical considerations, the gas capacity constraint for horizontal vessels thus becomes:

dH jgas ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 fHg qg p fAg rS $vT

(5)

where fHg and fAg are the fractions of height and cross sectional area occupied by the gas phase, respectively, which can be readily related to liquid phase wetted angle through geometrical considerations. Depending on the prescribed liquid level control, values can vary from completely dry (fHg ¼ fAg ¼ 1), 50% full (fHg ¼ fAg ¼ 0.50), to completely full of liquid (fHg ¼ fAg ¼ 0) but anywhere in between values of fHg and fAg are different at any given liquid level. In general, horizontal vessels are typically designed to operate 50% full of liquid in order to maximize available area for liquid/gas mass exchange. In the case of horizontal separators both gas and liquid capacity constraints limit the vessel diameter because both liquid and gas share the cross sectional area. These geometrical constraints yield the following liquid capacity constraint equation for horizontal vessels:

dH jliq ¼



4 tR $ql p fAl $rS

1 3

(6)

Table 1 Input neurons for the proposed ANN. Input parameter

Unit

Gravity difference, go  gg Gas oil ratio, GOR Gas flow rate, qg Oil gravity, go Gas gravity, gg Pressure

– scf/bbl MscfD – – psi

Table 4 Targets and range (testing sets). Target (testing)

Unit

Min.

Max.

Vertical separator diameter Vertical separator height Horizontal separator diameter Horizontal separator length

ft ft ft ft

2.34 7.39 1.64 5.70

7.00 19.40 5.70 17.12

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Fig. 8. dV prediction performance – training.

Fig. 9. dV prediction performance – testing.

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89

4. ANN model for separator design

Fig. 10. dV prediction performance cross-plot.

where fAl is the fraction of cross sectional area occupied by the liquid phase (fAl þ fAg ¼ 1). Since these equations provide the minimum diameter size required by the associated constraint, the larger diameter prevails:

i h dH ¼ max dH jgas ; dH jliq

(7)

Design is concluded with an iterative procedure in which vessel dimensions are determined for slenderness ratio values in the range [3–4] and the diameter-length couple that gives the smallest surface area (hence the material) is chosen. For horizontal separators, the slenderness ratio is defined as:

rS ¼

LH dH

(8)

The results of the Artificial Neural Network study for the case of separator design demonstrated that a feed-forward ANN architecture was adequate for the purpose of this study. The proposed network is presented in Fig. 7 and it is composed of a two hidden layers of thirty neurons each. The hyperbolic tangent sigmoid (tansig), log-sigmoid (logsig), and linear (purelin) functions were used as the transfer functions among the layers in Fig. 7, respectively. Information on the architecture of proposed ANN is presented in Table 1. In general, more neurons and layers usually result in better matching output but at the risk of overtraining or ‘‘memorization’’. In such cases, testing is not successful and the key point is achieving reasonable prediction performance while employing the simplest possible architecture. Fig. 7 presents the best combination of input parameters, hidden layers, and the number of neurons that this study was able to establish for the simultaneous prediction of both associated vertical vessel dimensions (dV and hV) and horizontal vessel dimensions (dH and LH). In the case of separator design, vessel dimensions (dV, hV, dH, LH) are functions of phase densities, oil and gas flow rates, operating pressure and temperature, fluid properties, geometrical considerations, and droplet size targets. It became clear during our studies that the best way of presenting this information to the network, in terms of best learning and predictive performance, was through the definition of the input neurons listed in Table 1. Among these, for example, the addition of the input neuron gravity difference, in addition to the specific gravity of each phase, significantly improved network performance. This was to be expected since vessel dimensions for a given set of conditions tend to decrease as the density contrast of the fluids increases, since gravity separation becomes more efficient. While density difference prevailed as one of the most important parameters, the ANN also recognized that actual values of liquid and gas densities have their own impact on the design in terms of the quantification of actual gas volume inside the vessel and liquid retention times, respectively. Input parameters and associated ranges used for the proposed neural network are given in Table 2. While separator operating pressure is considered as a design

Fig. 11. hV prediction performance – training.

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Fig. 12. hV prediction performance – testing.

variable, operating temperature is assumed to be constant at standard conditions (60F). Other typical design parameters are droplet diameter (assumed equal to 100 mm, based on customary practice described by Arnold and Sikes, 1986) and operating liquid fraction for horizontal separators (assumed equal to 50 % full of liquid in this work). Gas compressibility factors and gas viscosities are estimated using the Dranchuk and Abou-Kassem (1975) and Lee et al. (1966) models, respectively. Drag coefficient calculations follow the models presented by Arnold and Stewart (1998). At this point, the previously discussed separator design theory is implemented to generate a knowledgebase for a range of operating conditions in order to train and test the ANN. It is important to point out that once the ANN is trained and tested successfully using this knowledgebase, there is no further need to check its predictions with actual solutions as long as solution being sought is for the operating conditions within the range. Yet, at design engineer’s discretion, the range of the knowledgebase can be extended at anytime and consequently the ANN is further trained and tested to properly account for the new data range. Each generated input vector is a unique combination of the input parameters and thus a comprehensive database can be established. A total of 3125 training and 1024 testing data sets were generated with the ranges indicated in Table 2. Training and testing data sets were automatically generated using an in-house separator design expert based on the equations discussed in the preceding section. The testing data sets created in the study were chosen at random and were never shown to the network until the testing phase was conducted. This a customary step needed for the validation of ANN architectures in order to procure evidence that the network did not just ‘‘memorize’’ information but rather generalized it for all other possible input combinations. The MATLAB ANN toolbox was utilized to train the proposed ANN architecture (MathWorks, 2005) using the scaled conjugate gradient training algorithm (trainscg) as the backpropagation technique. Backpropagation is used for network training and it adjusts weights and biases of the network based on error performance. Input and target data for both training and testing are normalized (linearly scaled in the range [1, 1]) before they are supplied to the ANN.

Vessel dimensions for both vertical and horizontal separator designs are utilized as network targets in accordance with our objective. Ranges of calculated output targets are given in Tables 3 and 4 for training and testing data sets, respectively. Comparing the ranges for training and testing data sets reveals that limits of the training database demonstrates a good coverage of potential vessel dimensions, which has a positive influence on the network performance and reliability. 5. Results and discussion Training performance of the developed network for the case of the accurate prediction of vertical separator diameters (dV) is presented in Fig. 8. As can be observed from the error plot and error histogram, errors associated with the training process are less than 2% which is typically a good preliminary indicator of acceptable performance and learning of the ANN. Actual testing

Fig. 13. hV prediction performance cross-plot.

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91

Fig. 14. dH prediction performance – training.

performance of the network is shown in Fig. 9, where it is seen that model predicts test data quite well and associated errors are within the range 2.5% for data that it has never seen. Fig. 10 displays the cross-plot of targets (actual diameters) versus outputs (ANN predictions), for both training and testing data sets. A perfect match requires all of the points to be found on top of the cross-plot diagonal. Dashed red lines on both sides of the diagonal indicate the 10% error lines, which are the limits for acceptable ANN performance. We see that data points are fairly well

distributed along the diagonal or unit-slope line with minimal scatter. Both training and testing results are quite satisfactory; and thus, the proposed network is said to fully understand the prediction of diameter calculations for vertical vessels based on the input data. The histogram-based analysis of testing errors in Fig. 8 provides further evidence of the successful performance of the proposed network. The highest testing error frequency is found around 0%, with extremely low probabilities of finding testing errors above þ5%.

Fig. 15. dH prediction performance – testing.

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Fig. 16. dH prediction performance cross-plot.

Further evaluation of the ANN capabilities for natural gas separator design can be obtain by inspection of Figs. 11–19. For the case of vertical separator height (hV) predictions, Fig. 11 reveals ANN performance during training. Again, we see that errors are bounded within the range 2%. Similarly, and more importantly, the analysis of testing performance in Fig. 12 confirms the same error bounds for the data sets to which the network had not been previously exposed. Error histograms demonstrate a very dense concentration of points around very small error values during training and testing. Crossplot of actual versus predicted data in Fig. 13 is a bit more scattered at the outer end of the unit-slope line when compared to Fig. 10. Nevertheless, all the data points are near the diagonal and suggest a very good match and prediction performance. Horizontal separator diameter (dH) predictions during the ANN training session are shown in Fig. 14. Percent errors are significantly higher (as high as 10% at some instances) compared to the vertical

case. Nevertheless, error histogram shows that majority of the errors are within the 5% range. Test results given in Fig. 15 show that associated error is again within the range 2% and cross-plot of the testing data is very well aligned to the unit-slope line (see Fig. 16). By the same token, Fig. 17 shows the training results for horizontal separator length (LH). Errors grew beyond 2% but they are consistently maintained around 5%. Testing errors confirm this pattern in Fig. 18. Cross-plot given in Fig. 19 indicates that all the predictions are easily found well within the 10% error limit while the great majority of the data points are in a good alignment with the unit-slope line. Horizontal dimension predictions clearly posed more challenges for the ANN study than the vertical counterpart, but the proposed final architecture was able to successfully learn the intricacies of the design. At this point, it is clear that the developed ANN is able to predict appropriate separator designs for vertical and horizontal configurations. Since the required dimensions of the vertical and horizontal vessels are simultaneously calculated, a simple volume computation immediately guides the selection of one configuration over the other. The design configuration that can perform the fluid separation with the least volumetric requirement would always be preferred since it requires the least material for construction. Fast, reliable, and inexpensive results can be obtained using the proposed approach while still capturing most important design constraints and without recurring to detailed calculations. Once an ANN is in place and has been properly trained, it is particularly useful to determine the influence of each input parameter on the network performance. Relevancy is an important concept in the analysis of ANN performance since it can be used for the identification of the most influential input parameters of any problem of interest. This allows sorting out input parameters based on their level of influence on network response. In this study, the method proposed by Belue and Bauer (1995) is used in order to determine relevancies of each of the input parameters. For the problem under consideration, the relevancy plot is presented in Fig. 20, which was generated for all input parameters. It is evident from this figure that the gravity difference is the major driver of natural gas separator design, with the greatest impact (w23%) on the

Fig. 17. LH prediction performance – training.

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93

Fig. 18. LH prediction performance – testing.

Fig. 20. Relevancies of input parameters. Fig. 19. LH prediction performance cross-plot.

network performance. Phase gravities and prevailing pressure ranked in a higher level of importance than the flow rate information, although without major contrast in influence. Other than the density difference, the remaining input parameters exhibit a similar influence on the design of natural gas two-phase separators. 6. Concluding remarks A feed-forward Artificial Neural Network model with an arrangement of [6 30 30 4] neurons has been successfully developed for the reliable design and selection of natural gas two-phase separators. Error bounds of the proposed model are generally in the range 2% for dimensions of both vertical and horizontal vessels, with slightly higher prediction errors associated with horizontal design predictions. Cross-plot analysis indicates that predictions of the

network are well within the acceptable limits and align very well along the perfect-fit unit-slope line. Predictions allow the calculation of vessel dimensions and the selection of the best geometrical configuration based on fluid phase specific gravities, vessel pressure, GOR, and gas flow rate. The developed ANN covers the range of 1500 < GOR < 8000 scf/bbl, gas flow rates between 5000 and 30,000 MscfD, gas and condensate gravities ranging between 0.56– 1.20 and 0.7–1, respectively, and vessel operating pressures within the operational range of 200–800 psi. Using the concept of relevancy, it is corroborated that the fluid density contrast is the major driver of natural gas separation design. In this study, it has been demonstrated that a simple Artificial Neural Network can successfully replace conventional design strategy of two-phase natural gas separators during the basic engineering stage of surface production facilities. Future work should incrementally account for additional complexities and further details in design such as changes in operating

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conditions throughout reservoir life, temperature effects, and economical assessment of design options for instance. These proposed changes are ultimately aimed at helping the design engineer optimally explore better separator design alternatives. References Abdel-Aal, H.K., Aggour, M., Fahim, M.A., 2003. Petroleum and Gas Field Processing. Marcel Dekker, Inc., New York. Al-Farhan, F., Ayala H., Luis F., 2006. Optimization of surface separation conditions for natural gases using artificial intelligence. Journal of Petroleum Science and Engineering 53, 135–147. Arnold, K.E., Sikes, C.T., 1986. Droplet settling theory key to understanding separator-sizing correlations. July 21. Oil and Gas Journal, 60–64. Arnold, K., Stewart, M.,1998. Surface Production Operations. In: Design of Gas-Handling Systems and Facilities, second ed., vol. 1. Gulf Publishing Company, Houston, TX. Ayala H., Luis F., Ertekin, T., Adewumi, M., 2007. Study of gas-condensate reservoir exploitation using neuro-simulation. SPE Reservoir Evaluation and Engineering Journal 10 (2), 140–149. Ayala H., Luis F., Ertekin, T., 2007. Neuro-simulation analysis of pressure maintenance operations in gas-condensate reservoirs. Journal of Petroleum Science and Engineering 58, 207–226. Belue, L.M., Bauer, K.W., 1995. Determining input features of multilayer perceptrons. Neurocomputing 7 (2), 111–121. Campbell, J.M., 1994. Gas Conditioning and Processing. In: The Equipment Modules, seventh ed., vol. 2. Campbell Petroleum Series, Norman, OK. Chin, R., 2007. Oil and gas separators. In: Lake, L.W., Arnold, K.E. (Eds.), Petroleum Engineering Handbook. Facilities and Construction Engineering, vol. III. Society of Petroleum Engineers, Richardson, TX.

Dranchuk, P.M., Abou-Kassem, J.H., 1975. Calculation of Z-factors for natural gases using equations of state. Canadian Journal of Petroleum Technology July (14), 34–36. Gas Processors Suppliers Association (GPSA), 2004. GPSA Engineering Data Book, 12th ed Tulsa, OK. Gharbi, R.B.C., Mansoori, G.A., 2005. An introduction to artificial intelligence applications in petroleum exploration and production. Journal of Petroleum Science and Engineering 49 (3–4), 93–96. Guo, B., Ghalambor, A., 2005. Natural Gas Engineering Handbook. Gulf Publishing Company, Houston, TX. Guo, B., Lyons, W., Ghalambor, A., 2007. Petroleum Production Engineering: A Computer-Assisted Approach. Gulf Publishing Company, Houston, TX. Kidnay, A., Parrish, W., 2006. Fundamentals of Natural Gas Processing. Taylor and Francis Group, Boca Raton, FL. Kumar, S., 1987. Gas Production Engineering. Gulf Publishing Company, Houston, TX. Lee, A.L., Gonzalez, M.H., Eakin, B.E., 1966. Viscosity of natural gases. Journal of Petroleum Technology 18 (8), 997–1000. Mann, A., Ayala H., Luis F., 2009. Intelligent design of natural gas underground storage facilities. Int. J. of Modeling and Simulation 129 (2), 214–223. Manning, F.S., Thompson, R.E., 1991. Oilfield Processing Of Petroleum. In: Natural Gas, vol. 1. PennWell Books, Tulsa, OK. MathWorks, 2005. MATLABÓ User’s Guide Natick, MA. Mohaghegh, S.D., 2000. Virtual intelligence applications in petroleum engineering: Part I. Artificial neural networks. Distinguished Author Series, September. Journal of Petroleum Technology, 64–73. Peters, M.S., Timmerhaus, K.D., 1991. Plant Design and Economics for Chemical Engineers, fourth ed. McGraw-Hill, Inc. Svrcek, W.Y., Monnery, W.D., 1993. Design two-phase separators within the right limits. Chemical Engineering Progress 89, 53–60. Towler, G., Sinnott, R., 2008. Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design. Elsevier.