Patent Publication Number: US-9835026-B2

Title: High-speed transmission of annulus pressure-while-drilling by data compression

Description:
FIELD 
     Embodiments described herein generally relate to downhole tools. More particularly, such embodiments relate systems and methods for transmitting annulus pressure measurements from a downhole tool to a surface location. 
     BACKGROUND INFORMATION 
     Annulus pressure refers to the pressure of the fluid in an annulus between a drill string and the wellbore wall. Conventional managed pressure drilling (“MPD”) technology controls the annulus pressure within tight predetermined pressure limits throughout the drilling process to avoid the loss of drilling fluid and the influx of formation fluid, as well as to maintain the stability of the wellbore. The pressure limits are defined by the formation pore pressure and the fracture pressure, which is sometimes as narrow as a few hundred pounds per square inch (“psi”). 
     The MPD technology controls the annulus pressure-while-drilling (“APWD”) by adjusting the back pressure and causing drilling to be either at balance or slightly over or under balance. Thus, as will be appreciated, the MPD technology may perform better when APWD data is received faster and/or more frequently. For example, the rapid transmission of APWD data may enable a user to predict a sudden pressure change during a drilling job with a narrow pressure window and to react accordingly. 
     The APWD is impacted by many factors including hydrostatic pressure, friction pressure, back pressure, mud rheological properties, flow rate, cutting movement, pipe movement, drill string configuration, fractures and washouts, drilling noise, mud pulsers, etc. The effects of these factors make the APWD data noisy and discontinuous. The APWD data typically has a data range from about 0 psi to about 30,000 psi. The data measurements may go up and down by about 50 psi within a few seconds or by several hundred psi within a minute. 
     The current speed for mud-pulse telemetry is a few (e.g., 5) bits per second. Transmitting the high sampling rate APWD data along with other drilling and formation evaluation data, therefore, may be challenging. 
     SUMMARY 
     This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
     A method for transmitting data from a downhole tool to a surface location is disclosed. The method includes running a downhole tool into a wellbore. The downhole tool includes a pressure sensor. An annulus pressure in the wellbore is measured at a first time, using the pressure sensor, to produce a first pressure measurement. The first pressure measurement is compressed to produce a reference sample. The reference sample is transmitted to the surface location. The annulus pressure in the wellbore is measured at a second time, using the pressure sensor, to produce a second pressure measurement. A difference between the first pressure measurement and the second pressure measurement is determined to produce a first delta pressure measurement. The first delta pressure measurement is compressed to produce a first compressed delta pressure measurement. The first compressed delta pressure measurement is transmitted to the surface location. 
     In another embodiment, the method may include running a downhole tool into a wellbore. The downhole tool includes a pressure sensor. An annulus pressure in the wellbore is measured at a first time, using the pressure sensor, to produce a first pressure measurement. The first pressure measurement is confined to a first data range. The first pressure measurement is quantized. The annulus pressure in the wellbore is measured at a second time, using the pressure sensor, to produce a second pressure measurement. The second pressure measurement is confined to the first data range. The second pressure measurement is quantized. A difference between the first pressure measurement and the second pressure measurement is determined to produce a first delta pressure measurement. The first delta pressure measurement is confined to a second data range that is less than the first data range. 
     A method for decompressing data is also disclosed. The method may include receiving a first compressed pressure measurement. The first compressed pressure measurement is dequantized to produce a first uncompressed pressure measurement when the first compressed pressure measurement is less than or equal to a first predetermined number. A second compressed pressure measurement is received. A second predetermined number is subtracted from the second compressed pressure measurement to produce a first output when the second compressed pressure measurement is less than or equal to a third predetermined number. The first compressed pressure measurement is added to the first output to produce a second output. The second output is quantized to produce a second uncompressed pressure measurement. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the recited features may be understood in detail, a more particular description, briefly summarized above, may be had by reference to one or more embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings are illustrative embodiments, and are, therefore, not to be considered to limit the scope of the application. 
         FIG. 1  depicts a cross-sectional view of an illustrative downhole tool in a wellbore, according to an embodiment. 
         FIG. 2  depicts uncompressed APWD measurements in the left column and compressed APWD measurements in a repeating telemetry frame in the right column, according to an embodiment. 
         FIG. 3  depicts a graph showing the relation between the bandwidth consumption and the update spacing of the APWD measurements, according to an embodiment. 
         FIG. 4  depicts a graph showing the difference of the error corruption rates between the proposed method and the DPCM method, according to an embodiment. 
         FIGS. 5 and 6  depict graphs showing two cases of APWD measurements retrieved from compressed transmission, according to an embodiment. 
         FIG. 7  depicts a flowchart of a method for transmitting APWD measurements from a downhole tool to a surface location, according to an embodiment. 
         FIG. 8  depicts a flow chart of a method for compressing the APWD measurements, according to an embodiment. 
         FIG. 9  depicts a flow chart of a method for decompressing the APWD measurements, according to an embodiment. 
         FIG. 10  depicts a computing system for performing one or more of the methods disclosed herein, according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  depicts a cross-sectional view of an illustrative downhole tool  130  in a wellbore  100 , according to an embodiment. The downhole tool  130  may be run into the wellbore  100  on a drill string  120  that extends downward from a derrick assembly  110 . The downhole tool  130  may be or include a bottom hole assembly (“BHA”) that includes a telemetry module  135 , a logging-while-drilling (“LWD”) module  140 , a measuring-while-drilling (“MWD”) module  150 , a mud motor  160 , and drill bit  170 . 
     The telemetry module  135  may be configured to transmit data from the downhole tool  130  to a receiver at the surface, as discussed in more detail below. For example, the telemetry module  135  may transmit data from the LWD module  140  and/or the MWD module  150  to the receiver at the surface using mud pulses. The LWD module  140  may be configured to measure one or more formation properties and wellbore physical properties as the wellbore  100  is being drilled or at any time thereafter. The MWD module  150  may be configured to measure one or more physical properties as the wellbore  100  is being drilled or at any time thereafter. The formation properties may include resistivity, density, porosity, sonic velocity, gamma rays, and the like. The physical properties may include pressure, temperature, wellbore caliper, wellbore trajectory, a weight-on-bit, torque-on-bit, vibration, shock, stick slip, and the like. For example, the physical properties may include the annular pressure-while-drilling (“APWD”). 
     A pump  112  at the surface may cause a drilling fluid  114  to flow through the interior of the drill string  120 , as indicated by the arrow  115 . The drilling fluid  114  may flow through the mud motor  160 , which may cause the mud motor  160  to drive the drill bit  170 . After passing through the mud motor  160 , the drilling fluid  114  may flow out of the drill bit  170  and then circulate upwardly through the annulus between the outer surface of the drill string  120  and the wall of the wellbore  100 , as indicated by the directional arrows  116 . 
       FIG. 2  depicts uncompressed APWD measurements  201 - 207  in the left column and compressed APWD measurements  211 - 217  in a repeating telemetry frame  210  in the right column, according to an embodiment. The LWD module  140  and/or the MWD module  150  may obtain a plurality of (uncompressed) APWD measurements (seven are shown:  201 - 207 ) when the downhole tool  130  is in the wellbore  100 . The time spacing between each successive pair of APWD measurements (e.g., measurements  201 ,  202 ) may be from about 1 second to about 30 seconds, about 1 second to about 15 seconds, or about 1 second to about 5 seconds. The time spacing between successive measurements (e.g., measurements  201 ,  202 ) may be maintained evenly (e.g., within ±2 seconds) and close to the desired update rate. 
     A user may build the telemetry frame  210  starting by compressing the the first APWD measurement  201  to produce a reference sample  211 . The reference sample  211  may be represented by, for example, 12 bits. The telemetry frame  210  may then include a series of delta pressure measurements  212 - 217  that each represents the difference between one of the subsequent APWD measurements  202 - 207  and the first APWD measurement  201 . For example, the delta pressure measurement  212  may represent the difference between the second APWD measurement  202  and the first APWD measurement  201 , the delta pressure measurement  213  may represent the difference between the third APWD measurement  203  and the first APWD measurement  201 , and so on. 
     The delta pressure measurements  212 - 217  may include less data than their corresponding (e.g., uncompressed) APWD measurement  202 - 207 . For example, the delta pressure measurements  212 - 217  may be represented by six bits. The delta pressure measurements  212 - 217  may be able to catch up a pressure variation up to a pre-defined limit for the time period during which the APWD measurements  201 - 207  are obtained. For example, the limit may be set to ±300 psi. When larger dynamic pressure ranges are expected, additional reference samples may be inserted into the telemetry frame  210  to shorten the time spacing between the delta pressure measurements  212 - 217  and the corresponding reference sample  211 . 
     The delta pressure measurements (e.g., value  213 ) may be calculated from the reference APWD measurement  201 , rather than from the previous APWD measurement (e.g., value  202 ), as the delta-modulation does, to avoid propagation errors from telemetry or from APWD measurements beyond the designed limit (e.g., ±300 psi). The compression of the APWD measurements  211 - 217  may be on-demand. For example, when a request of a pressure sample from the telemetry module  135  arrives, the compressor  182  (see  FIG. 1 ) may locate the latest APWD measurement  201 - 207 , apply compression, and return the result to the telemetry module  135 . 
     Quantization and Encoding 
     Equation (1) may be used to quantize and encode the APWD measurements  201 - 207 :
 
 P   i   =[p   i   ·q]   (1)
 
     Where p i  represents the pressure value of the ith sample, P i  represents the corresponding quantized value, q represents the quantizer, and the square brackets [ ] represent the rounding operator. The quantizer q may be selected based on the desired accuracy. For example, selecting q=0.1 may yield a 10 psi resolution (e.g., ±5 psi quantization error). 
     The reference value  211  is denoted as P 0 , and the delta pressure measurements  212 - 217  are denoted as ΔP i . Thus, Equation (2) may be:
 
Δ P   i   =P   i   −P   0    (2)
 
     The reference value P 0  may be encoded with a 12-bit unsigned magnitude code. Thus, P 0  ε [0, 4095]. Choosing quantizer q=0.1, the quantization and coding scheme may allow p 0  ε [0, 40930] psi, as the values P 0 =4094 and 4095 may be used for exception handling. A reference pressure value outside the range may be truncated at the boundary limits. 
     The delta-values ΔP i  may be encoded with 6-bit signed magnitude codes. Choosing quantizer q=0.1, ΔP i  may be confined within the range [−31, 30], corresponding to pressure differences within [−310, 300] psi from the reference value. A pressure difference outside the range may be truncated at the limits. During coding, ΔP i  may be further shifted to an unsigned representation by Equation (3):
 
Δ P   i   =ΔP   i +31   (3)
 
     which makes ΔP i  fall in the range of 0˜61. Knowing that 6-bits may represent values of [0, 63], the values ΔP i =62 and 63 may again be used for exception handling. 
     Exception Handling 
     There may be cases of exceptions including (1) inaccurate APWD measurements  201 - 207  from the pressure gauge in the LWD module  140  and/or MWD module  150 , and/or (2) a communication error between the LWD module  140  and/or MWD module  150  and the telemetry module  135 . 
     The two scenarios may occur on both the reference sample  211  and the delta pressure measurements  212 - 217 . When an exception occurs to the reference sample  211 , both the reference sample  211  and the corresponding delta pressure measurements  212 - 217  may be discarded at the decompression end. When an exception occurs to one of the compressed delta values (e.g., value  213 ), the single APWD measurement (e.g., value  203 ), corresponding to the delta pressure measurement  213 , may be discarded. In the example shown in Table 1 example, the following values may be designated to indicate the above exceptions: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 Delta Pressure 
               
               
                   
                 Reference 
                 Measurement 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Communication Error 
                 4095 
                 63 
               
               
                   
                 Bad Pressure Reading 
                 4094 
                 62 
               
               
                   
                   
               
            
           
         
       
     
     Update Rate vs Bandwidth Consumption 
     The bandwidth usage for the transmission of the delta pressure measurements  212 - 217  may at least partially depend upon the desired sample update rate. The bandwidth usage may also be slightly affected by the repeating frame  210 . Equation (4) illustrates the relation between the bandwidth usage and the repeating frame  210 : 
     
       
         
           
             
               
                 
                   B 
                   = 
                   
                     
                       12 
                       × 
                       6 
                       × 
                       
                         [ 
                         
                           
                             floor 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     T 
                                     f 
                                   
                                   / 
                                   Δ 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                           - 
                           1 
                         
                         ] 
                       
                     
                     
                       T 
                       f 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where B represents the bandwidth usage in bits-per-second, Δt represents the sample update spacing in seconds, and T f  represents the repeating frame time in seconds. 
       FIG. 3  depicts a graph  300  showing the relation between the bandwidth consumption and the sample update spacing, according to an embodiment. To obtain a pressure sample at, for example, every six to 10 seconds, bandwidths from 1.0 bps down to 0.6 bps may be used. This indicates that sending the high sampling rate APWD measurements  201 - 207  may be achievable under the typical mud pulse telemetry running at a 3-6 bps data rate. 
     Error Rate 
     As mentioned the above, the proposed method of differential encoding may reduce error propagation compared to the conventional differential pulse code modulation (“DPCM”) or delta modulation methods.  FIG. 4  depicts a graph  400  showing the difference of the error corruption rates between the proposed method and the DPCM method, according to an embodiment. The example shown in  FIG. 4  corresponds to a telemetry frame that contains 20 samples of delta pressure measurements with one reference value at the beginning. The X-axis may be the telemetry error rate ranging from one-per-thousand to one percent. The Y-axis may be the error rate of delta pressure measurements (i.e., the fractions of the delta pressure measurements being corrupted due to telemetry corruptions). As may been seen, at the typical telemetry error rate of three-per-thousand, the delta pressure measurement error rate of the proposed method is about 5%, compared to 21% given by the DPCM method. Even under noisy telemetry conditions with a 1% error rate, the measurements transmitted by the proposed method still provide an update rate that drops about ⅙ of the corrupted samples, while the DPCM method yields about ⅔ of the corrupted samples. 
       FIGS. 5 and 6  depict graphs  500 ,  600 , respectively, showing two cases of APWD measurements retrieved from compressed transmission, according to an embodiment. The first graph  500  shows the comparison between the original APWD measurements sampled at a two-second rate before compression  502  and the surface received data after compression  504  sampled at an eight-second rate. The second graph  600  shows the moving averages of 32-second windows from the original data  602  and from the compressed data  604 . As may be seen, the curves before and after compression match very well, even in the area where the data is very noisy and presents dynamic ranges more than 200 psi within about 20 second time intervals. 
       FIG. 7  depicts a flowchart of a method  700  for transmitting APWD measurements  201 - 207  from a downhole tool  130  to a surface location, according to an embodiment. Although the method  700  is described with reference to APWD measurements  201 - 207 , it will be appreciated that the method  700  may also be applied to other types of measurements obtained by the LWD tool  140  or the MWD tool  150 . 
     The method  700  may begin by running the downhole tool  130  into the wellbore  100 , as at  702 . The method  700  may also include measuring the annulus pressure in the wellbore  100  at a first time to produce a first APWD measurement  201 , as at  704 . The annulus pressure may be measured with a pressure sensor  180  that is part of the downhole tool  130 . More particularly, the pressure sensor  180  may be part of the LWD tool  140  or the MWD tool  150 . The method  700  may then include compressing the first APWD measurement  201  to produce a compressed reference sample  211 , as at  706 . The compression device  182  (see  FIG. 1 ) may be positioned within the LWD tool  140  or the MWD tool  150  that obtains the APWD measurement  201 . The method  700  may then include modulating and transmitting the compressed reference sample  211  to a receiver at the surface location using the telemetry pulser  135 , as at  708 . 
     The method  700  may then include measuring the annulus pressure in the wellbore at a second time to produce a second APWD measurement  202 , as at  710 . The method  700  may then include determining a change in the annulus pressure between the first APWD measurement  201  and the second APWD measurement  202  to produce a first delta pressure measurement  212 , as at  712 . The method  700  may then include compressing the first delta pressure measurement  212 , as at  714 . The method  700  may then include modulating and transmitting the first delta pressure measurement  212  to the receiver at the surface location using the telemetry pulser  135 , as at  716 . 
     The method  700  may also include demodulating the compressed reference sample  211  and the first delta pressure measurement  212  using a demodulator  184  at the surface location, as at  718 . The method  700  may then include decompressing the compressed reference sample  211  and/or the first delta pressure measurement  212  using a decompressor  186  at the surface location, as at  720 . In response to receiving the compressed reference sample  211  and the first delta pressure measurement  212 , a user may reduce the weight of the mud that is being pumped into the wellbore from the surface, vary the flow rate of the mud that is being pumped into the wellbore from the surface, vary the weight on the drill bit, or a combination thereof. 
     If the (now uncompressed) delta pressure measurement is outside a predetermined range, a user may understand that the corresponding APWD measurements ( 201 - 207 ) are beyond the compressible data range of [−310, 300] from the reference sample ( 200 ) and determine whether the out or range APWD measurements may have gone beyond the pressure limits allowed by the designed MPD task. 
     The method  700  may be repeated for additional APWD measurements (e.g., value  203 ). Subsequent delta pressure measurements (e.g., value  213 ) may be produced by determining a change in the annulus pressure between the first APWD measurement  201  and the third APWD measurement  203  to produce a second delta pressure measurement  213 . The method  700  may then include compressing the second delta pressure measurement  213 . The method  700  may then include modulating and transmitting the second delta pressure measurement  213  to the receiver at the surface location using the telemetry pulser  135 . 
       FIG. 8  depicts a flow chart of a method  800  for compressing the APWD measurements  201 - 207 , according to an embodiment. The method  800  may include obtaining a first APWD measurement (e.g., value  201 ) using the pressure sensor  180  in the downhole tool  130 , as at  802 . The first APWD measurement  201  may be obtained in response to a request from the telemetry pulser  135  in the downhole tool  130 . The method  800  may then include compressing or confining the first APWD measurement  201  to a predetermined data range, as at  804 . The compression/confinement may be performed within the downhole tool  130  (e.g., within the compression device  182  in the downhole tool  130 ). The predetermined data range may be, for example, [0, 30000] psi. Data outside the predetermined range may be truncated. 
     The method  800  may also include quantizing the first APWD measurement  201 , as at  806 . The quantization may be performed within the downhole tool  130  (e.g., within the compression device  182  in the downhole tool  130 ). The quantization may be a linear quantization. The step size of the quantization may be from about 1 psi to about 100 psi or from about 2 psi to about 20 psi. For example, the step size may be about 10 psi. After the quantization, the first APWD measurement  201  may be represented by an integer including a plurality of bits. The number of bits may be from about 6 bits to about 18 bits or from about 8 bits to about 16 bits. For example, the first APWD measurement  201  may be represented by a 12-bit integer. Thus, the first APWD measurement may now be the reference sample  211 . 
     If the first APWD measurement  211  is to be used as the reference sample, then the method  800  may include copying or storing the first APWD measurement  211  into a reference sample location in the downhole tool  130  (e.g., a particular memory location), as at  808 . The method  800  may then include transmitting the first APWD measurement  211  to the telemetry pulser  135  in the downhole tool  130 , as at  810 . 
     The method  800  may also include obtaining a second APWD measurement  202  using the pressure sensor  180  in the downhole tool  130 , as at  812 . The second APWD measurement  202  may be obtained in response to another request from the telemetry pulser  135  in the downhole tool  130 . The method  800  may then include compressing or confining the second APWD measurement  202  to the predetermined data range, as at  814 . The predetermined data range may be the same as above, for example, [0, 30000] psi. Data outside the predetermined range may be truncated. 
     The method  800  may also include quantizing the second APWD measurement  202 , as at  816 . The quantization may be performed within the downhole tool  130  (e.g., within the compression device  182  in the downhole tool  130 ). The quantization may be a linear quantization. The step size of the quantization may be from about 1 psi to about 100 psi or from about 2 psi to about 20 psi. For example, the step size may be about 10 psi. After the quantization, the second APWD measurement  202  may be represented by an integer including a plurality of bits. The number of bits may be from about 6 bits to about 18 bits or from about 8 bits to about 16 bits. For example, the second APWD measurement  202  may be represented by a 12-bit integer. 
     If the second APWD measurement  202  is to be used to determine one of the delta pressure measurements (e.g., value  212 ), then the method  800  may include determining the difference between the second APWD measurement  202  and the first APWD measurement  201 , as at  818 . As this value may be negative in some embodiments, the method  800  may also include adding a predetermined number to the difference between the second APWD measurement  202  and the first APWD measurement  201  to produce a positive output value, as at  820 . The predetermined number may be from about 1 to about 63 (or more). For example, the predetermined number may be 61 corresponding to a 6 bit number (0-63), where 62 and 63 have been assigned already. 
     The method  800  may then include compressing or confining the positive output to a predetermined data range, as at  822 . The predetermined data range may be, for example, [0, 61]. Data outside the predetermined range may be truncated. The method  800  may then include transmitting the positive output (corresponding to the difference between the second APWD measurement  202  and the first APWD measurement  201 ) to the telemetry pulser  135  in the downhole tool  130 , as at  824 . 
       FIG. 9  depicts a flow chart of a method  900  for decompressing the APWD measurements  211 - 217 , according to an embodiment. The method  900  may begin by receiving a first compressed APWD measurement  211 - 217 , as at  902 . The first compressed APWD measurement  211 - 217  may be received by a decompressor  186  at a surface location. Prior to being received by the decompressor  186 , the compressed APWD measurement  211 - 217  may be transmitted from the downhole tool  130  (in the wellbore  100 ) to a demodulator  184  at the surface location, and the demodulator  184  may demodulate the compressed first APWD measurement  211 - 217  before sending the compressed first APWD measurement  211 - 217  to the decompressor  186 . 
     If the first compressed APWD measurement  211 - 217  is 12 bits, this may indicate that the first compressed APWD measurement  211 - 217  represents the reference sample (e.g., value  211 ). The method  900  may then include determining whether the first compressed APWD measurement  211  is greater than a first predetermined number, as at  904 . The first predetermined number may be from about 1 to about 4095 (or more). For example, the first predetermined number may be  4093  corresponding to a 12-bit number (0-4095), where 4094 and 4095 have been assigned already. 
     If the first compressed APWD measurement  211  is greater than the first predetermined number, an absent value may be assigned to the APWD measurement (e.g., value  201 ) corresponding to the first compressed APWD measurement  211 , indicating that the APWD measurement  201  is invalid. The APWD measurement  201  may be invalid for any of the reasons described above. If the first compressed APWD measurement  211  is less than the predetermined number, the first compressed APWD measurement  211  may be de-quantized to produce a decompressed APWD measurement, as at  906 . 
     The method  900  may also include receiving a second compressed APWD measurement  211 - 217 , as at  908 . If the second compressed APWD measurement  211 - 217  is 6 bits, this may indicate that the second compressed APWD measurement  211 - 217  represents one of the delta pressure measurements (e.g., value  212 ). The method  900  may then include determining whether the second compressed APWD measurement  212  is greater than a second predetermined number, as at  910 . The second predetermined number may be from about 1 to about 63 (or more). For example, the second predetermined number may be 61 corresponding to a 6 bit number (0-63), where 62 and 63 have been assigned already. 
     If the second compressed APWD measurement  212  is greater than the second predetermined number, an absent value may be assigned to the APWD measurement (e.g., value  202 ) corresponding to the second compressed APWD measurement  212 , indicating that the APWD measurement  202  is invalid. If the second compressed APWD measurement  212  is less than the second predetermined number, the second predetermined number may be subtracted from the second compressed APWD measurement  212  to produce a first output, as at  912 . 
     The first compressed APWD measurement  211  may be added to the first output to produce a second output, as at  914 . The second output may then be de-quantized to produce a decompressed APWD measurement (e.g., the APWD measurement  202 ), as at  916 . 
     The methods  700 ,  800 ,  900  disclosed herein allow transmitting the real-time APWD measurements at high sampling rates at an affordable cost of bandwidth under the normal MWD mud-pulse telemetry environment. The APWD measurements may be sent to the surface at any user desired update rates. Transmission at a 6-second update rate may cost about 1.0 bps bandwidth, and a 10-second update rate may cost about 0.64 bps. The methods  700 ,  800 ,  900  may also support a pressure range of 0-40 kpsi while providing a resolution of ±5 psi. The methods  700 ,  800 ,  900  may allow a pressure variation of ±300 psi within the time period of the telemetry frame  210 , (e.g., from 80 seconds to 200 seconds). A measurement with a pressure reading exceeding the specified data range may be truncated without affecting the subsequent measurements. The methods  700 ,  800 ,  900  may also allow the user to insert more reference samples in the telemetry frame to reduce the probability of pressure readings going beyond defined dynamic data range. The methods  700 ,  800 ,  900  may effectively avoid error propagation that presents under the standard DPCM compression schemes. Under typical mud-pulse telemetry error rate (e.g., three-per-thousand), the received sample corruption rate may be as low as 5%. The methods  700 ,  800 ,  900  do not introduce any additional transmission delay due to compression and, thus, make it possible for drilling operators to predict and to react promptly to a quick pressure change. 
       FIG. 10  depicts a computing system  1000  for performing the methods  700 ,  800 ,  900 , according to an embodiment. The computing system  1000  may include a computer or computer system  1001 A, which may be an individual computer system  1001 A or an arrangement of distributed computer systems. The computer system  1001 A may be at least partially disposed within the downhole tool  130 . The computer system  1001 A includes one or more analysis modules  1002  that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module  1002  executes independently, or in coordination with, one or more processors  1004 , which is (or are) connected to one or more storage media  1006 A. The processor(s)  1004  is (or are) also connected to a network interface  1007  to allow the computer system  1001 A to communicate over a data network  1009  with one or more additional computer systems and/or computing systems, such as  1001 B,  1001 C, and/or  1001 D (note that computer systems  1001 B,  1001 C and/or  1001 D may or may not share the same architecture as computer system  1001 A, and may be located in different physical locations, e.g., computer systems  1001 A and  1001 B may be located in a processing facility, while in communication with one or more computer systems such as  1001 C and/or  1001 D that are located in one or more data centers, and/or located in varying countries on different continents). 
     A processor can include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device. 
     The storage media  1006 A can be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of  FIG. 10  storage media  1006 A is depicted as within computer system  1001 A, in some embodiments, storage media  1006 A may be distributed within and/or across multiple internal and/or external enclosures of computing system  1001 A and/or additional computing systems. Storage media  1006 A may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURRY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above can be provided on one computer-readable or machine-readable storage medium, or alternatively, can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution. 
     In some embodiments, computing system  1000  contains one or more APWD compression module(s)  1008 . The APWD compression module  1008  may be configured to compress the APWD measurements  201 - 207  prior to transmitting the measurements to the surface location. 
     It should be appreciated that computing system  1000  is only one example of a computing system, and that computing system  1000  may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of  FIG. 10 , and/or computing system  1000  may have a different configuration or arrangement of the components depicted in  FIG. 10 . The various components shown in  FIG. 10  may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits. 
     Further, the steps in the processing methods described herein may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are all included within the scope of protection of the invention. 
     As used herein, the terms “inner” and “outer”; “up” and “down”; “upper” and “lower”; “upward” and “downward”; “above” and “below”; “inward” and “outward”; and other like terms as used herein refer to relative positions to one another and are not intended to denote a particular direction or spatial orientation. The terms “couple,” “coupled,” “connect,” “connection,” “connected,” “in connection with,” and “connecting” refer to “in direct connection with” or “in connection with via one or more intermediate elements or members.” 
     Although the preceding description has been described herein with reference to particular means, materials, and embodiments, it is not intended to be limited to the particulars disclosed herein; rather, it extends to all functionally equivalent structures, methods, and uses, such as are contemplated within the scope of the appended claims. While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof.