Method for relating multiple oil or gas wells to each other

A method of relating three or four producing wells in an existing fossil fuel drilling field utilizes the equation Y.sup.2 +X.multidot.Y-X.sup.2 =0. The independent variable X represents the distance between any two known producing wells in the field. The dependant variable Y represents a distance between a known producing well and another well location, wherein each of the known producing wells and well locations depend upon which method utilized. In one method, a first origin well can be selected as a known producing well and then a distance from the origin well to a second producing well can be determined. Utilizing the above equation, a third well location can be determined by calculating a distance Y from the origin well to the third location. This well location can represent either an existing producing well located a distance from the origin well, or a new location at which a producing well can be drilled within the existing drilling field. In another method, the distance X represents a distance between a first and a second known producing well. A third producing well is then selected within the existing field. The equation is then utilized to calculate a distance Y from the third producing well to a fourth well location. The fourth well location is either a location of an existing producing well in the field, or a location for drilling a new producing well in the field.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention is generally related to fossil fuel producing well
 fields, and more particularly to a system and method of mathematically
 relating two or three producing wells in the field either to locate
 another existing producing well or to locate a position that will yield
 another producing well.
 2. Description of the Related Art
 Presently, there are many oil or natural gas producing fields located
 around the world. Each of these fields includes a number of producing
 wells that generate a fossil fuel such as oil or natural gas. The wells
 are distributed over the area of a given field in what appears to be a
 haphazard manner.
 Each well position is originally located and selected for drilling by
 searching for oil and natural gas utilizing a number of different methods.
 One method is to simply look for ground seepage wherein oil or natural gas
 escapes from the earth through the ground into the atmosphere. Oil seepage
 can be located by visual inspection. Gas seepage can be traced by
 sensitive equipment that measures the presence or absence of natural gas
 in the atmosphere. These methods are known as surface methods. Another
 method is known as either gravity or magnetic survey wherein small changes
 in the electromagnetic field or gravitational force of the earth at a
 given area are measured relative to the surrounding areas. These small
 changes indicate underground formations that may be conducive to oil or
 natural gas reservoirs. A third method is commonly known as seismographic
 exploration that can be utilized to detect smaller and less obvious rock
 formations and underground traps that can include reservoirs of oil or
 natural gas that are otherwise not discoverable by the previous less
 sophisticated methods. Seismic surveying utilizes sound transmitted
 through the ground to indicate less obvious underground formations that
 can be conducive to oil or natural gas reservoirs. This procedure is
 repeated over wide areas to determine the possible locations of pockets or
 reservoirs of oil and/or natural gas.
 Heretofore, there has been no method known to somehow relate each and every
 oil well that exists in an oil field. There is further no presently known
 method of relating all existing oil wells in a given field for determining
 prime locations to drill additional oil wells in the field without
 resorting to the sophisticated, costly and time consuming methods of
 locating new well sites
 SUMMARY OF THE INVENTION
 The present invention for a method to mathematically relate each and every
 producing well in a given oil field. One object of the present invention
 is to provide a method of relating each and every oil producing well in a
 given field without resorting to more sophisticated and time consuming
 methods of locating one or more producing wells. Another object of the
 present invention is to provide a method of relating all of the oil
 producing wells in a given field in a manner that will yield other
 possible locations for new producing wells within the given field.
 To accomplish these and other objects, features and advantages of the
 present invention, a method of relating producing wells in a given fossil
 fuel drilling field is provided. In one embodiment, the method includes
 selecting a first origin well known to be a producing well. Next, a second
 well is selected that is also known to be a producing well. A distance X
 is then determined between the first origin well and the second well. A
 distance Y is then calculated from the first origin well to a third well
 location and using the equation
EQU Y.sup.2 +X.multidot.Y-X.sup.2 =0
 Next, the third well location is selected relative to the first origin well
 and having the distance Y from the first well.
 In one embodiment, the fossil fuel produced by the existing drilling field
 is a petroleum oil product. In another embodiment, the fossil fuel is a
 natural gas product.
 In one embodiment, the distance between the first origin well and the
 second well is calculated using Universal Transverse Mercator coordinates.
 In one embodiment, the third well location is calculated in order to locate
 an existing well known to be a producing well.
 In another embodiment, the third well location is determined in order to
 locate an area for drilling a new producing well.
 In another embodiment of the present invention, a method of relating
 producing wells in a given fossil fuel drilling field is provided. In this
 embodiment, the method includes selecting a first and a second well each
 of which are known to be producing wells. An origin distance X is then
 determined between the first well and the second well. A third well also
 known to be a producing well is then selected. A distance Y is then
 calculated from the third well to a fourth well location and using the
 equation
EQU Y.sup.2 +X.multidot.Y-X.sup.2 =0
 Next, the fourth well location is selected relative to the third well and
 having a distance Y from the third well.
 In one embodiment, the fourth well location is a known existing location of
 a producing well in the fossil fuel drilling field. In another embodiment,
 the fourth well location is determined for locating an area in which to
 drill a new producing well in the existing field.
 These and other objects, features and advantages of the present invention
 will become apparent upon a review of the written description and
 accompanying drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
 Referring now to the drawings, FIG. 1 illustrates a schematic chart showing
 the geographic location of each producing well in a productive oil field
 known as the Oseberg field in Norway. The units of the x-axis and the
 y-axis of the chart are each in metric meters. The intersection of the
 x-axis and y-axis for the chart is not zero but instead is the
 southernmost and westernmost location of producing wells in the entire
 field. The chart represents a coordinate system known as the Universal
 Transverse Mercator (UTM) geographical coordinate system and is based on
 data of 1927. In this system, there is one horizontal and vertical 0
 coordinate and then every geographic location is taken from the 0
 coordinate and measured in meters both horizontally and vertically
 relative to the origin. Therefore, the horizontal or x-axis of the chart
 represents the distance in meters along a horizontal axis from the 0
 coordinate of the UTM coordinate system. Similarly, the vertical or y-axis
 represents the distance in meters relative to the 0 coordinate along a
 vertical axis of the UTM coordinate system.
 FIG. 2 illustrates a simple schematic showing how, utilizing the UTM
 coordinate system, an actual distance in meters between two producing
 wells is calculated for the purposes of this invention. The lower left
 well identified by the coordinates (X0, Y0) is located spaced from a
 second well identified having the coordinates (X1, Y1). Utilizing the
 commonly known equation
EQU d= (X.sub.1 -X.sub.0).sup.2 +(Y.sub.1 -Y.sub.0).sup.2 (EQ. 1)
 This equation calculates the hyphothonus of a right triangle indicated by
 the dotted lines in FIG. 2. The horizontal dotted line represents the
 distance along the x- axis between the two wells and the vertical dotted
 line represents the distance along the y-axis between the wells. Utilizing
 the equation, the distance d between the two wells can be calculated as
 long as the coordinates in the UTM coordinate system are known for each
 producing well.
 The present invention provides a method for relating all of the producing
 wells in any given oil field wherein a mathematical relationship can be
 utilized for a number of different purposes. The relationship between each
 of the producing wells in a particular oil field is dependent upon the
 distances between all of the wells. By analyzing each of the distances
 between given pairs of producing wells in a number of different manners, a
 reoccurring relationship is discovered that relates all oil producing
 wells in a given field. An example is presented thoroughly explaining the
 inventive method and then the mathematical relationship that is realized
 is discussed. Two more examples are also presented and discussed in less
 detail herein.
 A first statistical analysis was conducted. Referring to FIG. 3, a chart
 representing each of the producing wells in the Oseberg field is
 illustrated wherein one of the wells identified as well O14 is selected as
 the origin well and a distance from the origin well to each other
 producing well of the field is calculated utilizing the equation 1 noted
 above. FIG. 4 illustrates the chart showing each of the wells of the
 Oseberg field except wherein the well O02 is selected as the origin well.
 The distance from the origin well to each of the remaining producing wells
 of the field is then calculated and also includes the distance from the
 origin well O02 to the previously selected origin well O14. This was done
 for each well selected as the origin well.
 Couples or pairs of distances having a common origin well were then
 compared for each producing well selected as the origin well. For example,
 as illustrated in FIG. 5, an origin well is O02 and one couple or pair of
 distances is illustrated including the distance from O02 to the well O04
 and the distance from O02 to the well O0902. FIG. 5 also illustrates the
 producing well O0902 selected as the origin well and illustrates one
 couple or pair of distances. One distance is from O0902 to the well O12
 and another distance is from O0902 to the well OC01. Therefore, for each
 well selected as the origin well in the Oseberg field, which includes
 nineteen total producing wells, there are eighteen distances between each
 origin well and the remaining producing wells in the field. Though these
 distances are repeated a number of times, there are a total of
 19.times.18=342 total distances possible for all wells selected as the
 origin well. For each well selected as the origin well, there are
 seventeen possible couples or pairs of distances from the origin well to
 two selected of the remaining producing wells. Therefore, there are
 19.times.17=323 total possible couples or pairs of distances without
 repeating any pairs or couples of distances and without repeating the
 origin well. The ratio of the smaller distance over the larger distance
 for every possible pair or couple of distances in the entire oil field of
 Oseberg was then analyzed and compared.
 A second statistical analysis was also conducted on the distance data for
 the producing wells of the Oseberg field. In the first statistical
 analysis noted above in FIG. 5, for comparing couples of distances having
 a common origin well, three producing wells were required. Referring to
 FIG. 6, the second statistical analysis was conducted selecting four
 producing wells at any one time. One distance is first selected as the
 origin distance. For example, the distance between the producing well
 O0912 and O0901, was selected as the origin distance and is shown in FIG.
 6. A third well such as the well O14 is next selected. The distance
 between the third well and each remaining unselected well is then
 calculated as is also illustrated in FIG. 6. Each of these distances is
 then separately compared to the origin distance to form separate pairs or
 couples of distances utilizing four producing wells. In this manner, each
 distance is separately selected as the origin distance between two given
 producing wells and compared to each other distance between any two of the
 remaining producing wells. An exhaustive analysis of each possible
 distance coupling or pairing utilizing four wells at a time was then
 studied without repeating distance pairings or couplings.
 As illustrated in FIG. 7, two examples of distance pairings or couplings
 are illustrated utilizing four separate wells for each pairing or
 coupling. For example, one origin distance is selected as the distance
 between the producing well O14 and the producing well O12. The coupled or
 paired distance was the distance between the producing well O17 and the
 producing well O09. A second exemplary pairing or coupling is the origin
 distance between the well O13 and the well O0912 and the coupled distance
 between the well O01 and well O0901. The ratio of each possible distance
 pairing or coupling utilizing four wells was then determined whereby the
 smaller distance of each pairing is divided by the larger distance.
 Upon reviewing the ratio data for each distance coupling or pairing for
 both statistical studies, one utilizing three wells having a common origin
 well and one utilizing four separate producing wells, reveal that a
 relatively large number of pairings or couplings produce the same constant
 ratio. Upon further analysis, each of the producing wells of the field at
 Oseberg was utilized at least once in the data producing the constant
 ratio. Every single well of the Oseberg field produced the same constant
 mathematical relationship at least once when compared to two or three
 other producing wells of the field. FIG. 8 illustrates each of the
 twenty-nine couples of distances or distance pairings of the Oseberg field
 that produced a constant distance ratio of 0.6178 (plus or minus a small
 statistical variation).
 FIG. 9 illustrates a data table including twenty-nine (29) pairs of
 distances which yield essentially the same constant ratio between the
 smaller distance Y over the larger distance X of each coupling or pairing.
 As can be seen in this data table, the couplings 4, 10 and 20 represent
 the first statistical study and utilize only three producing wells and
 have a common origin well. The remaining couplings or pairings represent
 the second statistical study and utilize four separate producing wells in
 comparing distances for each of the remaining couplings.
 FIG. 10 illustrates a-chart plotting the ratio of the distance couplings
 for each coupling or pairing 1 through 29 shown in the data table in FIG.
 9. The slope of the curve is linear and was calculated as B=0.6178017. The
 chart of FIG. 10 plots the larger distance X for each distance coupling
 along the horizontal axis and the smaller distance Y for each particular
 coupling along the vertical axis of the chart. This chart does not plot
 coordinates of the UTM system, but instead plots the distance in meters
 between producing wells for each pair or coupling indicated in the data
 table of FIG. 9.
 The data table of FIG. 11 illustrates comparative data wherein the
 independent variable X represent the larger distance between producing
 wells of each coupling or pairing of distances. The second column of the
 table indicates the actual smaller distance Y for each pairing. Column 3
 of the chart indicates a calculated variable Y' utilizing the average
 mathematical constant of the data of FIG. 8. The fourth column of the
 table of FIG. 11 denotes the difference in meters between the actual and
 the calculated dependent variable Y and Y, respectively, for determining a
 statistical deviation between the actual and calculated variables.
 FIG. 12 illustrates another schematic chart of each of sixteen producing
 wells in a oil field known as Captain field in the United Kingdom. Again,
 the geographical coordinates of each producing well are shown in the chart
 in meters and according to the UTM coordinate system.
 Similar to that of the Oseberg field discussed above, each possible pair or
 coupling of distances of producing wells in the Captain field was
 calculated both utilizing the three well statistically study and utilizing
 the four well statistical study. FIG. 13 illustrates an example of two
 different distance pairs or couplings wherein each pair or coupling has a
 common origin well. For example, the origin well C15 is selected and the
 distance from C15 to the producing well C06 and the distance from C15 to
 the producing well C08 makeup the two distances of the pair. As another
 example, the origin well C09A is selected and the distance between C09A
 and the producing well C11ST and from C09A to the producing well C16
 makeup the two distances of that particular pair.
 Similarly, FIG. 14 illustrates one example of a distance coupling or pair
 wherein the coupling or pair utilizes four separate producing wells. One
 distance of the pair is from the producing well C14 to C12s and the other
 distance of the pair is the distance from the well C13 to the well C10.
 Of all of the possible distance pairing combinations both utilizing three
 producing wells having a common origin well and utilizing four separate
 producing wells, twenty-seven (27) pairings or couplings yielded a common
 distance ratio of the smaller distance Y of each pairing over the larger
 distance X of each pairing and which utilized each and every producing
 well at least once for the entire Captain field. As shown in the table of
 FIG. 15, of the twenty-seven different couplings that produce the constant
 ratio, the couplings 1, 11, 12, 16, 18, 21 and 27 utilize three producing
 wells and a common origin well whereas the remaining couplings utilize
 four separate producing wells.
 FIG. 16 illustrates a chart comparing the larger distance X of each pair
 along the horizontal axis to the smaller distance Y of each pair along the
 vertical axis. The slope of the curve is again linear or constant and is
 B=0.6181176 for the captain field.
 FIG. 17 illustrates a data table comparing the actual larger distance X,
 smaller distance Y, calculated average smaller distance Y', and the
 difference of Y-Y' for each of the twenty-seven pairs or couplings that
 produce the constant ratio for the Captain field.
 As another example, FIG. 18 illustrates a schematic chart of the twelve oil
 producing wells of an oil field identified as Izozog Field, located in
 Argentina. Again, the chart includes units of meters and geographically
 locates the wells according to the UTM coordinate system.
 FIG. 19 illustrates three examples of distance couplings or pairings
 utilizing only three producing wells with one of the three origin well.
 For example, where the well IZ12 is the origin well, the distance from the
 IZ12 to the IZ4 well and the distance from IZ12 to the IZ8 well provide
 one distance pairing. Where the producing well IZ3 is the origin well, the
 distance from the IZ3 well to the IZ8 well and the distance from the IZ3
 well to the IZ7 well provides another distance pair. Also illustrated in
 FIG. 19, is one example of a distance pairing utilizing four separate oil
 producing wells. For example, the large distance X for this pairing is the
 distance from the well IZ6 to the well IZ1 and the small distance Y is the
 distance between the IZ5 well and the IZ3 well.
 Out of all the possible distance pairings utilizing either the three well
 or the four well statistical analysis, nine (9) pairings again produced
 the same constant and also utilized each and every well at least once for
 the entire Izozog field. The data for each of these nine pairings is shown
 in the table of FIG. 20. As shown in FIG. 20, pairing numbers 1, 2, 4, 6,
 8 and 9 utilize only three wells and the distance pairings 3, 5 and 7
 utilize four wells. Again, the ratio for each of these pairings identified
 as the small distance Y over the large distance X of each pairing equals a
 constant value B=0.6185382. FIG. 21 illustrates a chart having the large
 distance X of each pair plotted along the horizontal axis and the small
 distance Y of each pair plotted along the vertical axis. Again, the curve
 is linear and has a slope of B=0.6185382. This plot includes each of the
 well pairings shown in the table of FIG. 20.
 FIG. 22 illustrates a data table including the large distance X and the
 small distance Y for each pairing noted in table 20. This data table also
 includes the calculated average small distance Y' as well as the
 difference between the calculated distance Y' and the actual distance Y.
 In all, ten different oil fields in a number of different countries were
 statistically analyzed in the manner discussed above. FIG. 23 illustrates
 a chart or table listing the country and the oil field in that particular
 country that was analyzed. FIG. 23 also lists the number of producing
 wells in each field and the number of distance pairings or couplings
 producing the same mathematical relationship. FIG. 23 also lists the
 constant or slope B that was discovered for each of the particular oil
 fields analyzed. Surprisingly, in each oil field analyzed, a distance
 ratio among a number of distance pairings between three oil wells
 including an origin well or four separate oil wells, and wherein every
 producer well in each field was utilized at least once, the constant or
 slope B was found to be virtually identical.
 The average constant or slope B for all of the data obtained from the ten
 fields analyzed was B=0.61804. The significance of this constant B or
 slope obtained from all of these different and unrelated oil fields was
 further analyzed. Given that the constant or slope B represents a ratio of
 the smaller distance Y of a distance pairing over the larger distance X of
 the same distance pairing, if the ratio is equal to 0.61804, this relates
 to the equation 0.61804=Y.div.X, then the smaller distance Y is equal to
 the larger distance X multiplied by the constant ratio 0.61804.
 In solving an algebraic problem of comparing two lines X and Y of different
 length, and in making the bigger line X equal to one (X=1), the value of
 the smaller line Y is the dependent variable. Solving this problem results
 in the equation X.sup.2 =Y (Y+X). Making X equal to 1, and in solving this
 quadratic equation, Y=(-1)+1.sup.2 -4(31) (-1).sup.2 =0.618033.
 Surprisingly, this value is identical to the slope or constant B derived
 from analyzing each of the oil fields. Based upon the statistical data
 obtained from each of the oil fields and the result of equation 5, a new
 equation
EQU Y.sup.2 +X.multidot.Y-X.sup.2 =0 (EQ.2)
 is generated bu substituting the variable X for 1 in the equations 3 and 4
 above. Utilizing this equation, and knowing the independent variable X
 being the distance between two producing oil wells in any given oil field,
 one can calculate the dependent variable Y which can be utilized in a
 number of different ways.
 One use of the present invention can be performed using two existing well
 locations to find a third. If two existing producing wells are known and
 the distance is known between the two producing wells, this distance is
 the independent variable X, or the large distance in a distance coupling
 or pair. In one example, one of the two wells is selected as the origin
 well and Equation 2 is used to calculate a second smaller distance or
 dependent variable Y. A third producing well will be found on a circle
 having a radius of the distance Y from the origin well. This calculation
 can be utilized to locate an existing location of a third producing well
 or alternatively, can be utilized to locate a third well location where a
 new well can be drilled that will be a producing well within the existing
 field.
 Another use for the present invention can be performed using three existing
 well locations to find a fourth. Two existing producing wells are known in
 a given oil field and where the distance X between these two known wells
 is known. A third known producing well can be selected regardless of its
 position relative to the first two producing wells. Equation 2 can then be
 utilized to calculate a smaller distance or dependent variable Y from the
 third well to a fourth well location.
 This particular calculation can be used for two purposes. First, the
 calculation can be done to locate an existing location of a fourth
 producing well relative to the third known producing well. Alternatively,
 this calculation can be performed to locate a fourth well location to
 drill a new well a distance from the third known producing well anywhere
 on a circle having a radius the distance Y from the third well.
 Utilizing the methods of the invention, any known existing producing well
 in a given field can be utilized in conjunction with virtually any other
 known producing well to either locate an existing producing well without
 knowing its exact location and without resorting to sophisticated locating
 technology, or alternatively, can be utilized to locate an area where a
 new producing well can be drilled within the given oil field.
 Though specific embodiments of the present invention are described herein,
 the invention is not intended to be so limited. Modifications and changes
 can be made to the described embodiments and yet fall within the scope and
 spirit of the present invention. The invention is intended to be limited
 only by the appended claims.