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									           Petroleum Engineering 613
            Natural Gas Engineering
             Texas A&M University


                  Lecture 05:
            Gas Material Balance

          T.A. Blasingame, Texas A&M U.
       Department of Petroleum Engineering
               Texas A&M University
          College Station, TX 77843-3116
    +1.979.845.2292 — t-blasingame@tamu.edu
PETE 613           Gas Material
                                       Slide — 1
 (2005A)            Balance
Material Balance
  "Accounting" Concept of Material Balance:
     Require all inflows/outflows/generations.
     (Average) reservoir pressure profile is REQUIRED.
     Require rock, fluid, and rock-fluid properties (at some scale).
  Oil Material Balance:
     Less common than gas material balance (pressure required).
  Gas Material Balance:
     Volumetric dry gas reservoir (p/z versus Gp (straight-line)).
     Abnormally-pressured gas reservoirs (various techniques).
     Waterdrive/water influx cases (always problematic) (i.e., we
      don't know the influx, so we use a model).
  Material Balance yields RESERVOIR VOLUME!




PETE 613                      Gas Material
                                                              Slide — 2
 (2005A)                       Balance
Material Balance of a Petroleum Reservoir
 General Concept of Material Balance...




           a. Initial reservoir conditions.           b. Conditions after producing Np STB of oil,
                                                          and Gp SCF of gas, and Wp STB of water.
     From: Petroleum Reservoir Engineering
      — Amyx, Bass, and Whiting (1960).

  Material Balance: Key Issues
     Must have accurate production measurements (oil, water, gas).
     Estimates of average reservoir pressure (from pressure tests).
     Suites of PVT data (oil, gas, water).
     Reservoir properties: saturations, formation compressibility, etc.

PETE 613                                      Gas Material
                                                                                            Slide — 3
 (2005A)                                       Balance
Average Reservoir Pressure for Material Balance
 Average Reservoir Pressure




                                          From: Engineering Features of the Schuler Field and
                                           Unit Operation — Kaveler (SPE-AIME, 1944).

  Average Reservoir Pressure: Key Issues
     Must "average" pressures over volume or area (approximation).
     Pressure tests must be representative (pavg extrapolation valid).
     Can average using cumulative production (surrogate for volume).
PETE 613                       Gas Material
                                                                                   Slide — 4
 (2005A)                        Balance
Gas Material Balance Case                                                          (1/3)
 General Gas Material Balance:
   p
     1  ce ( p )( pi  p ) 
   z
         pi pi 1                                                            
             
         zi zi G 
                       Gp  Ginj  Wp Rsw  5.615  
                                                    1
                                                      (Wp  Winj ) Bw  We   
                                                                             
                                                  Bg                        
                                                                             

 "Dry Gas" Material Balance: (no reservoir liquids )
    p pi     1     
            1  Gp 
             G
    z zi           




PETE 613                                Gas Material
                                                                                 Slide — 5
 (2005A)                                 Balance
Gas Material Balance Case                                                               (2/3)
 General Gas Material Balance:
   p
     1  ce ( p )( pi  p ) 
   z
         pi pi 1                                                            
             
         zi zi G 
                       Gp  Ginj  Wp Rsw  5.615  
                                                    1
                                                      (Wp  Winj ) Bw  We   
                                                                             
                                                  Bg                        
                                                                             
 "Abnormal Pressure" Material Balance: (cf=f(p))
   p     pi            1              Gp 
                                     1
   z     zi 1  ce ( p )( pi  p ) 
                                        G
                                          
                  1                         VpNNP  VpAQ                    
   ce ( p )               S wi cw  c f                    (cw  c f   )
              (1  S wi ) 
                                             VpR   VpR
                                                             
                                                                                
                                                                                  
 "Quadratic Cumulative" Approximation:
   p pi        1              
          1  (   ) Gp  G 2 
       zi 
                              p
   z           G          G    


PETE 613                                Gas Material
                                                                                      Slide — 6
 (2005A)                                 Balance
Gas Material Balance Case                                                           (3/3)
 General Gas Material Balance:
    p
      1  ce ( p )( pi  p ) 
    z
          pi pi 1                                                            
              
          zi zi G 
                        Gp  Ginj  Wp Rsw  5.615  
                                                     1
                                                       (Wp  Winj ) Bw  We   
                                                                              
                                                   Bg                        
                                                                              
 "Water Influx" Material Balance:
                      1    Gp           
   p/z  pi /zi           1            
                 W B        G         
                1  e w               
                 GB gi 
                       
 "Cubic Cumulative" Approximation: (Current Research)
                                                      2               3
   p pi     1  (1   )  Gp                Gp            Gp    
                                (   )                    
   z   zi
                          G
                                
                                              G
                                                    
                                                              G
                                                                     
                                                                     
                                                                       

PETE 613                                 Gas Material
                                                                                  Slide — 7
 (2005A)                                  Balance
Volumetric Gas Material Balance




  "Dry Gas" Material Balance: Normally Pressured Reservoir Example
     Volumetric reservoir — no external energy (gas expansion only).
     p/z versus Gp yields unique straight-line trend.
     Linear extrapolation yield gas-in-place (G).

PETE 613                         Gas Material
                                                                        Slide — 8
 (2005A)                          Balance
Gas MBE Abnormally-Pressured Reservoir




   "Dry Gas" Material Balance: Abnormally Pressured Reservoir Example
      Volumetric reservoir — no water influx or leakage.
      p/z versus Gp yields unique quadratic trend (from approximated MBE).
      Quadratic extrapolation yield gas-in-place (G).

PETE 613                          Gas Material
                                                                        Slide — 9
 (2005A)                           Balance
Gas MBE "Water Influx" Case




a. Gas Material Balance Plot: p/z vs. Gp — simulated     b. Gas Material Balance Plot: p/z vs. Gp — simulated
   performance. Note effect of aquifer permeability on      performance. Note effect of displacement
   field performance.                                       efficiency (Ep).


  Gas Material Balance: Water Drive Gas Reservoir
       Pressure (hence p/z) is maintained during production via communication
        with an unsteady-state aquifer (this study).
       From: Unsteady-State Performance of Water Drive Gas Reservoirs, Agarwal
        (Texas A&M Ph.D., 1967).

PETE 613                                       Gas Material
                                                                                                Slide — 10
 (2005A)                                        Balance
Concept: p/z vs. Gp — Water Influx Case




  Simulated Performance: Agarwal Dissertation (1967)
     Recovery is a function of production rate, Ep, and kaquifer.
     p/z vs. Gp performance appears to be cubic (i.e., f(Gp3)).
PETE 613                      Gas Material
                                                               Slide — 11
 (2005A)                       Balance
           Petroleum Engineering 613
            Natural Gas Engineering
             Texas A&M University

                  Lecture 05:
            Gas Material Balance
                (End of Lecture)

          T.A. Blasingame, Texas A&M U.
       Department of Petroleum Engineering
               Texas A&M University
          College Station, TX 77843-3116
    +1.979.845.2292 — t-blasingame@tamu.edu
PETE 613            Gas Material
                                       Slide — 12
 (2005A)             Balance
           Petroleum Engineering 613
            Natural Gas Engineering
              Texas A&M University


     A Quadratic Cumulative Production Model
            for the Material Balance of
      Abnormally-Pressured Gas Reservoirs

                   F.E. Gonzalez
                 M.S. Thesis (2003)
            Department of Petroleum Engineering
                   Texas A&M University
              College Station, TX 77843-3116
PETE 613               Gas Material
                                                  Slide — 13
 (2005A)                Balance
Executive Summary — "p/z-Gp2" Relation                                     (1/4)
The rigorous relation for the material balance of a dry
gas reservoir system is given by Fetkovich, et al. as:
      p
        1  ce ( p)( pi  p)    pi
      z                            zi
             pi 1                       5.615                         
                 Gp  Ginj  W p Rsw        (W p Bw  Winj Bw  We )
             zi G 
                                         Bg                           
                                                                       

Eliminating the water influx, water production/injection,
and gas injection terms; defining Gp=ce(p)(pi-p) and
assuming that Gp<1, then rearranging gives the follow-
ing result:
                          p pi           1              
                                   1  (   ) Gp  G 2 
                                                        p
                          z   zi         G          G    


PETE 613                                Gas Material
                                                                    Slide — 14
 (2005A)                                 Balance
Executive Summary — "p/z-Gp2" Relation                                   (2/4)




Simulated Dry Gas Reservoir Case — Abnormal Pressure:
    Volumetric, dry gas reservoir — with cf(p) (from Fetkovich).
    Note extrapolation to the "apparent" gas-in-place (previous approaches).
    Note comparison of data and the new "Quadratic Cumulative Production" model.

PETE 613                         Gas Material
                                                                     Slide — 15
 (2005A)                          Balance
Executive Summary — "p/z-Gp2" Relation                                      (3/4)




Anderson L Reservoir Case — Abnormal Pressure:
    South Texas (USA) gas reservoir with abnormal pressure.
    Benchmark literature case.
    Note performance of the new "Quadratic Cumulative Production" model.

PETE 613                         Gas Material
                                                                     Slide — 16
 (2005A)                          Balance
Presentation Outline
  Executive Summary
  Objectives and Rationale
     Rigorous technique for abnormal pressure analysis.
  Development of the p/z-Gp2 model
     Derivation from the rigorous material balance.
  Validation — Field Examples
     Case 1 — Dry gas simulation (cf(p) from Fetkovich).
     Case 3 — Anderson L (South Texas, USA).
  Demonstration (MS Excel — Anderson L case)
  Summary
  Recommendations for Future Work



PETE 613                Gas Material
                                                 Slide — 17
 (2005A)                 Balance
Objectives and Rationale
Objectives:
    Develop a rigorous functional form (i.e., a model) for
    the p/z vs. Gp behavior demonstrated by a typical
    abnormally pressured gas reservoir.
   Develop a sequence of plotting functions for the
    analysis of p/z—Gp data (multiple plots).
   Provide an exhaustive validation of this new model
    using field data.
Rationale: The analysis of p/z—Gp data for abnorm-
 ally pressured gas reservoirs has evolved from empi-
 rical models and idealized assumptions (e.g., cf(p)=
 constant). We would like to establish a rigorous ap-
 proach — one where any approximation is based on
 the observation of some characteristic behavior, not
 simply a mathematical/graphical convenience.
PETE 613                 Gas Material
                                                   Slide — 18
 (2005A)                  Balance
Development of the p/z-Gp2 model
Concept:
    Use the rigorous material balance relation given by
     Fetkovich, et al. for the case of a reservoir where
     cf(p) is NOT presumed constant.
    Use some observed limiting behavior to construct a
     semi-analytical relation for p/z—Gp behavior.
Implementation:
    Develop and apply a series of data plotting functions
     which clearly exhibit unique behavior relative to the
     p/z—Gp data.
    Use a "multiplot" approach which is based on the
     dynamic updating of the model solution on each
     data plot.
    Develop a "dimensionless" type curve approach that
     can be used to validate the model and estimate G.
PETE 613                Gas Material
                                                  Slide — 19
 (2005A)                 Balance
p/z-Cumulative Model:                                                               (1/3)
The rigorous relation for the material balance of a dry
gas reservoir system is given by Fetkovich, et al. as:
      p
        1  ce ( p)( pi  p)    pi
      z                            zi
             pi 1                       5.615                         
                 Gp  Ginj  W p Rsw        (W p Bw  Winj Bw  We )
             zi G 
                                         Bg                           
                                                                       

Eliminating the water influx, water production/injection,
and gas injection terms, then rearranging gives the
following definition:

                     p i /z i     Gp     
            p/z                 1       [where Gp  c e ( p )( p i  p )]
                  (1  Gp      )
                                     G   
                                          


PETE 613                                Gas Material
                                                                                 Slide — 20
 (2005A)                                 Balance
p/z-Cumulative Model:                                                  (2/3)
Considering the condition where:
                                 D  Gp  1

Then we can use a geometric series to represent the D
term in the governing material balance. The appropriate
geometric series is given by:
             1 / 1  x  1  x  x 2  x3  ...    (1  x  1)
or, for our problem, we have:
                     1
                            1  Gp            (1  Gp  1)
                (1  Gp )
Substituting this result into the material balance relation,
we obtain:
                     p pi        1              
                            1  (   ) Gp  G 2 
                         zi 
                                                p
                     z           G          G    

PETE 613                         Gas Material
                                                                    Slide — 21
 (2005A)                          Balance
p/z-Cumulative Model:                                               (3/3)
A more convenient form of the p/z-cumulative model is:
                       p pi
                             Gp   G 2
                                         p
                       z zi
                           1       pi            pi
                     (     )        
                           G       zi           G zi
We note that these parameters presume that  is con-
stant. Presuming that  is linear with Gp, we can derive
the following form:
           p pi    1       pi       a          pi 2 b pi 3
                (  a)      Gp  (  b)         Gp       Gp
           z zi    G       zi       G          zi      G zi
                           where   a  bGp

Obviously, one of our objectives will be the study of the
behavior of  vs. Gp (based on a prescribed value of G).
PETE 613                     Gas Material
                                                                 Slide — 22
 (2005A)                      Balance
-Gp Performance (Case 1)                                                                        (1/2)




  a. Case 1: Simulated Performance Case — Plot of     b. Case 1: Simulated Performance Case — Plot of
      versus Gp (requires an estimate of gas-in-        p/z versus Gp. The constant and linear  trends
     place). Note the apparent linear trend of the       match well with the data — essentially a con-
     data. Recall that Gp=ce(pp-p).                     firmation of both models.




Simulated Dry Gas Reservoir Case — Abnormal Pressure:
     A linear trend of  vs. Gp is reasonable and should yield an accurate model.
      is approximated by a constant value within the trend.
     A physical definition of  is elusive — Gp=ce(p)(pi-p) implies that  has units of
      1/volume, which suggests  is a scaling variable for G.

PETE 613                                      Gas Material
                                                                                           Slide — 23
 (2005A)                                       Balance
-Gp Performance (Case 3)                                                                           (2/2)




  a. Case 3: Anderson L Reservoir Case (South                b. Case 3: Anderson L Reservoir Case (South
     Texas, USA) — Plot of  versus Gp (requires an             Texas, USA) — Plot of p/z versus Gp. Both
     estimate of gas-in-place). Some data scatter               models are in strong agreement.
     exists, but a linear trend is evident (recall that
     Gp=ce(p )(pi-p)).




Anderson L Reservoir Case — Abnormal Pressure:
     Field data will exhibit some scatter, method is relatively tolerant of data scatter.
     Constant  approximation is based on the "best fit" of several data functions.
     The linear approximation for  is reasonable (should favor later data).

PETE 613                                           Gas Material
                                                                                               Slide — 24
 (2005A)                                            Balance
Validation of the p/z-Gp2 model: Orientation
Methodology:
    All analyses are "dynamically" linked in a spread-
      sheet program (MS Excel). Therefore, all analyses
      are consistent — should note that some functions/
      plots perform better than others — but the model
      results are the same for every analysis plot.
Validation: Illustrative Analyses
    p/z-Gp2 plotting functions — based on the proposed
     material balance model.
    -Gp performance plots — used to calibrate analysis.
    Gan analysis — presumes 2-straight line trends on a
     p/z-Gp plot for an abnormally pressured reservoir.
    pD-GpD type curve approach — use p/z-Gp2 material
     balance model to develop type curve solution — this
     approach is most useful for data validation.
PETE 613                Gas Material
                                                  Slide — 25
 (2005A)                 Balance
p/z-Gp2 Plotting Functions: Case 1                                                                                         (1/5)




                 pi p                                                                              Gp
                                                                                                   0
                                                  1                                          1
  a. Δ( p/z )       vs. Gp                b.    Δ( p/z ) vs. Gp                      c.               Δ( p/z ) dGp vs. Gp
                 zi z                          Gp                                         Gp
                      




             Gp                                                                                                 Gp                
            0                                                                                                  0
       1                                                    Gp                             1                1
                                                           0
                                                       1                                       Δ( p/z )             Δ( p/z ) dGp  vs. Gp
  d.              Δ( p/z ) dGp vs. Gp   e. Δ( p/z )             Δ( p/z ) dGp vs. Gp   f.
       G2                                             Gp                                  Gp   
                                                                                                          Gp                      
                                                                                                                                   
        p


PETE 613                                           Gas Material
                                                                                                                      Slide — 26
 (2005A)                                            Balance
-Gp Plotting Functions: Case 1                                                                      (2/5)




 a. Case 1: Simulated Performance Case — Plot of           b. Case 1: Simulated Performance Case — Plot of
    ce(p)(pi-p) versus Gp (requires estimate of G).           1/ce(p)(pi-p) versus Gp (requires estimate of G).




 c. Case 1: Simulated Performance Case — Plot of      d. Case 1: Simulated Performance Case — Plot of 
    versus Gp (requires estimate of G).                   versus Gp/G (requires estimate of G).


PETE 613                                        Gas Material
                                                                                               Slide — 27
 (2005A)                                         Balance
-Gp Plotting Functions: Case 1                                              (3/5)




Simulated Dry Gas Reservoir Case — Abnormal Pressure:
    Summary p/z—Gp plot for  =constant and  =linear cases.
    Good comparison of trends,  =linear trend appears slightly conservative as it
    emerges from data trend — but both solutions appear to yield same G estimate.

PETE 613                           Gas Material
                                                                         Slide — 28
 (2005A)                            Balance
Gan-Blasingame Analysis (2001): Case 1                                                                  (4/5)




 a. Case 1: Simulated Performance Case — Gan Plot 1          b. Case 1: Simulated Performance Case — Gan Plot 2
    ce(p)(pi-p) versus (p/z)/(pi/zi) (requires est. of G).      (p/z)/(pi /zi ) versus (Gp/G) (requires est. of G).


                                                              Gan-Blasingame Analysis:
                                                                Approach considers the "match"
                                                                 of the ce(p)(pi-p) — (p/z)/(pi/zi)
                                                                 data and "type curves."
                                                                Assumes that both abnormal
                                                                 and normal pressure p/z trends
                                                                 exist.
                                                                Straight-line extrapolation of the
 c. Case 1: Simulated Performance Case — Gan Plot 3              "normal" p/z trend used for G.
    (p/z) versus Gp (results plot).


PETE 613                                           Gas Material
                                                                                                   Slide — 29
 (2005A)                                            Balance
pD-GpD Type Curve Approach: Case 1                                                                   (5/5)




  a. pD-GpD Type curve solution based on the p/z-Gp2     b. Case 1: Simulated Performance Case — Type
     model. pD= [(pi/zi)-(p/z)]/(pi/zi) and GpD=Gp/G —      curve analysis of (p/z)-Gp data, this case is
     both pD and pDi functions are plotted.                 "force matched" to the same results as all of the
                                                            other plotting functions.



PETE 613                                         Gas Material
                                                                                                Slide — 30
 (2005A)                                          Balance
p/z-Gp2 Plotting Fcns: Case 3 (Anderson L)                                                                                   (1/5)




                 pi p                                                                              Gp
                                                                                                   0
                                                  1                                          1
  a. Δ( p/z )       vs. Gp                b.    Δ( p/z ) vs. Gp                      c.               Δ( p/z ) dGp vs. Gp
                 zi z                          Gp                                         Gp
                      




             Gp                                                                                                 Gp                
            0                                                                                                  0
       1                                                    Gp                             1                1
                                                           0
                                                       1                                       Δ( p/z )             Δ( p/z ) dGp  vs. Gp
  d.              Δ( p/z ) dGp vs. Gp   e. Δ( p/z )             Δ( p/z ) dGp vs. Gp   f.
       G2                                             Gp                                  Gp   
                                                                                                          Gp                      
                                                                                                                                   
        p


PETE 613                                           Gas Material
                                                                                                                      Slide — 31
 (2005A)                                            Balance
-Gp Plotting Functions: Case 3                                                                            (2/5)




 a. Case 3: Anderson L (South Texas) — Plot of                   b. Case 3: Anderson L (South Texas) — Plot of
    ce(p)(pi-p) versus Gp (requires estimate of G).                 1/ce(p)(pi-p) versus Gp (requires estimate of G).




 c. Case 3: Anderson L (South Texas) — Plot of              d. Case 3: Anderson L (South Texas) — Plot of 
    versus Gp (requires estimate of G).                         versus Gp/G (requires estimate of G).


PETE 613                                              Gas Material
                                                                                                      Slide — 32
 (2005A)                                               Balance
-Gp Plotting Functions: Case 3                                           (3/5)




Case 3 — Anderson L Reservoir (South Texas (USA))
    Summary p/z—Gp plot for  =constant and  =linear cases.
    Good comparison of trends,  =constant and  =linear cases in good agreement.
    Data trend is very consistent.

PETE 613                          Gas Material
                                                                      Slide — 33
 (2005A)                           Balance
 Gan-Blasingame Analysis (2001): Case 3                                                                   (4/5)




a. Case 3: Anderson L Reservoir — Gan Plot 1 ce(p)(pi-p)   b. Case 3: Anderson L Reservoir — Gan Plot 2 (p/z)/(pi /zi )
   versus (p/z)/(pi/zi) (requires est. of G).                 versus (Gp/G) (requires est. of G).


                                                            Gan-Blasingame Analysis:
                                                                We note an excellent "match" of
                                                                 the ce(p)(pi-p) — (p/z)/(pi/zi) data
                                                                 and the "type curves."
                                                                Both the abnormal and normal
                                                                 pressure p/z trends appear ac-
                                                                 curate and consistent.
                                                                Straight-line extrapolation of the
  c. Case 3: Anderson L Reservoir — Gan Plot 3 (p/z)             "normal" p/z trend used for G.
     versus Gp (results plot).


PETE 613                                         Gas Material
                                                                                                     Slide — 34
 (2005A)                                          Balance
pD-GpD Type Curve Approach: Case 3                                             (5/5)




Case 3 — Anderson L Reservoir (South Texas (USA))
    pD-GpD type curve solution matched using field data.
    Note the "tail" in the pD trend for small values of GpD (common field data event).
    "Force matched" to the same results as each of the other plotting functions.

PETE 613                            Gas Material
                                                                            Slide — 35
 (2005A)                             Balance
Example Analysis Using MS Excel: Case 3
  Case 3 — Anderson L (South Texas (USA))
    Literature standard case.
    A 3-well reservoir, delimited by faults.
    Good quality data.
    Evidence of overpressure from static pressure tests.


  Analysis: (Implemented using MS Excel)
    p/z-Gp2 plotting functions.
    -Gp performance plots.
    Gan analysis (2-straight line trends on a p/z-Gp plot).
    pD-GpD type curve approach.




PETE 613                 Gas Material
                                                    Slide — 36
 (2005A)                  Balance
Summary:                                                                  (1/3)
  Developed a new p/z-Gp2 material balance model for
   the analysis of abnormally pressured gas reservoirs:
     p pi        1                      where:         1
            1  (   ) Gp  G 2                        ce ( p)( pi  p)
         zi 
                                p
     z           G          G                          Gp

   The -function is presumed (based on graphical
   comparisons) to be either constant, or approximately
   linear with Gp. For the =constant case, we have:
                           p pi
                                 Gp   G 2
                                             p
                           z zi

                              1       pi           pi
                        (     )          
                              G       zi          G zi


PETE 613                        Gas Material
                                                                      Slide — 37
 (2005A)                         Balance
Summary:                                                                                               (2/3)
  Base relation: p/z-Gp2 form of the gas material balance
          p pi                                       1         pi                    pi
                  Gp   G 2
                              p                (     )                  
          z zi                                       G         zi    G zi
    a. Plotting Function 1:                           d. Plotting Function 4 :
                  (quadratic)                                             (linear)
                       p   p                                       Gp
                                                                    0
                                                               1
            Δ( p/z )   i   vs. Gp                                     Δ( p/z ) dGp vs. Gp
                        zi z 
                                                           G2
                                                              p

    b. Plotting Function 2:                           e. Plotting Function 5 :
                     (linear)                                        (quadratic)
                                                                            Gp
                                                                          0
                                                                     1
                 1
                   Δ( p/z ) vs. Gp                     Δ( p/z )                 Δ( p/z ) dGp vs. Gp
                Gp                                                  Gp

    c. Plotting Function 3:                           f. Plotting Function 6:
                  (quadratic)                                             (linear)
                 Gp                                                           Gp                
                0                                                          0
            1                                          1                1
                      Δ( p/z ) dGp vs. Gp                  Δ( p/z )               Δ( p/z ) dGp  vs. Gp
           Gp                                         Gp              Gp                        
                                                                                                

PETE 613                                    Gas Material
                                                                                                Slide — 38
 (2005A)                                     Balance
Summary:                                               (3/3)
  The plotting functions developed in this work have
   been validated as tools for the analysis reservoir
   performance data from abnormally pressured gas
   reservoirs. Although the straight-line functions (PF2,
   PF4, and PF6) could be used independently, but we
   recommend a combined/simultaneous analysis.
  The -Gp plots are useful for checking data con-
   sistency and for guiding the selection of the -value.
   These plots represent a vivid and dynamic visual
   balance of all of the other analyses.
  The Gan analysis sequence is also useful for orient-
   ing the overall analysis — particularly the ce(p)(pi-p)
   versus (p/z)/(pi/zi) plot.
  The pD-GpD type curve is useful for orientation —
   particularly for estimating the  or (D ) value.
PETE 613                 Gas Material
                                                    Slide — 39
 (2005A)                  Balance
Recommendations for Future Work:
   Consider the extension of this methodology for
    cases of external drive energy (e.g., water influx, gas
    injection, etc.).
   Continue the validation of this approach by applying
    the methodology to additional field cases.
   Implementation into a stand alone software.




PETE 613                  Gas Material
                                                    Slide — 40
 (2005A)                   Balance
           Petroleum Engineering 613
            Natural Gas Engineering
              Texas A&M University

     A Quadratic Cumulative Production Model
            for the Material Balance of
      Abnormally-Pressured Gas Reservoirs
               (End of Presentation)

                   F.E. Gonzalez
                 M.S. Thesis (2003)
            Department of Petroleum Engineering
                   Texas A&M University
              College Station, TX 77843-3116
PETE 613               Gas Material
                                                  Slide — 41
 (2005A)                Balance

								
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