An improved computer-implemented method for generating a three dimensional geological representation of a subsurface reservoir

Abstract

The method (100) generates a 3D geological representation (R) of a subsurface reservoir, by, during a sampling phase : - sampling (110), using a normal distribution, a value for each of the N parameters of a reduced set of parameters (s); transforming (120) the reduced set of parameters (s) into an extended set of parameters (E), that comprises M parameters, M being equal to the number of cells of the 3D geological representation; applying (130) a trained deep learning algorithm onto the extended set of parameters (E) to generate the 3D geological representation (R), the deep learning algorithm being a diffusion model algorithm, the trained deep learning algorithm resulting from a training phase of the method (100) using training 3D geological representations (TR) of a subsurface reservoir.

Description

[0001] TITLE

[0002] An improved computer-implemented method for generating a three dimensional geological representation of a subsurface reservoir

[0003] TECHNICAL FIELD OF THE INVENTION

[0004] The present invention concerns a method for geological modeling a subsurface reservoir. The present invention also concerns a computer program product and a readable information carrier.

[0005] BACKGROUND OF THE INVENTION

[0006] The subsurface reservoir of interest is any type of geological reservoir, used to extract or to store a fluid (like oil, gas or carbon dioxide). It is made of one or several underground layers of permeable rocks, porous rocks, rock fractures and / or unconsolidated materials (gravel, sand, or silt).

[0007] Methods of geological modelling a reservoir aims at obtaining a three-dimensional - 3D geological representation of said reservoir.

[0008] In such a 3D geological representation, the volume of the reservoir is divided into cells. A local value of at least one geological property is attached to each cell. The relevant geological properties to be considered are for example the porosity, the permeability, categorial facies index, etc. A geological property may be a discrete or a continuous quantity.

[0009] The number of cells representing the reservoir being of the order of several millions, a 3D geological representation has a high dimensionality.

[0010] The 3D geological representation is obtained by running a numerical geological simulation using field data. Well-known geological simulations are for example “Truncated Gaussian Simulation - TGS or “U-Like”.

[0011] The field data are geological properties measured on cores extracted during the drilling of the well(s), seismic imagery of the reservoir, and other pieces of information or geological assumptions. The field data are geo-localized.

[0012] One 3D geological representation is used to forecast some production quantities at a well drilled into the reservoir. Examples of production quantities are fluid flow rate (liquid, gas), pressure, etc. These are dynamical time varying data.

[0013] For this forecasting purpose, a numerical flow simulation is run on the 3D geological representation in order to determine an estimated time series of each relevant production quantity at each well of the subsurface reservoir. This numerical flow simulation may be a high precision physical model based on partial derivative flow equations in porous medium ora low precision physical model based on an artificial intelligence model properly trained.However, the 3D geological representation used in this forecasting process has to be properly calibrated to be able to precisely estimate future values of production quantities.

[0014] The calibration process is performed using an history of the production quantities, i.e. an observed time series of each relevant production quantity at each well of the reservoir of interest.

[0015] History matching therefore consists in finding the values of the geological properties of the 3D geological representation allowing to reproduce the observed time series of the production quantities.

[0016] History matching is a highly complex inverse problem, since it requires to adjust the values of the geological properties of the 3D geological representation, characterized by a high dimensionality, with one or several observed production data (for example four quantities measured each day over several months for one well), characterized by a low dimensionality.

[0017] In addition, adjusting the values of the geological properties of the 3D geological representation is an iterative process that requires, at each iteration, to run the numerical geological simulation, what can take several weeks to several months.

[0018] Many approaches have been proposed to ease the calibrate process for history matching.

[0019] Among these approaches, Artificial Intelligence based methods for history matching, such as GAN-HM have been proposed. Such an approach is for example presented in the article D. Busby and al., “3D-GAN to Model Uncertainty and to Perform Effective History Matching of a Complex Turbidite Field Case”, ECMOR 2022, Sep 2022, Volume 2022, p.1 -19 (doi: https: / / doi.org / 10.3997 / 2214-4609.202244073).

[0020] It consists in using an adversarial net to train, with a sample of 3D geological representations obtained through numerical geological simulations of the reservoir of interest, an Al model that will be able to generate 3D geological representations .

[0021] Advantageously, the latent space of the entry parameters of this Al model has a reduced dimensionality.

[0022] At present, GANs can reproduce the results of geological modeling, but with learning times that are still too long (typically superior to four weeks), and with results that are inferior to those obtained from conventional geological simulations.

[0023] Hence, there exists a need for an improved method for generating 3D geological representations of a reservoir of interest.

[0024] SUMMARY OF THE INVENTION

[0025] To this end, the invention relates to a method for generating a 3D geological representation of a subsurface reservoir, the 3D geological representation comprising anumber of cells, each cell being associated with a value of at least one geological property, the method comprising, during a sampling phase, the steps of : sampling, using a normal distribution, a value for each parameter of a reduced set of parameters, the reduced set of parameters comprising N parameters ; transforming the reduced set of parameters into an extended set of parameters, the extended set of parameters comprising M parameters, M being equal to the number of cells of the 3D geological representation; applying a trained deep learning algorithm onto the extended set of parameters to generate the 3D geological representation (R), the deep learning algorithm being a diffusion model algorithm, the trained deep learning algorithm resulting from a training phase of the computer-implemented method using training 3D geological representations of a subsurface reservoir.

[0026] The method according to the invention may comprise one or more of the following features considered alone or in any combination that is technically possible:

[0027] - the step of transforming the reduced set of parameters into an extended set of parameters involves applying successively at least one duplication operation, at least one permutation operation and at least one normalization operation.

[0028] - the diffusion model algorithm is used without conditioning or with conditioning, the conditioning being then preferably data relative to a production quantity of the subsurface reservoir.

[0029] - the diffusion model algorithm is either a « Denoising diffusion implicit models » - DDIM algorithm or a “Probabilistic Diffusion Model” - PDM algorithm.

[0030] - the training 3D geological representations of a subsurface reservoir used for the training phase are obtained by a geological simulation of the subsurface reservoir.

[0031] - the geological simulation is computed based on filed data measured on the subsurface reservoir.

[0032] - a flow simulation is applied on the training 3D geological representations to obtain estimated production data, the estimated production data being used for conditioning the diffusion model algorithm during its training.

[0033] - the training phase involves a data compressor, preferably a “Variational Upper Bound” compressor.

[0034] - said at least geological property is chosen among facies and petrophysical properties thereof, such as porosity, permeability, clay content, saturation and bulk density.

[0035] - the method further comprising a phase of history matching, consisting in: applying a flow simulation on the 3D geological representation of a subsurface reservoir to estimate production data relative to said subsurface reservoir; comparing the estimated production data with observed production data relative to said subsurface reservoir; updating the reduced setof parameters based on the result of the step of comparing, the method (100) being iterated with the updated reduced set of parameters until a convergence criteria is met.

[0036] The invention also relates to a computer program product comprising a readable information carrier having stored thereon a computer program comprising program instructions, the computer program being loadable onto a data processing unit and causing the previous method to be carried out when the computer program is carried out on the data processing unit.

[0037] The invention also relates to a readable information carrier on which the previous computer program product is stored.

[0038] BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The invention and its features will be easier to understand in view of the following description, provided solely as an example and with reference to the appended drawings, in which:

[0040] Figure 1 schematically illustrates a first and preferred embodiment of the method according to the invention;

[0041] Figure 2 schematically illustrates a second embodiment and a third embodiment of the method according to the invention; and,

[0042] Figure 3 are graphs illustrating the benefits of each of the three embodiments.

[0043] DETAILED DESCRIPTION

[0044] Figure 1 shows a preferred embodiment of the method 100 according to the invention. Method 100 is computer implemented.

[0045] It aims at generating a 3D geological representation of a reservoir of interest. This 3D geological representation comprises M cells. M is an integer of for example the order of 107.

[0046] The method 100 starts, in step 110, with running a generator. The generator is configured with a normal distribution N of N variables.

[0047] The generator outputs an initial set s of N values (one for each variables) selected randomly according to the normal distribution N.

[0048] Thus, the set s corresponds to a vector of N coordinates in a reduced latent space £w. This latent space is characterised by a dimensionality equal to N. N is for example equal to 64 or 128.

[0049] In step 120, a transformation T is applied in order to transform the vector s into a vector E belonging to an extended latent space 8M.This extended latent space £Mis characterised by a dimensionality equal to M, i.e. the number of cells of the 3D geological representation to be generated.

[0050] In step 130, a trained diffusion model is applied on vector E, as an entry, to output one 3D geological representation R of the reservoir of interest. This representation comprises M cells, each cell being associated with the value of at least one geological property P.

[0051] Advantageously, the 3D geological representation R is used for history matching. Thus method 100 continues with step 140, wherein a numerical flow simulation is applied on the 3D geological representation R to get, in particular, estimates of production time series of the reservoir. These estimated data are labelled D*.

[0052] In step 150, an history matching module is executed to compare the estimated data D* with corresponding measured data D. Data D are obtained directly from the reservoir of interest.

[0053] The result A of the comparison performed in step 150 is used in step 160 to update the set s for the next iteration of steps 120 to 160.

[0054] Step 160 is an optimization step that for example computes the gradient of a function of A, to define a trajectory of evolution of set s in space £w.

[0055] With iterations of the loop of the steps shown in figure 1, history matching is performed in order to optimize the parameters of the normal function N. The optimised parameters are those that lead to the generation of the best 3D geological representation by the diffusion model algorithm in terms of estimated versus measured production time series.

[0056] As it appears in the previous description of the preferred embodiment, the method 100 is based on a deep learning algorithm that implements a generative approach based on a diffusion model.

[0057] More specifically, the diffusion model used may be either a « Denoising diffusion Implicit Model » - DDIM or a “Probabilistic Diffusion Model” - PDM.

[0058] DDIM algorithms are for example disclosed in document authored by Jiaming Song et al. “DENOISING DIFFUSION IMPLICIT MODELS”, ICLR2021 (https: / / arxiv.orq / pdf / 2010.02502).

[0059] DDIM algorithms can be stochastic or deterministic, in the sampling (i.e. inference) phase. In our case the deterministic sampling approach.PDM algorithms are for example presented in the article by Jonathan Ho et al, “Denoising Diffusion Probabilistic Models”, 34th Conference on Neural Information Processing Systems (NeurlPS 2020), Vancouver, Canada, (https: / / arxiv.org / abs / 2006.11239).

[0060] DDIM I PDM algorithms are known from the technical field of text, image, or video to image, or video, according to which a virtual image or a video is generated from a prompt.

[0061] DDIM I PDM algorithms are here applied in the context of geological modelling in order to generate 3D geological representations.

[0062] In particular, in this first embodiment, the DDIM I PDM algorithms are used without a prompt, i.e. without conditioning.

[0063] DDIM algorithms require a reduced number of sampling step compared to PDM algorithms, for an identical training step. Thus DDIM algorithms are preferred in the present invention.

[0064] Diffusion model algorithms present the benefit (as GANs do) that the at least one property P of the 3D geological representation R that is generated may either be discrete or continuous.

[0065] However, such an application requires a very high precision, i.e. the number of cells of the 3D geological representations R is high. The number of cells M is the dimensionality of the 3D geological representation.

[0066] Since the latent space £Mof the entry of a diffusion model algorithm need to be of the same dimensionality as its output, i.e. the 3D geological representation R, this latent space is characterised by a high dimensionality, i.e. vectors of M coordinates.

[0067] In order to remedy these issues, the method according to the invention applies, upstream the DDIM algorithm, the transformation T which allows the passage from a reduced latent space ENto the extended latent space £Mof the diffusion model algorithm.

[0068] The reduced latent space £wis characterised by a number of dimensions N which is reduced compared to the number M of dimensions of the latent space £M.

[0069] For example, the number N is equal to 64 or 128.

[0070] The transformation T is based on a normalized Gaussian random projection on the coordinates of reduced vector s to obtain the corresponding extended vector E.

[0071] The transformation T is a fellow:

[0072] a random Gaussian projection is fitted to project a small Gaussian noise to a large Gaussian noise;

[0073] once the random Gaussian projection has been fitted, it is used to upsample Gaussian noise vectors.

[0074] The random Gaussian projection is thus applied on the latent vector s of size N, to obtain the latent vector E of size M.Note that vector E must comply with a normal distribution. This is a constraint imposed by diffusion model algorithms on their entries. With such a transformation T, this constraint is always respected.

[0075] Then, step 130 of the method allows to go from vector E, sampled from EM, to the final 3D geological representation R through K successive sampling steps. For example K = 50 steps.

[0076] The training step 230 of the diffusion model algorithm that is used in step 130 is performed using a sample of training 3D geological representations R**. Preferably the training 3D geological representations R** are all associated with the same reservoir, in particular the reservoir of interest, on which the measurements D are done for the history matching.

[0077] The training 3D geological representations R** derived from field data, P**, i.e. geological property measured on the reservoir. Preferably, a numerical geological simulation is used is step 220 to generate the sample of training 3D geological representations R**. Additional techniques may be used to increase the number of training 3D geological representations R** from an initial sample.

[0078] The training step 230 may be performed using for example a data compressor of the type “Variational upper bound” - VAEs, for faster and better training. Such a compressor is for example disclosed in the article Robin Rombach et al. “High-Resolution Image Synthesis with Latent Diffusion Models”, 2022 IEEE / CVF Conference on Computer Vision and Pattern Recognition, (https: / / api.semanticscholar.Org / CorpuslD:245335280).

[0079] Figure 2 represents a second embodiment of the invention.

[0080] Method 200 starts with the same steps 110 of initializing the value of the latent vector s and 120 of projecting the vector s into a vector E, as in the first embodiment.

[0081] In step 110, the normal distribution N generator is run to output a reduced vector s of N coordinates belonging to the reduced latent space £w.

[0082] In step 120, a transformation T is applied in order to transform the reduced vector s into an extended vector E belonging to the extended latent space 8M.

[0083] In step 330, a trained diffusion model is applied on vector E, as an entry, to output one 3D geological representation R of the reservoir of interest.

[0084] However, in this second embodiment, the diffusion model algorithm is used with a prompt, i.e. with conditioning. Consequently, a conditioning data D’ is also inputted as an entry to the diffusion model algorithm in addition to vector E. The data D’ used as a prompt is preferably a data relative to a production quantity of the reservoir of interest, in particular a time series. For example D’ is a seismic observation of the reservoir to be modelled orfacieses in the vicinity of the wells of that reservoir.Ideally, the training step of the diffusion model algorithm used in step 330 is such that, when the data D’ used for conditioning the diffusion model algorithm correspond to real data measured on the reservoir of interest, the representation R output by step 330 is the optimal representation of that reservoir. In this second embodiment, there is no need for history matching, since it is redundant with what is done during the training step.

[0085] The training phase involves, in addition to step 220 (wherein a numerical geological simulation is used on a property P to generate the sample of training 3D geological representations R**), a step 240.

[0086] In step 240 a numerical flow simulation is applied on the 3D geological representation R** to get estimated production data D**, in particular time series.

[0087] Pairs of R** and D** are then used in step 430 to trained the diffusion model, the estimated production data D** being used for conditioning the diffusion model algorithm during its training.

[0088] In a third embodiment, also illustrated in figure 2 with dash lines, the second embodiment is completed with the history matching steps of the first embodiment.

[0089] In fact, the drawback of the second embodiment is that it needs an extensive time for the computation, in sufficient number and with the required high precision, of both the representations R** and the time series D**.

[0090] To alleviate this drawback, the constraint on the training phase is reduced by performing a rough data estimation from the representation and to use this rough data in step 240.

[0091] Then, when used in inference in step 330, the conditioned diffusion model provides representations which are not optimal, but nearer the optimal representation than if the diffusion model were used free of conditioning (first embodiment). Consequently the history matching step provides the optimal representation faster (total number n of iterations reduced compared to the first embodiment) or with more precision (the n iterations are neared the optimal representation compared to the first embodiment).

[0092] It is precisely what is illustrated in Figure 3. Figure 3 are graphs of a production quantity Prod over time T.

[0093] Graph A represents various production data time series D* computed on representations of the reservoir of interest generated using the first embodiment (diffusion model without conditioning) for different values of set s (for example s1 and s2). These simulated time series are to be compared with the data D observed on the reservoir of interest.

[0094] Graph B represents various production data time series D* computed on representations of the reservoir of interest generated using the third embodiment (diffusion model with “partial”conditioning) for different values of set s (for example s1 and s2). These simulated time series are to be compared with the data D observed on the reservoir of interest.

[0095] With the third embodiment, the representations generated are far more realistic than with the first representation. The convergence of the method is thus obtained with a reduced number of iterations.

[0096] ALTERNATIVES AND ADVANTAGES

[0097] The method for generating a 3D geological representation is deterministic, i.e. the same set s of parameters of the reduced latent space always leads to the same 3D geological representation R.

[0098] The method according to the invention provides a 3D geological representation of a good quality in a short period of time in terms of computational cycles.

[0099] This method benefits from the known advantages of diffusion model algorithms in terms of training, diversity and high-quality images.

[0100] The process of history matching involving the generation of 3D geological representation through a diffusion model algorithm is faster than the numerical geological simulation, but also other generating approaches like GAN.

Claims

CLAIMS1.- A computer-implemented method (100) for generating a three dimensional - 3D geological representation (R) of a subsurface reservoir, the 3D geological representation comprising a number of cells, each cell being associated with a value of at least one geological property, the method comprising, during a sampling phase, the steps of :- sampling (110), using a normal distribution, a value for each parameter of a reduced set of parameters (s), the reduced set of parameters comprising N parameters ;- transforming (120) the reduced set of parameters (s) into an extended set of parameters (E), the extended set of parameters comprising M parameters, M being equal to the number of cells of the 3D geological representation;- applying (130) a trained deep learning algorithm onto the extended set of parameters (E) to generate the 3D geological representation (R), the deep learning algorithm being a diffusion model algorithm,the trained deep learning algorithm resulting from a training phase of the computer-implemented method (100) using training 3D geological representations (TR) of a subsurface reservoir.2.- The method according to claim 1, wherein the step of transforming (120) the reduced set of parameters into an extended set of parameters involves applying successively at least one duplication operation, at least one permutation operation and at least one normalization operation.

3. The method according to claim 1 or claim 2, wherein the diffusion model algorithm is used without conditioning or with conditioning, the conditioning being then preferably data relative to a production quantity of the subsurface reservoir.

4. The method according to any one of claims 1 to 3, wherein the diffusion model algorithm is either a « Denoising diffusion implicit models » - DDIM algorithm ora “Probabilistic Diffusion Model” - PDM algorithm.

5. The method according to any one of claims 1 to 4, the training 3D geological representations (R**) of a subsurface reservoir used for the training phase are obtained by a geological simulation of the subsurface reservoir.

6. The method according to claim 5, wherein the geological simulation is computed based on filed data (P**) measured on the subsurface reservoir.

7. The method according to claim 5 or claim 6, wherein a flow simulation is applied on the training 3D geological representations (R**) to obtain estimated production data (D**), the estimated production data being used for conditioning the diffusion model algorithm during its training.

8. The method according to any one of claim 5 to 7, wherein the training phase involves a data compressor, preferably a “Variational Upper Bound” compressor.

9. The method according to any one of claims 1 to 8, wherein said at least geological property is chosen among facies and petrophysical properties thereof, such as porosity, permeability, clay content, saturation and bulk density.

10. The method according to any one of claims 1 to 9, further comprising a phase of history matching, consisting in:- applying (140) a flow simulation on the 3D geological representation (R) of a subsurface reservoir to estimate production data (D*) relative to said subsurface reservoir;- comparing (150) the estimated production data (D*) with observed production data (D) relative to said subsurface reservoir;- updating (160) the reduced set of parameters (s) based on the result of the step of comparing,the method (100) being iterated with the updated reduced set of parameters (s) until a convergence criteria is met.11.- A computer program product comprising a readable information carrier having stored thereon a computer program comprising program instructions, the computer program being loadable onto a data processing unit and causing a method according to any one of claims 1 to 10 to be carried out when the computer program is carried out on the data processing unit.12.- A readable information carrier on which a computer program product according to claim 11 is stored.

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