Virtual Multiphase Flow Meter using combination of Ensemble Learning and first principle physics based

The test pilot was set up to get real-time measurements from the OSIsoft™ PI server through PI web Application Program Interface (API). The developed system was tested in an online pilot in an offshore field with two oil-producing wells. The details of the pilot test are shown in Table 1.

Wells 101 and 102 together with physical multi-phase flow meter (MPFM) are shown in Figure 3.

Figure 3

Both of the wells were tested on a monthly basis by diverting the manual valve for an 8-hr duration. This data dataset is called a Well Test Report in a format shown in Table 2. Both wells have close to 2 years of historical Well Test data. Based on the dataset, well 101 flows only oil and gas while 102 also contains a significant amount of water.

The VFM system architecture is shown in Figure 4. Sensor measurements come from OSIsoft™ PI, while the well-test dataset is uploaded from Excel sheets.

Figure 4

Both the measurements and the reference well-test results are fed into individual VFMs, and the outputs are stored in a database. The combiner subsystem uses the outputs from the individual VFMs to estimate flow rates along with the confidence level indicator. All the data is then stored in the database and visualized using a real-time dashboard. The system is flexible such that more than one VFM model can be running for the same asset. The combiner is also flexible as it can accept one or more models to run the combining algorithm and can also handle missing values correctly.

For this project, the chosen data-driven VFM (DD-VFM) uses ensemble learning methods as per developed previously using the same dataset by (AL-Qutami et al., 2018). This choice is supported independently by Bikmukhametov (AL-Qutami, 2017; Bikmukhametov and Jäschke, 2020b). Ensemble methods take multiple models which normally considered as “weak learners: and combine them together to form a more powerful model overall. There are 3 different approaches of Ensemble Learning i.e. Bagging, Boosting and Stacking (Opitz and Maclin, 1999).

Bagging (also called bootstrap aggregating) combine homogenous “weak learners”. Homogeneous means each earlier weak learner is of the same type (e.g. all decision trees) These weak learners are trained independently in parallel. The output from weak learners are then combined with some type of aggression technique like voting for binary classification or averaging regression use case. From this definition, Random Forest is indeed a type of Bagging (Naik, 2019a).

In Boosting, models are trained sequentially. Weak learners are therefore not independent. Model at the current step depends on models at previous steps. There are further 3 methods of Boosting i.e. AdaBoost (Adaptive Boosting), Gradient Boosting and XGBoost (Extreme Gradient Boosting) (Naik, 2019b). In AdaBoost, at each step, the weights of the observations that were previously misclassified are increased making the better the weak learner the higher its weight. The “strong learner” (final model) is a weighted sum of the weak learners.

With Gradient Boosting, the final model is also weighted sum of the weak learners, however, gradient descent is used to determine how to improve at each step in the sequence. Gradient boosting is a generalisation of boosting where optimization can be based on any arbitrary differentiable loss function.

Theoretically, comparing the two methods using bias-variance trade off as shown in Figure 5; with bagging, the goal is to reduce the variance in model while with boosting, the goal is to increase the prediction accuracy or the bias of the model (Naik, 2020; Powerhouse, 2020). On the dataset partition, in bagging, the data partition is random, while in boosting, mis-classified data is given higher importance.

Figure 5

Finally, stacking is ensemble method that combine heterogenous weak learners (Wolpert, 1992). For example, a combination of neural networks with decision trees, linear model and so on. Bagged or Boosted models could as well be used as those weak learners. For this reason, stacked models can be very difficult to interpret meaningfully.

Ensemble Learning is preferred especially in this application for multiphase flow prediction because interpretability is not our top priority with high accuracy take higher precedence. The complete workflow of the data-driven VFM using ensemble learning is shown in Figure 6. The implementation of Ensemble Learning in Python is described by (Semicolon, 2017).

Figure 6

Three separate data-driven models were developed, as shown in Figure 7. The subsurface model uses measurements taken from downhole and from upstream of the choke valve. The surface model uses measurements from upstream of choke valve and downstream of choke. Lastly, the full model covers all the above, utilising measurements from downhole to downstream of the choke valve.

Figure 7

Each phase flow rate was modeled independently resulting in three ML estimators for the same production well. A further three categories of models were developed based on the measurements fed to each estimator. The summary of the different trained estimators is shown in Table 3.

The possible inputs to the machine learning model are Choke opening (C_V), Flowing tubing head pressure (FTHP), Flowing tubing head temperature (FTHT), differential pressure across the well (dP_Well), differential temperature across the well (dT_Well), differential pressure across the choke (dP_Choke), differential temperature across the choke (dT_Choke). dP_Well and dT_Well are the differences between downhole P/T and flowing tubing head P/T.

The outputs of the VFMs are gas flow rate (Q_gas), oil flow rate (Q_oil), and water flow rate (Q_water). Each model was trained using the pool of algorithms and a hyperparameter space to produce the best performing model.

In this project, the Physics-based virtual flow meter (VFM) uses Flux Simulator from Turbulent Flux (Turbulent Flux, https://turbulentflux.com) to construct the physics model. TF-VFM will be used as the abbreviation for the VFM from Turbulent Flux’s Flux Simulator.

The workflow requires two general steps to work properly.

Physics and static tuning

As shown in Figure 8, static information about the well is used, such as well geometry, PVT, and choke characteristics to tune the physical and system parameters. Using description by Mokhtari Jadid (2017) and Figure 7 as reference, the Physics model can be constructed suing the following:

Fluid properties characterization

Wellbore model

Choke valve model

Enthalpy model

Figure 8

Fluid properties characterization: From the supplied fluid property (also known as PVT data), Multiflash^® software can be used to generate the model as shown in Figure 9.

Figure 9

Wellbore model: are represented by Inflow Performance Relationship (IPR) and Vertical Lift Performance (VLP), as shown in Figures 10 and 11. IPR is defined as the well flowing bottom-hole pressure (Pwf) as a function of production rate. It describes the flow in the reservoir. The Pwf is defined in the pressure range between the average reservoir pressure and atmospheric pressure.

Figure 10

Figure 11

Vertical Lift Performance Relationship (VLP) is name also Outflow, describes the bottom-hole pressure as a function of flow rate. The VLP depends on many factors including fluid PVT properties, well depth, tubing size, surface pressure, water cut and GOR. It describes the flow from the bottom-hole of the well to the wellhead. Both the Inflow Performance Relationship and the Vertical Lift Performance Relationship relate the wellbore flowing pressure to the surface production rate. While the IPR represents what the reservoir can deliver to the bottom hole, the VLP represents what the well can deliver to the surface. The intersection of the IPR with the VLP, called the operating point, yields the well deliverability, an expression of what a well will actually produce for a given operating condition as in Figure 12.

Figure 12

Choke Flow Model: the model represent an equipment used to regulate well production rate. Choke valve opening is regulated in such a way the opening is not too small to impede production and not too big causing sand, water accumulating at the well bore. No universal equation exists that can predict pressure drop across the Choke for different wells and fluid properties. Flow-through choke can be Sonic (critical) or Subsonic (subcritical). Sonic flow is the most common type and happens when fluid flow velocity reaches the speed of sound, hence upstream pressure is independent of pressure downstream the choke. Literatures are full of choke flow models that were designed for sonic and subsonic flow. Many empirical choke models are generally represented by the following: P_wh = CR^mQ/Sⁿ where P_wh is the upstream (wellhead) pressure (psia), Q is gross production rate (bbl/day), R is gas-liquid- ratio (Mcf/bbl), S is the choke size (in 1/64 of inch), C, m and n are empirical constants provided by each choke valve manufacturer.

Enthalpy Model: Application of energy conservation can also be used to predict the fluid temperature and used to correlate the flow rate in the wellbore as a function of depth versus temperature, as shown in Figure 13.

Figure 13

Autonomous calibration

As shown in Figure 14, Flux Simulator uses an optimizer that runs periodically and corrects the system based on measurements from the well. No reference flow rates are required to perform this step.

Figure 14

The combiner is an algorithm that aggregates estimations from different VFM models (be it either data-driven or physics-driven), and finds the optimal flow rate estimates along with an indication of confidence level. The combiner tracks the performance of different models using periodically updated and validated well-tests. The contribution of each model to the final estimate is dependent on its performance compared to historical well-tests, and the confidence decay factor which indicates the model relevance over time and concept drift. The general combiner workflow is shown in Figure 15.

Figure 15

Confidence decay factor λ: is calculated based on the time difference between the last estimator tuning and the current sample time. Decay coefficient δ is a constant selected based on the estimator behaviors and the well conditions. For example, a physics-driven estimator can have a small δ since it can have a wider operating envelope compared to data-driven estimators which was trained on a small window of the operating envelope. Wells that are rapidly changing should also have a large δ since the estimator’s performance tends to degrade rapidly over time due to the changing operating conditions and concept drift. λi=1−|Δt|δi:range[0,1] {\lambda _i} = 1 - \left| {\Delta t} \right|{\delta _i}:range\left[ {0,1} \right]

Accuracy contribution factor α_i: for estimator i is calculated from Mean Absolute Percent Error (MAPE) of the estimator and the last known reference point at time t – r where r is the time of last known reference data available. α_I is normalized by the sum of errors of all estimators such that ∑N=1Nαn=1 \sum\nolimits_{N = 1}^N {{\alpha _n} = 1} , where N is the number of estimators involved. MAPEi=|Yt−r−Ht−riYt−r| {MAPE_i} = \left| {{{{Y_{t - r}} - H_{t - r}^i} \over {{Y_{t - r}}}}} \right| acci=1−MAPEi∑n=1NMAPEn {acc_i} = 1 - {{{MAPE_i}} \over {\sum\nolimits_{n = 1}^N {{MAPE_n}} }} αi=acci∑n=1Naccn {\alpha _i} = {{{acc_i}} \over {\sum\nolimits_{n = 1}^N {{acc_n}} }}

Confidence Interval (CI): of the combined flow rate is calculated from the pair-wise sample standard deviation s_t. st=∑i=1N(Ht−Hti)2N−1 {s_t} = \sqrt {\sum\limits_{i = 1}^N {{{{{\left( {{H_t} - H_t^i} \right)}^2}} \over {N - 1}}} } CIt=H^t±t*stN C{I_t} = {\hat H_t} \pm {{t*{s_t}} \over {\sqrt N }} where Ĥ_t represents the outcome of the combiner and t is the student’s t-distribution score which is a parameter based on the confidence level and degrees of freedom. If there are enough samples, the normal distribution can be used instead of t-distribution.

Downsampling by f: the results are passed through a downsampler to produce estimates at the desired frequency f which should be slower than the estimator frequency to introduce a smoothing effect.

Figure 16 shows the detailed block diagram and data flow of the combiner. Only two estimators (1 and i) are shown for simplicity.

Figure 16

The combiner is used to improve the overall performance of the VFM over time, by combining different estimators (data-driven and physics-driven), taking into consideration the weaknesses of these estimators, and performance degradation over time. A total of 24 Hybrid VFMs have been tested in this study. Each of them takes a different set of input estimators as shown in Table 4 with the explanation for each combiner group is described in Table 5.

To evaluate the developed VFMs and confirm they will perform satisfactorily; a set of evaluation metric must be devised. Following the published standards such as API MPMS (PETRONAS, 2015; Mokhtari Jadid, 2017), the metrics listed in Figure 17 are used to evaluate VFM performance. However, the main indicator will be the mean absolute percent error.

Figure 17

In addition to quantitative performance measures, there are also visual quality plots that are recommended by the Norwegian Society for Oil and Gas Measurement (Norwegian Society for Oil and Gas Measurement NFOGM, 2005). The two visual quality plots that will be used here are:

Cumulative deviation plot: which will be used to indicate the percentage of test points that are below specified deviation criteria. The error percentage between actual and VFM estimates is calculated for each test sample. Then, the number of samples with error percentage below a specified deviation percentage (5%, 10%, 15%, etc.) are counted. The counts are then divided by the total number of test samples and plotted against deviation percentage.

In Tables 6 and 7, the performance of each data-driven VFM without combiner and with combiner are shown. MAPE of Q_water is not included since the water flow rate has zero values which would result in undefined MAPE. All models achieved a satisfactory performance. We can observe that data-driven VFM with combiner does not introduce much improvement over the individual estimators. Only when all the individual estimators have high errors will the combiner result have overall lower error than individual estimators.

In this section the overall VFM performance (data-driven VFM, physics-based from Flux Simulator and VFM with combiner) will be presented. In Tables 8 and 9, we can see the MAPE and flow rate deviation performance of each VFM type. DD-VFM is using the full-type estimator in this comparison. The combiner (now called Hydrid VFM) combines all three DD-VFM types (full, surface and subsurface) along with TFVFM. Full+TF Hybrid-VFM is combining the full-type DD-VFM with TF-VFM. Surface+TF Hybrid-VFM is combining the surface-type DD-VFM with TF-VFM (Table 9).

All models achieved a satisfactory performance i.e., deviation less than 20%. We can observe that, in general, Hybrid-VFMs achieved better results compared to independent VFMs.

Figures 18 and 19 show the cumulative percentage deviation for each VFM for both wells 101 and 102. Q_water is not shown here since the water flow rate has zero values and cannot be represented in MAPE. The performance of the best model (combiner) can keep over 90% of the samples within a deviation of 20%. Most of the deviations above 20% are justified and attributed to physical meter abnormalities, well-test abnormalities, or process upsets such as downstream process changes.

Figure 18

Figure 19

Figures 20 and 21 show the percent deviation of estimations from the well-test test points. We can observe the following:

Performance of individual models is satisfactory,

Figure 20

Figure 21

In this section, we show a visual trend of well-test flow rates over the pilot period. We can observe from Figures 22–24 that DD-VFMs try to estimate the confidence interval but the confidence is very poor. TF-VFMs don’t provide any confidence indicators. Hybrid-VFMs through the combiner provide both better flow rate estimations and better confidence interval indicator. Notice here that the confidence band increases when the base estimators disagree but otherwise will decrease.

Figure 22

Figure 23

Figure 24

In summary the following observations can be made by comparing the standalone VFM versus the combiner (Hybrid VFM):

Combiner VFM indeed produces good confidence interval indication,