Patent Publication Number: US-7212923-B2

Title: Inferred production rates of a rod pumped well from surface and pump card information

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates generally to oilfield equipment for monitoring and controlling wells that are produced by rod pumping where subsurface fluid pumps are driven via a rod string which is reciprocated by a pumping, unit located at the surface. The pumping unit may be of the predominate beam type or any other type that reciprocates the rod string. 
   In particular, this invention concerns using a down hole dynagraph, i.e., a pump card, with information as to the size of the down hole pump, to infer automatically the hydrocarbon production of the well. 
   Still more particularly, the invention concerns methods for use in a Well Monitor Controller where surface and pump cards are produced, whereby traditional well tests of a producing well can be eliminated. 
   2. Description of the Prior Art 
   Traditional Production Testing 
   A production test is a time-honored procedure in oil producing operations. It is involved in several activities including operation of the oilfield as a business venture, governmental regulation, well troubleshooting, and reserve estimates. With respect to its business role, it provides for division of leaseholder royalties and costs. To encourage prudent operation and enhance the stability of the nation, conservation authorities usually require periodic production tests. Also the production test is employed as a diagnostic indicator which calls attention to well problems that need to be addressed. It is important in reserve estimates, because cumulative production from each well needs to be known. 
   The use of the production test as a diagnostic indicator is perhaps the most recognized application among production specialists. A decline in production rate compared with a previous test can indicate a mechanical problem. The down hole pump may be worn or a tubing leak may have developed. The mechanical malfunction should be identified and remedied. The decline may also be caused by a change in reservoir conditions in the drainage area of the well. The receptivity of an offset injection well may have diminished. This may have resulted in a producing pressure decline and a decrease in production rate. The problem in the secondary recovery system should be rectified. 
   Conversely, an increase in productivity as measured by a well test may indicate that the well is responding to secondary recovery efforts. In this case, the well should be pumped more aggressively to obtain the increased production that is available. 
   The production test is a good tool for sensing that a change in the well has occurred, but it does not pinpoint the exact reason for the change. Usually a unique cause and effect relationship does not exist between a change in production rate and its cause. Because different causes may lead to the same effect, ambiguity exists. For example, a production decrease can have any number of causes such as a worn pump, a tubing leak, a failed tubing anchor, the onset of free gas production, secondary recovery deficiency, etc. 
   In the early years of the oil industry, each well had its own tankage and oil-gas-water separation equipment. The well was tested by measuring daily production into its tank. To decrease capital and operating costs, the handling and measurement system evolved into a centralized facility with flow lines extending from the individual wells. Production from the individual wells comes to a header. At the header a given well is placed either “on test” or has its production sent with that of other wells through a separate facility for separating and treating salable products. Ultimately the oil produced from the well(s) on test is combined with production from the remainder of the wells. The total production is then measured a final time and sold. The individual well test is used to determine the contribution of the subject well to total production from the lease  230 . As mentioned previously, individual well tests are also used to equitably divide operating costs between the wells and to provide information for reserve estimates  230 . 
   Meter malfunction is a significant problem for traditional production tests. In addition, the well test can be wrong even when the meters are working perfectly. Actual production is normally much lower than the test, primarily because of down time for equipment failures or other reasons. In principle, downtime is noted and accounted for, but down time measurement accuracy is poor. Downtime is often neglected entirely. The net effect is that traditional tests and actual production from individual wells can differ substantially, as much as from 10 to 20 percent. Accurately knowing actual production from each well is not only important for effective production operations but is also important for reservoir management  230 . 
   Well test systems have evolved significantly. Automatically controlled diverting valves have replaced manual valves. Computers for scheduling well tests have been introduced. Significant improvements in the accuracy and reliability of measuring devices have also been made. Traditional production testing has come a long way since the pumper manually operated the system and recorded the results in an oily notebook with a stubby pencil. 
   Diagnostic Methods 
   As mentioned above, a production test has been used as a diagnostic tool to discover that a change has occurred in the well  230 . The test itself does not point to the cause for the change. To determine specific cause(s) for change, diagnostic methods are employed. The best diagnostic methods are based on dynamometer analyses. Trial and error searches with the service rig (pulling unit) can also be used, but these searches are more costly to perform. Trial and error solutions require more time, and revenue is lost before the problem is identified. 
   Like the production test, a fluid level instrument is not capable of identifying the specific cause for a change. A change in fluid level can indicate several causes. If a relatively high fluid level is found, for example, the well operator only knows that the well is not producing at capacity. More investigation with diagnostic methods is required to identify the cause: it could be a worn pump, tubing leak, secondary recovery problem or something else. 
   Modern diagnostic analysis with the dynamometer began in the 1960&#39;s. The epochal development was the method for inferring the down hole pump card from surface dynamometer data. It was described in U.S. Pat. No. 3,343,409 (Gibbs). The down hole pump card (hereinafter called the “pump card”) was originally introduced in 1936. It was measured directly with a dynamometer located at the subsurface pump. The measured pump card had to be retrieved by a costly process of pulling the rods and pump. By 1960, computers were available which could solve the complicated equations required to calculate the pump card from data measured at the surface of the well. To produce the pump card  212 , solutions to the wave equation are obtained which satisfy dynamometer time histories of surface rod load  208  and position  210 . 
   Qualitative Evaluation of Down Hole Pump from the Shape of Pump Card 
   The pump card is very useful. Its shape reveals defective pumps, completely filled pumps, gassy or pounding wells, unanchored tubing, parted rods, etc. The pump card can also be used to compute producing pressure, liquid and gas throughput, and oil shrinkage effects. It can also be used to sense tubing leaks. 
   Quantitative Determination of Pump Leakage 
   Quantitative computation of pump leakage from pump cards was described in “ Quantitative Determination of Rod - Pump. Leakage with Dynamometer Techniques ”, Nolen, Gibbs, SPE Production Engineering, August 1990. Prior to this work, pump mechanical condition was obtained by (1) pulling the pump or (2) comparing the production test with estimates of pump capacity or (3) qualitative eyeballing of valve leakage rates measured with the dynamometer. The quantitative methods of Nolen and Gibbs to determine leakage involved use of scaled traveling or standing valve tests and information as to the manner in which the surface unit stops when turned off and information as to: the pump velocity measured from the pump card. These methods are discussed below in greater detail. 
   Pump Off Control Technology 
   Pump off control (POC) attained status as a viable method in the early 1970&#39;s. It was originally intended merely for stopping the well to prevent the mechanical damage of fluid pound and the power waste associated with operating an incompletely filled pump. From this humble beginning, the POC evolved into a distributed diagnostic system with well management capabilities  230 . Gradually the phrase “pump off control” was replaced with terms like “Well Manager,” “Pump Rod Controller,” etc. (Lufkin Automation uses the trademark SAM to identify its Well Manager system). These new terms imply more than pump off control. The modern systems include diagnostic capability, collection and analysis of performance data and operation of the well in an economic fashion  230 . The term WM is used below in this specification as an abbreviation for Well Manager of the type presently available through Lufkin Automation. 
   Over the years, POCs have used different algorithms to sense pump off. Some of these involve surface load change, motor current, motor speed, set points, dynamometer card area, and the down hole pump card. U.S. Pat. No. 5,252,031 to Gibbs describes pump off control through the use of “pump” cards. Because of its ability to sense liquid and gas throughput using the subsurface pump as a meter, POCs which use the pump card for control are desired for implementing Inferred Production (IP). 
   Inferred Production (IP) using a POC Well Manager (WM) 
   Current WMs infer production rate with considerable accuracy by using the subsurface pump as a flow meter. In other words inferred production (IP) can be determined without continuous use of traditional metering equipment. The current WM accumulates inferred fluid production with time and displays it for (1) manual recording and dissemination or (2) automatic transmittal to a central location via SCADA. A SCADA or telemetry system is helpful but not an absolute requirement. The WM always displays inferred production that can be retrieved during periodic visits by the pumper. However when a group of pumping wells is already under SCADA surveillance, IP is interfaced with SCADA for unattended telemetry of inferred production to a central collection point. The pump card based WM excels in the IP application over a SCADA produced pump card system. This is because the WM is monitoring its well continuously, stroke after stroke. The SCADA system can interrogate the well only a few times each day to retrieve dynamometer data. Therefore down hole or “pump” cards can be computed in SCADA only a few times each day. This causes errors in inferred production, particularly in wells where pump fillage varies rapidly. 
   Even in its incomplete state, the present system of gathering production data has the advantage of providing continuous well tests. This decreases the time lag between discovery and remediation of problems that affect production. Traditional well tests are often brief in duration (4 hours or less). In many cases these are not representative of true production rate. If the test system is serving a large number of wells, the traditional tests are infrequent, maybe only monthly. This acts to increase the time lapse between problem discovery and remediation. 
   It is important to identify the assumptions upon which a production test is inferred with a current prior art system.
         1) The pump is in good mechanical condition and leakage is minimal.   2) The tubing is anchored at or near the pump.   3) Free gas volume in the pump is negligible at the time of traveling valve (TV) opening.   4) Oil shrinkage effects are negligible.       

     FIG. 1  shows a typical rod pumping system, generally indicated by reference number  10 , including a prime mover  12 , typically an electric motor. The power output from the prime mover  12  is transmitted by a belt  14  to a gear box unit  16 . The gear box unit  16  reduces the rotational speed generated by prime mover  12  and imparts a rotary motion to a pumping unit counterbalance, a counterweight  18 , and to a crank arm  20  which is journaled to a crank shaft end  22  of gear box unit  16 . The rotary motion of crank arm  20  is converted to reciprocating motion by means of a walking beam  24 . Crank arm  20  is connected to walking beam  24  by means of a Pitman  26 . A walking horsehead  28  and a cable  30  hang a polished rod  32  which extends through a stuffing box  34 . 
   A rod string  36  of sucker rods hangs from polished rod  32  within a tubing  38  located in a casing  40 . Tubing  38  can be held stationary to casing  40  by anchor  37 . The rod string  36  is connected to a plunger  42  of a subsurface pump  44 . Pump  44  includes a traveling valve  46 , a standing valve  48  and a pump barrel  50 . In a reciprocation cycle of the structure, including the walking beam  24 , polished rod  32 , rod string  36  and pump plunger  42 , fluids are lifted on the upstroke. When pump fillage occurs on the upstroke between the traveling valve  46  and the standing valve  48 , the fluid is trapped above the standing valve  48 . A portion of this fluid is displaced above the traveling valve  46  when the traveling valve moves down. Then, this fluid is lifted toward the surface on the upstroke. A schematic description of pump valve operation is illustrated in  FIGS. 2A and 2B . 
   As shown in  FIG. 2A , when the rod string  36  is in an upstroke, the traveling valve  46  is closed and the fluid is lifted upward in the tubing  38 . During the upstroke, fluid is drawn upward into the pump barrel  50  through the open standing valve  48 . Referring to  FIG. 2B  for a description of the down stroke, as the plunger  42  is lowered, the traveling valve  46  is open thereby permitting fluid within the pump barrel  50  to pass through the valve to allow the plunger  42  to move downward. The fluid within the tubing  38  and the barrel  50  is held fixed in place by the closed standing valve  48 . The rod string  36  does not carry any weight of fluid during the down stroke, but does lift the entire column of fluid during the upstroke. 
   A well manager unit  52  (see  FIG. 1 ) receives or derives surface rod and load information  210 ,  208  (or equivalent measurements), draws a surface card and computes a pump card  212 . Information about the subsurface pump  44 , including surface and pump cards can be sent to a central location via telemetry equipment including antenna  54 . 
   A current Inferred Production System can be described by reference to  FIGS. 3 and 4 . These Figures show traveling and standing valve action and the shape of typical pump cards that are computed by WM  52 .  FIG. 3E  shows the familiar rectangular pump card shape  500  indicating full liquid fillage of the pump.  FIG. 3F  depicts a “fluid pound” card  510  showing incomplete liquid fillage. In both cases the pump is in good mechanical condition and the tubing is anchored near the pump. At low producing pressure, oil shrinkage effects and the volume of free gas at TV opening are negligible. Under pump off control, the pump normally fills completely with liquid for a time after startup. At a later time depending upon the well, pump fillage decreases and fluid pound develops. Eventually the WM  52  will stop the pumping unit  10  to prevent waste of power and the damaging effects of fluid pound. In  FIG. 3E  the gross stroke S g  and the net stroke S n  are shown. When the pump is filling completely with liquid, there is no free gas passing through the pump and S n =S g . The net liquid stroke is the distance traveled by the pump from TV opening (Point C) to the bottom of its stroke (Point D)  FIG. 3E . 
     FIG. 3F  represents the situation of an incompletely filled pump with a volume of liquid and low pressure free gas therein. At point B, the pump is at top of its stroke, and the standing valve (SV) has just closed.  FIG. 3D . Later, on the down stroke (Point C) the traveling valve opens. The free gas has been compressed into a tiny volume that satisfies Assumption 3. The computer in the WM  52  is programmed to determine  214  when the traveling valve opens. Thus, the net liquid stroke is defined  232  with little error as the distance the pump travels from TV opening to the bottom of its stroke. See S n  in  FIG. 3F . 
   In most cases the shut-down criterion for pump off control is based on liquid fillage of the pump. Fillage is defined as 
                 Φ   =       100   ⁢           ⁢     S   n         S   g               (   1   )               
in which Θ is fillage percentage. The term fillage is defined by equation 1, and is commonly used and understood by practioners of rod pumping. The shut down percentage is chosen by the well technician and causes the WM  52  to stop the unit  10  when the calculated fillage drops below a preset value. For example a cut-off fillage of 90 percent causes the unit to shut down when liquid fillage drops below 90 percent of the full barrel volume. The digital computer in the WM is programmed to recognize when the traveling valve  46  opens, and this helps define the net liquid stroke S n .
 
   Using the Subsurface Pump as a Meter 
   The subsurface pump can be used as a meter to measure liquid and gas volumes. On a given stroke, the liquid volume (oil and water) passing through the pump is 
                   Δ   ⁢           ⁢     V   l       =       π   4     ⁢     d   2     ⁢     S   n               (   2   )               
in which ΔV 1  is measured in cubic inches and d is the diameter of the pump measured in inches. Equation 2 is the formula for computing the volume of a cylinder of diameter d and height S n . If the unit  10  is turned off by the WM  52 , the liquid volume is
 Δ V   1 =0 
   The prior art WM  52  is programmed to obtain an estimate of liquid production passing through the pump in an interval of time. Stroke after stroke the WM derives the liquid stroke (i.e., S n  from  FIG. 3E  or  3 F) from the pump card and computes the liquid volume from Equation (2). It accumulates (integrates) the liquid volumes during pumping strokes, whatever the fillage. The WM  52  has information when the unit  10  is stopped and no fluid is passing through the pump. The WM controls when the unit runs and when it is stopped. When 24 hours have passed, the WM  52  computes the inferred daily production rate R IP    228  in barrels per day from the elapsed time and accumulated volumes. This is expressed analytically as, 
                   R   IP     =     8.905   ⁢       ∑           ⁢     Δ   ⁢           ⁢     V   l           (       T   d     +     T   p       )                 (     3   ⁢   a     )               
in which T d  and T p  are the accumulated downtimes and pumping times during the day, expressed in seconds. The coefficient 8.905 converts cubic inches per second into barrels per day. The integrated volume of liquid passing through the pump, stroke after stroke, is the sum, ΣΔV 1 .
 
   Equation (3a) defines the prior art method for Inferred Production IP of liquids using the WM  52  or unit  10 . Such equation, as described above, is based on assumptions of 
   (1) negligible pump leakage, 
   (2) anchored tubing, 
   (3) negligible free gas volume in pump at time of traveling valve (TV) opening, and 
   (4) oil shrinkage effects are negligible. 
   The prior art method for determining liquid volume daily production rate R IP  (equation 3a) has been to provide a “k” factor to account for differences between measured production and inferred production using the pump as a meter. But when any of the basic assumptions above are not correct, the accuracy of the IP method decreases. The prior art “k” factor is 
                 k   =       R   t       R   IP               (   4   )               
in which R t  is the daily production rate measured in a traditional well test and R IP  is the unadjusted inferred daily liquid rate. The k factor is multiplied by the unadjusted inferred daily liquid rate (determined from eq. 3a) to estimate the actual daily liquid rate of the well without actually measuring it by a traditional well test. The formula is,
   R   t   =k R   IP ,  (5) 
where R t  is the adjusted value that is taken to be equivalent to the traditional well test. Ideally, the k factor is just below 1.0, for example in the range of 0.85 to 0.9. This factor accounts for the fact that the fundamental assumptions above are not always correct. All pumps leak, at least slightly. Tubing is not always anchored at or near the pump. A small volume of free gas is often present in the pump at the instant of traveling valve opening. If pressure in the pump is relatively high (the well is not completely pumped-off), the volume of free gas in the pump may not be small at all. Finally, most oil shrinks as gas evolves from it while passing up the tubing to the stock tank. Ideally the combined effect of these departures from the assumptions is small such that the k factor is slightly less than one as mentioned above.
 
   The prior art method of using the subsurface pump as a meter for liquid volume inferred production (IP) is illustrated in the examples below. 
   EXAMPLE 1 
   A 1.5 inch subsurface pump is being used to infer production with typical full fillage and fluid pound pump cards shown in  FIGS. 3E and 3F . 
   Determine: 
   (1) The incremental volume of liquid handled by the pump on the complete liquid fillage stroke of  FIG. 3E , and 
   (2) The incremental volume of liquid handled by the pump on the fluid pound stroke of  FIG. 3F . 
   Solution: 
   (1) From  FIG. 3E , the net liquid stroke S n  is 117.5 inches (full liquid fillage). From eq. 2, 
   
     
       
         
           
             Δ 
             ⁢ 
             
                 
             
             ⁢ 
             
               V 
               l 
             
           
           = 
           
             
               
                 π 
                 4 
               
               ⁢ 
               
                 
                   ( 
                   1.5 
                   ) 
                 
                 2 
               
               ⁢ 
               
                 ( 
                 117.5 
                 ) 
               
             
             = 
             
               207.64 
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   in 
                   3 
                 
                 . 
               
             
           
         
       
     
   
   (2) From  FIG. 3F , the net liquid stroke is 46.77 inches (incomplete fillage). From eq. 2 
   
     
       
         
           
             Δ 
             ⁢ 
             
                 
             
             ⁢ 
             
               V 
               l 
             
           
           = 
           
             
               
                 π 
                 4 
               
               ⁢ 
               
                 
                   ( 
                   1.5 
                   ) 
                 
                 2 
               
               ⁢ 
               
                 ( 
                 46.77 
                 ) 
               
             
             = 
             
               82.65 
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   in 
                   3 
                 
                 . 
               
             
           
         
       
     
   
   Equation 3a is used with the ΔV l  values so calculated to infer liquid production. 
   EXAMPLE 2 
   A rod pumping well  10  is being monitored with a pump card WM  52 . Unadjusted inferred production is 289 BFPD. A traditional well test during the same period is 263 BFPD. A month later, a larger unadjusted inferred production of 310 BFPD is noticed. The well is in a water flood. 
   Determine: 
   (1) The k factor. 
   (2) The inferred production rate one month later. 
   (3) The possible causes for the production increase. 
   Solution: 
   (1) The k factor is 
   
     
       
         
           k 
           = 
           
             
               263 
               289 
             
             = 
             
               0.91 
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 
                   see 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   eq 
                   ⁢ 
                   
                     . 
                   
                   ⁢ 
                   4 
                 
                 ) 
               
             
           
         
       
     
   
   (2) Inferred production one month later is,
 
 R   t   =k R   IP =0.91(310)=282  BFPD   (see eq. 5)
 
   (3) Since the well is in a water flood, possible causes for the production increase are (a) further response to secondary recovery efforts, and (b) effect of a rod part in an offset producer and the attendant down time of that well. 
   The k factor is a useful but imperfect concept. One disadvantage is that it is not constant. For example, as the subsurface pump wears, the k factor decreases. Indeed if any of the quantities assumed to be negligible change, the k factor changes. Most significant of all, it would not be possible to compute the k factor if the traditional well test were to be entirely eliminated in favor of Inferred Production methods (see eq. 5 again). 
   3. Identification of Objects of the Invention 
   A primary object of this invention is to use a Well Manager in combination with a rod pumping unit to infer liquid production and gas production of a well with high accuracy. 
   Another object of the invention is to entirely eliminate traditional well tests for a rod pumped well by inferring liquid and gas production with high accuracy with a Well Manager Unit in combination with a rod pumping unit. 
   Another object of the invention is to remove limiting assumptions of negligible pump leakage, anchored tubing, negligible free gas and negligible oil shrinkage effects from prior art methods of inferring production when using a well manager with a rod pumping unit. 
   Another object of the invention is to provide inferred production methods that do not have timing and administrative problems inherent with traditional well testing. 
   SUMMARY OF THE INVENTION 
   The objects identified above along with other advantages and features are provided by a method and system in which pump leakage determinations are incorporated in the Well Manager, unanchored tubing determinations are incorporated in the Well Manager, and free gas remaining in the pump at TV opening are measured for each pump cycle. Furthermore, a method for inferring the rate of free gas production through the tubing is provided. Such measurements are incorporated in Inferred Production determinations such that accuracy is achieved which makes traditional well testing of the well unnecessary. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic illustration of a prior art rod pumping unit for a well with a reciprocating pump and with a Well Manager Unit for controlling operation of the rod pumping unit; 
       FIGS. 2A and 2B  are schematic illustrations of a prior art reciprocating pump showing operation of a standing valve and a traveling valve during upstroke and down stroke operation of the pump; 
       FIGS. 3A ,  3 B,  3 C, and  3 D illustrate operational conditions of a prior art reciprocating pump in conjunction with  FIG. 3E  which shows a typical down hole pump card where liquid in the well completely fills the pump on the up stroke and with  FIG. 3F  which shows a typical down hole pump card where liquid in the well only partially fills the pump on the up stroke; 
       FIG. 4  shows a down hole card and an aligned pump velocity versus pump position graph which illustrates a method for determining valve leakage of a down hole reciprocating pump as in  FIGS. 1–3 ; 
       FIG. 5  shows aligned graphs of surface rod position and load versus time for the rod pumping unit of  FIG. 1  which illustrates another method for determining valve leakage of a down hole reciprocating pump as in  FIGS. 1–3 ; 
       FIG. 6  shows aligned graphs of surface rod position and load versus time for the rod pumping unit of  FIG. 1  which illustrates yet another method for determining valve leakage of a down hole reciprocating pump as in  FIGS. 1–3 ; 
       FIGS. 7A–7D  illustrate a subsurface reciprocating pump in which tubing is not adequately anchored to the well casing, the Figures showing the shape of a down hole pump card by which tubing anchor inadequacy can be identified; 
       FIGS. 8A–8D  illustrate a subsurface reciprocating pump which is not completely filled with liquid on the down stroke of the pump and for which gas in the pump is at high pressure; 
       FIGS. 9A–9B  illustrate a well which has a pump leakage with the pump card and pump velocity versus position graphs used to compute pump leakage; 
       FIGS. 10A–10B  illustrate a gassy well with high pump intake pressure; 
       FIG. 11  illustrates the relationship among S g , S g adj , S n , and S l  with adjustments for unanchored tubing and pump leakage at pump conditions and the relationship of oil at stock tank conditions; 
       FIGS. 12 ,  13 , and  14  illustrate a method for determination of pump intake pressure and corresponding shrinkage factor of Gas Oil Ratio remaining in solution; and 
       FIGS. 15 ,  16 , and  17  illustrate flow chart schematic diagrams according to one or more methods of the invention. 
   

   DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION 
   As was discussed above, the prior art includes a method for inferring the liquid volume (oil and water) passing through the pump. Refer to equations (2) and (3a) above. 
   Inferred Measurement of Gas Production 
   One aspect of this invention concerns a method for measuring gas production. See  FIG. 3F  for an example of a well in which the pump is not completely filled with liquid on the pump downstroke. 
   The volume of gas passing through the pump on the stroke in question  220  is 
                   Δ   ⁢           ⁢     V   g       =         π   4     ⁢     d   2     ⁢           ⁢     (       S   g     -     S   n       )       =       π   4     ⁢     d   2     ⁢     S   gas                 (   6   )               
Gas volume, like liquid volume (equation 2 of the prior art method), is also measured in cubic inches. To obtain gas volume in standard cubic feet, gas pressure and temperature must be known. Similarly when the WM  52  has the unit  10  turned off,
 Δ V   g =0. 
   Similar to the derivation of inferred liquid production of the prior art of equation (3a), a method  200  has been developed for inferring the daily rate of free gas production, G IP , (SCF/day) through the tubing, 
                   G   IP     =       50       T   d     +     T   p         ⁢     (       P   i       P   x       )     ⁢     (       z   s       z   i       )     ⁢     (       T   s       T   i       )     ⁢           ⁢     ∑           ⁢     Δ   ⁢           ⁢     V   g                   (     3   ⁢   b     )               
where P s , z s , and T s  are standard pressure (14.65 psia), gas compressibility factor at standard pressure, and standard temperature of 520 deg R, respectively. The same quantities subscripted i are evaluated at pump intake pressure and pump temperature. The factor  50  converts cubic inches per second into cubic feet per day.
 
Improvements in Inferred Production
 
   This invention also concerns improvements in the methods and apparatus described above by which a Well Manager (WM) in combination with a rod pumping unit infers production from a well. The improvements allow for determination of Inferred Production of the well by eliminating assumptions of the prior art technique, thereby allowing measurement of the production with information from the down hole pump and obviating the need for periodic traditional well testing. 
   The description of the invention presented below uses relationships measured in common English measurements such as inches, cubic inches, barrels, etc. The invention can be used with measurements expressed in other measurement systems such as the metric system. The use of the English measurement system is not intended to limit the invention, but merely to show units consistency among the variables presented. 
   Elimination of Assumption of Negligible Pump Leakage 
   The first improvement concerns adding a method  202  which can be practiced by software in the WM by which the assumption of negligible pump leakage is eliminated. In other words, existing WM determination of inferred production of a rod pumped well, liquid production according to equations 3a and a new determination of gas determination according to equation 3b described above, are automatically augmented with techniques of the August 1990 SPE Production Engineer publication described above. 
   TV Pump leakage from Down Hole Pump Dynamometer Card and Pump Velocity: “Pump Card” Method 
   This method uses the pump card and pump velocity to determine the critical point at which upward displacement rate equals, leakage rate. The method applies when the pump card shape shows abnormal pump leakage. 
   When a severe traveling valve (or plunger) leak exists, the characteristic pump card shows a delayed load pickup and a premature load release. The standing valve opens when the upward lifting rate (measured in BPD) begins to exceed the downward slippage rate (BPD). The lifting rate depends on pump diameter and pump velocity. Pump velocity is derived from the pump card by numerical differentiation. The formula for TV/plunger slippage rate is
 
 L   TV =6.99  d   2   C   p   V   crit   (7)
 
in which C p  is a coefficient derived from the pump card, V crit  is the critical pump velocity (in/sec) at standing valve opening (C p  is sometimes taken to be 0.5), and d is the pump diameter (inches). See Appendix A for a derivation of C p    402 . Pump diameter is the only additional parameter needed over and above those already required for computing the pump card. The pump card method for evaluating pump leakage works best for severely worn pumps. For the example pump card  520  and pump velocity versus pump position plot  522  shown in  FIG. 4 , for a 1.25 in. pump (and C p =0.47 derived from the pump card) L TV =6.99 (1.25) 2  (0.47) (26.6)=137 B/D. Analogous methods for sensing standing valve leakage using the pump card are also available.
 
   The computer program in WM is written to estimate the point of standing valve opening and closing and traveling valve opening and closing  400 . See  FIGS. 3E and 3F  for example pump cards  500 ,  510  where traveling and standing valves are in good working order. One way to determine the point on the pump card where standing valve opens is to determine that point from TV closure where the pump load rises to 90% of the fluid load. Another way is to look for a change in direction of the pump card trace when fluid load pickup transitions to fluid lifting. Thus, for the pump card method of automatically determining pump leakage of the rod pumping system  10  of  FIG. 1 , the following steps are performed, 
   Referring to  FIG. 4 ,
         1) Determine C p    402  (i.e., estimate C p ≅0.5, or measure C p  according to method of Appendix A).   2) Determine  404  a pump velocity versus pump position relationship  522  from the pump card  520  being generated periodically in the WM.   4) Determine critical pump velocity V crit  relative to standing valve status
           a) determine V crit  at SV opening  406     b) determine V crit  at SV closing  410     
           5) Determine Traveling Valve Leakage L TV  
           a) determine L TV  at SV opening  408 
 
 L   TV =6.99 d   2   C   p  ( V   crit ) SV opening  
   b) determine L TV  at SV closing  412 
 
 L   TV =6.99 d   2   C   p  ( V   crit ) SV closing  
   
           6) Chose L TV  from 5 a) or from 5 b) or the average of L TV  from 5 a) and 5 b)  414     7) Determine TV opening and TV closing points  400     8) Determine critical pump velocity V crit , relative to Traveling Valve status
           a) determine V crit  at TV opening  416     b) determine V crit  at TV closing  420     
           9) Determine Standing Valve Leakage L SV  
           a) L SV =6.99d 2 (1−C p )(V crit ) TV opening    418     b) L SV =6.99d 2  (1−C p )(V crit ) TV closing    422     
           10) Chose L SV  from either 9a) or 9b) or the average of L SV  from 9a) and 9b)  424         

   TV Pump Leakage From Surface Rod Load and Position Time Histories (“Rolling Stop” Method) 
   Another method for sensing pump leakage is shown in  FIG. 5  which involves analyzing  426  surface rod load and position time histories  530 ,  532 . This method works best for shallow wells with small to severe pump leakage rates. In shallow wells, the pump card looks much like the surface dynamometer card. Further, the critical pump velocity V crit  is closely approximated by the critical velocity shown at the surface. This is called the “rolling stop” method and uses the same concept as the pump card method described above. The only difference is that the pump card method involves an increase in pump velocity whereas the method of  FIG. 5  observes the rod string slowing down. When rods slow down, the surface load begins to decrease when the load begins to be transferred from the traveling valve to the standing valve. Lifting rate (BPD) is again equal to downward slippage rate (BPD). The points  1 ,  2  and  3  in  FIG. 5  are used to compute the critical velocity (by differentiation) needed in eq. 7. An analogous procedure is available for sensing standing valve leakage. For an Inferred Production program in WM, the points  1 ,  2  and  3  are determined, a curve is found through them and critical velocity is determined by differentiating the position versus time relation for such curve. 
   Referring to  FIG. 5 ,
         1) Determine a curve through points  1 ,  2  and  3  where the rod-pumping unit is rising and the unit&#39;s upward velocity is maintaining polished rod load fairly constant. Identify point  1  where a small decrease in upward velocity causes the polished-rod load to decrease signifying the time at which upward velocity is no longer sufficient to keep the standing valve open, and determine V crit  on SV closing (for TV leakage)  428 .   2) Determine V crit    428  at point  1  by differentiating a curve which passes through points  1 ,  2 ,  3 ,   3) Compute TV leakage  412  from
 
 L   TV =6.99 d   2   C   p (V crit ) point  1 
 
An analogous procedure can be used for SV leakage. While the unit is moving downward, find points  4 ,  5 ,  6  such that at point  4  the downward velocity is no longer adequate to keep the TV open  430 . At this point, surface load beings to increase.
   4) Compute SV leakage  422  from
 
 L   SV =6.99 d   2 (1 −C   p )( V   crit ) point  4 
 
In deep wells pump velocity is no longer approximately equal to surface velocity. This results from greater rod stretch and time lag of traveling waves which are significant in deep wells. An analogous method uses pump velocity and load (instead of surface velocity and load) can be derived from the wave equation.
       

   Deriving TV/Plunger Leakage from Traveling Valve Load Loss Rate 
   Another quantitative method for deriving pump leakage is shown using surface rod load and position time histories  540 ,  542  of  FIG. 6 . This senses TV/plunger leakage by recognizing that the rods contract as fluid slips by the TV/plunger assembly causing the load to be transferred from the traveling valve to the standing valve. The volume of slippage during this time is the product of the pump area and the rod contraction distance. The rate of load loss is related to leakage  434  by means of the equation, 
   
     
       
         
           
             
               
                 
                   
                     L 
                     TV 
                   
                   = 
                   
                     6.99 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       d 
                       2 
                     
                     ⁢ 
                     
                       C 
                       p 
                     
                     ⁢ 
                     
                       k 
                       rt 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             ⅆ 
                             F 
                           
                           
                             ⅆ 
                             t 
                           
                         
                         ) 
                       
                       max 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   where 
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       L 
                       
                         
                             
                         
                         TV 
                       
                     
                     = 
                     
                       leakage 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       rate 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       of 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       TV 
                       ⁢ 
                       
                         / 
                       
                       ⁢ 
                       plunger 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       assembly 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       in 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       BPD 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           k 
                           rt 
                         
                         = 
                           
                         ⁢ 
                         
                           the 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           combined 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           stretched 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           constant 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           the 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           rod 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           string 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           unanchored 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           tubing 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               in 
                               ⁢ 
                               
                                 / 
                               
                               ⁢ 
                               lb 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 ⅆ 
                                 F 
                               
                               
                                 ⅆ 
                                 t 
                               
                             
                             ) 
                           
                           max 
                         
                         = 
                         ⁠ 
                         ⁢ 
                         
                             
                           
                             the 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             maximum 
                             ⁢ 
                             
                               
                                   
                               
                               ⁢ 
                               
                                   
                               
                             
                             ⁢ 
                             rate 
                             ⁢ 
                             
                               
                                   
                               
                               ⁢ 
                               
                                   
                               
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             traveling 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             load 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             loss 
                           
                           ⁢ 
                           
                               
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               lb 
                               ⁢ 
                               
                                 / 
                               
                               ⁢ 
                               sec 
                             
                             ) 
                           
                           . 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   The maximum load loss rate occurs at point  1  in  FIG. 6  and is evaluated  432  by differentiating a second degree polynomial passed through points  1 ,  2  and  3 . This method works in all cases as long as the load loss trace is not nearly vertical. In such cases, the “rolling stop” method of  FIG. 5  is preferable. An analogous method  436  is available for sensing standing valve leakage from maximum load increase rate. 
   For automatic application of the maximum load loss rate method of  FIG. 6 , the load loss trace for load versus time  530  is determined, a polynomial is passed through points  1 ,  2  and  3 , and F t  as a function of time is determined. The derivative is determined from that curve and a 
             (       ⅆ   F       ⅆ   t       )     max         
is found for application in equation 8.
 
   Adjusting for Pump Leakage Based on Time on 
   Automatic sensing of pump leakage is a great improvement to the methods of the prior WM. The equation, 
   
     
       
         
           
             stroke 
             ⁢ 
             
                 
             
             ⁢ 
             distance 
           
           = 
           
             bpd 
             
               0.1166 
               ⁢ 
               
                 ( 
                 
                   d 
                   2 
                 
                 ) 
               
               ⁢ 
               
                 ( 
                 SPM 
                 ) 
               
             
           
         
       
     
   
   where
         stroke distance denotes the equivalent pump stroke proportional to pump leakage, for example   d denotes the diameter of the pump in inches   SPM denotes the pump speed of the surface unit, strokes per minute   bpd denotes the volume of production corresponding to stroke distance, for example, lost by pump leakage, barrels per day, (See also Appendix B, infra),       

   is used to compute the effective stroke lost to pump leakage, S leak    216 . Such pump leakage must be adjusted in accordance with on-time percentage, because the TV/plunger only leaks when the pump is running. The increment of liquid production on a given stroke is computed from, 
   
     
       
         
           
             Δ 
             ⁢ 
             
                 
             
             ⁢ 
             
               V 
               net 
             
           
           = 
           
             
               π 
               4 
             
             ⁢ 
             
               
                 d 
                 2 
               
               ⁡ 
               
                 ( 
                 
                   
                     S 
                     l 
                   
                   - 
                   
                     
                       % 
                       on 
                     
                     ⁢ 
                     
                       S 
                       leak 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     
       
         where 
       
     
     
       
         
           
             % 
             on 
           
           = 
           
             
               T 
               P 
             
             
               
                 T 
                 P 
               
               + 
               
                 T 
                 d 
               
             
           
         
       
     
   
   and S leak  is based on the full daily leakage in bpd. 
   Eliminating the Assumption of Anchored Tubing 
   As illustrated in  FIG. 1 , the tubing  38  can be fixed to casing  40  by a tubing anchor  37 . Tubing is anchored primarily for three reasons: (1) to prevent tubing movement thereby increasing net liquid stroke, (2) to prevent relative motion between casing and tubing and the tubular wear that it causes, and (3) to prevent the tubing from parting due to cyclic load fatigue failure. Tubing is anchored in most wells when pumps are set at 2000 ft or deeper. Sometimes tubing anchors fail to hold. Thus, it is not sufficient to assume that the tubing is not moving just because the records say that a tubing anchor is installed. The pump card must be examined to make sure. 
     FIG. 7  illustrates the generation of a pump card  550  for a pumping unit where tubing is not anchored to the casing by means of an anchor  37  shown in  FIG. 1 . As illustrated in  FIGS. 7   a  and  7   b , the pump  44  moves a distance S t  between TV closing ( FIG. 7   a ) and SV opening ( FIG. 7   b ) when pump load is put on the plunger  42  and removed from the tubing  38 . The pump  44  moves an equal and opposite distance S t  between SV closing ( FIG. 7   c ) and TV opening ( FIG. 7   d ). 
     FIG. 7   d  shows a pump card  550  with full liquid fillage and unanchored tubing. The card  550  has a rhombus shape rather than a rectangular shape. According to the invention, tubing stretch S t  is automatically determined so that a net liquid stroke S n  can be determined  232 . For full liquid fillage and unanchored tubing S n =S g −S t  as  FIG. 7   d  shows. As always TV opening is used to determine liquid stroke. Pump cards with incomplete fillage and unanchored tubing show the TV opening further to the left, i.e. the plunger has moved further into the down stroke than the distance S t . The load trace between SV closing and TV opening also shows evidence of gas compression. In many cases the magnitude of the tubing stretch S t  is closely approximated  204  by Hooke&#39;s law, statically applied, 
                   S   t     ≅     12   ⁢         L   f     ⁢     D   p           E   t     ⁢     A   t                   (   9   )               
where, S t  is tubing stretch in inches, L f  is the fluid load read from the pump card (lb), D p  is the pump setting depth (ft), E t  is the modulus of elasticity of the tubing (psi) and A t  is the cross sectional area of the tubing (in 2 ). The factor  12  converts tubing stretch from feet to inches.
 
Eliminating the Assumptions of Free Gas and Oil Shrinkage
 
     FIGS. 8A–8D  show a pump card  560  being generated where free gas is in the pump at the time of TV opening.  FIG. 8A  shows the volume of the liquid  562  and free gas  564  in the incompletely filled pump  44 .  FIG. 8C  shows that the volume of free gas after it is compressed is not necessarily small. The controlling factor is the pressure of the gas as it enters the pump (the pump intake pressure). As this pressure increases, the volume of the free gas at TV opening increases such that it may no longer be negligible. In this most general case, the formula for liquid stroke  224  is,
   S   t   =S   n   −S   gas   (10) 
in which S t  is the liquid stroke (in) and S gas  is the stroke corresponding to the volume of free gas remaining in the pump at TV opening (Assumption 3). S n  remains the distance traveled by the pump from TV opening to the bottom of the stroke  232 . When S gas  is negligibly small, the liquid stroke is simply S n .
 
   The prior art has obtained pump intake pressure  206  for many years in equipment as in  FIG. 1  where a well manager is provided in conjunction with a rod-pumping unit  10 . Pump-intake pressure is determined by the equation, 
                   P   i     =       P   a     -       L   f       A   p                 (   11   )               
where P i  is the pump intake pressure (psi), P a  is the pressure above the pump plunger caused by tubing head pressure and hydrostatic effects of oil-gas-water in the tubing (psi), L f  is the fluid load which is derived from the pump card (lb) and confirmed with valve checks, and A p  is the area of the plunger (in 2 ).
 
   Equation (11) is solved in a software system called PIP provided in WM  52  of  FIG. 1 . (See Appendix B for a detailed description of the method  206  for determining Pump Intake Pressure. PIP is an acronym for Pump Intake Pressure.) The basic idea of the PIP program is to use the subsurface pump to meter liquid and gas into the tubing (in well test amounts) at a pressure that satisfies eq. 11. Shrinkage is also considered  229  knowing that oil in the pump at P i  has a larger volume than in the stock tank, because oil shrinkage occurs as gas separates from it while enroute from the pump to the stock tank. The PIP program uses “Nolen” non-dimensional curves for solution gas and oil shrinkage as functions of pressure. Such “Nolen” curves are illustrated in  FIGS. 13 ,  14  and described in Appendix B. The PIP program assumes  300  a small starting value of P i . It calculates  302  solution gas and shrinkage factor from the Nolen correlations. Then it computes  304  the volume of free gas at P i  (initially) using eq. 
             Δ   ⁢           ⁢     V   g       =       π   4     ⁢         d   2     ⁡     (       S   g     -     S   n       )       .             
It then determines  306  total gas (as SCF) passing through the pump by adding free and solution gas volumes. This establishes  308  the tubing GLR (gas/liquid ratio). If multiphase flow considerations at this GLR do not produce  310  a P a  which satisfies  312 ,  311  eq. 11, P i  is increased  314  and the process is repeated. This process eventually defines the S gas  needed to determine  224 ,  316  the correct S l . Oil shrinkage can be found  302  from the Nolen correlation once P i  is calculated.
 
   According to the invention, the volumes of free gas  220 ,  305  and oil shrinkage  302 ,  229  are determined by running a PIP analysis for each generation of a pump card. A more direct iterative procedure based on Newton&#39;s method can be employed. 
   Using the WM to Infer Production Without the Need for Well Tests 
   As described above, assumptions which limit the accuracy of using the rod-driven down hole pump as a flow meter have been removed. According to the invention, the rod-driven down hole pump can accurately infer well production by removing prior assumptions, thereby eliminating the need for traditional well tests. Two examples are presented below which show the accuracy of inferred production according to the invention. 
   EXAMPLE 1 
   This illustration is taken from an actual well in West Texas 
   A new production test of 400 BFPD (35 BOPD plus 365 BWPD) was obtained on a well having a Well Manager System with an Inferred Production IP System. In a manual mode, IP indicated a production rate of 524 BFPD based on a previously determined k factor of 0.9. The difference of 124 BPD had to be explained. WM indicated that the well pumps continually, i.e. does not pump off. The dynamometer data used by WM for control was exported to a program named DIAG for extracting information from the pump card. The pump card  570  re-created by DIAG is shown in  FIG. 9A  which also shows the surface card  572 .  FIG. 9B  shows the velocity plot  574  corresponding to the pump card  570 . The pump card method (described above) was used to compute pump leakage. Evidence of leakage is present on the pump card  570 , i.e. delayed load pickup and premature load release. Eq. 7 indicates that TV/plunger leakage is 64 BPD as follows
 
 L   TV =6.99 d   2   C   p   V   crit =6.99(2.25) 2 (0.53) (3.41)=64 BPD.
 
   The pump card  570  shows no evidence of a standing valve leak. The fluid load and net and gross strokes were measured from the pump card  570  and the PIP program was run. A pump intake pressure (see Equation 11) of 890 psi was indicated. An oil shrinkage factor of 1.234 was computed which means that the 35 BOPD of stock tank oil occupies a volume of 43 (35×1.234) BOPD at pump intake pressure. The accounting of fluid through the pump is then 
   Gross pump capacity: 595 BPD (from the pump card) 
   Pump leakage: 64 BPD (from eq. 8) 
   Oil at pump conditions: 43 BPD (shrinkage effect computed by PIP) 
   Free gas: 0 BPD (no gas interference noted on pump card) 
   Produced water: 488 BPD (obtained by difference). 
   This accounting leads to a stock tank volume of 523 BFPD (35 BOPD plus 488 BWPD). Water shrinkage is not considered since gas does not dissolve appreciably in water. As a result of this investigation, the oil operator examined the metering equipment and found that the water measurement was incorrect and should have been 493 BWPD instead of 365 BWPD as reported. The new well test should have been 528 BFPD (35+493) which compares to the IP value of 524 BFPD based on a k factor of 0.9. Thus the IP system was within 4 BFPD of the actual measured production. It would be justified to adjust the k factor (where using the manual method) slightly to a new value of 
   
     
       
         
           k 
           = 
           
             
               
                 R 
                 t 
               
               
                 R 
                 IP 
               
             
             = 
             
               
                 528 
                 595 
               
               = 
               
                 0.89 
                 . 
               
             
           
         
       
     
   
   But when the pump leakage and PIP routines are run automatically in WM, the k factor method of intermittently running a well test can be totally eliminated. In other words, complete determination of well production can be made without the need for traditional well tests. 
   EXAMPLE 2 
   The previous example shows, among other things, the uncertainties caused by an inaccurate well test and a severely worn pump. This example shows how the prior IP system can be improved for a gassy well with a good oil cut and a high pump intake pressure. 
     FIG. 10A  shows the pump dynamometer card  580  and surface card  582  of such a well that is producing full-time.  FIG. 10B  shows a velocity plot  584  corresponding to pump card  580 . Table I presented below for this example 2 is a PIP program analysis showing additional information that is available to IP according to the invention when the PIP program runs automatically in WM. The following accounting shows how the prior art IP system (unadjusted with a k factor) deals with the well.
         Gross pump capacity: 457 BPD (from the pump card)   Net liquid (oil plus water): 395 BPD (from the pump card and Assumption 3, S n =110.7   Free gas production: 62 BPD (by difference or eq. 4 extended to 24 hours).
 
Based on a reported well test of 277 BPD, a k factor of 0.7 would be indicated. This low factor, which is much less than 1, is a tip-off that the limiting assumptions are hurting the accuracy of IP.
       
   The PIP program when incorporated into IP according to the invention yields a better accounting. 
   Gross pump capacity: 457 BPD (from the pump card) 
   Pump leakage: 10 BPD 
   Unanchored tubing: 5 BPD 
   Net liquid (oil plus water): 329 BPD (based on S l  of 92.2 inches)
         158 BOPD plus 129 BWPD at stock tank conditions (based on measured oil cut of 0.55)       

   Free gas production: 113 BPD (by difference). Assumption 3 is eliminated. 
   The IP system according to the invention produces a report  230  of liquid production at stock tank conditions comprising 
   158 BWPD 
   129 BOPD (based on the shrinkage factor of 1.266 computed by PIP) 
   287 BFPD total liquid. 
   This refined accounting, which does not include a k factor, compares with the traditional well test of 277 BFPD. The well test may or may not be exceedingly precise. This illustration shows that consideration of oil shrinkage is important in wells with a good oil cut and high producing pressure. It also shows the importance of computing (not neglecting) the volume of free gas in the pump when the traveling valve opens in wells with high producing pressure. 
   This example 2 illustrates the IP process as implemented by the invention incorporated in the PIP program.  FIG. 11  illustrates the relationship among S l , S n , S g adj , S gas  at P i , S gas  at P a , and S g . The effect of oil shrinkage is also indicated by a comparison of the volume of fluid (oil and dissolved gas plus water) at pump conditions  600  and the volume of fluid (dead oil plus water) at stock tank conditions  602 . The prior art PIP program did not determine pump leakage when calculating pump intake pressure, shrinkage, stock tank production, etc. An embodiment of the invention is provided for an improved PIP program that runs in WM  52  to handle valve leakage with accuracy. 
   The gross stroke in Table I below is taken to be 128.3 inches as also illustrated in  FIG. 11  where pump positions are read from the pump card  580  ( FIG. 10A ) in inches from the bottom of the stroke. Differences in position signify portions of the gross stroke that represent gas, oil, water, pump leakage, unanchored tubing, etc. 
   The procedure  218  according to an embodiment of the invention is to subtract stroke segments representing unanchored tubing  204  and leakage  216  from the gross stroke. Then the pump intake pressure, shrinkage factor, and oil, water, and gas volumes in the pump on that stroke are determined. Finally, shrinkage is considered to compute stock tank oil and water volumes on that stroke. 
   
     
       
         
             
           
             
               TABLE I 
             
             
                 
             
             
               for Example 2 
             
             
               Pump Intake Pressure Program 
             
             
                 
             
           
          
             
               SUBSURFACE PUMP ANALYSIS 
             
             
                 
             
          
         
         
             
             
          
             
               Pump Bore Size (in): 1.75 
               Setting Depth (ft): 4332 
             
          
         
         
             
          
             
               Actual Pump Conditions ************** 
             
          
         
         
             
             
          
             
               Pump Intake Pressure (psi): 920 
               Pumping Speed (spm): 9.98 
             
             
               Gross Stroke (in): 128.3 
               Net Stroke (in): 92.2 
             
             
               Gas Interference: 
               Fluid Pound: None 
             
             
               MODERATE–SEVERE 
               Pump Leakage (bpd): 10 
             
             
               Fluid Load (lbs): 1040 
             
          
         
         
             
          
             
               Crude Shrinkage Factor from Pump to Stock Tank (bbl per bbl): 1.266 
             
             
               Tubing Gas Liquid Ratio (cu ft per bbl): 272 
             
             
                 
             
          
         
         
             
          
             
               Pump Volumetric Displacements 
             
          
         
         
             
             
             
          
             
                 
               Based on 
               Based on Adjusted 
             
             
                 
               Net Stroke 
               Gross Stroke 
             
             
                 
                 
             
             
                 
               329 bpd 
               442 bpd 
             
             
                 
               (287 bpd @ Stock Tank Conditions) 
             
             
                 
                 
             
          
         
         
             
          
             
               Pump Efficiencies 
             
          
         
         
             
             
             
             
          
             
                 
                 
               Based on Test 
               Based on Test 
             
             
                 
                 
               and Gross Stroke 
               and Net Stroke 
             
             
                 
                 
               (percent) 
               (percent) 
             
             
                 
                 
             
             
                 
               Crude Shrinkage 
               62.6 
               84.3 
             
             
                 
               not considered: 
             
             
                 
               Crude Shrinkage 
               71.8 
               96.5 
             
             
                 
               considered: 
             
             
                 
                 
             
          
         
         
             
          
             
               OTHER DIAGNOSTIC INDICATORS 
             
             
                 
             
          
         
         
             
             
          
             
               Down Hole Friction: MODERATE 
               Lost Displacement (bpd): 5 
             
             
               PUMP FRICTION 
               Avg Tbg Grad (psi per ft): .283 
             
             
               Tubing or Annulus Check 
             
             
               Valve Leak: None Likely 
             
             
               Tubing Movement (in): 1.4 
             
             
               Tubinghead Pressure (psi): 125 
             
          
         
         
             
          
             
               Pump Power Without Slippage and Shrinkage (hp): 3.3 
             
             
                 
             
          
         
         
             
          
             
               WELL TEST AND FLUID PROPERTY DATA 
             
             
                 
             
          
         
         
             
             
          
             
               Test Date: Apr. 29, 2003 
               BOPD: 153 
             
             
               BFPD: 277 
               Oil Cut (%): 55.2 
             
             
               BWPD: 124 
               Test SPM: 9.98 
             
             
               GOR: Unknown 
               Water Gravity (sg): 1.18 
             
             
               Pumping Unit Stroke: 120.25 
               Solution GOR (cu ft/bo): 640 est. 
             
             
               Oil Gravity (api): 38. 
             
             
               Bubble Point (psi): 1760 est. 
             
             
               Formation Volume Factor 
             
             
               (bbl per bbl): 1.37 est. 
             
             
                 
             
          
         
       
     
   
   APPENDIX A 
   From a down hole pump card, a single pump-slippage coefficient (usually estimated to be C p =0.5) can be estimated from 
   
     
       
         
           
             C 
             P 
           
           = 
           
             k 
             ⁢ 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   r 
                 
               
               ⁢ 
               
                 
                   [ 
                   
                     
                       0.5 
                       ⁢ 
                       
                         ( 
                         
                           
                             F 
                             i 
                             P 
                           
                           + 
                           
                             F 
                             
                               i 
                               + 
                               1 
                             
                             P 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       F 
                       min 
                       P 
                     
                   
                   ] 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       t 
                       
                         i 
                         + 
                         1 
                       
                     
                     - 
                     
                       t 
                       i 
                     
                   
                   ) 
                 
               
             
           
         
       
     
   
   where 
   
     
       
         
           k 
           = 
           
             1 
             
               
                 ( 
                 
                   
                     F 
                     max 
                     P 
                   
                   - 
                   
                     F 
                     min 
                     P 
                   
                 
                 ) 
               
               ⁢ 
               Θ 
             
           
         
       
     
       
       
         
           F i   P =pump loads used to construct pump card, lbf i=1, 2 . . . r 
           F max   P =maximum pump load, lbf 
           F min   P =minimum pump load, lbf 
           Θ=pumping period, sec/cycle 
         
       
     
  
   Alternatively, two pump slippage coefficients C TV  and C SV  can be defined. Such coefficients refer to traveling valve/plunger leakage and standing valve leakage. These can be defined as 
   
     
       
         
           
             
               
                 
                   C 
                   TV 
                 
                 = 
                 
                   k 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         i 
                         = 
                         r 
                       
                     
                     ⁢ 
                     
                       
                         [ 
                         
                           
                             0.5 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   F 
                                   i 
                                   P 
                                 
                                 + 
                                 
                                   F 
                                   
                                     i 
                                     + 
                                     1 
                                   
                                   P 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             F 
                             min 
                             P 
                           
                         
                         ] 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             t 
                             
                               i 
                               + 
                               1 
                             
                           
                           - 
                           
                             t 
                             i 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               1 
             
           
           
             
               
                 
                   C 
                   SV 
                 
                 = 
                 
                   k 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         i 
                         = 
                         r 
                       
                     
                     ⁢ 
                     
                       
                         [ 
                         
                           
                             F 
                             max 
                             P 
                           
                           - 
                           
                             0.5 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   F 
                                   i 
                                   P 
                                 
                                 + 
                                 
                                   F 
                                   
                                     i 
                                     + 
                                     1 
                                   
                                   P 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             t 
                             
                               i 
                               + 
                               1 
                             
                           
                           - 
                           
                             t 
                             i 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               2 
             
           
         
       
     
   
   where 
   
     
       
         
           
             
               
                 k 
                 = 
                 
                   1 
                   
                     
                       ( 
                       
                         
                           F 
                           max 
                           P 
                         
                         - 
                         
                           F 
                           min 
                           P 
                         
                       
                       ) 
                     
                     ⁢ 
                     Θ 
                   
                 
               
             
             
               3 
             
           
         
       
     
   
   The term C TV  is a non-dimensional number that expresses the pressure difference across the traveling valve/plunger and the time of application of that pressure difference. Similarly C SV  expresses the difference of pressure and time of application across the standing valve. Algebraic manipulation of eqs. 1, 2, and 3 provides that
 
 C   TV   +C   SV =1
 
when it is recognized that
 
   
     
       
         
           
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   r 
                 
               
               ⁢ 
               
                 
                   F 
                   min 
                   P 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       t 
                       
                         i 
                         + 
                         1 
                       
                     
                     - 
                     
                       t 
                       i 
                     
                   
                   ) 
                 
               
             
             = 
             
               
                 F 
                 min 
                 P 
               
               ⁢ 
               Θ 
             
           
           , 
           
             etc 
             . 
           
         
       
     
   
   As seen above, a generic coefficient C p  is used for C TV . To save computer time by eliminating the need for calculating C SV  the term (1−C p ) is used when standing valve leakage is being computed. The sum of coefficients being unity results from the fact that both valves can not be open at the same time. The valves are frequently closed at the same time. An open valve can not leak, but a closed valve can. A closed valve leaks at a rate which is proportional to the pressure difference across it. The leakage coefficients defined above acknowledge the fact that a valve is closed part of the time and the pressure difference across it varies continually. 
   APPENDIX B 
   Method for Determining Pump Intake Pressure (PIP) Pump intake pressure is an important quantity in operating a rod pumped well. If this pressure is high, more production is available. If the pressure is low, little additional production is available at the present pump depth. Pump intake pressure also governs the volume of free gas in the pump and the amount of dissolved gas remaining in the oil. The quantity of dissolved gas affects the amount of shrinkage that the oil suffers in traveling up the tubing to the stock tank. 
   Using a wave equation derived pump card, the pump intake pressure in a well can be calculated with acceptable precision. The PIP procedure is described in the following stepwise procedure. The procedure determines P i  subject to pressure balance considerations, multiphase flow concepts, and pressure-volume-temperature (PVT) characteristics of the produced oil, water and gas. Along with P i  the PIP procedure computes oil shrinkage and liquid and gas passing through the pump. 
   Step 1. From multiphase flow (oil-water-gas) considerations, determine P a  (psi) as a function of tubing gas/liquid ratio (GLR in SCF/bbl of liquid)  310 . Denote this relationship as Table 1. SCF denotes gas in cubic feet at standard conditions of 14.65 psi and 520 deg R. 
   
     
       
         
             
             
             
             
           
             
                 
               TABLE 1 
             
             
                 
                 
             
           
          
             
                 
               TRIAL P i   
               P a   
               GLR 
             
             
                 
                 
             
          
         
       
     
   
   Step 2. Obtain a downhole pump card  212  using the wave equation. Identify fluid load L f  (lbs)  214 , gross pump stroke S g (inches)  214 , net pump stroke S n  (inches)  232  and tubing stretch S t  (inches)  204  from the pump card. 
   Step 3. Using processes described herein, determine pump leakage (bpd)  202 . Convert pump leakage to equivalent inches of stroke  216 , 
                 stroke   =     bpd     0.1166   ⁢     (     d   2     )     ⁢     (   SPM   )                 B   ⁢     -     ⁢   1   ⁢   a               
in which
         stroke denotes the pump stroke, in this case lost by pump leakage (S leakage ), inches   d denotes the diameter of the pump, inches   SPM denotes the pumping speed of the surface unit, strokes per minute   bpd denotes the volume of production corresponding to stroke, in this case lost by pump leakage, barrels per day.
 
Another version,
 
 bpd =0.1166( d   2 )( SPM )(stroke)  B-1b
 
can be used to compute volume rate expressed in bpd using pump stroke expressed in inches. These relations can be used at will  305  to convert stroke increment into volume increment, and vice versa.
       
   Step 4. Determine the adjusted gross stroke  218 ,
 
 S   g adj   =S   g   −S   t   −S   leakage   B-2
 
   Step 5. Conceptually, construct the pressure balance relationship  206  between P i  and P a , 
                   P   i     =       P   a     -       L   f       A   p                 B   ⁢     -     ⁢   3               
where
     P i  is pump intake pressure below the standing valve, psia   P a  is the pressure above the pump at the foot of the tubing caused by tubing head pressure and hydrostatic pressure effects of oil, water and gas in the tubing above the pump, psia. This can also be called pump outlet pressure.   L f  is the fluid load read from the pump card, lbs   A p  is the plunger area of the down hole pump, in.   Refer to  FIG. 12  where the P i  is plotted as a function of P a .   True P i  lies somewhere on the straight line  610  of  FIG. 12 .   
   Step 6. Assume a low trial P i    300 . 
   Step 7.
         a) Compute the oil shrinkage factor F shrinkage  and the gas remaining in solution (SCF/bbl of oil) at the trial P i    302 .   b) Using gas laws, compute S gas  based on the trial P i    318 . Compute S l    316  from
 
 S   l   =S   n   −S   gas  
   c) Determine oil cut at pump conditions from the shrinkage factor and measured oil cut at surface conditions  320 .   d) Determine the instantaneous BOPD and BWPD at trial P i  using oil cut at pump conditions, S l  and eq. B-1  322 . Instantaneous rate is the rate on the stroke in question.   e) Determine free gas volume (SCF/day)  220 ,  305  at trial P i  using gas equations, eq. B-1 and
           S free gas =S g adj −S l    304 .   
           f) Determine dissolved gas volume (SCF/day) at trial P i  using the BOPD and gas remaining in solution  326 .   g) Determine total gas (SCF/day) passing through pump into tubing by adding free gas volume to dissolved gas volume  306 .   h) Determine tubing GLR  308  from       

   
     
       
         
           GLR 
           = 
           
             
               total 
               ⁢ 
               
                 
                     
                 
                 ⁢ 
                 
                     
                 
               
               ⁢ 
               gas 
             
             
               BOPD 
               + 
               BWPD 
             
           
         
       
     
   
   Step 8. Using Table 1 created in Step 1, determine P a  corresponding to trial P i    310  using the GLR computed above in Step 7. Conceptually plot this P a  (which corresponds to the trial P i ) as point  1  on  FIG. 12 . If point  1  does not fall on (or close enough to) the straight line pressure balance relationship  311 , the true P i  has not been found. Change the trial P i    314  and return to Step 7. Repeat this process until the true P i  is found  312 . 
   As the trial P i  is increased, the corresponding P a  will decrease. This results because more gas is computed to be entering the tubing which diminishes the hydrostatic pressure effect, hence P a . The line drawn through trials points  1 ,  2 ,  3 , . . . . will intersect the pressure balance line to reveal the true P i    328 . The convergence process can be sped up using Newton&#39;s Method to select new trial P i  values. The process described herein uses trial P i  values spaced equal pressure increments apart. 
   After the pump intake pressure P i  has been finally determined use non-dimensional curves  620 ,  630  of  FIGS. 13 and 14 , respectively, to determine oil shrinkage factor and GOR remaining in solution that correspond to the P i    302 . 
   Step 9. Determine stock tank liquid and tubing gas production increments using the oil shrinkage factor  302 , BOPD, BWPD  322 , free and dissolved gas volumes  305 ,  326  corresponding to the true P i  found in Step 8.