Production analysis and/or forecasting methods, apparatus, and systems

Abstract

Methods and apparatus for modeling well production. Such methods comprise modeling a production of a well (perhaps an open universe, generative model). Methods also comprise determining probability distributions for physical parameters associated with the well by training the model with historic well production data (perhaps using sparse sampling). Such methods also comprise determining a posterior distribution for the model by sampling probability distributions for the parameters. Some methods further comprise determining a posterior distribution for the well's production using the model's posterior distribution. Non-Gaussian (Laplacian) noise can be added to the model. Methods can comprise financially modeling the well. Some methods comprise using MCMC sampling to converge the parameter posterior distribution for the well's production. An EUR for the well can be determined as well as an uncertainty associated with the posterior distribution for the production. If desired, some methods comprise modeling multi-phase flow in the well.

1 . A method comprising:
 modeling a production of a well using Bayesian statistics thereby accounting for noise in measurements of the production of the well wherein the model of the well is an open universe, generative model;   adding Laplacian noise to the Bayesian model of the production of the well in accordance with geophysical properties of the well and using the processor;   training the Bayesian model of the production of the well with historic data which was gathered at a monthly rate and which is pertinent to the production of the well thereby determining probability distributions for physical parameters associated with the well using the processor;   sampling the probability distributions associated with the physical parameters associated with the well thereby determining a posterior distribution for the Bayesian model of the production of the well using the processor;   determining a posterior distribution for a future production of the well using the posterior distribution for the Bayesian model of the production of the well and the processor;   outputting at least one curve illustrating the posterior distribution for the future production of the well based on the Bayesian model of the production of the well with the Laplacian noise added thereto using the processor;   monitoring the future production of the well; and   raising an alarm responsive to the future production of the well falling below a user-selected probabilistic threshold.   
     
     
         2 . A method comprising:
 modeling a production of a well using a processor;   determining probability distributions for physical parameters associated with the well by training the model of the well with historic data pertinent to the production of the well and using the processor;   determining a posterior distribution for the model of the well by sampling the probability distributions for the physical parameters associated with the well and using the processor; and   outputting the posterior distribution for the model of the well via an interface in communication with the processor.   
     
     
         3 . The method of  claim 2  further comprising adding Laplacian noise to the model of the well in accordance with geophysical properties of the well. 
     
     
         4 . The method of  claim 2  further comprising modeling a financial model of the well based on at least the model of the well. 
     
     
         5 . The method of  claim 2  further comprising using Markov Chain Monte Carlo sampling to converge on the posterior distributions for the model of the well. 
     
     
         6 . The method of  claim 2  wherein the training of the model of the well further comprises using historical data associated with an initial completion of the well, a shut-in of the well, a secondary stimulation of the well, or a combination thereof. 
     
     
         7 . The method of  claim 2  wherein the model of the well is an open universe, generative model. 
     
     
         8 . The method of  claim 2  further comprising determining a posterior distribution for a future production of the well using the posterior distributions for the model of the well and using the processor and outputting the posterior distribution for the future production of the well based on the model of the well and using the processor. 
     
     
         9 . The method of  claim 8  further comprising determining an estimated ultimate recovery estimate for the well using the posterior distribution for the future production of the well. 
     
     
         10 . The method of  claim 8  further comprising quantifying an uncertainty associated with the posterior distribution for the future production of the well. 
     
     
         11 . The method of  claim 8  further comprising comparing the posterior distribution for the future production of the well to a manually-fit production forecast. 
     
     
         12 . An apparatus comprising:
 a processor;   an interface in communication with the processor; and   a memory in communication with the processor and storing processor executable instructions which when executed by the processor cause the processor to perform a method comprising:   modeling a production of a well using a processor;   determining probability distributions for physical parameters associated with the well by training the model of the well with historic data pertinent to the production of the well and using the processor;   determining a posterior distribution for the model of the well by sampling the probability distributions for the physical parameters associated with the well and using the processor; and   outputting the posterior distribution for the model of the well via an interface in communication with the processor.   
     
     
         13 . The method of  claim 12  further comprising adding Laplacian noise to the model of the well in accordance with geophysical properties of the well. 
     
     
         14 . The method of  claim 12  further comprising modeling a financial model of the well based on at least the model of the well. 
     
     
         15 . The method of  claim 12  further comprising using Markov Chain Monte Carlo sampling to converge on the posterior distributions for the model of the well. 
     
     
         16 . The method of  claim 12  wherein the training of the model of the well further comprises using historical data associated with an initial completion of the well, a shut-in of the well, a secondary stimulation of the well, or a combination thereof. 
     
     
         17 . The method of  claim 12  wherein the model of the well is an open universe, generative model. 
     
     
         18 . The method of  claim 12  further comprising determining a posterior distribution for a future production of the well using the posterior distributions for the model of the well and using the processor and outputting the posterior distribution for the future production of the well based on the model of the well and using the processor. 
     
     
         19 . The method of  claim 18  further comprising determining an estimated ultimate recovery estimate for the well using the posterior distribution for the future production of the well. 
     
     
         20 . The method of  claim 18  further comprising quantifying an uncertainty associated with the posterior distribution for the future production of the well. 
     
     
         21 . The method of  claim 12  wherein the outputting of the posterior distribution of the well further comprises outputting a plurality of curves representing the posterior distribution of the well. 
     
     
         22 . The method of  claim 12  further comprising monitoring a future production of the well and raising an alarm responsive to the future production of the well decreasing to a user-selected probablistic threshold. 
     
     
         23 . A computer readable storage medium storing instructions which when executed by a processor cause the processor to perform a method comprising:
 modeling a production of a well using a processor;   determining probability distributions for physical parameters associated with the well by training the model of the well with historic data pertinent to the production of the well via sparse sampling and using the processor;   determining a posterior distribution for the sparsely-sampled model of the well by sampling the probability distributions for the physical parameters associated with the well using the processor; and   outputting the posterior distribution for the sparsely-sampled model of the well using an interface in communication with the processor.   
     
     
         24 . The computer readable storage medium of  claim 23  wherein the method further comprises adding non-Gaussian noise to the model of the well. 
     
     
         25 . The computer readable storage medium of  claim 24  wherein the non-Gaussian noise is Laplacian noise. 
     
     
         26 . A computer readable storage medium storing processor executable instructions which when executed by the processor cause the processor to perform a method comprising:
 modeling a production of a well using a processor and using non Gaussian noise;   determining probability distributions for physical parameters associated with the well by training the model of the well with historic data pertinent to the production of the well and using the processor;   determining a posterior distribution for the model of the well by sampling probability distributions associated for the physical parameters associated with the well using the processor; and   outputting the posterior distribution of the model of the well using an interface in communication with the processor.   
     
     
         27 . The computer readable storage medium of  claim 26  wherein the non-Gaussian noise is Laplacian noise. 
     
     
         28 . The computer readable storage medium of  claim 26  wherein the training the model of the well with historic data pertinent to the well is performed via sparse sampling.