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CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 09/621,398 filed on Jul. 21, 2000, now U.S. Pat. No. 6,478,096, the specification of which is incorporated herein by reference, and is related to U.S. provisional patent application Ser. No. 60/219,741 filed on Jul. 20, 2000, the specification of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention generally relates to the testing of underground formations or reservoirs. More particularly, this invention relates to a reduced volume method and apparatus for sampling and testing a formation fluid using multiple regression analysis. 
     2. Description of the Related Art 
     To obtain hydrocarbons such as oil and gas, well boreholes are drilled by rotating a drill bit attached at a drill string end. The drill string may be a jointed rotatable pipe or a coiled tube. A large portion of the current drilling activity involves directional drilling, i.e., drilling boreholes deviated from vertical and/or horizontal boreholes, to increase the hydrocarbon production and/or to withdraw additional hydrocarbons from earth formations. Modern directional drilling systems generally employ a drill string having a bottomhole assembly (BHA) and a drill bit at an end thereof that is rotated by a drill motor (mud motor) and/or the drill string. A number of downhole devices placed in close proximity to the drill bit measure certain downhole operating parameters associated with the drill string. Such devices typically include sensors for measuring downhole temperature and pressure, azimuth and inclination measuring devices and a resistivity-measuring device to determine the presence of hydrocarbons and water. Additional downhole instruments, known as measurement-while-drilling (MWD) or logging-while-drilling (LWD) tools, are frequently attached to the drill string to determine formation geology and formation fluid conditions during the drilling operations. 
     One type of while-drilling test involves producing fluid from the reservoir, collecting samples, shutting-in the well, reducing a test volume pressure, and allowing the pressure to build-up to a static level. This sequence may be repeated several times at several different reservoirs within a given borehole or at several points in a single reservoir. This type of test is known as a “Pressure Build-up Test.” One important aspect of data collected during such a Pressure Build-up Test is the pressure build-up information gathered after drawing down the pressure in the test volume. From this data, information can be derived as to permeability and size of the reservoir. Moreover, actual samples of the reservoir fluid can be obtained and tested to gather Pressure-Volume-Temperature data relevant to the reservoir&#39;s hydrocarbon distribution. 
     Some systems require retrieval of the drill string from the borehole to perform pressure testing. The drill string is removed, and a pressure measuring tool is run into the borehole using a wireline tool having packers for isolating the reservoir. Although wireline conveyed tools are capable of testing a reservoir, it is difficult to convey a wireline tool in a deviated borehole. 
     The amount of time and money required for retrieving the drill string and running a second test rig into the hole is significant. Further, when a hole is highly deviated wireline conveyed test figures cannot be used because frictional force between the test rig and the wellbore exceed gravitational force causing the test rig to stop before reaching the desired formation. 
     A more recent system is disclosed in U.S. Pat. No. 5,803,186 to Berger et al. The &#39;186 patent provides a MWD system that includes use of pressure and resistivity sensors with the MWD system, to allow for real time data transmission of those measurements. The &#39;186 device enables obtaining static pressures, pressure build-ups, and pressure draw-downs with a work string, such as a drill string, in place. Also, computation of permeability and other reservoir parameters based on the pressure measurements can be accomplished without removing the drill string from the borehole. 
     Using a device as described in the &#39;186 patent, density of the drilling fluid is calculated during drilling to adjust drilling efficiency while maintaining safety. The density calculation is based upon the desired relationship between the weight of the drilling mud column and the predicted downhole pressures to be encountered. After a test is taken a new prediction is made, the mud density is adjusted as required and the bit advances until another test is taken. 
     A drawback of this type of tool is encountered when different formations are penetrated during drilling. The pressure can change significantly from one formation to the next and in short distances due to different formation compositions. If formation pressure is lower than expected, the pressure from the mud column may cause unnecessary damage to the formation. If the formation pressure is higher than expected, a pressure kick could result. Consequently, delay in providing measured pressure information to the operator may result in drilling mud being maintained at too high or too low a density. 
     Another drawback of the &#39;186 patent, as well as other systems requiring large fluid intake, is that system clogging caused by debris in the fluid can seriously impede drilling operations. When drawing fluid into the system, cuttings from the drill bit or other rocks being carried by the fluid may enter the system. The &#39;186 patent discloses a series of conduit paths and valves through which the fluid must travel. It is possible for debris to clog the system at any valve location, at a conduit bend or at any location where conduit size changes. If the system is clogged, the tool must be retrieved from the borehole for cleaning causing delay in the drilling operation. Therefore, it is desirable to have an apparatus with reduced risk of clogging. 
     Another drawback of the &#39;186 patent is that it has a large system volume. Filling a system with fluid takes time, so a system with a large internal volume requires more time for the system to respond during a drawdown cycle. Therefore it is desirable to have a small internal system volume in order to reduce sampling and test time. 
     SUMMARY OF THE INVENTION 
     The present invention addresses some of the drawbacks discussed above by providing a measurement while drilling apparatus and method which enables sampling and measurements of parameters of fluids contained in a borehole while reducing the time required for taking such samples and measurements and reducing the risk of system clogging. 
     One aspect of the present invention provides a method for determining a parameter of interest of a formation while drilling. The method comprises conveying a tool on a drill string into a borehole traversing the formation and extending at least one selectively extendable probe disposed on the tool to make sealing engagement with a portion of the formation. A port is exposed to the sealed portion of the formation, the port providing fluid communication between the formation and a first volume within the tool. The first volume is varied with a volume control device using a plurality of volume change rates. The method includes determining at least one characteristic of the first volume using a test device at least twice during each of the plurality of volume change rates, and using multiple regression analysis to determine the formation parameter of interest using the at least one characteristic determined during the plurality of volume change rates. 
     Another aspect of the present invention provides a method for determining a parameter of interest of a formation while drilling. The method comprises conveying a tool on a drill string into a borehole traversing the formation and extending at least one selectively extendable probe disposed on the tool to make sealing engagement with a portion of the formation. A port is exposed to the sealed portion of the formation, the port providing fluid communication between the formation and a first volume within the tool, the first volume being selectively variable between zero cubic centimeters and 1000 cubic centimeters. The first volume is varied with a volume control device using a plurality of volume change rates. The method includes determining at least one characteristic of the first volume using a test device at least twice during each of the plurality of volume change rates, and determining the formation parameter of interest using the at least one sensed characteristic sensed during the plurality of volume change rates. 
     The novel features of this invention, as well as the invention itself, will be best understood from the attached drawings, taken along with the following description, in which similar reference characters refer to similar parts. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an elevation view of an offshore drilling system according to one embodiment of the present invention. 
     FIG. 2 shows a preferred embodiment of the present invention wherein downhole components are housed in a portion of drill string with a surface controller shown schematically. 
     FIG. 3 is a detailed cross sectional view of an integrated pump and pad in an inactive state according to the present invention. 
     FIG. 4 is a cross sectional view of an integrated pump and pad showing an extended pad member according to the present invention. 
     FIG. 5 is a cross sectional view of an integrated pump and pad after a pressure test according to the present invention. 
     FIG. 6 is a cross sectional view of an integrated pump and pad after flushing the system according to the present invention. 
     FIG. 7 shows an alternate embodiment of the present invention wherein packers are not required. 
     FIG. 8 shows and alternate mode of operation of a preferred embodiment wherein samples are taken with the pad member in a retracted position. 
     FIG. 9 shows a plot illustrating a method according to the present invention. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 is a typical drilling rig  102  with a borehole  104  being drilled into subterranean formations  118 , as is well understood by those of ordinary skill in the art. The drilling rig  102  has a drill string  106 . The present invention may use any number of drill strings, such as, jointed pipe, coiled tubing or other small diameter work string such as snubbing pipe. The drill string  106  has attached thereto a drill bit  108  for drilling the borehole  104 . The drilling rig  102  is shown positioned on a drilling ship  122  with a riser  124  extending from the drilling ship  122  to the sea floor  120 . 
     If applicable, the drill string  106  can have a downhole drill motor  110  for rotating the drill bit  108 . Incorporated in the drill string  106  above the drill bit  108  is at least one typical sensor  114  to sense downhole characteristics of the borehole, the bit, and the reservoir. Typical sensors sense characteristics such as temperature, pressure, bit speed, depth, gravitational pull, orientation, azimuth, fluid density, dielectric, etc. The drill string  106  also contains the formation test apparatus  116  of the present invention, which will be described in greater detail hereinafter. A telemetry system  112  is located in a suitable location on the drill string  106  such as uphole from the test apparatus  116 . The telemetry system  112  is used to receive commands from, and send data to, the surface. 
     FIG. 2 is a cross section elevation view of a preferred system according to the present invention. The system includes surface components and downhole components to carry out “Formation Testing While Drilling” (FTWD) operations. A borehole  104  is shown drilled into a formation  118  containing a formation fluid  216 . Disposed in the borehole  104  is a drill string  106 . The downhole components are conveyed on the drill string  106 , and the surface components are located in suitable locations on the surface. A surface controller  202  typically includes a communication system  204  electronically connected to a processor  206  and an input/output device  208 , all of which are well known in the art. The input/out device  208  may be a typical terminal for user inputs. A display such as a monitor or graphical user interface may be included for real time user interface. When hard-copy reports are desired, a printer may be used. Storage media such as CD, tape or disk are used to store data retrieved from downhole for future analyses. The processor  206  is used for processing (encoding) commands to be transmitted downhole and for processing (decoding) data received from downhole via the communication system  204 . The surface communication system  204  includes a receiver for receiving data transmitted from downhole and transferring the data to the surface processor for evaluation recording and display. A transmitter is also included with the communication system  204  to send commands to the downhole components. Telemetry is typically relatively slow mud-pulse telemetry, so downhole processors are often deployed for preprocessing data prior to transmitting results of the processed data to the surface. 
     A known communication and power unit  212  is disposed in the drill string  106  and includes a transmitter and receiver for two-way communication with the surface controller  202 . The power unit, typically a mud turbine generator, provides electrical power to run the downhole components. Alternatively, the power unit  212  may be a battery package or a pressurized chamber. 
     Connected to the communication and power unit  212  is a controller  214 . As stated earlier, a downhole processor (not separately shown) is preferred when using mud-pulse telemetry; the processor being integral to the controller  214 . The controller  214  uses preprogrammed commands, surface-initiated commands or a combination of the two to control the downhole components. The controller controls the extension of anchoring, stabilizing and sealing elements disposed on the drill string, such as grippers  210  and packers  232  and  234 . The control of various valves (not shown) can control the inflation and deflation of packers  232  and  234  by directing drilling mud flowing through the drill string  106  to the packers  232  and  234 . This is an efficient and well-known method to seal a portion of the annulus or to provide drill string stabilization while sampling and tests are conducted. When deployed, the packers  232  and  234  separate the annulus into an upper annulus  226 , an intermediate annulus  228  and a lower annulus  230 . The creation of the intermediate annulus  28  sealed from the upper annulus  226  and lower annulus  230  provides a smaller annular volume for enhanced control of the fluid contained in the volume. 
     The grippers  210 , preferably have a roughened end surface for engaging the well wall  244  to anchor the drill string  106 . Anchoring the drill string  106  protects soft components such as the packers  232  and  234  and pad member  220  from damage due to tool movement. The grippers  210  would be especially desirable in offshore systems such as the one shown in FIG. 1, because movement caused by heave can cause premature wear out of sealing components. 
     The controller  214  is also used to control a plurality of valves  241  combined in a multi-position valve assembly or series of independent valves. The valves  241  direct fluid flow driven by a pump  238  disposed in the drill string  106  to control a drawdown assembly  200 . The drawdown assembly  200  includes a pad piston  222  and a drawdown piston or otherwise called a draw piston  236 . The pump  238  may also control pressure in the intermediate annulus  228  by pumping fluid from the annulus  228  through a vent  218 . The annular fluid may be stored in an optional storage tank  242  or vented to the upper  226  or lower annulus  230  through standard piping and the vent  218 . 
     Mounted on the drill string  106  via a pad piston  222  is a pad member  220  for engaging the borehole wall  244 . The pad member  220  is a soft elastomer cushion such as rubber. The pad piston  222  is used to extend the pad  220  to the borehole wall  244 . A pad  220  seals a portion of the annulus  228  from the rest of the annulus. A port  246  located on the pad  220  is exposed to formation fluid  216 , which tends to enter the sealed annulus when the pressure at the port  246  drops below the pressure of the surrounding formation  118 . The port pressure is reduced and the formation fluid  216  is drawn into the port  246  by a draw piston  236 . The draw piston  236  is integral to the pad piston  222  for limiting the fluid volume within the tool. The small volume allows for faster measurements and reduces the probability of system contamination from the debris being drawn into the system with the fluid. A hydraulic pump  238  preferably operates the draw piston  236 . Alternatively, a mechanical or an electrical drive motor may be used to operate the draw piston  236 . 
     It is possible to cause damage downhole seals and the borehole mudcake when extending the pad member  220 , expanding the packers  232  and  234 , or when venting fluid. Care should be exercised to ensure the pressure is vented or exhausted to an area outside the intermediate annulus  228 . FIG. 2 shows a preferred location for the vent  218  above the upper packer  232 . It is also possible to prevent damage by leaving the pad member  220  in a retracted position with the vent  218  open until the upper and lower packers  232  and  234  are set. 
     FIGS. 3 through 6 illustrate components of the drawdown assembly  200  in several operational positions. FIG. 3 is a cross sectional view of the fluid sampling unit of FIG. 2 in its initial, inactive or transport position. In the position shown in FIG. 3, the pad member  220  is fully retracted toward a tool housing  304 . A sensor  320  is disposed at the end of the draw piston  236 . Disposed within the tool housing  304  is a piston cylinder  308  that contains hydraulic oil or drilling mud  326  in a draw reservoir  322  for operating the draw piston  236 . The draw piston  236  is coaxially disposed within the piston cylinder  308  and is shown in its outermost or initial position. In this initial position, there is substantially zero volume at the port  246 . The pad extension piston  222  is shown disposed circumferentially around and coaxially with the draw piston  236 . A barrier  306  disposed between the base of the draw piston  236  and the base of the pad extension piston  222  separates the piston cylinder  308  into an inner (or draw) reservoir  322  and an outer (or extension) reservoir  324 . The separate extension reservoir  324  allows for independent operation of the extension piston  222  relative to the draw piston  236 . The hydraulic reservoirs are preferably balanced to hydrostatic pressure of the annulus for consistent operation. 
     Referring to FIGS. 2 and 3, the drawdown assembly  200  has dedicated control lines  312 - 318  for actuating the pistons. The draw piston  236  is controlled in the “draw” direction by fluid  326  entering a “draw” line  314  while fluid  326  exits through a “flush” line  312 . When fluid flow is reversed in these lines, the draw piston  236  travels in the opposite or outward direction. Independent of the draw piston  236 , the pad extension piston  222  is forced outward by fluid  328  entering a pad deploy line  316  while fluid  328  exits a pad retract line  318 . Like the draw piston  236 , the travel of the pad extension piston  222  is reversed when the fluid  328  in the lines  316  and  318  reverses direction. As shown in FIG. 2, the downhole controller  214  controls the line selection, and thus the direction of travel, by controlling the valves  241 . The pump  238  provides the fluid pressure in the line selected. 
     Referring now to FIG. 4, the pad extension piston  222  of drawdown assembly  200  is shown at its outermost position. In this position, the pad  220  is in sealing engagement with the borehole wall  244 . To get to this position, the pad extension piston  222  is forced radially outward and perpendicular to a longitudinal axis of the drill string  106  by fluid  328  entering the outer reservoir  324  through the pad deploy line  316 . The port  246  located at the end of the pad  220  is open, and formation fluid  216  will enter the port  246  when the draw piston  236  is activated. 
     Test volume can be reduced to substantially zero in an alternate embodiment according to the present invention. Still referring to FIG. 4, if the sensor  320  is slightly reconfigured to translate with the draw piston  236 , and the draw piston is extended to the borehole wall  244  with the pad piston  222  there would be zero volume at the port  246 . One way to extend the draw piston  236  to the borehole wall  244  is to extend the housing assembly  304  until the pad  220  contacts the wall  244 . If the housing  304  is extended, then there is no need to extend the pad piston  222 . At the beginning of a test with the housing  304  extended, the pad  220 , port  246 , sensor  320 , and draw piston  236  are all urged against the wall  244 . Pressure should be vented to the upper annulus  226  via a vent valve  240  and vent  218  when extending elements into the annulus to prevent over pressurizing the intermediate annulus  228 . 
     Another embodiment enabling the draw piston to extend does not include the barrier  306 . In this embodiment (not shown separately), the flush line  312  is used to extend both pistons. The pad extension line  316  would then not be necessary, and the draw line  314  would be moved closer to the pad retract line  318 . The actual placement of the draw line  314  would be such that the space between the base of the draw piston  236  and the base of the pad extension piston  222  aligns with the draw line  314 , when both pistons are fully extended. 
     Referring now to FIG. 5, a cross-sectional view of the drawdown assembly  200  is shown after sampling. Formation fluid  216  is drawn into a sampling reservoir  502  when the draw piston  236  moves inward toward the base of the housing  304 . As described earlier, movement of the draw piston  236  toward the base of the housing  304  is accomplished by hydraulic fluid or mud  326  entering the draw reservoir  322  through the draw line  314  and exiting through the flush line  312 . Clean fluid, meaning formation fluid  216  substantially free of contamination by drilling mud, can be obtained with several draw-flush-draw cycles. Flushing, which will be described in detail later, may be required to obtain clean fluid for sample purposes. The present invention, however, provides sufficiently clean fluid in the initial draw for testing purposes. 
     Fluid drawn into the system may be tested downhole with one or more sensors  320 , or the fluid may be pumped through valves  243  to optional storage tanks  242  for retrieval and surface analysis. The sensor  320  may be located at the port  246 , with its output being transmitted or connected to the controller  214  via a sensor tube  310  as a feedback circuit. The controller may be programmed to control the draw of fluid from the formation based on the sensor output. The sensor  320  may also be located at any other desired suitable location in the system. If not located at the port  246 , the sensor  320  is preferably in fluid communication with the port  246  via the sensor tube  310 . 
     Referring to FIGS. 2 and 6, a cross sectional view of the drawdown assembly  200  is shown after flushing the system. The system draw piston  236  flushes the system when it is returned to its pre-draw position or when both pistons  222  and  236  are returned to the initial positions. The translation of the fluid piston  236  to flush the system occurs when fluid  326  is pumped into the draw reservoir through the flush line  312 . Formation fluid  216  contained in the sample reservoir  502  is forced out of the reservoir as shown in FIG. 5. A check valve  602  may be used to allow fluid to exit into the annulus  228 , or the fluid may be forced out through the vent  218  to the annulus  226 . 
     FIG. 7 shows an alternative embodiment of the present invention wherein packers are not required and the optional storage reservoirs are not used. A drill string  106  carries downhole components comprising a communication/power unit  212 , controller  214 , pump  708 , a valve assembly  710 , stabilizers  704 , and a drawdown assembly  200 . A surface controller sends commands to and receives data from the downhole components. The surface controller comprises a two-way communications unit  204 , a processor  206 , and an input-out device  208 . 
     In this embodiment, stabilizers or grippers  704  selectively extend to engage the borehole wall  244  to stabilize or anchor the drill string  106  when the drawdown assembly  200  is adjacent a formation  118  to be tested. A pad extension piston  222  extends in a direction generally opposite the grippers  704 . The pad  220  is disposed on the end of the pad extension piston  222  and seals a portion of the annulus  702  at the port  246 . Formation fluid  216  is then drawn into the drawdown assembly  200  as described above in the discussion of FIGS. 4 and 5. Flushing the system is accomplished as described above in the discussion of FIG.  6 . 
     The configuration of FIG. 7 shows a sensor  706  disposed in the fluid sample reservoir of the drawdown assembly  200 . The sensor senses a desired parameter of interest of the formation fluid such as pressure, and the sensor transmits data indicative of the parameter of interest back to the controller  214  via conductors, fiber optics or other suitable transmission conductor. The controller  214  further comprises a controller processor (not separately shown) that processes the data and transmits the results to the surface via the communications and power unit  212 . The surface controller receives, processes and outputs the results described above in the discussion of FIGS. 1 and 2. 
     The embodiment shown in FIG. 7 also includes a secondary tank  716  coupled to the drawdown assembly  200  via a flowline  720  and a valve  718 . The tank is used when additional system volume is desirable. Additional system volume is desirable, for example, when determining fluid compressibility. 
     The valve  718  is a switchable valve controlled by the downhole controller  214 . The use of the switchable valve  718  enables faster formation tests by allowing for smaller system volume when desired. For example, determinations of mobility and formation pressure do not require the additional volume of the secondary tank  716 . Moreover, having smaller system volume decreases test time. 
     Modifications to the embodiments described above are considered within scope of this invention. Referring to FIG. 2 for example, the draw piston  236  and pad piston  222  may be operated electrically, rather than hydraulically as shown. An electrical motor, such as a spindle motor or stepper motor, can be used to reciprocate each piston independently, or preferably, one motor controls both pistons. Spindle and stepper motors are well known, and the electrical motor could replace the pump  238  shown in FIG.  2 . If a controllable pump power source such as a spindle or stepper motor is selected, then the piston position can be selectable throughout the line of travel. This feature is preferable in applications where precise control of system volume is desired. 
     Using either a stepper motor or a spindle motor, the selected motor output shaft is connected to a device for reciprocating the pad and draw pistons  222  and  236 . A preferred device is a known ball screw assembly (BSA). A BSA uses circulating ball bearings (typically stainless steel or carbon) to roll along complementary helical groves of a nut and screw subassembly. The motor output shaft may turn either the nut or screw while the other translates linearly along the longitudinal axis of the screw subassembly. The translating component is connected to a piston, thus the piston is translated along the longitudinal axis of the screw subassembly axis. 
     Now that system embodiments of the invention have been described, a preferred method of testing a formation using the preferred system embodiment will be described. Referring first to FIGS. 1-6, a tool according to the present invention is conveyed into a borehole  104  on a drill string  106 . The drill string is anchored to the well wall using a plurality of grippers  210  that are extended using methods well known in the art. The annulus between the drill string  106  and borehole wall  244  is separated into an upper section  226 , an intermediate section  228  and a lower section  230  using expandable packers  232  and  234  known in the art. Using a pad extension piston  222 , a pad member  220  is brought into sealing contact with the borehole wall  244  preferably in the intermediate annulus section  228 . Using a pump  238 , drilling fluid pressure in the intermediate annulus  228  is reduced by pumping fluid from the section through a vent  218 . A draw piston  236  is used to draw formation fluid  216  into a fluid sample volume  502  through a port  246  located on the pad  220 . At least one parameter of interest such as formation pressure, temperature, fluid dielectric constant or resistivity is sensed with a sensor  320 , and a downhole processor processes the sensor output. The results are then transmitted to the surface using a two-way communications unit  212  disposed downhole on the drill string  106 . Using a surface communications unit  204 , the results are received and forwarded to a surface processor  206 . The method further comprises processing the data at the surface for output to a display unit, printer, or storage device  208 . 
     A test using substantially zero volume can be accomplished using an alternative method according to the present invention. To ensure initial volume is substantially zero, the draw piston  236  and sensor are extended along with the pad  220  and pad piston  222  to seal off a portion of the borehole wall  244 . The remainder of this alternative method is essentially the same as the embodiment described above. The major difference is that the draw piston  236  need only be translated a small distance back into the tool to draw formation fluid into the port  246  thereby contacting the sensor  320 . The very small volume reduces the time required for the volume parameters being sensed to equalize with the formation parameters. 
     FIG. 8 illustrates another method of operation wherein samples of formation fluid  216  are taken with the pad member  220  in a retracted position. The annulus is separated into the several sealed sections  226 ,  228  and  230  as described above using expandable packers  232  and  234 . Using a pump  238 , drilling fluid pressure in the intermediate annulus  228  is reduced by pumping fluid from the section through a vent  218 . With the pressure in the intermediate annulus  228  lower than the formation pressure, formation fluid  216  fills the intermediate annulus  228 . If the pumping process continues, the fluid in the intermediate annulus becomes substantially free of contamination by drilling mud. Then without extending the pad member  220 , the draw piston  236  is used to draw formation fluid  216  into a fluid sample volume  502  through a port  246  exposed to the fluid  216 . At least one parameter of interest such as those described above is sensed with a sensor  320 , and a downhole processor processes the sensor output. The processed data is then transmitted to the surface controller  202  for further processing and output as described above. 
     A method of evaluating a formation using a probe with small system volume is provided in another embodiment of the present invention. The method includes using a tool with small system volume, such as the drawdown assembly  200  described above and shown in FIGS. 1-7. 
     The method includes sealing a portion of a well borehole wall with the extendable drawdown assembly  200  as described. In a preferred method, the system volume of the tool is then increased using the draw piston  236 . Once the system pressure is drawn below the formation pressure, the piston draw rate is adjusted. The draw rate is adjusted in steps, and a plurality of measurements are taken at each step. This stepwise drawdown is illustrated in FIG.  9 . 
     FIG. 9 is a plot representing a single cycle of a drawdown test using the method of the present invention. One curve  902  represents piston draw rate of the draw piston  236  or simply piston rate, which is measured in cubic centimeters per second (cm3/s). A set of other curves  904  represents pressure response of the system volume or test volume influenced by fluid flow from the formation. The pressure response is measured in pounds per square inch (psi). 
     The pressure response curves  904  comprise separate curves  906 ,  908  and  910  determined using data rates of 1 Hz, 4 Hz and 20 Hz, respectively. In most applications using the method, data rate of 4 Hz or higher is preferred to ensure multiple data points are available for the multiple regression analysis. The data rate used, however, may vary below 4 Hz when well conditions allow. 
     The method of the present invention enables determinations of mobility (m), fluid compressibility (C) and formation pressure (p*) to be made during the drawdown portion of the cycle by varying the draw rate of the system during the drawdown portion. This early determination allows for earlier control of drilling system parameters based on the calculated p*, which improves overall system performance and control quality. 
     For formations having low mobility, the method may be concluded at the end of the drawdown portion. A desirable feature of the method is the added ability to vary buildup rates on the latter portion of the drawdown/build up cycle i.e., the build up portion. Determinations of m and p* at this point improves the accuracy of the overall determination of the parameters. This added determination, may only be desirable for formations having relatively low mobility, and this aspect of the present invention is optional. 
     For determining mobility (m), C is not used in the calculations. Therefore, C need not be assumed as in previous methods of determining m, and the determination becomes more accurate. Additionally, the determination of m does not rely on system volume, thus enabling the use of a small-volume system such as the system of the present invention. With the use of a highly accurate control system for controlling the draw rate, determining mobilities ranging from 0.1 to 2000 mD/cP is possible. In a preferred embodiment, a down hole micro-processor based controller  214  is used to control the draw rate. 
     If determining C is desirable, the determination may be made using a system according to the present invention. Referring now to FIG. 7, one embodiment of the system of the present invention includes a separate tank  716  that is connected to the system volume. The tank  716  is coupled to the system volume by a flow line  720  and having a valve  718 . The controller  214  actuates the valve  718  to switch the valve from a closed position to an open position thereby increasing the overall system volume by adding the tank volume to the system volume for the purpose of calculating C. 
     The larger system volume is necessary only for determining C. In all other determinations, C is not necessary and the system volume may be switched to include only its volume of the drawdown assembly  200  by using the switching valve  718 . Using the smaller system volume enables faster system response to varying draw rates. In a preferred embodiment, the system volume is variable between 0 cm 3  and 1000 cm 3 . 
     FIG. 9 shows that the system pressure will substantially stabilize at a given piston rate, even though the test volume is changing. And having a data rate sufficient for acquiring at least two measurements at each given piston rate, the method then utilizes Formation Rate Analysis (FRA) to determine desired formation parameters such as fluid compressibility, mobility and formation pressure. 
     U.S. Pat. No. 5,708,204 to Kasap, which is incorporated herein by reference, describes FRA. FRA provides extensive analysis of pressure drawdown and build-up data. The mathematical technique employed in FRA is called multi-variant regression. Using multi-variant regression calculations, parameters such as formation pressure (p*), fluid compressibility (C) and fluid mobility (m) can be determined simultaneously when data representative of the build up process are available. 
     Equation 1 represents the FRA mathematically.                p        (   t   )       =       p   *     -       (     μ     k                   G   0          r   i         )          (         C   sys          V   sys               p          t         +     q   dd       )                 Equation                 1                                
     where, p(t) is the system pressure as a function of time; p* is the formation pressure as a calculated value; k/μ is mobility; G 0  is a dimensionless geometric factor; r i  is the inner radius of the port  246 ; C sys  is the compressibility of fluid in the system; V sys  is the total system volume; dp/dt is the pressure gradient within the system with respect to time; and q dd  is the draw down rate. 
     By rearranging Equation 1 and using the time-derivative of dp/dt terms, the equation becomes:                p        (   t   )       =       p   *     -           μC   sys          V   sys         k                   G   0          r   i                     p        (   t   )              t         -       μ     k                   G   0          r   i              q   dd                 Equation                 2                                
     wherein dp(t)/dt is the pressure change rate at time t and q dd  is the draw down rate. These terms are the only variables. Equation 2 is in the mathematical form of a linear equation y=b−m 1 x 1 −m 2 x 2 , which can be solved using multiple regression analysis techniques to determine the coefficients m1 and m2. Determining m1 and m2 then leads to determining mobility k/μ and compressibility C sys  when desired. 
     The method of the present invention provides a faster evaluation of formations by using variable rates of piston drawdown and pressure build up enabled by the various embodiments of the apparatus according to the present invention. 
     While the particular invention as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages hereinbefore stated, it is to be understood that this disclosure is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended other than as described in the appended claims.

Summary:
A minimum volume apparatus and method is provided including a tool for obtaining at least one parameter of interest of a subterranean formation in-situ, the tool comprising a carrier member, a selectively extendable member mounted on the carrier for isolating a portion of annulus, a port exposable to formation fluid in the isolated annulus space, a piston integrally disposed within the extendable member for urging the fluid into the port, and a sensor operatively associated with the port for detecting at least one parameter of interest of the fluid.