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• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N20/00—Machine learning
  • G06N20/10—Machine learning using kernel methods, e.g. support vector machines [SVM]
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N20/00—Machine learning
  • G06N20/20—Ensemble learning
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/0499—Feedforward networks
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods
  • G06N3/09—Supervised learning
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N7/00—Computing arrangements based on specific mathematical models
  • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
• • G—PHYSICS
  • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
  • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
  • G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
  • G16C20/30—Prediction of properties of chemical compounds, compositions or mixtures
• • G—PHYSICS
  • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
  • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
  • G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
  • G16C20/70—Machine learning, data mining or chemometrics
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/20—Design optimisation, verification or simulation

Definitions

• This disclosure relates to reservoir simulation, and more particularly to identifying isothermal phase behavior for reservoir simulation.
• composition of the reservoir fluids can be described using different models.
• petroleum can be modeled as including one oil and one gas component.
• These components can be pseudo-components, in that they may not refer to any specific chemical components, such as methane or octane, but refer to a collection of components that can exhibit similar phase behavior.
• reservoir fluids can be described as a mixture of several pure chemical components, such as carbon dioxide (C02), hydrogen sulphide (H2S), low-carbon alkanes (for example, methane and ethane), and pseudo-components for heavier hydrocarbons.
• compositional fluid models are increasingly used to simulate production from conventional reservoirs and fields developed using enhanced oil recovery techniques (EOR) (for example, surfactant flooding, polymer flooding, and miscible gas injection), since such models can be more accurate than traditionally used black oil models.
• EOR enhanced oil recovery techniques
• reservoir fluid behavior can be generally modeled using an equation of state (EOS) and phase equilibrium calculations that require solving nonlinear systems of equations. These types of equations can be solved for phase stability analysis to determine the number of stable phases at equilibrium for a given composition, temperature, and pressure.
• EOS equation of state
• phase-split or flash
• the present disclosure describes isothermal phase behavior identification for reservoir simulation.
• a training data set using negative flash calculations is generated.
• a first machine learning algorithm to identify a supercritical phase and a subcritical phase, a second machine learning algorithm to identify a number of stable phases in the subcritical phase, and a third machine learning algorithm to determine a phase split of the subcritical phase that has more than one identified stable phase are trained.
• the previously described implementation is implementable using a computer-implemented method; a non-transitory, computer-readable medium storing computer-readable instructions to perform the computer-implemented method; and a computer-implemented system comprising a computer memory interoperably coupled with a hardware processor configured to perform the computer-implemented method/the instructions stored on the non-transitory, computer-readable medium.
• the machine learning algorithm can reduce computation time for phase equilibrium calculations, which in turn, can reduce the overall run time of a compositional reservoir simulation. As such, more simulations can be performed in a fixed time frame, or the computational savings can be used to include more components in a fluid model or include more cells in a geologic model.
• the reduced computation time can be beneficial in simulating reservoirs that contain fluids near the critical boundary.
• These reservoirs often include gas-condensate reservoirs, volatile oil reservoirs, and reservoirs injected with supercritical CO2 for EOR.
• the machine-learning-based algorithm uses a relevance vector machine (RVM) model to determine whether a fluid mixture is supercritical or not, which can avoid performing a large amount of iterations to make the simulation run faster.
• RVM relevance vector machine
• the desired speedup by using the machine learning algorithm can be selected based on an error tolerance. Since the RVM models provide both a prediction of the fluid phase (for example, whether the fluid is supercritical or not) and a confidence estimate, the machine learning algorithm can allow the prediction to be supplanted by a negative flash calculation if the confidence estimate falls below a threshold. By decreasing the threshold, lower-confidence predictions may be accepted and the accuracy of the algorithm may decrease while the speedup may increase. For example, accepting an error of approximately 5%, the algorithm can provide a speed-up of greater than 90%.
• FIG 1A is a phase diagram showing an example supercritical and subcritical phase-point classification, according to some implementations of the present disclosure.
• FIG IB is a phase diagram showing an example supercritical and subcritical phase-point classification, and single-phase and two-phase subcritical phase-point classification, according to some implementations of the present disclosure.
• FIG 2 is a flow chart showing an example machine learning method for determining phase equilibrium determination, according to some implementations of the present disclosure.
• FIG. 3 is a flow chart showing an example algorithm for phase equilibrium calculations based on machine learning methods, according to some implementations of the present disclosure.
• FIG. 4A is a phase diagram showing an example phase behavior of a hydrocarbon mixture at a given temperature and pressure, according to some implementations of the present disclosure.
• FIG 4B is a phase diagram showing examples of models trained using machine learning methods to classify the phase behavior of a hydrocarbon mixture at a given temperature and pressure into supercritical , sub-critical single phase, and sub- critical two-phase regions, according to some implementations of the present disclosure.
• FIG 5 is a diagram showing example misclassification error and average absolute relative error with respect to a speed gain using a rapid flash algorithm, according to some implementations of the present disclosure.
• FIG. 6 is a block diagram illustrating an example computer system used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure, according to some implementations of the present disclosure.
• negative flash calculations can be used to generate training data sets including inputs and outputs to train the MLAs.
• the negative flash calculations can be used to distinguish the super-critical phase state, subcritical single-phase state, and subcritical two-phase states.
• the inputs and the solutions of the negative flash calculations can be stored as input-output examples to build the training data set to train the MLAs.
• the training of the machine learning method can include three high- level steps.
• a MLA can be trained to identify a first classifier used to identify if the input conditions correspond to a supercritical region or a subcritical region.
• a MLA can be trained to identify a second classifier to identify the number of stable phases in the subcritical region.
• a relevance vector machine RVM
• the RVM can determine the posterior probabilities for each class, which can be subsequently used to construct a criterion for accepting the predicted phase state.
• the phase split can be determined by training a MLA to predict equilibrium vapor-liquid distribution ratios (K-values) for a given pressure and composition.
• an artificial neural network (ANN) algorithm can be used as the MLA to determine the phase split.
• FIG. 1A corresponds to the first training step that identifies a first classifier to classify supercritical region and subcritical region.
• FIG. IB corresponds to the second training step that identifies a second classifier to classify single-phase and two-phase subcritical region.
• FIG 1A is a phase diagram showing an example 100a supercritical and subcritical phase-point classification, according to some implementations of the present disclosure.
• two input variables xl and x2 are used to train a first machine-learning model.
• the input variables xl and x2 can represent mole fractions of two components in a feed.
• the mole fraction can be defined as the amount of a component (expressed in moles) divided by the total amount of all components (expressed in moles) in the feed.
• the first MLA is trained to identify a first classifier 130 (shown in FIG.
• the first MLA can be algorithms such as support vector machines (SVMs), RVMs, AN s, and decision trees.
• SVMs support vector machines
• RVMs RVMs
• AN s subcritical region 120
• decision trees decision trees.
• the first MLA may be trained by a plurality of input pairs (xl, x2) to identify the first classifier 130. Once the first MLA is optimized, the first classifier is said to be trained and can be used to predict the supercritical and subcritical phase behavior of any input pairs. For example, if an input pair is located in the supercritical region 110, the output of the fist classifier is a supercritical phase label.
• FIG IB is a phase diagram showing an example 100b supercritical and subcritical phase-point classification, and a single-phase and two-phase subcritical phase-point classification, according to some implementations of the present disclosure.
• a second MLA can be trained to identify a second classifier 140 (shown in FIG 1A as a boundary curve) that can separate each input pair (xl, x2) in the subcritical region 120 into a single-phase subcritical region 122 (between the boundary line 130 and the boundary curve 140) and a two-phase subcritical region 124 (lower left of the boundary curve 140).
• the second MLA can be any algorithms such as SVMs, RVMs, ANNs, and decision trees.
• RVMs can be used as the first MLA and the second MLA, because not only can it identify the classifier, but it can also determine how accurate the classification is.
• both the first classifier 130 and the second classifier 140 are optimized to determine whether an input pair is a supercritical, single-phase subcritical, or two-phase subcritical phase point.
• the training of the MLAs for identifying the first classifier 130 and the second classifier 140 can use the results of negative flash calculations.
• the third MLA is used to make quantitative predictions about the phase composition and the amount of each phase.
• the fraction of phase 1 can be expressed as a regression function of the input pairs (xl , x2), such that for any input pair, the fraction of phase 1 can be determined based on the regression function.
• the third MLA can be used to identify the form of the regression function through optimization.
• the third MLA can be any machine learning based regression model, such as AN s, SVMs, RVMs, Decision forest regression, and Boosted regression tree regression.
• an ANN can be used as the third MLA since it is accurate once trained and has low computational complexity.
• the machine learning based regression algorithms can identify the regression function that predicts the fraction of phase for a given input pair (xl , x2). The regression function can then be used to predict the fraction of phase 1 for any input pair during reservoir simulation.
• the trainings for the first, second, and third MLAs are performed before the start of the reservoir simulation.
• the first classifier 130, the second classifier 140, and the regression function can be used to calculate the phase behavior for each reservoir cell.
• FIG 2 is a flowchart showing an example machine learning method 200 for determining phase equilibrium determination.
• method 200 can be performed, for example, by any suitable system, environment, software, and hardware, or a combination of systems, environments, software, and hardware, as appropriate.
• various steps of method 200 can be run in parallel, in combination, in loops, or in any order.
• Machine learning techniques are used to model complex relationships between inputs and outputs, if provided with adequate training information.
• the inputs are the fluid composition, ⁇ zij, and pressure, P, of a simulation cell and the output is the equilibrium phase state, which is the number of stable phases and their compositions.
• the relationships of interest are the phase boundaries in the corresponding phase diagram.
• Machine learning techniques are used to generate models that predict phase behavior.
• a training data set of input-output examples are calculated by solving a negative flash problem over a feed composition and pressure range of interest. MLAs are then trained using the training data set to predict a solution of the phase equilibrium problem.
• training data set is generated using negative flash calculations.
• the training data set can be generated by solving the two-phase isothermal negative flash problem over the reservoir pressure and composition range.
• the advantages of this method include: (1) the phase stability and the phase split problems are solved simultaneously, and (2) the negative flash procedure can distinguish between the supercritical and subcritical phase state.
• the solution to the problem is determined by f a ' — 1 9
• L and ⁇ denote the liquid and vapor phase
• x ⁇ and ⁇ are the mole fractions of component z in the liquid and vapor phase
• ⁇ is the fugacity coefficient
• the component K-values and P can be calculated iteratively, using the successive substitution method.
• One Rachford-Rice iteration can be defined as an update of P at fixed followed by an update of with P held constant.
• Wilson's correlation can be used to seed the method with initial estimates for , f . The procedure converges as long as the feed composition is positive and if P is in the range ma Convergence to a non-trivial
• the negative flash calculations can be performed for a large number of inputs ( ⁇ ' ⁇ ).
• the inputs and the solutions ( ⁇ ' ⁇ ⁇ > ⁇ ' > ⁇ ) from the negative flash calculations can be stored as input-output examples in order to build the training data set.
• the input vectors can be drawn randomly from the ( n + 1 )-dimensional space spanned by the range of pressures and compositions the reservoir can exhibit under operating conditions. While the pressure can be freely picked in the operating range, the feed mole fractions can be drawn from a ( " " ⁇ -dimensional unit simplex in order to satisfy the constraint that the mole fractions sum to one, which is obtained by following the Bayesian bootstrap method. From 210 example method 200 proceeds to 220.
• a first machine algorithm is trained for identifying a supercritical phase and a subcritical phase.
• the first task of the algorithm identifying the presence of a supercritical phase, can be treated as a classification problem. This is based on the observation that the negative flash converges to the trivial solution, xi - y t - zi ⁇ m( ma ⁇ me length of the tie-line, t , is zero for any point in the supercritical region.
• the length of the tie-line can be defined as:
• the tie-line length is greater than zero for any hydrocarbon mixture in the subcritical region irrespective of the number of stable phases present at equilibrium. Based on this observation, the length of the tie-line can be used to recast the supercritical phase detection problem as a binary classification problem with the following rule:
• the classification problem can be solved based on discriminant functions generated by training SVMs. For any input, the discriminant function is evaluated to assign the label without considering the confidence level of the prediction. Instead, the classification problem is split into two steps - the inference step of training the model and a decision step using the posterior probability of the predicted label and a threshold value for acceptance.
• the advantage of this method over discriminant functions is that the misclassification rate can be reduced by rejecting predictions with a probability less than the discriminant threshold
• RVMs can be used to fit the decision boundary that separates the subcritical and supercritical regions in phase space.
• the confidence estimate of the trained model is improved by increasing the density of training points in the vicinity of the surface separating the two regions.
• a second MLA is trained for identifying a number of stable phases in the subcritical phase.
• identifying the number of stable phases at equilibrium can also be re-formulated as a multi-class classification problem, solved by training another RVM model.
• training data set is pruned by removing points belonging to the supercritical region. For points in the subcritical region, the phase label is assigned using P from the negative flash solution as follows:
• siisgfc- hase liquid, if ⁇ 0
• Phase is fen-phase smxhiii:, if ⁇ ⁇ ⁇ ⁇ I
• the RVM model can represent an approximation for the bubble point curve ( P ⁇ ) and the dew point curve ( P ⁇ ⁇ ). Therefore, models with better predictive capability are generated by selecting training points that lie in the vicinity of the two curves, as measured by the value ⁇ .
• P(#ph) is used to implement a rejection criterion by comparing it
• a third MLA is trained for determining a phase split of the subcritical phase that has more than one identified stable phase.
• the third step of solving the phase equilibrium problem is to determine the compositions of the liquid and vapor phases in a two-phase mixture by solving the equal fugacity constraint and
• Rachford-Rice equation simultaneously for and P This step is accelerated by generating initial K-value estimates using a function that is tailored for the phase diagram under consideration as opposed to using an empirical relationship such as Wilson's correlation.
• the acceleration can be attributed to the fact that the predicted , f can either satisfy the equal fugacity constraint to within some tolerance, ° , eliminating Rachford-Rice iterations or provide an accurate guess that reduces the number of iterations for convergence.
• nonlinear regression can be used to obtain more accurate initial K-value estimates.
• Nonlinear regression can be used to fit a function, 2 ; to predict ⁇ ⁇ ' ' for a given pressure and composition by optimizing its parameters, w , to match the EOS-based solution:
• ANN can be used for function regression to eliminate the need for a user-defined function for 2 .
• Another advantage of ANNs is that they can capture complex nonlinear relationships with relatively few parameters, enabling cheap computations of S .
• the function weights, w are optimized to minimize the mean squared error between the predicted ⁇ ⁇ and the training data set.
• the ⁇ 2 ' ⁇ and P corresponding to negative flash solutions in the two phase region can be selected to build the data set for training the ANN. Overfitting is avoided by using early -stopping and minimizing the number of neurons in the hidden layer of the ANN required to produce a satisfactory fit.
• FIG 3 is a flow chart showing an example algorithm 300 for phase equilibrium calculations using the trained machine learning models, according to some implementations of the present disclosure.
• method 300 can be performed, for example, by any suitable system, environment, software, and hardware, or a combination of systems, environments, software, and hardware, as appropriate.
• various steps of method 300 can be run in parallel, in combination, in loops, or in any order.
• the trained models that is, the supercritical RVM classifier, the number of phases RVM classifier, and the phase split ANN regression model, can be linked together to create a new algorithm for calculating the equilibrium phase state.
• the example method uses three MLAs. First, it uses a relevance vector machine (RVM) to determine whether a fluid is supercritical or subcritical. If the fluid is not supercritical, it uses another RVM to determine if it is a liquid, a vapor, or a two-phase fluid. For a two-phase fluid, it uses an artificial neural network (ANN) to determine the phase split.
• RVM relevance vector machine
• ANN artificial neural network
• the example algorithm 300 starts at 305. [0048] At 310, the simulation cell is queried for the feed composition, 1 , and pressure, P .
• the supercritical RVM model is evaluated to obtain the class label, SC, and the corresponding probability value, P(SC).
• the RVM classifier is evaluated to determine the number of stable phases, #ph, and its probability, P(#ph).
• the phase split is calculated by running a phase-split ANN regression model.
• the K-values ( ⁇ ' ⁇ ) are calculated by evaluating the trained phase split regression model.
• the fugacity for each component is checked. If the fugacities of all components in both phases are equal to within some error tolerance, 0 , the
• the 300 stops at 365. If the component fugacities are not equal, the predicted is used as an initial guess for the negative flash method at 360 and the algorithm stops at 365 after a solution is obtained.
• the results of the algorithm can be compared with the negative flash results for the same inputs to determine the accuracy and computational speedup.
• the error may arise from two sources: misclassification rate of the RVMs and the average absolute relative error (AARE) in the vapor fraction as a result of not satisfying the equal fugacity constraint in the two-phase region.
• the misclassification rate can be defined as:
• Yj is the class label calculated using the negative flash method.
• the AARE in the vapor fraction is calculated as follows:
• the speedup can be measured as the difference in the mean number of Rachford-Rice iterations required for convergence in the algorithm and the negative flash method. This measure does not include the computational cost of evaluating the trained models but the additional cost incurred can be small relative to the cost of a Rachford-Rice iteration and will not change the results.
• the speedup and accuracy of the algorithm can be tailored by ⁇ ⁇
• the algorithm for rapid phase behavior determination can be tested using three different reservoir fluid mixtures of increasing complexity: three, six, and thirteen component mixtures. In all cases, the ranges of pressure and composition for which the phase diagram includes supercritical and subcritical regions are considered.
• FIG 4A is a phase diagram 400a showing an example phase behavior of a hydrocarbon mixture at a given temperature and pressure, according to some implementations of the present disclosure.
• the phase diagram is for a CH 4 - C2H 6 - CO2 ternary system at 260 Kelvin (K) and 7 megaPascal (MPa).
• the phase behavior of the CH4 - C2H6 - CO2 mixture is generated using negative flash calculations with respect to the mole fractions of C2H6 and CH4 at 260 K and 7 MPa.
• the phase diagram 400a shows a critical surface 490a separating the supercritical region 410a and subcritical regions.
• the subcritical regions include a liquid region 420a, a vapor and liquid mixture region 430a, and a vapor region 440a.
• the phase diagram 400a also shows the bubble-point curve 450a and dew-point curve 460a that bound the two-phase region.
• FIG 4B is a phase diagram 400b showing another example phase behavior of a hydrocarbon mixture at a given temperature and pressure along with two machine-learning models trained to classify the supercritical phase, the sub-critical liquid phase, the sub-critical vapor phase, and sub-critical two-phase region, according to some implementations of the present disclosure.
• a data set for this phase diagram is calculated using the negative flash method, and the data set is used to train two RVMs.
• One RVM model classifies the input fluid as either supercritical 410b or subcritical. For this model, relevance vectors are shown as open circles 490b.
• Another RVM model classifies the fluid as a liquid 420b, a vapor 440b, or a two-phase mixture 430b. For this model, relevance vectors lie on the two-phase boundary and are shown as open stars 470b.
• the phase diagram data are used to train the three machine-learning models.
• the trained RVM models can predict the critical behavior and number of stable phases at equilibrium with an accuracy greater than ⁇ ⁇
• the RVM models for predicting the critical phase and number of stable phases for the three component mixture at 260 K and 7 MPa are illustrated in Fig. 4B.
• the second RVM model identifies the single- phase liquid, single-phase vapor, and two-phase regions using relevance vectors to represent the two-phase boundary.
• the ANN regression models use 25 to 50 neurons in the hidden layer to predict to within 10 4 of the value calculated from the EOS- based model across the fluid mixtures of interest.
• FIG 5 is a diagram showing example 500 misclassification error and average absolute relative error with respect to a speed gain using a rapid flash algorithm, according to some implementations of the present disclosure.
• the error is the sum of the misclassification error and the average absolute relative error (AARE) in the vapor fraction of two-phase results.
• AARE average absolute relative error
• the speedup is defined as the relative decrease in the number of Rachford-Rice iterations between the algorithm and conventional negative flash.
• the algorithm offers a speed gain of greater than 90% with a maximum error of 5% across all the cases. As shown in FIG. 5, the algorithm can reduce the computational cost of phase equilibrium calculations by over 20% with an error on the order of 10 relative to the EOS solution.
• the machine-learning-based algorithm for equilibrium phase determination offers several advantages over the negative flash method alone.
• One of the main advantages is the reduction in computation time. This reduction can decrease the overall run time of a compositional reservoir simulation, which would provide reservoir simulation engineers with several benefits: they can complete more simulations in a fixed time frame, or use the computational savings to include more components in the fluid model or more cells in the geologic model.
• the reduced computation time can be particularly advantageous in simulating reservoirs that contain fluids near the critical boundary.
• These reservoirs often include gas-condensate reservoirs, volatile oil reservoirs, and reservoirs injected with supercritical CO2 for EOR.
• the negative flash method requires a large number of iterations for fluids near the critical boundary when compared to systems that are far away from the critical boundary. Since the machine-learning- based algorithm uses a RVM model to determine whether a fluid mixture is supercritical or not, these iterations can be avoided and the simulation may run faster.
• Another advantage of the machine-leaming-based algorithm is that the desired speedup can be chosen according to one's error tolerance. This capability derives from the use of RVMs. Since our RVM models provide both a prediction of the fluid phase (for example, the fluid is supercritical or not) and a confidence estimate, our algorithm allows the prediction to be supplanted by a negative flash calculation if the confidence estimate is less than a threshold. By decreasing the threshold, lower- confidence predictions are accepted and the accuracy of the algorithm decreases, but the speedup increases.
• This trade-off curves are plotted for three fluid samples in FIG 5, including CI-C2-CO2 mixture trade-off curve 510, Pedersen 13 component mixture trade-off curve 520, and SPE5 6 component mixture trade-off curve 530. These types of plots can be used by reservoir simulation engineers to set the desired accuracy for a given run time. If an engineer chooses to accept an error of less than 0.01%, our results suggest that the algorithm would still provide a speed-up of greater than 20%. This ability to reject low-confidence solutions and thereby trade accuracy for run time is not possible using SVMs.
• the machine-learning-based algorithm is extensible.
• the method can be extended to EOS other than Peng-Robinson (PR) or Soave-Redlich-Kong (SRK), including non- cubic EOS such as perturbed-chain statistical association fluid theory (PC-SAFT) and cubic-plus-association (CPA), without sacrificing speed since it depends on phase behavior calculations only for the training stage.
• Non-cubic EOS can be more accurate than cubic EOS, but are less used in reservoir simulation since the phase behavior calculations for non-cubic EOS can be three times as expensive as those for cubic EOS.
• Multi-class classification can be used to assign labels to each region of phase space, similar to how different labels are assigned for a single-phase vapor, a single-phase liquid, and a two- phase mixture.
• the machine-leaming-based algorithm also requires low data storage and is not sensitive to changes in the fluid composition of a grid cell over time, when compared to other methods.
• the algorithm requires less data storage than methods such as compositional space parameterization (CSP), compositional space tabulation (CST), and compositional space adaptive tabulation (CSAT), which store and search tie-line lists. As these lists become larger, the speed of these methods also decreases.
• CSP compositional space parameterization
• CST compositional space tabulation
• CSAT compositional space adaptive tabulation
• the speed of the algorithm is not affected by how the fluid composition in a grid cell changes over time. In contrast, methods that use the phase equilibrium solution from the previous time step will provide a smaller speed up if that solution does not accurately approximate the current solution. This feature of the algorithm can be important for reservoir simulations with billions of simulation cells.
• the numerical dissipation can be less than in lower resolution simulations and, as a result, the fluid composition in a grid cell may exhibit larger changes between time steps.
• the machine-learning-based algorithm could benefit other applications in the oil industry. It could reduce the simulation time of processes that require determining the phase equilibrium, such as the separation of production fluids in surface facilities, the flow of hydrocarbons in pipelines, and the distillation of crude oil.
• Another disadvantage of this method is that the models are applicable only over the pressure range used in the training stage. If the pressure exceeds these bounds, the method may not provide any speedup. In such cases, a conventional phase calculation can be used for pressures outside the training range or, if deemed necessary, the models can be re-trained over the phase diagram corresponding to the extended pressure range.
• FIG. 6 is a block diagram of an example computer system 600 used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, as described in the instant disclosure.
• the illustrated computer 602 is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including physical or virtual instances (or both) of the computing device.
• PDA personal data assistant
• the computer 602 can comprise a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer 602, including digital data, visual, or audio information (or a combination of information), or a graphical-type user interface (UI) (or GUI).
• an input device such as a keypad, keyboard, touch screen, or other device that can accept user information
• an output device that conveys information associated with the operation of the computer 602, including digital data, visual, or audio information (or a combination of information), or a graphical-type user interface (UI) (or GUI).
• UI graphical-type user interface
• the computer 602 can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure.
• the illustrated computer 602 is communicably coupled with a network 630.
• one or more components of the computer 602 can be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).
• the computer 602 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer 602 can also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, or other server (or a combination of servers).
• an application server e-mail server, web server, caching server, streaming data server, or other server (or a combination of servers).
• the computer 602 can receive requests over network 630 from a client application (for example, executing on another computer 602) and respond to the received requests by processing the received requests using an appropriate software application(s).
• requests can also be sent to the computer 602 from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.
• Each of the components of the computer 602 can communicate using a system bus 603.
• any or all of the components of the computer 602 hardware or software (or a combination of both hardware and software), can interface with each other or the interface 604 (or a combination of both), over the system bus 603 using an application programming interface (API) 612 or a service layer 613 (or a combination of the API 612 and service layer 613).
• the API 612 can include specifications for routines, data structures, and object classes.
• the API 612 can be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs.
• the service layer 613 provides software services to the computer 602 or other components (whether or not illustrated) that are communicably coupled to the computer 602.
• the functionality of the computer 602 can be accessible for all service consumers using this service layer.
• Software services, such as those provided by the service layer 613 provide reusable, defined functionalities through a defined interface.
• the interface can be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or other suitable format.
• XML extensible markup language
• alternative implementations can illustrate the API 612 or the service layer 613 as stand-alone components in relation to other components of the computer 602 or other components (whether or not illustrated) that are communicably coupled to the computer 602.
• any or all parts of the API 612 or the service layer 613 can be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.
• the computer 602 includes an interface 604. Although illustrated as a single interface 604 in FIG. 6, two or more interfaces 604 can be used according to particular needs, desires, or particular implementations of the computer 602.
• the interface 604 is used by the computer 602 for communicating with other systems that are connected to the network 630 (whether illustrated or not) in a distributed environment.
• the interface 604 comprises logic encoded in software or hardware (or a combination of software and hardware) and is operable to communicate with the network 630. More specifically, the interface 604 can comprise software supporting one or more communication protocols associated with communications such that the network 630 or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer 602.
• the computer 602 includes a processor 605. Although illustrated as a single processor 605 in FIG. 6, two or more processors can be used according to particular needs, desires, or particular implementations of the computer 602. Generally, the processor 605 executes instructions and manipulates data to perform the operations of the computer 602 and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure. Example processors include central processing unit (CPU), graphic processing unit (GPU), microcontroller (MCU), and many integrated core (MIC). [0079] The computer 602 also includes a database 606 that can hold data for the computer 602 or other components (or a combination of both) that can be connected to the network 630 (whether illustrated or not).
• a database 606 can hold data for the computer 602 or other components (or a combination of both) that can be connected to the network 630 (whether illustrated or not).
• database 606 can be an in-memory, conventional, or other type of database storing data consistent with this disclosure.
• database 606 can be a combination of two or more different database types (for example, a hybrid in-memory and conventional database) according to particular needs, desires, or particular implementations of the computer 602 and the described functionality.
• two or more databases can be used according to particular needs, desires, or particular implementations of the computer 602 and the described functionality.
• database 606 is illustrated as an integral component of the computer 602, in alternative implementations, database 606 can be external to the computer 602.
• the computer 602 also includes a memory 607 that can hold data for the computer 602 or other components (or a combination of both) that can be connected to the network 630 (whether illustrated or not).
• Memory 607 can store any data consistent with this disclosure.
• memory 607 can be a combination of two or more different types of memory (for example, a combination of semiconductor and magnetic storage) according to particular needs, desires, or particular implementations of the computer 602 and the described functionality. Although illustrated as a single memory 607 in FIG. 6, two or more memories 607 (of the same or combination of types) can be used according to particular needs, desires, or particular implementations of the computer 602 and the described functionality. While memory 607 is illustrated as an integral component of the computer 602, in alternative implementations, memory 607 can be external to the computer 602.
• the application 608 is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer 602, particularly with respect to functionality described in this disclosure.
• application 608 can serve as one or more components, modules, or applications.
• the application 608 can be implemented as multiple applications 608 on the computer 602.
• the application 608 can be external to the computer 602.
• the computer 602 can also include a power supply 614.
• the power supply 614 can include a rechargeable or non-rechargeable battery that can be configured to be either user- or non-user-replaceable.
• the power supply 614 can include power-conversion or management circuits (including recharging, standby, or other power management functionality).
• the power-supply 614 can include a power plug to allow the computer 602 to be plugged into a wall socket or other power source to, for example, power the computer 602 or recharge a rechargeable battery.
• computers 602 there can be any number of computers 602 associated with, or external to, a computer system containing computer 602, each computer 602 communicating over network 630.
• clients can be used interchangeably, as appropriate, without departing from the scope of this disclosure.
• this disclosure contemplates that many users can use one computer 602, or that one user can use multiple computers 602.
• Described implementations of the subject matter can include one or more features, alone or in combination.
• a computer-implemented method comprises, generating a training data set using negative flash calculations, training a first machine learning algorithm to identify a supercritical phase and a subcritical phase, training a second machine learning algorithm to identify a number of stable phases in the subcritical phase and training a third machine learning algorithm to determine a phase split of the subcritical phase that has more than one identified stable phase.
• a first feature combinable with any of the following features, wherein the training data set includes input data points and output data points, and the output data points are calculated using the negative flash calculations based on the input data points.
• a second feature combinable with any of the previous or following features, wherein the output data points include supercritical data points, subcritical single-phase data point, and subcritical two-phase data points.
• a third feature combinable with any of the previous or following features, wherein the first machine learning algorithm is a RVM algorithm.
• a fourth feature combinable with any of the previous or following features, wherein the first machine learning algorithm is trained by solving a classification problem.
• a fifth feature combinable with any of the previous or following features, wherein the second machine learning algorithm is a RVM algorithm.
• a sixth feature combinable with any of the previous or following features, wherein the second machine learning algorithm is trained by solving a multi- class classification problem.
• a seventh feature combinable with any of the previous or following features, wherein the third machine learning algorithm is an artificial neural network algorithm.
• determining the phase split includes determining a mole fraction and a molar composition for each of the more than one stable phase.
• a ninth feature combinable with any of the previous or following features, further comprises using the trained first machine learning algorithm, the second trained machine learning algorithm, and the third trained machine learning algorithm to calculate isothermal phase equilibria.
• a tenth feature combinable with any of the previous or following features, further comprises constructing one or more Jacobian matrices for reservoir simulation based on the calculated isothermal phase equilibria.
• Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
• Software implementations of the described subject matter can be implemented as one or more computer programs, that is, one or more modules of computer program instructions encoded on a tangible, non-transitory, computer-readable computer-storage medium for execution by, or to control the operation of, data processing apparatus.
• the program instructions can be encoded in/on an artificially generated propagated signal, for example, a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.
• the computer-storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer-storage mediums.
• Configuring one or more computers means that the one or more computers have installed hardware, firmware, or software (or combinations of hardware, firmware, and software) so that when the software is executed by the one or more computers, particular computing operations are performed.
• NRT near(ly) real-time
• quadsi real-time or similar terms (as understood by one of ordinary skill in the art), means that an action and a response are temporally proximate such that an individual perceives the action and the response occurring substantially simultaneously.
• the time difference for a response to display (or for an initiation of a display) of data following the individual's action to access the data can be less than 1 ms, less than 1 sec, or less than 5 sees.
• data processing apparatus refers to data processing hardware and encompass all kinds of apparatus, devices, and machines for processing data, including by way of example, a programmable processor, a computer, or multiple processors or computers.
• the apparatus can also be, or further include special purpose logic circuitry, for example, a CPU, an FPGA (field programmable gate array), or an ASIC (application-specific integrated circuit).
• the data processing apparatus or special purpose logic circuitry can be hardware- or software-based (or a combination of both hardware- and software-based).
• the apparatus can optionally include code that creates an execution environment for computer programs, for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments.
• code that constitutes processor firmware for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments.
• the present disclosure contemplates the use of data processing apparatuses with or without conventional operating systems, for example LINUX, UNIX, WINDOWS, MAC OS, ANDROID, IOS, or any other suitable conventional operating system.
• a computer program which can also be referred to or described as a program, software, a software application, a module, a software module, a script, or code can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
• a computer program can, but need not, correspond to a file in a file system.
• a program can be stored in a portion of a file that holds other programs or data, for example, one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, for example, files that store one or more modules, sub-programs, or portions of code.
• a computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.
• the methods, processes, or logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output.
• the methods, processes, or logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, for example, a CPU, an FPGA, or an ASIC.
• Computers suitable for the execution of a computer program can be based on general or special purpose microprocessors, both, or any other kind of CPU.
• a CPU will receive instructions and data from and write to a memory.
• the essential elements of a computer are a CPU, for performing or executing instructions, and one or more memory devices for storing instructions and data.
• a computer will also include, or be operatively coupled to, receive data from or transfer data to, or both, one or more mass storage devices for storing data, for example, magnetic, magneto-optical disks, or optical disks.
• mass storage devices for storing data, for example, magnetic, magneto-optical disks, or optical disks.
• a computer need not have such devices.
• a computer can be embedded in another device, for example, a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device, for example, a universal serial bus (USB) flash drive, to name just a few.
• PDA personal digital assistant
• GPS global positioning system
• USB universal serial bus
• Computer-readable media suitable for storing computer program instructions and data includes all forms of permanent/non-permanent or volatile/non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, for example, random access memory (RAM), read-only memory (ROM), phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices; magnetic devices, for example, tape, cartridges, cassettes, internal/removable disks; magneto-optical disks; and optical memory devices, for example, digital video disc (DVD), CD-ROM, DVD+/-R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY, and other optical memory technologies.
• RAM random access memory
• ROM read-only memory
• PRAM phase change memory
• SRAM static random access memory
• DRAM dynamic random access memory
• EPROM erasable programmable
• the memory can store various objects or data, including caches, classes, frameworks, applications, modules, backup data, jobs, web pages, web page templates, data structures, database tables, repositories storing dynamic information, and any other appropriate information including any parameters, variables, algorithms, instructions, rules, constraints, or references. Additionally, the memory can include any other appropriate data, such as logs, policies, security or access data, reporting files, as well as others.
• the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
• implementations of the subject matter described in this specification can be implemented on a computer having a display device, for example, a CRT (cathode ray tube), LCD (liquid crystal display), LED (Light Emitting Diode), or plasma monitor, for displaying information to the user and a keyboard and a pointing device, for example, a mouse, trackball, or trackpad by which the user can provide input to the computer.
• a display device for example, a CRT (cathode ray tube), LCD (liquid crystal display), LED (Light Emitting Diode), or plasma monitor
• a keyboard and a pointing device for example, a mouse, trackball, or trackpad by which the user can provide input to the computer.
• Input can also be provided to the computer using a touchscreen, such as a tablet computer surface with pressure sensitivity, a multi-touch screen using capacitive or electric sensing, or other type of touchscreen.
• a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user's client device in response to requests received from the web browser.
• GUI graphical user interface
• GUI can be used in the singular or the plural to describe one or more graphical user interfaces and each of the displays of a particular graphical user interface. Therefore, a GUI can represent any graphical user interface, including but not limited to, a web browser, a touch screen, or a command line interface (CLI) that processes information and efficiently presents the information results to the user.
• a GUI can include a plurality of user interface (UI) elements, some or all associated with a web browser, such as interactive fields, pull-down lists, and buttons. These and other UI elements can be related to or represent the functions of the web browser.
• UI user interface
• Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, for example, as a data server, or that includes a middleware component, for example, an application server, or that includes a front-end component, for example, a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components.
• the components of the system can be interconnected by any form or medium of wireline or wireless digital data communication (or a combination of data communication), for example, a communication network.
• Examples of communication networks include a local area network (LAN), a radio access network (RAN), a metropolitan area network (MAN), a wide area network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a wireless local area network (WLAN) using, for example, 802.11 a/b/g/n or 802.20 (or a combination of 802. l lx and 802.20 or other protocols consistent with this disclosure), all or a portion of the Internet, or any other communication system or systems at one or more locations (or a combination of communication networks).
• the network can communicate with, for example, Internet Protocol (IP) packets, Frame Relay frames, Asynchronous Transfer Mode (ATM) cells, voice, video, data, or other suitable information (or a combination of communication types) between network addresses.
• IP Internet Protocol
• ATM Asynchronous Transfer Mode
• the computing system can include clients and servers.
• a client and server are generally remote from each other and typically interact through a communication network.
• the relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
• any claimed implementation is considered to be applicable to at least a computer-implemented method; a non-transitory, computer- readable medium storing computer-readable instructions to perform the computer- implemented method; and a computer system comprising a computer memory interoperably coupled with a hardware processor configured to perform the computer- implemented method or the instructions stored on the non-transitory, computer- readable medium.

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