Abstract:
A method for determining a parameter of interest of a formation fluid, comprises moving a tool attached to a tubular member along a borehole in a subterranean formation. The tool is used to determine a formation fluid pressure and a formation fluid temperature at predetermined locations along the borehole and calculating a formation fluid density along the borehole therefrom. A density of a reference fluid is determined along the borehole and is related to the formation fluid pressure and the formation fluid temperature. The parameter of interest of the formation fluid is determined at a predetermined location from a comparison of the corresponding formation fluid density and the reference fluid density at the predetermined location.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to the testing of underground formations or reservoirs. More particularly, this invention relates to an apparatus and a method for determining properties of formation fluids by interpreting formation fluid pressure and temperature measurements. 
   2. Description of the Related Art 
   When a wellbore is drilled, fluids from the drilling process, called filtrate, may be forced into the pore spaces of some of the earth formations, changing their fluid content and therefore their fluid properties. The process of the filtrate being forced into the pore spaces is generally referred to as “invasion”. The formation fluids may be hydrocarbon liquids and gases, and aqueous liquids, including brine. Well logging operations, either by wireline or while drilling, are used to determine properties of the formation fluids, in order to determine the potential hydrocarbon content and the locations of formation water and gas interfaces. Many of the logging systems detect the formation properties relatively close to the borehole such that the invaded zone affects the measurements. For example, when interpreting deep-reading electric well logs, it is important to know the true formation brine resistivity, which is a function of the brine salinity. When drilling with fresh water based drilling mud, the filtrate in the invaded zone can alter the resistivity of the filtrate contaminated brine in the invaded zone and substantially bias the resistivity reading. In addition, some of the highly saline brines encountered have resistivity readings that are beyond the range of presently available sensors. 
   Likewise, when attempting to determine gas properties in a reservoir, the filtrate in the invasion zone, affects the readings of the gas property measurements. The filtrate may also plug and contaminate sensors designed for such gas measurements. For example, it is known in the art to take a sample of the gas using a tool such as a formation tester and to pass the gas by a sensor in a flow passage in the tool for analysis. The presence of the filtrate from the invasion zone may clog such a device and/or bias the readings of such an analytical device. 
   A formation pressure test may be taken at multiple locations along the borehole as a formation test tool is conveyed by wireline, or in a drill string, downward through a borehole. The difference between formation pressures at two locations divided by the vertical distance between the locations produces the average pressure gradient over the interval between the test locations. The pressure gradient may be used to determine fluid density in-situ and the interface or contact points between gas, oil and water when these fluids are present in a single reservoir. 
   Thus there is a demonstrated need for a system and method for determining formation fluid properties that are not substantially biased by the presence of a filtrate invasion zone proximate the borehole. 
   SUMMARY OF THE INVENTION 
   In one aspect of the present invention, a method for determining a parameter of interest of a formation fluid comprises moving a tool attached to a tubular member along a borehole in a subterranean formation. The tool is used to determine a formation fluid pressure and a formation fluid temperature at predetermined locations along the borehole and calculating a formation fluid density along the borehole therefrom. A density of a reference fluid is determined along the borehole and is related to the formation fluid pressure and the formation fluid temperature. The parameter of interest of the formation fluid is determined at a predetermined location from a comparison of the corresponding formation fluid density and the reference fluid density at the predetermined location. 
   In another aspect, a system for determining a formation fluid parameter of interest comprises a tool attached to a tubular member in a borehole, where the tool is adapted to determine a formation fluid pressure and a formation fluid temperature along the borehole. A controller acting under programmed instructions determines a formation fluid density along the borehole from the formation fluid pressure. A model of a reference fluid is stored in the controller for determining a reference fluid density at a predetermined location in the borehole. An empirical correlation is stored in the controller, where the correlation relates the formation parameter of interest to a comparison of the formation fluid density to the reference fluid density. 
   Examples of the more important features of the invention thus have been summarized rather broadly in order that the detailed description thereof that follows may be better understood, and in order that the contributions to the art may be appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form the subject of the claims appended hereto. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For detailed understanding of the present invention, references should be made to the following detailed description of the preferred embodiment, taken in conjunction with the accompanying drawings, in which like elements have been given like numerals, wherein: 
       FIG. 1  is an elevation view of an offshore drilling system according to one embodiment of the present invention; 
       FIG. 2  shows a portion of drill string incorporating the present invention; 
       FIG. 3  is a system schematic of the present invention; 
       FIG. 4  is an elevation view of a wireline embodiment according to the present invention; and 
       FIG. 5  is a flow chart describing the process of determining a formation fluid parameter according to embodiments of the present invention. 
   

   DETAILED DESCRIPTION 
   The system and methods of the present invention overcome the foregoing disadvantages of the prior art by determining formation fluid density from pressure gradient measurements and relating the formation fluid density to desired formation fluid parameters of interest. Many logging tools, for example, resistivity tools, commonly detect parameters of the formation fluid within a few meters of the borehole. The invasion zone may be a substantial portion of the detection region and thus bias the measurement so as to be of little value. Other logging tools, such as formation testers, detect the fluid pressure of the formation fluid at a predetermined location along the borehole. Whether using wireline or measurement while drilling (MWD) systems, the formation tester systems commonly measure pressure by drawing down the pressure of a portion of the formation adjacent the borehole to a point below the expected formation pressure at an established rate until the formation fluid entering the tool stabilizes the tool pressure. Then the pressure is allowed to rise and stabilize by stopping the drawdown. As one skilled in the art will appreciate, when the measurement stabilizes, the formation pressure determined in such a manner is indicative of the formation pressure extending tens to hundreds of meters surrounding the borehole. The size of the invasion zone in such a measurement is considered so small as to have a negligible effect on the formation pressure measurement. The formation pressure may be determined at predetermined locations along the wellbore. From this formation pressure data, a formation pressure gradient may be determined between two locations along the wellbore where the formation fluid pressure gradient is substantially unaffected by filtrate contamination. As one skilled in the art will appreciate, the pressure gradient is related to the fluid density between the measurement stations. Any formation tester system is deemed suitable for use with the present invention. Examples of such systems are described in U.S. Pat. Nos. 5,377,755 A, 5,708,204 A, 5,803,186 A, 6,568,487 B2, 6,585,045 B2, each of which is incorporated herein by reference. 
     FIGS. 1–4  describe exemplary systems that may be used in the present invention.  FIG. 1  is a drilling apparatus according to one embodiment of the present invention. A typical drilling rig  202  with a borehole  204  extending therefrom is illustrated, as is well understood by those of ordinary skill in the art. The drilling rig  202  has a work string  206 , which in the embodiment shown is a drill string. The drill string  206  has attached thereto a drill bit  208  for drilling the borehole  204 . The present invention is also useful in other types of work strings, and it is useful with a wireline, jointed tubing, coiled tubing, or other small diameter work string such as snubbing pipe. The drilling rig  202  is shown positioned on a drilling ship  222  with a riser  224  extending from the drilling ship  222  to the sea floor  220 . However, any drilling rig configuration such as a land-based rig may be adapted to implement the present invention. 
   If applicable, the drill string  206  can have a downhole drill motor  210 . Incorporated in the drill string  206  above the drill bit  208  is a typical testing unit, which can have at least one sensor  214  to sense downhole characteristics of the borehole, the bit, and the reservoir, with such sensors being well known in the art. A useful application of the sensor  214  is to determine direction, azimuth and orientation of the drill string  206  using an accelerometer or similar sensor. The BHA also contains the formation test apparatus  216  of the present invention, which will be described in greater detail hereinafter. A telemetry system  212  is located in a suitable location on the work string  206  such as above the test apparatus  216 . The telemetry system  212  is used for command and data communication between the surface and the test apparatus  216 . 
     FIG. 2  is a section of drill string  206  incorporating the present invention. The tool section is commonly located in a BHA close to the drill bit (not shown). The tool includes a communication unit and power supply  320  for two-way communication to the surface and supplying power to the downhole components. In one embodiment, the tool requires a signal from the surface only for test initiation. A downhole controller and processor (not shown) carry out all subsequent control. The power supply may be a generator driven by a mud motor (not shown) or it may be any other suitable power source. Also included are multiple stabilizers  308  and  310  for stabilizing the tool section of the drill string  206  and packers  304  and  306  for sealing a portion of the annulus. A circulation valve disposed in the present example above the upper packer  304  is used to allow continued circulation of drilling mud above the packers  304  and  306  while rotation of the drill bit is stopped. A separate vent or equalization valve (not shown) is used to vent fluid from the test volume between the packers  304  and  306  to the upper annulus. This venting reduces the test volume pressure, which is required for a drawdown test. It is also contemplated that the pressure between the packers  304  and  306  could be reduced by drawing fluid into the system or venting fluid to the lower annulus, but in any case some method of increasing the volume of the intermediate annulus to decrease the pressure will be required. 
   In one embodiment of the present invention an extendable pad-sealing element  302  for engaging the well wall  3  is disposed between the packers  304  and  306  on the test apparatus  216 . The pad-sealing element  302  could be used without the packers  304  and  306 , because a sufficient seal with the well wall can be maintained with the pad  302  alone. If packers  304  and  306  are not used, a counterforce is required so pad  302  can maintain sealing engagement with the wall of the borehole  204 . The seal creates a test volume at the pad seal and extending only within the tool to the pump rather than also using the volume between packer elements. 
   One way to ensure the seal is maintained is to ensure greater stability of the drill string  206 . Selectively extendable gripper elements  312  and  314  could be incorporated into the drill string  206  to anchor the drill string  206  during the test. The grippers  312  and  314  are shown incorporated into the stabilizers  308  and  310  in this embodiment. The grippers  312  and  314 , which would have a roughened end surface for engaging the well wall, would protect soft components such as the pad-sealing element  302  and packers  304  and  306  from damage due to tool movement. The grippers  312  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. 
     FIG. 3  shows the tool of  FIG. 2  schematically with internal downhole and surface components. Selectively extendable gripper elements  312  engage the borehole wall  204  to anchor the drill string  206 . Packer elements  304  and  306  well known in the art extend to engage the borehole wall  204 . The extended packers separate the well annulus into three sections, an upper annulus  402 , an intermediate annulus  404  and a lower annulus  406 . The sealed annular section (or simply sealed section)  404  is adjacent a formation  218 . Mounted on the drill string  206  and extendable into the sealed section  404  is the selectively extendable pad sealing element  302 . A fluid line providing fluid communication between pristine formation fluid  408  and tool sensors such as pressure sensor  424  is shown extending through the pad member  302  to provide a port  420  in the sealed annulus  404 . The preferable configuration to ensure pristine fluid is tested or sampled is to have packers  304  and  306  sealingly urged against the wall  204 , and to have a sealed relationship between the wall and extendable element  302 . Reducing the pressure in sealed section  404  prior to engaging the pad  302  will initiate fluid flow from the formation into the sealed section  404 . With formation flowing when the extendable element  302  engages the wall, the port  420  extending through the pad  320  will be exposed to pristine fluid  408 . Control of the orientation of the extendable element  302  is highly desirable when drilling deviated or horizontal wells. The preferred orientation is toward an upper portion of the borehole wall. A sensor  214 , such as an accelerometer, can be used to sense the orientation of the extendable element  302 . The extendable element can then be oriented to the desired direction using methods and not-shown components well known in the art such as directional drilling with a bend-sub. For example, the drilling apparatus may include a drill string  206  rotated by a surface rotary drive (not shown). A downhole mud motor (see  FIG. 1  at  210 ) may be used to independently rotate the drill bit. The drill string can thus be rotated until the extendable element is oriented to the desired direction as indicated by the sensor  214 . The surface rotary drive is halted to stop rotation of the drill string  206  during a test, while rotation of the drill bit may be continued using the mud motor of desired. 
   A downhole controller  418  preferably controls the test. The controller  418  is connected to at least one system volume control device (pump)  426 . The pump  426  is a preferably small piston driven by a ball screw and stepper motor or other variable control motor, because of the ability to iteratively change the volume of the system. The pump  426  may also be a progressive cavity pump. When using other types of pumps, a flow meter should also be included. A valve  430  for controlling fluid flow to the pump  426  is disposed in the fluid line  422  between a pressure sensor  424  and the pump  426 . A test volume  405  is the volume below the retracting piston of the pump  426  and includes the fluid line  422 . The pressure sensor is used to sense the pressure within the test volume  404 . The sensor  424  is connected to the controller  418  to provide the feedback data required for a closed loop control system. The feedback is used to adjust parameter settings such as a pressure limit for subsequent volume changes. The downhole controller may incorporate a processor (not separately shown) for further reducing test time, and an optional database and storage system may be incorporated to save data for further analysis and for providing default settings. 
   When drawing down the sealed section  404 , fluid is vented to the upper annulus  402  via an equalization valve  419 . A conduit  427  connecting the pump  426  to the equalization valve  419  includes a selectable internal valve  432 . If fluid sampling is desired, the fluid may be diverted to optional sample reservoirs  428  by using the internal valves  432 ,  433   a,  and  433   b  rather than venting through the equalization valve  419 . For typical fluid sampling, the fluid contained in the reservoirs  428  is retrieved from the well for analysis. 
   One embodiment for testing low mobility (tight) formations includes at least one pump (not separately shown) in addition to the pump  426  shown. The second pump should have an internal volume much less than the internal volume of the primary pump  426 . A suggested volume of the second pump is 1/100 the volume of the primary pump. A typical “T” connector having selection valve controlled by the downhole controller  418  may be used to connect the two pumps to the fluid line  422 . 
   In a tight formation, the primary pump is used for the initial draw down. The controller switches to the second pump for operations below the formation pressure. An advantage of the second pump with a small internal volume is that build-up times are faster than with a pump having a larger volume. 
   Results of data processed downhole may be sent to the surface in order to provide downhole conditions to a drilling operator or to validate test results. The controller passes processed data to a two-way data communication system  416  disposed downhole. The downhole system  416  transmits a data signal to a surface controller  412  that contains a processor and memory storage. There are several methods and apparatuses known in the art suitable for transmitting data. Any suitable system would suffice for the purposes of this invention. Once the signal is received at the surface, a surface controller  412  and processor  410  converts and transfers the data to a suitable output or storage device  414 . As described earlier, surface controller  412  is also used to send the test initiation command. 
     FIG. 4  is a wireline embodiment according to the present invention. A well  502  is shown traversing a formation  504  containing a reservoir having gas  506 , oil  508  and water  510  layers. A wireline tool  512  supported by an armored cable  514  is disposed in the well  502  adjacent the formation  504 . Extending from the tool  512  are optional grippers  312  for stabilizing the tool  512 . Two expandable packers  304  and  306  are disposed on the tool  512  are capable of separating the annulus of the borehole  502  into an upper annulus  402 , a sealed intermediate annulus  404  and a lower annulus  406 . A selectively extendable pad member  302  is disposed on the tool  512 . The grippers  312 , packers  304  and  306 , and extendable pad element  302  are essentially the same as those described in  FIGS. 2 and 3 , therefore the detailed descriptions are not repeated here. 
   Telemetry for the wireline embodiment is a downhole two-way communication unit  516  connected to a surface two-way communication unit  518  by one or more conductors  520  within the armored cable  514 . The surface communication unit  518  is housed within a surface controller  412  that includes a processor, memory, and output device  414  as described in  FIG. 3 . A typical cable sheave  522  is used to guide the armored cable  514  into the borehole  502 . The tool  512  includes a downhole controller  418  having a processor and memory for controlling formation tests in accordance with methods to be described in detail later. 
   The embodiment shown in  FIG. 4  is desirable for determining contact points  538  and  540  between the gas  506  and oil  508  and between the oil  508  and water  510 . To illustrate this application a plot  542  of pressure versus depth is shown superimposed on the formation  504 . The downhole tool  512  includes a pump  426 , a plurality of sensors  424  and optional sample tanks  428  as described above for the embodiment shown in  FIG. 3 . These components are used to measure formation pressure at varying depths within the borehole  502 . The pressures plotted as shown are indicative of fluid or gas density, which varies distinctly from one fluid to the next. Therefore, having multiple pressure measurements M 1 –M n  provides data necessary to determine the contact points  538  and  540 . 
   As described previously, when interpreting electric well logs in regions having brine formation fluids, it is important to know the formation brine resistivity. In one embodiment, the present invention relates the formation fluid density, determined from the formation fluid pressure gradient, to the formation fluid salinity. The formation fluid resistivity is then determined using published data relating fluid salinity to resistivity. This process is described in the flow chart of  FIG. 5 . In step  600 , a formation test tool, such as one of the exemplary tools described previously, is traversed along the borehole and stopped at predetermined locations of interest along the borehole. At each predetermined location, the tool is used to determine the formation fluid pressure and the formation fluid temperature  610 . Such data may be transmitted to surface processor  412  and/or downhole processor  418  for analysis. The pressure gradient is determined from the pressure and temperature data  620 . 
   The gradient may be determined directly from the pressures measured at two predetermined locations divided by the vertical distance between the predetermined locations. The vertical distance between the predetermined locations can be determined from direct measurement in vertical holes and from directional survey data in inclined holes. The formation fluid density is determined from the pressure gradient  630  using techniques known in the art. Certain parameters of interest of the formation can be determined by comparing the formation fluid density to the density of a reference fluid at the downhole conditions  650 . In the case where the formation fluid is a brine solution, the formation fluid density may be measurably different from that of pure water at the downhole pressure and temperature. By comparing the formation brine density to a calculated density of pure water at the downhole conditions, the present invention determines the salinity of the formation fluid  660 . The density of pure water at downhole pressure and temperature is determined from empirical models of water  640 . For example, for pressures less than 100 MPa (14,500 psi) and temperatures to 325 C, correlations are available such as the IAPWS-97 model of the International Association for the Properties of Water and Steam available from the National Institute of Standards and Technology(NIST) of Gaitherburg, Md. Alternatively, a correlation covering the range of 25 C to 250 C and atmospheric to 206 MPA (30,000 psi) is calculated using the data for the density of water at varying pressure and temperature gathered from the NIST database (see Table 1). The data are correlated for the density of pure water as a function of pressure and temperature using a commercial statistical package, such as the STATISTICA™ brand of statistical software marketed by StatSoft®, Inc. of Tulsa, Okla. The resulting equation is based on 336 data points, has an R 2 =0.99986, a standard error of 0.00073 g/ml, and is given by:
 
ρ water (g/ml)=1.00806−2.27533×10 −6   *T   2 +2.7666583×10 −3   *P+ 5.906096×10 −8   *PT   2 −2.706382×10 −4   *T− 2.81544×10 −7   *P   2   T− 50.79548* T   3 +4.764802×10 −7   *P   3 −1.220952×10 −5   *P   2   (1)
 
where T is the measured formation temperature in ° C., and P is the measured formation pressure in kpsi (1 kpsi=6.89 kPa). It is commonly known that the dissolved solids in brine solution are predominately NaCl having a published density of 2.165 to 2.2 g/ml with an average density of about 2.17 g/ml. By comparing the measured density of the brine solution ρ brine  to the density of pure water at the downhole conditions, the salinity of the brine solution can be determined from the following:
 
   Let the fraction by weight of salt=f ws , and the fraction by volume of salt=f vs , then
 
 f   vs =(ρ brine −ρ water )/(ρ salt −ρ water )  (2)
 
and, f ws  can be determined from f vs  using
 
 f   ws =1/[(((1/ f   vs )−1)/(ρ salt /ρ water ))+1]  (3)
 
where f ws  is also called the salinity, S, and is often expressed as parts per million (ppm).
 
   Using correlations known in the art, a salinity is related to resistivity  680 . For example, the salinity is compared to published charts of salinity versus resistivity. Such charts include “Log Interpretation Charts/Dresser Atlas”, Houston, Tex., Dresser Atlas Division of Dresser Industries, 1979 (now Baker Atlas, Division of Baker Hughes Incorporated). Also see “Log Interpretation Charts”, Houston, Tex., Schlumberger Inc., 1972 and 1979. Alternatively, such chart correlations, or their underlying data, may be converted to a multi-variable correlation model of brine resistivity as a function of brine salinity, downhole pressure, and downhole temperature, using techniques known in the art. One such exemplary model, published by Baker Atlas in the Log Interpretation Charts described above, is of the form:
 
 R   brineT ={0.0123+[3647.5/( S ) 0.955 ]}*[45.4/( T+ 21.5)]  (4)
 
where R brineT  is the resistivity in ohm-meter at the measured downhole temperature, T in ° C., and S is the salinity (NaCl concentration in ppm) determined from Eq. 3.
 
   Such a model may be stored in surface processor  412  and/or downhole processor  518  for analysis of the formation pressure and temperature measurements, in situ. Therefore, the present embodiment provides resistivity of the formation fluid from measurements of the formation fluid pressure and formation fluid temperature at predetermined locations along the borehole  670 . 
   In another embodiment, still referring to  FIG. 5 , formation fluid pressure and formation fluid temperature may be used to determine the composition of natural gas and the gas dryness in the formation. Steps  600 – 650  are performed as described above. Here, however, the model of the reference fluid in step  640  is a model of the properties of pure methane at downhole conditions. Gas dryness is commonly defined in the art as the ratio of the molar concentration of methane molecules (C 1 ) to the molar concentration of heavier hydrocarbon molecules such as ethane, propane, butane and pentane, etc. (collectively referred to herein as C 2+ ). One may determine the density of formation gas using the measurements of formation pressure  630 . According to Gas Research Institute Report #82/0037, on average, out of 100 molecules of natural gas, 93 are methane, 3 are ethane, 1 is propane, 0.5 is butane, with smaller numbers for higher molecular weight molecules. There are about thirteen times as many methane molecules as non-methane molecules. Thus, the methane-methane molecular forces and molecular size are substantially dominant in determining the density of molecules per unit volume in a natural gas mixture. Thus, the number of molecules per unit volume of pure methane may be estimated to be substantially the same as the number of molecules of all molecular types in a 90 mole percent mixture of methane with a few heavier hydrocarbon gases, as commonly occurs with natural gas. The density of pure methane at measured downhole conditions is determined using an empirical correlation of available data shown in Table 2. The data were correlated using the Statistica™ brand statistical package described previously to provide methane density as a function of downhole formation pressure and formation temperature. The correlation for determining methane density is based on 234 data points, has an R 2 =0.99914, a standard error of 0.00392 g/ml, and is given by:
 
ρ methane (g/ml)=2.770625×10 −3 +2.480415×10 −5   *P− 1.120014×10 −9   *P   2 +1.808398×10 −14   *P   3 −1.307547×10 −7*   T+ 1.455411×10 −3 *( P/T )−4.922499×10 −6 *( P/T ) 2 +5.933963×10 −9* ( P/T ) 3   (5)
 
where T is the measured formation temperature in ° C., and P is the measured formation pressure in kpsi (1 kpsi=6.89 kPa). Then the calculated density of the pure methane at downhole conditions may be divided by methane&#39;s mass per mole (16.04 g/mole) to estimate the number of moles of gas per ml at downhole conditions. Dividing the measured density of the formation gas by the number of moles per ml, the average molecular weight of the formation gas is determined  700 . The greater the deviation of the average molecular weight of the formation gas from the molecular weight of pure methane (16.04), the “wetter” the gas is considered to be. Conversely, the closer the average molecular weight of the formation gas is to the molecular weight of pure methane, the “drier” the gas is considered to be.
 
   Having determined the average molecular weight of the formation gas, it is desirable to determine the breakdown of the constituents. For a particular region of the world, the ratios of the heavier molecules, C 2 + along with N 2  and CO 2 , are often known and available in databases of prior reservoir analyses in that region  720 . The ratio of C 1 (methane) to the overall mixture is, however, more variable because methane is created by multiple processes, including biological and geological processes. The following analysis provides a method for estimating the molecular breakdown, also called composition, of the formation gas knowing the average molecular weight determined from the formation pressure gradient described previously. The average molecular weight of a natural gas is the molar fraction, f i , of the i-th pure gas component times the molecular weight of that component. For example, assuming that the gas components of interest are the C1–C6 hydrocarbons, nitrogen and carbon dioxide, then
 
 MW   avg   =f   C1   *MW   C1   +f   C2   *MW   C2   +f   C3   *MW   C3   +f   C4   *MW   C4   +f   C5*   MW   C5   +f   C6   *MW   C6   +f   N2   *MW   N2   +f   CO2   *MW   CO2   (6)
 
   then, assuming these are the only gases in significant amounts, the sum of their molar fractions is unity.
 
1 =f   C1   +f   C2   +f   C3   +f   C4   +f   C5   +f   C6   +f   N2   +f   CO2 =Σ i   f   i   (7)
 
   The ratio of C 1  to the other gases is quite variable, but the ratio of C 2  to the other gases is less variable such that the molar ratio of the i-th gas to C 2  is defined as r i2 =f i /f C2 . Then,
 
1 =f   C1   +f   C2 (1 +r   32   +r   42   +r   52   +r   62   +r   N2C2   +r   CO2C2 )  (8a)
 
1 =f   C1   +f   C2 (1+Σ i   r   i )  (8b)
 
   Remembering that, for a particular region of the world, the ratios of the concentrations of heavier molecules C 2 + to each other and to the concentrations of N 2  and CO 2  are often known, then
 
( MW   avg   −f   C1   *MW   C1 )= f   C2   *D=f   C2   *[MW   C2   +r   32*   MW   C3   +r   42   *MW   C4   +r   52   *MW   C5   +r   62   *MW   C6   +r   N2C2   *MW   N2   +r   CO2C2   *MW   CO2 ]  (9)
 
( MW   avg   −fC 1 *MW   C1 )=(1 −fC 1)* D/ (1+Σ i   r   i )  (10)
 
 f   C1   =[MW   avg   −D /(1+Σ i   r   i )]/[ MW   C1   −D/( 1+Σ i   r   i )]  (11)
 
   Noting that, D/(1+Σ i r i )=MW avg−C1  is the average molecular weight of all of the non-methane gases in the natural gas mixture, (the average when excluding C 1 ), and
 
 f   C1   =[MW   avg   −MW   avg−C1   ]/[MW   C1   −MW   avg−C1 ]  (12)
 
where MW avg  is measured from downhole formation pressure measurements; MW C1  is the molecular weight of pure methane (16.04); and MW avg−C1  is determined from database information related to the ratios of the non-methane gases catalogued for various regions in commercially available databases. With f C1  determined, the constituent makeup of the formation gas can then be established  710 .
 
   The present invention has been described as a method and apparatus operating in a downhole environment. However, the present invention may also be embodied as a set of instructions on a computer readable medium comprising ROM, RAM, CD ROM, DVD, FLASH or any other computer readable medium, now known or unknown, that when executed causes a computer such as, for example, a processor in downhole controller  418  and/or a processor in surface controller  412 , to implement the method of the present invention. 
   The foregoing description is directed to particular embodiments of the present invention for the purpose of illustration and explanation. It will be apparent, however, to one skilled in the art that many modifications and changes to the embodiment set forth above are possible. It is intended that the following claims be interpreted to embrace all such modifications and changes. 
   
     
       
             
           
             
             
           
             
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Density of Water (g/ml) vs. Pressure (psi) and Temperature (C.) (NIST data) 
             
           
        
         
             
                 
               T [C.] 
             
           
        
         
             
               P [psi] 
               25 
               50 
               75 
               100 
               125 
               150 
               175 
               200 
               225 
               250 
             
             
                 
             
           
        
         
             
               14.7 
               0.99705 
               0.98804 
               0.97484 
               0.95835 
                 
                 
                 
                 
                 
                 
             
             
               29.4 
               0.99709 
               0.98808 
               0.97489 
               0.95840 
             
             
               33.7 
                 
                 
                 
                 
               0.93902 
             
             
               44.1 
               0.99714 
               0.98812 
               0.97493 
               0.95844 
               0.93906 
             
             
               58.8 
               0.99718 
               0.98817 
               0.97498 
               0.95849 
               0.93911 
             
             
               69.1 
                 
                 
                 
                 
                 
               0.91701 
             
             
               73.5 
               0.99723 
               0.98821 
               0.97502 
               0.95854 
               0.93916 
               0.91703 
             
             
               88.2 
               0.99728 
               0.98826 
               0.97507 
               0.95859 
               0.93922 
               0.91708 
             
             
               100.0 
               0.99731 
               0.98829 
               0.97510 
               0.95863 
               0.93926 
               0.91713 
             
             
               129.5 
                 
                 
                 
                 
                 
                 
               0.89228 
             
             
               200.0 
               0.99762 
               0.98859 
               0.97541 
               0.95895 
               0.93961 
               0.91752 
               0.89260 
             
             
               225.5 
                 
                 
                 
                 
                 
                 
                 
               0.86466 
             
             
               300.0 
               0.99793 
               0.98889 
               0.97572 
               0.95927 
               0.93996 
               0.91791 
               0.89304 
               0.86505 
             
             
               369.8 
                 
                 
                 
                 
                 
                 
                 
                 
               0.83375 
             
             
               400.0 
               0.99824 
               0.98919 
               0.97602 
               0.95959 
               0.94031 
               0.91830 
               0.89349 
               0.86557 
               0.83394 
             
             
               500.0 
               0.99855 
               0.98949 
               0.97632 
               0.95991 
               0.94066 
               0.91869 
               0.89393 
               0.86609 
               0.83458 
             
             
               576.7 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               0.79889 
             
             
               600.0 
               0.99886 
               0.98979 
               0.97663 
               0.96023 
               0.94100 
               0.91907 
               0.89437 
               0.86661 
               0.83521 
               0.79908 
             
             
               700.0 
               0.99917 
               0.99009 
               0.97693 
               0.96055 
               0.94135 
               0.91946 
               0.89481 
               0.86713 
               0.83584 
               0.79988 
             
             
               800.0 
               0.99948 
               0.99038 
               0.97723 
               0.96087 
               0.94170 
               0.91985 
               0.89525 
               0.86764 
               0.83646 
               0.80068 
             
             
               900.0 
               0.99978 
               0.99068 
               0.97754 
               0.96119 
               0.94204 
               0.92023 
               0.89569 
               0.86816 
               0.83708 
               0.80147 
             
             
               1000.0 
               0.99700 
               0.99098 
               0.97784 
               0.96151 
               0.94239 
               0.92061 
               0.89613 
               0.86867 
               0.83770 
               0.80225 
             
             
               2000.0 
               1.00010 
               0.99392 
               0.98083 
               0.96466 
               0.94579 
               0.92438 
               0.90040 
               0.87365 
               0.84369 
               0.80976 
             
             
               3000.0 
               1.00310 
               0.99682 
               0.98377 
               0.96774 
               0.94912 
               0.92805 
               0.90454 
               0.87843 
               0.84937 
               0.81676 
             
             
               4000.0 
               1.00610 
               0.99967 
               0.98666 
               0.97077 
               0.95237 
               0.93163 
               0.90856 
               0.88304 
               0.85479 
               0.82334 
             
             
               5000.0 
               1.00910 
               1.00250 
               0.98951 
               0.97375 
               0.95556 
               0.93512 
               0.91246 
               0.88748 
               0.85997 
               0.82954 
             
             
               6000.0 
               1.01200 
               1.00530 
               0.99231 
               0.97668 
               0.95869 
               0.93853 
               0.91625 
               0.89178 
               0.86495 
               0.83543 
             
             
               7000.0 
               1.01490 
               1.00800 
               0.99508 
               0.97955 
               0.96176 
               0.94187 
               0.91994 
               0.89594 
               0.86973 
               0.84104 
             
             
               8000.0 
               1.01770 
               1.01070 
               0.99780 
               0.98238 
               0.96477 
               0.94513 
               0.92354 
               0.89998 
               0.87433 
               0.84640 
             
             
               9000.0 
               1.02050 
               1.01340 
               1.00050 
               0.98517 
               0.96772 
               0.94833 
               0.92705 
               0.90390 
               0.87878 
               0.85153 
             
             
               10000.0 
               1.02330 
               1.01600 
               1.00310 
               0.98791 
               0.97063 
               0.95146 
               0.93048 
               0.90771 
               0.88309 
               0.85647 
             
             
               11000.0 
               1.02600 
               1.01860 
               1.00570 
               0.99061 
               0.97348 
               0.95453 
               0.93384 
               0.91143 
               0.88726 
               0.86122 
             
             
               12000.0 
               1.02870 
               1.02120 
               1.00830 
               0.99327 
               0.97629 
               0.95754 
               0.93712 
               0.91505 
               0.89131 
               0.86581 
             
             
               13000.0 
               1.03140 
               1.02370 
               1.01090 
               0.99589 
               0.97905 
               0.96050 
               0.94033 
               0.91858 
               0.89524 
               0.87025 
             
             
               14000.0 
               1.03400 
               1.02620 
               1.01340 
               0.99847 
               0.98177 
               0.96340 
               0.94347 
               0.92203 
               0.89907 
               0.87454 
             
             
               15000.0 
               1.03660 
               1.02860 
               1.01580 
               1.00100 
               0.98444 
               0.96626 
               0.94656 
               0.92540 
               0.90280 
               0.87871 
             
             
               16000.0 
               1.03910 
               1.03110 
               1.01830 
               1.00350 
               0.98708 
               0.96906 
               0.94959 
               0.92870 
               0.90643 
               0.88276 
             
             
               17000.0 
               1.04170 
               1.03350 
               1.02070 
               1.00600 
               0.98968 
               0.97182 
               0.95255 
               0.93193 
               0.90998 
               0.88669 
             
             
               18000.0 
               1.04420 
               1.03590 
               1.02310 
               1.00850 
               0.99224 
               0.97454 
               0.95547 
               0.93510 
               0.91345 
               0.89053 
             
             
               19000.0 
               1.04660 
               1.03820 
               1.02540 
               1.01090 
               0.99476 
               0.97721 
               0.95834 
               0.93820 
               0.91684 
               0.89426 
             
             
               20000.0 
               1.04910 
               1.04060 
               1.02780 
               1.01330 
               0.99725 
               0.97985 
               0.96115 
               0.94124 
               0.92015 
               0.89790 
             
             
               22000.0 
               1.05620 
               1.04510 
               1.03230 
               1.01800 
               1.00210 
               0.98500 
               0.96665 
               0.94716 
               0.92658 
               0.90493 
             
             
               24000.0 
               1.06080 
               1.04960 
               1.03680 
               1.02250 
               1.00690 
               0.99000 
               0.97197 
               0.95287 
               0.93276 
               0.91166 
             
             
               26000.0 
               1.06530 
               1.05400 
               1.04120 
               1.02700 
               1.01150 
               0.99487 
               0.97714 
               0.95840 
               0.93871 
               0.91811 
             
             
               28000.0 
               1.06970 
               1.05830 
               1.04550 
               1.03140 
               1.01610 
               0.99962 
               0.98216 
               0.96375 
               0.94445 
               0.92431 
             
             
               30000.0 
               1.07400 
               1.06250 
               1.04970 
               1.03560 
               1.02050 
               1.00420 
               0.98704 
               0.96894 
               0.95001 
               0.93029 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
           
             
             
             
             
             
             
             
           
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Density of Methane (g/ml) vs. Pressure (psi) and Temperature (C.) 
             
           
        
         
             
                 
               T (C.) 
             
           
        
         
             
                 
               75 
               100 
               125 
               150 
               175 
               200 
             
           
        
         
             
               P (psi) 
               Density (g/cc) 
             
             
                 
             
           
        
         
             
               100 
               0.0038457 
               0.0035816 
               0.0033522 
               0.0031508 
               0.0029725 
               0.0028136 
             
             
               200 
               0.0077397 
               0.0071954 
               0.0067252 
               0.0063145 
               0.0059524 
               0.0056305 
             
             
               300 
               0.0116810 
               0.0108400 
               0.0101180 
               0.0094090 
               0.0089386 
               0.0084498 
             
             
               400 
               0.0156680 
               0.0145140 
               0.0135290 
               0.0126760 
               0.0119300 
               0.0112710 
             
             
               500 
               0.0196990 
               0.0182150 
               0.0169560 
               0.0158720 
               0.0149260 
               0.0140920 
             
             
               600 
               0.0237720 
               0.0219420 
               0.0203990 
               0.0190750 
               0.0179250 
               0.0169140 
             
             
               700 
               0.0278850 
               0.0256930 
               0.0238550 
               0.0222850 
               0.0209260 
               0.0197340 
             
             
               800 
               0.0320360 
               0.0294650 
               0.0273230 
               0.0255010 
               0.0239280 
               0.0225520 
             
             
               900 
               0.0362200 
               0.0332570 
               0.0308000 
               0.0287200 
               0.0269290 
               0.0253680 
             
             
               1000 
               0.0404360 
               0.0370650 
               0.0342850 
               0.0319410 
               0.0299290 
               0.0281790 
             
             
               2000 
               0.0833620 
               0.0751400 
               0.0691010 
               0.0639300 
               0.0595930 
               0.0558850 
             
             
               3000 
               0.1242300 
               0.1120100 
               0.1023300 
               0.0944430 
               0.0878610 
               0.0822670 
             
             
               4000 
               0.1593700 
               0.1444300 
               0.1323200 
               0.1223000 
               0.1138900 
               0.1067000 
             
             
               5000 
               0.1880600 
               0.1719200 
               0.1584100 
               0.1470100 
               0.1372800 
               0.1288900 
             
             
               6000 
               0.2113500 
               0.1949300 
               0.1808000 
               0.1686100 
               0.1580500 
               0.1488200 
             
             
               7000 
               0.2305400 
               0.2142900 
               0.2000100 
               0.1874600 
               0.1764100 
               0.1666500 
             
             
               8000 
               0.2466700 
               0.2308000 
               0.2166100 
               0.2039600 
               0.1926800 
               0.1826000 
             
             
               9000 
               0.2605100 
               0.2450800 
               0.2311200 
               0.2185300 
               0.2071700 
               0.1969200 
             
             
               10000 
               0.2725800 
               0.2576200 
               0.2439400 
               0.2314900 
               0.2201600 
               0.2098500 
             
             
               11000 
               0.2832800 
               0.2687500 
               0.2553900 
               0.2431200 
               0.2318800 
               0.2215800 
             
             
               12000 
               0.2928700 
               0.2787600 
               0.2657000 
               0.2536400 
               0.2425300 
               0.2322900 
             
             
               13000 
               0.3015600 
               0.2878400 
               0.2750800 
               0.2632400 
               0.2522700 
               0.2421200 
             
             
               14000 
               0.3095100 
               0.2961400 
               0.2836700 
               0.2720500 
               0.2616400 
               0.2511900 
             
             
               15000 
               0.3168300 
               0.3037900 
               0.2915900 
               0.2801800 
               0.2695300 
               0.2596000 
             
             
               16000 
               0.3236100 
               0.3108900 
               0.2989400 
               0.2877300 
               0.2772500 
               0.2674300 
             
             
               17000 
               0.3299400 
               0.3174900 
               0.3057800 
               0.2947800 
               0.2844500 
               0.2747600 
             
             
               18000 
               0.3358700 
               0.3236800 
               0.3122000 
               0.3013800 
               0.2912100 
               0.2816400 
             
             
               19000 
               0.3414400 
               0.3295000 
               0.3182300 
               0.3075900 
               0.2975700 
               0.2881200 
             
             
               20000 
               0.3467100 
               0.3350000 
               0.3239200 
               0.3134600 
               0.3035800 
               0.2942400 
             
             
               21000 
               0.3517000 
               0.3402000 
               0.3293100 
               0.3190100 
               0.3092700 
               0.3000500 
             
             
               22000 
               0.3564500 
               0.3451500 
               0.3344400 
               0.3242900 
               0.3146800 
               0.3055700 
             
             
               23000 
               0.3609700 
               0.3498600 
               0.3393100 
               0.3293100 
               0.3198300 
               0.3108300 
             
             
               24000 
               0.3652900 
               0.3543500 
               0.3439700 
               0.3341000 
               0.3247400 
               0.3158500 
             
             
               25000 
               0.3694300 
               0.3586600 
               0.3484200 
               0.3386900 
               0.3294500 
               0.3206600 
             
             
               26000 
               0.3734000 
               0.3627900 
               0.3526900 
               0.3430900 
               0.3339500 
               0.3252600 
             
             
               27000 
               0.3772200 
               0.3667500 
               0.3567900 
               0.3473100 
               0.3382800 
               0.3296900 
             
             
               28000 
               0.3808900 
               0.3705700 
               0.3607400 
               0.3513700 
               0.3424500 
               0.3339500 
             
             
               29000 
               0.3844400 
               0.3742500 
               0.3645400 
               0.3552900 
               0.3464600 
               0.3380500 
             
             
               30000 
               0.3878700 
               0.3778100 
               0.3682100 
               0.3590600 
               0.3503300 
               0.3420000