Fourier transform-based machine learning for well placement

Abstract

Systems and methods of the present disclosure provide systems and methods that include obtaining properties related to an underground reservoir and encoding the properties into a latent space. A first portion of the encoded properties is then transformed using a Fourier transform. In the Fourier space, the transformed first portion of the encoded properties is convolved using a trained neural network. The convolved first portion of the encoded properties is then inversely Fourier transformed. A second portion of the encoded properties is locally convolved. The convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties are then combined. Predicted results are decoded where the results are related to a potential well location based at least in part on the combination of the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties.

What is claimed is: 
     
         1 . A method, comprising:
 obtaining properties related to an underground reservoir;   encoding the properties into a latent space;   performing a Fourier transform on a first portion of the encoded properties to obtain a transformed first portion;   convolving the transformed first portion of the encoded properties using a neural network to obtain a convolved first portion;   performing an inverse Fourier transform on the convolved first portion of the encoded properties to obtain an inversely transformed convolved first portion;   performing local convolution on a second portion of the encoded properties to obtain a convolved second portion;   combining the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties; and   decoding predicted results related to a potential well location based at least in part on the combination of the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties.   
     
     
         2 . The method of  claim 1 , wherein encoding the properties into a latent space comprises encoding the properties using a fully connected neural network. 
     
     
         3 . The method of  claim 1 , wherein decoding the predicted results based at least in part on the combination of the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties comprises decoding the predicted results based at least in part on the combination of the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties using a fully connected neural network. 
     
     
         4 . The method of  claim 1 , wherein combining the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties comprises summing the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties and applying an activation function. 
     
     
         5 . The method of  claim 4 , wherein the activation function comprises a Gaussian error logic unit activation function. 
     
     
         6 . The method of  claim 1 , comprising iteratively performing Fourier transformations and convolutions on the combination of the convolved second portion of the encoded properties and the inversely transformed convolved first portion of the encoded properties a plurality of times, and the predicted results are based at least in part on the iterative transformations and convolutions. 
     
     
         7 . The method of  claim 1 , comprising filtering frequencies in the Fourier space before convolution. 
     
     
         8 . The method of  claim 1 , wherein the obtained properties comprise a stack of images showing one or more conditions related to the underground reservoir. 
     
     
         9 . The method of  claim 8 , wherein the stack of images comprise representations of measurements related to horizontal permeability, vertical permeability, porosity, water levels, depth, well locations/control, or a combination thereof. 
     
     
         10 . The method of  claim 9 , wherein the potential well location corresponds to a potential well location to be used for carbon capture and storage. 
     
     
         11 . The method of  claim 10 , wherein the predicted results comprise data indicating carbon dioxide gas saturation, an amount or percentage of carbon dissolved in water, capillary capture, and/or reactions after carbon injection as part of carbon capture and storage. 
     
     
         12 . The method of  claim 11 , wherein multiple predicted results are generated using a plurality of neural networks that comprises the neural network. 
     
     
         13 . A method, comprising:
 obtaining data related to an underground reservoir;   obtaining subsequent conditions of the underground reservoir after placement of a well at a potential location; and   training one or more neural networks to map input conditions in the data to the subsequent conditions after placement of the well using discrete Fourier transform (DFT) forms.   
     
     
         14 . The method of  claim 13 , wherein obtaining the subsequent conditions comprises simulating the subsequent conditions from the input conditions in the data. 
     
     
         15 . The method of  claim 13 , wherein obtaining the subsequent conditions comprises using data from a subsequent time compared to the data at which the input conditions are obtained. 
     
     
         16 . The method of  claim 13 , wherein the subsequent conditions correspond to a final resting condition after well placement at a later time. 
     
     
         17 . A system, comprising:
 a memory storing instructions; and   a processor configured to execute the instructions to cause the system to:
 encode first and second properties corresponding to an underground reservoir into a latent space to obtain first and second encoded properties; 
 perform a Fourier transform on the first encoded properties to obtain transformed first encoded properties; 
 perform low pass filtration on the transformed first encoded properties to obtain filtered first encoded properties; 
 convolve the filtered first encoded properties in a neural network to obtain convolved first encoded properties; 
 perform an inverse Fourier transform on the convolved first encoded properties to obtain inversely transformed first encoded properties; 
 perform a local convolution on the second encoded properties to obtain convolved second encoded properties; 
 combine the convolved second encoded properties and the inversely transformed first encoded properties; and 
 decode predicted results related to a potential well location based at least in part on the combination of the convolved second encoded properties and the inversely transformed first encoded properties. 
   
     
     
         18 . The system of  claim 17 , wherein the neural network is implemented at least in part using the processor. 
     
     
         19 . The system of  claim 17 , comprising one or more fully connected neural networks that are configured to:
 encode the first and second properties corresponding to the underground reservoir into the latent space; and   decode the predicted results related to the potential well location based at least in part on the combination of the convolved second encoded properties and the inversely transformed first encoded properties.   
     
     
         20 . The system of  claim 17 , wherein the processor is configured to execute the instructions to cause the system to perform iterative Fourier-based convolutions on the combination of the convolved second encoded properties and the inversely transformed first encoded properties, wherein the predicted results are based at least in part on the iterative Fourier-based convolutions.