System And Method for Removing Noise From Measurement Data

Abstract

System and/or methods for removing noise from measurement data are disclosed. For example, pressure measurements may be used to identify a flow regime using the derivative of each of the pressure measurements. A time window may be defined about each pressure measurement and numerous or even all pressure measurements within the time window may be used to calculate the pressure derivative of each pressure measurement. A least-squares method or a least-absolute-deviations method may be used to compute a pressure-derivative curve. The iteratively-reweighted least-squares method may be used to solve least-absolute-deviation problems to compute a pressure-derivative curve with enhanced smoothing.

We claim: 
     
         1 . A method comprising:
 drawing reservoir fluid in a formation about a wellbore into a downhole tool;   ceasing to draw the reservoir fluid into the downhole tool;   obtaining pressure measurements with respect to time of the reservoir fluid after ceasing to draw the reservoir fluid into the downhole tool;   defining a time window about a first pressure measurement of the pressure measurements;   obtaining a derivative of the first pressure measurement with respect to time by utilizing the first pressure measurement, a plurality of the pressure measurements within the time window and obtained prior to the first pressure measurement, and a plurality of the pressure measurements within the time window and obtained after the first pressure measurement; and   identifying a reservoir flow regime based on the derivative.   
     
     
         2 . The method of  claim 1 , wherein the derivative is determined using a least-squares method, a least-absolute-deviations method, or an iteratively-reweighted least-squares method. 
     
     
         3 . The method of  claim 1 , wherein the size of the time window varies for each pressure measurement. 
     
     
         4 . The method of  claim 1 , wherein the size of the time window is fixed. 
     
     
         5 . The method of  claim 1 , wherein the time window is based on a function of time change. 
     
     
         6 . The method of  claim 5 , wherein the function of time change is logarithmic. 
     
     
         7 . The method of  claim 1 , wherein all of the pressure measurements in the time window are used to obtain the derivative. 
     
     
         8 . A method comprising:
 drawing reservoir fluid in a formation about a wellbore into a downhole tool;   ceasing to draw the reservoir fluid into the downhole tool;   obtaining pressure measurements of the reservoir fluid with respect to time after ceasing to draw the reservoir fluid into the downhole tool;   defining a time window about each of the pressure measurements;   obtaining, for each of the pressure measurements, a derivative of a given pressure measurement of the pressure measurements with respect to time by utilizing the given pressure measurement, a plurality of the pressure measurements within the time window of the given pressure measurement and obtained prior to the given pressure measurement, and a plurality of the pressure measurements within the time window of the given pressure measurement and obtained after the given pressure measurement; and   identifying a reservoir flow regime based on the derivative for each of the pressure measurements.   
     
     
         9 . The method of  claim 8 , wherein the derivative is calculated using a least-squares technique, a least-absolute-deviations technique, or an iteratively-reweighted least-squares technique. 
     
     
         10 . The method of  claim 8 , wherein the size of the time window varies based on a logarithmic function of time. 
     
     
         11 . The method of  claim 8 , wherein the size of the time window is equal for each pressure measurement. 
     
     
         12 . The method of  claim 8  further comprising the steps of:
 determining a function indicative of the data points; and 
 performing an iteration of a least-absolute-deviations problem to solve the function. 
 
     
     
         13 . The method of  claim 12  further comprising a step of:
 performing one or more additional iterations until consecutive solutions are within a given range. 
 
     
     
         14 . The method of  claim 8 , wherein more than three pressure measurements are used in the derivative calculation. 
     
     
         15 . A method for computing a pressure derivative in a wellbore, the method comprising:
 drawing reservoir fluid in a formation about a wellbore into a downhole tool at a substantially constant rate;   obtaining pressure measurements of the reservoir fluid with respect to time while drawing reservoir fluid into the downhole tool;   defining a time window about each of the pressure measurements;   obtaining, for each of the pressure measurements, a derivative of a given pressure measurement of the pressure measurements with respect to time by utilizing the given pressure measurement, a plurality of the pressure measurements within the time window of the given pressure measurement and obtained prior to the given pressure measurement, and by utilizing a plurality of the pressure measurements within the time window of the given pressure measurement and obtained after the given pressure measurement; and   identifying a flow regime based on the derivative for each of the pressure measurements.   
     
     
         16 . The method of  claim 15 , wherein the derivative is determined using a least-squares method, a least-absolute-deviations method, or an iteratively-reweighted least-squares method. 
     
     
         17 . The method of  claim 15 , wherein the time window is determined using a time function. 
     
     
         18 . The method of  claim 17 , wherein the size of the time window is equal for each pressure measurement. 
     
     
         19 . The method of  claim 15 , wherein the flow regime is spherical or radial. 
     
     
         20 . The method of  claim 15 , wherein the size of the time window is equal for each pressure measurement.