System and methods for cross-sensor linearization

Abstract

A method includes obtaining a plurality of master sensor responses with a master sensor in a set of training fluids and obtaining node sensor responses in the set of training fluids. A linear correlation between a compensated master data set and a node data set is then found for a set of training fluids and generating node sensor responses in a tool parameter space from the compensated master data set on a set of application fluids. A reverse transformation is obtained based on the node sensor responses in a complete set of calibration fluids. The reverse transformation converts each node sensor response from a tool parameter space to the synthetic parameter space, and uses transformed data as inputs of various fluid predictive models to obtain fluid characteristics. The method includes modifying operation parameters of a drilling or a well testing and sampling system according to the fluid characteristics.

What is claimed is: 
     
         1 . A method, comprising:
 obtaining a plurality of master sensor responses with a master sensor in a set of training fluids;   obtaining a plurality of node sensor responses with a plurality of node sensors in the set of training fluids;   finding a linear correlation between a compensated master data set and a node data set for the set of training fluids;   generating a plurality of node sensor responses in a tool parameter space from the compensated master data set on a set of application fluids;   obtaining a reverse transformation based on the plurality of node sensor responses in a complete set of calibration fluids, the reverse transformation transforming each node sensor response from a tool parameter space to a synthetic parameter space;   obtaining fluid characteristics with synthetic fluid predictive models using reverse-transformed inputs from at least one of the node sensor responses to a fluid measurement; and   modifying operation parameters of a drilling or a well testing and sampling system according to the fluid characteristics, wherein the complete set of calibration fluids comprises the set of training fluids and the set of application fluids.   
     
     
         2 . The method of  claim 1 , further comprising:
 selecting a weighting factor to compensate the master sensor responses with the node sensor responses according to the linear correlation between the compensated master data set and the node data set.   
     
     
         3 . The method of  claim 2 , wherein selecting the weighting factor comprises selecting a weighting factor that results in a high linear correlation between the compensated master data set and the node data set, wherein the high linear correlation indicates a low data transformation error. 
     
     
         4 . The method of  claim 2 , wherein selecting the weighting factor comprises determining a set of cross-sensor linearized coefficients comprising the weighting factor for each channel pair, using an exhaustive searching loop through multi-iteration training. 
     
     
         5 . The method of  claim 1 , further comprising selecting the master sensor and at least one of the plurality of node sensors from two sensors having a same design, two sensors having a same configuration, and two sensors from a fabrication batch. 
     
     
         6 . The method of  claim 1 , further comprising selecting the master sensor and at least one of the plurality of node sensors from different fabrication batches, and from two sensors having a same design and having a same configuration. 
     
     
         7 . The method of  claim 1 , further comprising selecting the master sensor and at least one of the plurality of node sensors from different fabrication batches having a different design, and with a same number of elements having the same denomination. 
     
     
         8 . The method of  claim 1 , further comprising selecting the master sensor and at least one of the plurality of node sensors from different designs, from different configurations, and originating from different fabrication batches. 
     
     
         9 . The method of  claim 1 , further comprising truncating a master data set to a same number of samples as a node data set, wherein each sample in the master data set comprises a measurement having a temperature setting and pressure setting similar to a temperature setting and a pressure setting of at least one measurement in the node data set. 
     
     
         10 . The method of  claim 1 , wherein finding a linear correlation between a compensated master data and the node data set comprises applying a weight factor to a difference between a synthetic node sensor response and a synthetic master sensor response for a reference fluid selected from the set of training fluids, and adding the weighted difference to a master sensor response measured from the reference fluid. 
     
     
         11 . The method of  claim 1 , further comprising determining at least one of a node sensor response and a master sensor response in the synthetic parameter space with a dot product of a fluid spectral response vector and a convolved spectral response vector for one of the at least one node sensor or the master sensor. 
     
     
         12 . The method of  claim 1 , further comprising obtaining fluid characteristics with a synthetic fluid predictive model using the reverse transformed inputs from at least one of the node sensor responses to a fluid measurement. 
     
     
         13 . The method of  claim 1 , wherein obtaining a plurality of node sensor responses with a plurality of node sensors on the set of training fluids comprises measured and simulated node sensor responses from reference fluids at broad ranges of temperature settings and pressure settings. 
     
     
         14 . The method of  claim 1 , further comprising:
 collecting optical responses from a plurality of petroleum fluids with known characteristics using the selected master sensor;   generating a plurality of synthetic node sensor responses associated with the plurality of petroleum fluids using the reverse transformation with cross-sensor linearized node sensor inputs in tool parameter space; and   calibrating a fluid characterization model using the plurality of synthetic node sensor responses.   
     
     
         15 . A method, comprising:
 determining a value for a node sensor response in synthetic parameter space using a two-dimensional temperature and pressure interpolation with given node sensor responses at specified temperatures and pressures;   determining a value for a master sensor response in synthetic parameter space using the two-dimensional temperature and pressure interpolation with given master sensor response at specified temperatures and pressures;   determining a difference between the value for a node sensor response and the value for a master sensor response;   determining a set of cross-sensor linearized model coefficients in an optimization loop;   adjusting a master sensor channel selection to simulate a channel response of the node sensor;   obtaining a reverse transformation using the simulated channel responses of the node sensor; and   modifying operation parameters of a drilling or a well testing and sampling system according to a fluid characteristic obtained with a synthetic fluid predictive model using node sensor responses as input to the reverse transformation.   
     
     
         16 . The method of  claim 15 , wherein determining the value for a node sensor response and determining the value for a master sensor response comprises varying temperature and pressure conditions for a plurality of node sensor responses and master sensor responses. 
     
     
         17 . The method of  claim 15 , wherein adjusting the master sensor channel selection to simulate a channel response of the node sensor comprises:
 identifying a set of cross-sensor linearized coefficients for a node sensor channel based on a plurality of training fluids; and   obtaining the channel response of the node sensor on a plurality of application fluids with the set of cross-sensor linearized model coefficients.   
     
     
         18 . The method of  claim 15 , wherein obtaining a reverse transformation using the simulated channel responses of the node sensor comprises combining the node sensor response on a plurality of training fluids and a plurality of application fluids to develop the reverse transformation model with a neural network. 
     
     
         19 . The method of  claim 15 , further comprising adjusting a master sensor channel selection from a master sensor to simulate a node sensor channel response from a node sensor. 
     
     
         20 . The method of  claim 19 , wherein the master sensor channel has the same or different nominal element as the node sensor channel. 
     
     
         21 . A method, comprising:
 introducing a tool into a wellbore drilled into one or more subterranean formations, the tool having been previously calibrated for operation by:
 obtaining a plurality of master sensor responses with a master sensor in a set of training fluids; 
 obtaining a plurality of node sensor responses with a plurality of node sensors in the set of training fluids, each of the plurality of node sensors and the master sensor including an optical element; 
 finding a linear correlation between a compensated master data set and a node data set for the set of training fluids; 
 generating a plurality of node sensor responses in a tool parameter space from the compensated master data set on a set of application fluids; and 
 obtaining a reverse transformation based on the plurality of node sensor responses in a complete set of calibration fluids, wherein the complete set of calibration fluids comprises the set of training fluids and the set of application fluids; 
   determining a fluid characteristic from the plurality of node sensor responses in the synthetic parameter space using the reverse transformation and a synthetic fluid predictive model; and   modifying operation parameters of a drilling or a well testing and sampling according to the fluid characteristic.   
     
     
         22 . The method of  claim 21 , wherein obtaining a plurality of node sensor responses with a plurality of node sensors in the set of training fluids during the tool calibration comprises determining a temperature setting and a pressure setting of the reduced set of training fluids according to a temperature setting and a pressure setting of the master set of training fluids. 
     
     
         23 . The method of  claim 21 , further comprising, during the tool calibration, selecting one of the plurality of master sensors and one of the plurality of node sensors from two sensors having at least one of different designs, different configurations, or different fabrication batches.