A METHOD OF MODELLING A PRODUCTION WELL

Abstract

A method of modelling one of a plurality of hydrocarbon production wells, wherein each production well is associated with at least one control point in a flow path associated therewith. The method comprises: (i) generating a first model capable of describing for any one of the first plurality of production wells a relationship between flow parameters, well parameters and/or an associated status of the at least one control point, wherein the first model is parameterised by a set of first parameters representative of properties common to all of the first plurality of production wells. The model can be applied to estimate well parameters, flow parameters and/or the status of control points. In addition, the resultant models can be used to optimise production of the production well.

Claims

1. A method of modelling one of a first plurality of hydrocarbon production wells, each production well being associated with at least one control point in a flow path associated therewith, the method comprising: (i) generating a first model capable of describing for any one of the first plurality of production wells a relationship between flow parameters, well parameters and/or an associated status of the at least one control point, wherein the first model is parameterised by a set of first parameters representative of properties common to all of the first plurality production wells.

2. A method according to claim 1, further comprising: (ii) generating at least one further first model capable of describing for any one of a further, different plurality of production wells a relationship between flow parameters, well parameters, and/or an associated status of the at least one control point, wherein the at least one further first model is parameterised by a further set of first parameters representative of properties common to all of the further plurality of production wells; and (iii) combining the first model with the at least one further first model to form a combined model capable of describing for any one of the wells in the first plurality and the at least one further plurality of production wells a relationship between flow parameters, well parameters and/or associated status of the at least one control point to which it relates.

3. A method as claimed in claim 2, further comprising: generating a plurality of further first models, each first model capable of describing for a respective further different plurality of production wells a relationship between flow parameters, well parameters, and/or an associated status of the at least one control point, wherein each further first model is parametrised by a set of first parameters representative of properties common to the respective further plurality of production wells; and combining the first model with the plurality of further first models to form a combined model capable of describing for any one of the wells in both the first plurality and each of the at least one further pluralities of production wells a relationship between flow parameters, well parameters and/or associated status of the at least one control point to which it relates.

4. A method as claimed in claim 2 or 3, wherein at least some of the production wells within the, or each, further plurality of productions wells are also in the first plurality of production wells.

5. A method as claimed in claim 4, wherein all of the productions wells within the, or each, further plurality of production wells are in the first plurality of production wells, and wherein the first plurality of production wells additionally includes further production wells.

6. A method as claimed in claim 3 or 4, wherein at least some of the production wells within the, or each, further plurality of productions wells are not included in the first plurality of production wells.

7. A method as claimed in any preceding claim, comprising: generating a second model that is capable of describing a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for only one production well, wherein the second model is parameterised by a set of second parameters that are representative of properties that are specific to the production well to which it relates; and combining the second model with the first model, and optionally the, or each, further first model to form a combined model that is capable of describing a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for only the one production well.

8. A method as claimed in claim 7, wherein the one well to which the second model relates is comprised within the first plurality of production wells and/or the, or each, further plurality of production wells.

9. A method as claimed in claim 7, wherein the one well to which the second model relates is not comprised within the first plurality of production wells and/or the, or each, further plurality of production wells.

10. A method as claimed in any of claims 7 to 9, comprising: generating a plurality of second models, each second model capable of describing a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for a respective production well, each second model being parameterised by a set of second parameters that are representative of properties that are specific to the production well to which it relates; and combining each second model with the first model, and optionally the, or each, further first model to form combined models that are each capable of describing a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for the respective production well to which it relates.

11. A method as claimed in any preceding claim, comprising generating a flow composition model that is capable of describing a relationship between the flow composition of the fluid produced from any one of a second plurality of production wells and the flow parameters, well parameters, an associated status of the at least one control point, and/or time, wherein the flow composition model is parameterised by a first set of flow composition parameters that are representative of the flow composition common to all of the second plurality production wells; and combining the flow composition model with the first model, and optionally each first model and/or the, or each, second model to form a combined model that is capable of describing a relationship between flow parameters, wells parameters, an associated status of the a least one control point, and/or time, for any one of the wells within the second plurality and the first plurality of production wells, and optionally the, or each, further plurality of production wells and/or the, or each, well upon which the second model(s) is/are based.

12. A method as claimed in claim 11, wherein at least some of the production wells within the second plurality of production wells are comprised within the first plurality of production wells, the further plurality of production wells, and/or each further plurality of production wells.

13. A method as claimed in claim 12, wherein all of the productions wells within the second plurality of production wells are comprised within the first plurality of production wells, the further plurality of production wells and/or each further plurality of production wells.

14. A method as claimed in claim 13, wherein the first plurality of production wells, the further plurality of production wells and/or each further plurality of production wells additionally include(s) further production wells.

15. A method as claimed in claim 11 or 12, wherein at least some of the production wells within the second plurality of production wells are not included in the first plurality of production wells, the and/or each further plurality of production wells.

16. A method as claimed in any of claims 11 to 15, comprising: generating a plurality of flow composition models, each flow composition model capable of describing a relationship between the flow composition of the fluid produced from any one of a respective second plurality of production wells and the flow parameters, well parameters, an associated status of the at least one control point, and/or time, wherein each flow composition model is parameterised by a first set of flow composition parameters that are representative of the flow composition common to all of the respective second plurality production wells to which it relates; combining each flow composition model with the first model, and optionally the further first model, or each further first model and/or the, or each, second model to form a combined model that is capable of describing a relationship between flow parameters, wells parameters, an associated status of the a least one control point, and/or time, for any one of the wells within any one of the second plurality of production wells and the first plurality of production wells, and optionally the, or each, further plurality of production wells and/or the, or each, well upon which the second model(s) is/are based.

17. A method as claimed in any preceding claim, comprising: generating a well specific flow composition model that is capable of describing a relationship between the flow composition of the fluid produced from only one production well and flow parameters, well parameters, an associated status of the at least one control point, and/or time, wherein the well specific flow composition model is parameterised by a second set of flow composition parameters that are representative of the flow composition specific to the production well to which it relates; combining the well specific flow composition model with the first model and optionally the, or each, further first model, the, or each, second model, and/or the, or each, well composition model to form a combined model that is capable of describing a relationship between flow parameters, well parameters, an associated status of the at least one control point and/or time for only the one production well.

18. A method as claimed in claim 17, wherein the one well to which the well specific model relates is comprised within the first plurality of production wells, the, or each, further plurality of production wells, and/or the, or each, second plurality of production wells.

19. A method as claimed in claim 17, wherein the one well to which the well specific model relates is not comprised within the first plurality of production wells, the, or each, further plurality of production wells, and/or the, or each, second plurality of production wells.

20. A method as claimed in claim 17, 18 or 19, wherein the one well to which the well specific model relates is the same as the one well to which the, or at least one of the second model(s) relate(s).

21. A method as claimed in any of claims 17 to 20, comprising: generating a plurality of well specific flow composition models, each well specific flow composition model capable of describing a relationship between the flow composition of the fluid produced from only one, respective well and flow parameters, well parameters, an associated status of the at least one control point, and/or time, each well specific model being parameterised by a second set of flow composition parameters that are representative of the flow composition that is specific to the only one, respective production well to which it relates; combining each well specific flow composition model with the first model, and optionally the, or each further first model, the, or each, second model and/or the, or each, flow composition model to form combined models that are each capable of describing a relationship between flow parameters, wells parameters, an associated status of the at least one control point, and/or time, for each respective well.

22. A method as claimed in any preceding claim, comprising: generating a prediction model, the prediction model capable of predicting for any one of a third plurality of production wells a change in a flow parameter, well parameter and/or a status of the at least one control point based on a hypothetical change in the status of the at least one control point, a hypothetical change in a well parameter and/or a hypothetical change in a flow parameter, wherein the prediction model is parameterised by a set of prediction parameters that are representative of properties that are common to the third plurality of production wells; and combining the prediction model with the first model, and optionally the, or each, further first model, the, or each, second model, the, or each, flow composition model, and/or the, or each, well specific flow composition model to form a combined model that is capable of predicting a flow parameter, a well parameter and/or the status of the at least one control point resulting from a hypothetical change in the status of the at least one control point, the hypothetical change in a well parameter and/or the hypothetical change in a flow parameter for any one of the wells within the third plurality of production wells and the first plurality of production wells, and optionally the, or each, further plurality of production wells, the, or each, well upon which the second model(s) is/are based, the, or each, second plurality of production wells and/or the, or each, well upon which the well specific composition model(s) is/are based.

23. A method as claimed in claim 22, wherein at least some of the production wells within the third plurality of production wells are comprised within the first plurality of production wells, the further plurality of production wells, each further plurality of production wells, the second plurality of production wells, and/or each second plurality of production wells.

24. A method as claimed in claim 23, wherein all of the productions wells within the third plurality of production wells are comprised within the first plurality of production wells, the further plurality of production wells, each further plurality of production wells, the second plurality of production wells and/or each second plurality of production wells.

25. A method as claimed in claim 24, wherein the first plurality of production wells, the further plurality of production wells, each further plurality of production wells, the second plurality of production wells, and/or each second plurality of production wells additionally include(s) further production wells.

26. A method as claimed in claim 22 or 23, wherein at least some of the production wells within the third plurality of production wells are not included in the first plurality of production wells, the further plurality of production wells, each further plurality of production wells, the and/or each second plurality of production wells.

27. A method as claimed in any of claims 22 to 26, comprising: generating a plurality of prediction models, each prediction model capable of predicting for any one of a respective third plurality of production wells a change in a flow parameter, a well parameter and/or the status of at least one control point based on a hypothetical change in the status of the at least one control point, a hypothetical change in a well parameter and/or a hypothetical change in a flow parameter, wherein each prediction model is parameterised by a set of prediction parameters that are representative of properties that are common to each respective third plurality of production wells; combining each prediction model with the first model, and optionally the, or each, further first model, the, or each, second model, the, or each, flow composition model, and/or the, or each, well specific flow composition model to form a combined model that is capable of predicting a flow parameter, a well parameter and/or a status of the at least one control point resulting from a hypothetical change in the status of the at least one control point, a hypothetical change in a well parameter and/or the hypothetical change in a flow parameter for any one of the wells within any one of the third plurality of production wells and the first plurality of production wells, and optionally the, or each, further plurality of production wells, the, or each, well upon which the second model(s) is/are based, the, or each, second plurality of production wells and/or the, or each, well upon which the well specific composition model(s) is/are based.

28. A method as claimed in any preceding claim, comprising: generating a well-specific prediction model, the well-specific prediction model capable of predicting for only one production well a change in a flow parameter, a well parameter and/or the status of the at least one control point based on a hypothetical change in the status of at the least one control point, a hypothetical change in a well parameter and/or a hypothetical change in a flow parameter, wherein the well-specific prediction model is parameterised by a set of well-specific prediction parameters that are representative of properties specific to that production well; combining the well-specific prediction model with the first model, and optionally the, or each, further first model, the, or each, second model, the, or each, flow composition model, the, or each, well specific flow composition model, and/or, the, or each, prediction model to form combined models that are each capable of predicting a flow parameter, a well parameter and/or the status of the at least one control point resulting from a hypothetical change in the status of the at least one control point, the hypothetical change in a well parameter and/or the hypothetical change in a flow parameter for only the one production well.

29. A method as claimed in claim 28, wherein the one well to which the well-specific prediction model relates is comprised within the first plurality of production wells, the, or each, further plurality of production wells, the, or each, second plurality of production wells, and/or the, or each, third plurality of production wells.

30. A method as claimed in claim 28, wherein the one well to which the well-specific prediction model relates is not comprised within the first plurality of production wells, the, or each, further plurality of production wells, the, or each, second plurality of production wells, and/or the, or each, third plurality of production wells.

31. A method as claimed in any preceding claim, wherein the one well to which the well-specific prediction model relates is the same as the one well to which the, or at least one of the second model(s) relate(s) and/or the same as the one well to which the, or at least one of the well-specific flow composition model(s) relate(s).

32. A method as claimed in any of claims claim 28 to 31, comprising: generating a plurality of well-specific prediction models, each well-specific prediction model capable of predicting for only one, respective production well a change in a flow parameter, a well parameter and/or the status of the least one control point based on a hypothetical change in the status of at the least one control point, a hypothetical change in a well parameter and/or a hypothetical change in a flow parameter, wherein each well-specific prediction model is parameterised by a set of well-specific prediction parameters that are representative of properties that are specific to the production well to which it relates; combining each well-specific production model with the first model, and optionally the, or each, further first model, the, or each, second model, the, or each, flow composition model, the, or each, well specific flow composition model, and/or, the, or each, prediction model to form combined models that are each capable of predicting a flow parameter, a well parameter and/or the status of the at least one control point resulting from the hypothetical change in the status of the at least one control point, the hypothetical change in a well parameter and/or the hypothetical change in a flow parameter for each respective production well.

33. A method of predicting a flow parameter, well parameter and/or the status of the at least one control point for at least one production well, comprising: modelling in accordance with any of claims 22-32; inputting a hypothetical change in the status of the at least one control point, a hypothetical change in a well parameter and/or a hypothetical change in a flow parameter associated with the at least one production well into the (respective) combined model and thereby obtaining a predicted flow parameter, well parameter and/or status of the at least one control point for the at least one production well.

34. A method of optimising hydrocarbon production from at least one hydrocarbon production well, comprising: predicting a flow parameter, a well parameter and/or the status of at the least one control point for at least one hydrocarbon production well in accordance with claim 33; repeating the prediction of claim 33 based on a different hypothetical change to the status of the at least one control point, a different hypothetical change to the well parameter and/or a different hypothetical change to the flow parameter; and determining an optimised status of the at least one control point, the flow parameter and/or the well parameter and thereby optimised hydrocarbon production.

35. A method as claimed in claim 34, wherein the prediction of claim 32 is repeated a plurality of times based on a plurality of different hypothetical changes to the status of the at least one control point, different hypothetical change to the flow parameter and/or different hypothetical changes to the well parameter.

36. A method as claimed in claim 34 or 35, wherein an optimisation algorithm is used to determine the status of the at least one control point, the well parameter and/or the flow parameter that results in an optimised flow parameter, well parameter and/or status of the at least one control point and thereby optimised hydrocarbon production.

37. A method as claimed in any of claims 33 to 36 used in a ‘what-if’ study.

38. A method of estimating a flow parameter, a well parameter and/or the status of at least one control point for at least one hydrocarbon production well, the method comprising: modelling in accordance with any of claims 1 to 20; and determining an estimated flow parameter, well parameter and/or status of at least one control point for the at least one hydrocarbon production well by inputting to the first model or the (respective) combined model a state of the at least one production well, the state comprising a flow parameter, a well parameter and/or an associated status of the at least one control point of the at least one production well.

39. A method as claimed in claim 38, wherein the state of the at least one of the plurality of production wells is a historical state, a real-time state or a future state.

40. A method as claimed in any of claims 33 to 39, wherein the estimated/predicted flow parameter, well parameter and/or the estimated status of the at least one control point is a well health indicator, a water cut (WC) of the produced hydrocarbon fluid, a gas to oil ratio (GOR) of the produced fluid, a liquid loading risk indicator, a total produced fluid flow rate (by volume, mass or flow speed/velocity), a gas flow rate, an oil flow rate, a water flow rate, a liquid flow rate, a hydrocarbon flow rate, a carbon dioxide fluid flow rate, a hydrogen sulphide fluid flow rate, a multiphase fluid flow rate, a slug severity, an oil fraction, a gas fraction, a water fraction, a carbon dioxide fraction, a multiphase fluid fraction, a hydrogen sulphide fraction, a ratio of gas to liquid, density, viscosity, pH, productivity index (PI), BHP and wellhead pressures, rates after topside separation, separator pressure, other line pressures, flow velocities or a sand production.

41. A method as claimed in claim 40, wherein estimating/predicting a gas flow rate, an oil flow rate, a water flow rate, carbon dioxide flow rate or a hydrogen sulphide flow rate comprises modelling using the, or each, flow composition model, and/or the, or each, well specific flow composition model.

42. A method as claimed in any preceding claim, wherein one, or more, of the model(s) form part of a statistical approach such that a flow parameter, a well parameter and/or a status of the at least one control point output by the one, or more, model(s) is output as a probability distribution with an associated degree of uncertainty.

43. A method as claimed in any preceding claim, wherein the at least one control point comprises at least one of: a flow control valve; a pump; a compressor; a gas lift injector; an expansion devices; a choke control valve; gas lift valve settings or rates on wells or riser pipelines; ESP (Electric submersible pump) settings, effect, speed or pressure lift; down hole branch valve settings, down hole inflow control valve settings; or topside and subsea control settings on one or more: separators, compressors, pumps, scrubbers, condensers/coolers, heaters, stripper columns, mixers, splitters, chillers.

44. A method as claimed in any preceding claim, wherein the flow parameters include one or more of pressures; flow rate, a gas flow rate, an oil flow rate, a water flow rate a liquid flow rate, a hydrocarbon flow rate, a flow rated that is the sum of one or more of any of the previous rates (by volume, mass or flow speed); an oil fraction, a gas fraction, a carbon dioxide fraction, a multiphase fluid fraction, a hydrogen sulphide fraction, a multiphase fluid fraction, temperatures, a ratio of gas to liquid, densities, viscosities, molar weights, pH, water cut (WC), productivity index (PI), Gas Oil Ratio (GOR), BHP and wellhead pressures, rates after topside separation, separator pressure, other line pressures, flow velocities or sand production.

45. A method as claimed in any preceding claim, wherein the well parameters include one or more of: depth, length, number and type of joints, inclination, cross-sectional area (e.g. diameter or radius) within/of a production well, wellbore, well branch, pipe, pipeline or sections thereof; choke valve Cv-curve; choke valve discharge hole cross-sectional area; heat transfer coefficient (U-value); coefficients of friction; material types; isolation types; skin factors; and external temperature profiles.

46. A method as claimed in any preceding claim, comprising the further steps of: (ii) training the first, or combined, model on data relating to flow parameters, well parameters and/or an associated status of the at least one control point from at least two production wells; (iii) obtaining an updated set of first parameters from the training of the first model, wherein the updated set of first parameters more accurately parameterise the properties common to all of the first plurality production wells; and (iv) updating the first, or combined, model based on the updated set of first parameters, wherein the updated first model allows for a more accurate modelling of any one of the plurality of production wells.

47. A computer system for modelling one of a plurality of production wells, for estimating a flow parameter, a well parameter and/or the status of at least one control point for at least one hydrocarbon production well, and/or for predicting a flow parameter, a well parameter and/or the status of at least one control point for at least one hydrocarbon production well, wherein the computer system is configured to perform the method of any preceding claim.

48. A computer program product comprising instructions for execution on a computer system arranged to receive data relating to flow parameters, well parameters and/or an associated status of the at least one control point from the plurality of production wells; wherein the instructions, when executed, will configure the computer system to carry out a method as claimed in any of claims 1 to 46.

Description

[0186] Certain embodiments of the present invention will now be described, by way of example, and with reference to the accompanying drawings, in which:

[0187] FIG. 1 is a schematic of a generic architecture for modelling flow rate for one of a plurality of production wells in accordance with an embodiment of the invention;

[0188] FIG. 2 is a schematic of an architecture for modelling choke flow in accordance with an embodiment of the invention;

[0189] FIG. 3 is a schematic of an architecture for wellbore modelling in accordance with an embodiment of the invention; and

[0190] FIG. 4 is a schematic of an alternative generic architecture for modelling in accordance with an embodiment of the invention.

[0191] FIG. 1 shows a transfer learning architecture having a first model 1 comprised of a neural network and a second model structure 3 comprising of a plurality of second models 5. In this embodiment, each second model 5 consists of a set of second parameters β in vector form. As such, the second model structure 3 can be considered as a second model matrix

[0192] The first model 1 is capable of modelling the fluid flow rate from any one of a plurality of hydrocarbon production wells, and comprises therein a set 7 of first parameters θ. The first model 1 is generated initially from a desired specification, which includes the variables that are to be input to the model, the desired output variables (in the present case, fluid flow rate), the model architecture, and the model/number of model parameters. Once the first model 1 has been generated in accordance with the desired specification, the set 7 of first parameters θ are stochastically generated and input to the first model 1 to initialise the first model 1. The set 7 of first parameters θ within the first model are representative of the physical properties and characteristics common to all of the plurality production wells and allow for the model to account for such behaviours when modelling a particular production well.

[0193] Each second model 5 represents one of the plurality of production wells and is capable of describing a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for that production well. As noted above, in this embodiment, each second model 5 consists of a set of second parameters β. The set of second parameters β are specific to the related production well within the plurality and are representative of properties that are specific to that production well. After initial generation of each of the second models 5, the second parameters β are stochastically generated to initialise each of the second models 5.

[0194] The second model structure 3 is generated from the plurality of second models 5. This comprises a concatenation of each of the plurality of second models 5.

[0195] After initial generation of the first model 1 and the second model structure 3, the step of training the first model 1 is commenced. The aim of the training is to update the first parameters θ and the second parameters β within the first model 1 and second model structure 3 respectively such that the first parameters θ more accurately parameterise those properties common to all of the plurality of production wells and the second parameters β more accurately parameterise the properties specific to each of the plurality of the production wells. As a result, the first model 1 will more accurately describe for any one of the plurality of production wells a relationship between flow parameters, well parameters and/or an associated status of the at least one control point as compared to the originally initialised first model 1 comprising stochastically generated first parameters θ. Similarly, as a result of the training, each second model 5 will more accurately describe a relationship between flow parameters, well parameters and/or an associated status of the at least one control point for its production well as compared to each of the respective initialised second models comprising the stochastically assigned parameters.

[0196] The training is achieved by inputting data 9 relating to flow parameters, well parameters and/or an associated status of at least one control point associated with each of the plurality of production wells into the first model 1. In this embodiment, the data 9 input, and which underpins the training procedure, is data 9 from each (i.e. all) of the plurality of production wells.

[0197] In this embodiment, the training of the first model 1 initially comprises determining a number of training steps that are to form the basis of the training procedure before termination (though in other embodiments an adaptive training regime may be implemented, e.g. wherein a termination condition determines the number of training steps rather than a pre-determined number of steps). Once the number of training steps is determined, training commences by stochastically selecting a batch of data from the total data 9 available relating to the plurality of production wells. The batch of data may contain data from a single well within the plurality, from multiple wells, or may contain topside data representative of multiple wells. The exact nature of each batch of data will be determined prior to training of the first model 1 is commenced and will be dependent on the specific iterative training regime to be implemented.

[0198] After selection of a batch of data, a signal 11 is created for the batch of data. The signal 11 is specific to only those of the plurality of production wells which the batch of data is from. The effect of the signal 11 is such that upon input of the signal 11 into the second model structure 3 only those second models 5 relating to those wells from which the batch of data has been collected (i.e. only those second parameters β that relate to the wells from which the batch of data has been collected) remain within the second model structure 3. As such, after input of the well specific signal 11, the second model structure 3 is specifically tailored for modelling only those of the plurality of production wells to which the signal 11 relates.

[0199] In the present embodiment, the signal 11 input into the second model structure 3 is in the form of a binary vector. As such, the operation of inputting the signal 11 into the second model structure 3 involves a simple vector-matrix multiplication, wherein the result is a contracted, tailored second model structure 3 containing only those second models 5 relating to the second models from which the data in the training batch has been derived.

[0200] Once the tailored second model structure 3 is produced such that only those second parameters β relating to the production wells which the batch of training data is from, the second model structure 3 is input into the first model 1. In this particular embodiment, this is achieved by producing a plurality of copies of the first model 1 equal to the number of second models 5 in the second model structure 3. Subsequently, each second model 5 from the tailored second model structure is fed into its own respective copy of the first model 1 to form a combined model. The resultant combined models will thus be tailored to modelling the specific well to which the input second model 5 relates.

[0201] At this stage, the data 9 from the selected batch is run through the (copies of) the combined model. Only the data 9 relating specifically to the production well which the (or each copy of the) tailored combined model relates is fed into the (or each copy of the) combined model.

[0202] The data 9 input to each of the combined models, which may also be considered as tailored first models 1, results in an output of an estimated flow rate for the specific production well which the tailored first model relates. This estimated flow rate is then compared to a flow rate 13 actually measured for that production well at a time when the input data had been collected. This comparison allows for the computation of a batch loss, which can be considered as an error of each tailored first model 1 on the data in the batch (i.e. a discrepancy between the estimated and measured flow rate 13). From this batch loss, gradients of the batch loss with respect to the first θ and second β model parameters can be calculated. These gradients are then used to update the first θ and second β model parameters in order to create a first model 1 and second model structure 3 having a decreased batch loss. This update of the first θ and second β model parameters to decrease batch loss occurs in parallel across each copy of the first model 1 required for training in that step on that batch of data. This training step is then terminated, and the first model 1 and the second model structure 3 are updated based on the resultant updated first θ and second β model parameters.

[0203] Subsequent to the termination of this iterative training step, a new batch from the data 9 is stochastically selected and the resultant training stages as set out above are repeated to obtain further updated first θ and second β model parameters. This is iterated for data from each of the plurality of production wells until the predetermined number of training steps has been completed.

[0204] Further specifics of the training of the model are set out in equation (4) below:

(θ*,β*.sub.1, . . . ,β*.sub.M)=argmin.sub.(θ,β.sub.1.sub., . . . ,β.sub.M.sub.)=Σ.sub.j=1.sup.MΣ.sub.i=1.sup.N.sup.j(y.sub.ij−h.sub.θ,β.sub.j(u.sub.ij,x.sub.ij)).sup.2  (4)

[0205] In equation (4) u.sub.ij, x.sub.ij represents the batch of data input in each iterative step of the method. Here each batch is of size one (i.e. consists of a single data point i for well j), and includes both control variables u.sub.ij and measurements of the state x.sub.ij. h.sub.θ,β.sub.j represents the tailored first model 1 (i.e. the combined model), which has the second model structure 3 relating to the production wells from which the batch of data has been derived incorporated therein. (θ*,β*.sub.1, . . . ,β*.sub.M) represents the updated first parameters θ and second parameters β achieved from the training of the well. M represents the number of production wells within the plurality, j represents the index of each well and N.sub.j represent the data points for each well. The model is trained by solving equation (4) using a stochastic gradient descent method (SGD) as outlined in broad terms above.

[0206] After completion of the training, an updated first model 1 and second model structure 3 are arrived at, with updated first θ and second β model parameters resulting from the iterative training regime. These updated parameters provide both the first model 1 and the second model structure 5 with an improved accuracy in modelling the well-generic behaviours and well-specific behaviours, respectively.

[0207] The resultant trained first model 1 and second model structure 5 can then be used to estimate the flow rate for any of the plurality of the production wells. As such, estimations based on a state comprising flow parameters, well parameters and/or an associated status of the at least one control point of the one of the plurality of production wells may be made for any of the plurality of production wells. This would involve the input of such a state into the trained model 1 with the additional input of those second parameters β (i.e. that second model 5) relating to the production well for which the estimation is being made. The relevant second parameters β can again be selected out from the second model structure 3 via input of an appropriate well specific signal into the second model structure 3. Equation (5) sets out an estimation made using the trained first model 1 and second model structure 3.

=h.sub.θ*,β*.sub.j(u.sub.ij,x.sub.ij)  (5)

[0208] Here, u.sub.ij, x.sub.ij pertains to the state of the production well for which the estimation is being carried out for, h.sub.θ*,β*.sub.j represents the trained first model 1 (incorporating the updated first parameters θ*) having the relevant trained second model structure 3 (incorporation the updated second parameters β*.sub.j) input therein so as to form a combined model, and represents the estimated flow rate of the production well.

[0209] The fact that the training in this embodiment is based on data 9 from each of the wells within the plurality of production wells ensures that, in particular, the first model 1 has improved accountability of, for instance, the reservoir effect. It also helps to ensure that the first model 1 is not solely influenced on the limited data from a single well. As such any estimations made through use of the trained first model 1 and second model structure 5 can, by virtue of the training, be ensured to have improved accuracy with a reduced likelihood of error resulting from a poor accountability of, for instance, the reservoir effect and/or a limited training data set.

[0210] Furthermore, not only can the estimations made account for those properties and behaviours that are common across the plurality of production wells without being heavily misguided by ill account of the reservoir effect and/or a limited training data set by virtue of the first model 1, by virtue of the refined second parameters β within the second model structure 3 the estimations made using the combination of the trained first model 1 and second model structure 3 can accurately account for those properties and behaviours specific to each of the plurality of production wells.

[0211] FIG. 2 is a schematic of a transfer learning architecture specifically designed for modelling choke flow through choke valves within the flow paths associated with each of the plurality of production wells. The FIG. 2 architecture can be seen to be a more specific example of the architecture underlying the FIG. 1 embodiment, and thus shares many of the same corresponding features. For instance, the FIG. 2 architecture comprises a first model 1 in the form of a neural network and a second model structure 3 comprising of a plurality of second models 5.

[0212] As in the above embodiment, the second model structure 3 initially incorporates a second model 5 for each of the plurality of production wells. Each second model 5 comprises a set of second parameters β representative of behaviours and properties specific to each of the plurality of production wells. Then, upon input of a well specific signal 11 relating to those production wells from which the training data has been obtained, a tailored second model structure 3 comprising only those second models 5 relating to those production wells from which the training data has been obtained is produced. This is the second model structure 3 shown in FIG. 2, with the step of inputting the well specific signal 11 to contract the second model structure 3 down into its tailored form as described above not being shown in this Figure.

[0213] As is also the case for the FIG. 1 embodiment, the first model 1 of the FIG. 2 embodiment comprises a set of first parameters θ representative of behaviours and properties common to each of the plurality of production wells.

[0214] In this embodiment, the second model structure 3 maps choke position to “choke conductivity” (which can be thought of as the resistance to flow through each of the choke valves). In view of this, the second model structure 3 of the FIG. 2 embodiment differs from that of the FIG. 1 embodiment in that the second models 5 comprise more than just the second model parameters β; they additionally comprise an element allowing for the input of a position 21 of a choke valve such that resistance to flow as compared to the position 21 of the choke valve can be mapped by each of the second models 5. As such, the second model structure 3 of the FIG. 2 embodiment allows for a simpler interpretation of each of the second models 5, the second parameters β and its output.

[0215] The type and sizing of the choke valve may differ from well to well, and it is therefore desired to have a well-specific model 5 that maps choke position 21 to choke conductivity for each of the plurality of production well.

[0216] The training and subsequent estimation carried out using the model architecture of FIG. 2 largely corresponds to the training and the estimation described above in relation to the FIG. 1 embodiment, and as such it will not be described again here in detail. Where the training/estimation of the FIG. 2 embodiment differs however is that, in addition to the well specific signal 11, the choke position 21 is input into the second model structure 3 prior to each iterative training step and/or estimation. From said input, a mapping of the choke position to the choke conductivity 23 is output from the second model structure 3, and it is this second model output 23 that is input into the first model 1, along with data 9, prior to each iterative training step and/or an estimation of a well characteristic 13 using the second model architecture.

[0217] The model architecture of the FIG. 2 embodiment can account for both the behaviours and properties that are common to each of the plurality of production wells by virtue of the first model 1, and can additionally account for the choke conductivity, which is a behaviour/property that is specific to each of the plurality of production well, by virtue of the second model structure 3.

[0218] FIG. 3 is a schematic of a further transfer learning architecture. The FIG. 3 transfer learning architecture is specifically designed for wellbore modelling. The FIG. 3 architecture can be seen to be a more specific example of the architecture underlying the FIG. 1 embodiment, and thus shares many of the same corresponding features. For instance, the FIG. 2 architecture comprises a first model 1 in the form of a neural network and a second model structure 3 comprising of a plurality of second models 5.

[0219] As in the above embodiment, the second model structure 3 initially incorporates a second model 5 for each of the plurality of production wells. Each second model 5 comprises a set of second parameters β representative of behaviours and properties specific to each of the plurality of production wells. Then, upon input of a well specific signal 11 relating to those production wells from which the training data has been obtained, a tailored second model structure 3 comprising only those second models 5 relating to those production wells from which the training data has been obtained is produced. This is the second model structure 3 shown in FIG. 3, with the step of inputting the well specific signal 11 to contract the second model structure 3 down into its tailored form is thus not being shown in this Figure.

[0220] As is also the case for the FIG. 1 embodiment, the first model 1 comprises a set of first parameters θ representative of behaviours and properties common to each of the plurality of production wells.

[0221] In the embodiment of FIG. 3, the second model structure 3 merely consists of the second model parameters β, which help to capture the unique relationship for each well bore between the total flow rate and the data 9 relating to flow parameters, well parameters and/or an associated status of the at least one control point from the production well associated with that wellbore. That is, the second model parameters β capture those properties unique to each well bore, and which cannot be generalised across all wells within the first parameters θ.

[0222] The training and subsequent estimation carried out using the model architecture of FIG. 3 largely corresponds to the training and the estimation described above in relation to the FIG. 1 embodiment, and as such it will not be described again here in detail.

[0223] The model architecture of the FIG. 3 embodiment can account for both the behaviours and properties that are common to each of the plurality of production wells by virtue of the first model 1, and can additionally account for those that are a unique result of the well bore to which each production well is connected by virtue of the second model structure 3.

[0224] FIG. 4 shows an alternative generic architecture for modelling in accordance with alternative embodiments. The architecture of FIG. 4 shares many similarities with that represented in FIG. 1. In particular, the architecture of FIG. 4 comprises a first model 1 comprised of a neural network and a second model structure 3 comprising of a plurality of second models 5. As for FIG. 1, each second model 5 consists of a set of second parameters β in vector form. As such, the second model structure 3 can be considered as a second model matrix. The first model 1 and second model structure 3 of FIG. 4 are directly comparable to the corresponding models discussed above in connection with FIG. 1, and can be trained and used as the basis for estimation in a manner correspondent to that which was described above in connection the architecture of FIG. 1.

[0225] Where the architecture of FIG. 4 differs to that described above in connection with FIG. 1 however, is that rather than incorporating each second model 5 into a respective copy of the first model 1 prior to input of the data 9 (whether that be during training or estimation as described above in connection with FIG. 1), the relevant data 9 is input into the first model 1 prior to input of the second model 5 into the respective first model 1. This is an alternative approach to the modelling architecture to that discussed above, and is a common approach for neural network based modelling. That is, in the resultant neural network forming the combined model (i.e. the tailored first model 1) in the context of the FIG. 4 embodiment, the shared (hard) parameters form part of the first layers of the architecture, and the specific parameters form part of the last layer (or layers) of the neural network.

[0226] The above described embodiments set out in detail the aspects of the invention relating to the first model, the second model and their combination with one another. It also sets out in detail how the first and second models might be trained, and how an estimation might be achieved using the combined model resulting from the first and second model. This description therefore gives an appreciation of specific embodiments of the invention, and it will be apparent to the skilled how these aspects of the invention that have been described in detail can map on to those that do not form part of the specific embodiments herein.

[0227] For instance, from the discussion above in connection with the first model, and how it is generated, trained and used as the basis of estimation, the skilled person will gain an understanding of how the, or each, further first model, the, or each, prediction model, and the, or each, flow composition model may be generated, trained and used as the basis of estimation and/or prediction given the correspondence between the structure and architecture of these models.

[0228] Similarly, from the discussion above in connection with the second model, and how it is generated, trained and used as the basis of estimation, the skilled person will gain an understanding of how the, or the, or each, well specific prediction model, and the, or each, well specific flow composition model may be generated, trained and used as the basis of estimation and/or prediction given the correspondence between the structure and architecture of these models.

[0229] The combination of the first and second models as described above also provides an understanding of how any of the models of the invention may be combined with one another as part of a combined model for modelling and later use in estimation, prediction and optimisation.