A

Arps equations

• bounds of, 11

• degree of curvature, 5

• exponential curve

  • Arps nominal decline, 7

  • b-exponent term, 6

  • Cartesian rate vs. cumulative production plots, 9

  • constant and continuous declines, 7–8

  • constant percentage exponential decline, 6–7

  • EUR, 7

  • exponential rate vs. time expression, 6

  • hyperbolic rate-time expression, 6

  • rate vs. cumulative production plot, 8–9

  • rate vs. time plot, 8, 9

  • semilog rate vs. time, 9

• harmonic equations, 10–11

• hyperbolic equations, 9–10

• initial decline rate, 5

• initial producing rate, 5

• loss ratio, 5

Arps (1945) late-time production decline model behavior, 89–91

B

Blasingame et al. method

• assumptions and characteristics, 97–98

• composite type curve, 98

• correlating functions, 98–101

• decline curve solution, 102

• empirical scaling term, 102

• horizontal well decline curves, 102

• integral and integral-derivative function transformations, 85

• matching procedure, 101–102

• normalized rate and pressure changes, 97

• production rate normalization, 97

• step- and ramp-rate boundary flux models, 102

Bollycotton Gas Field

• Cartesian rate vs. cumulative production, 40, 42

• G_a and OGIP plot, 40

• initial condition (p/z) relationship, 39

• logarithmic rate vs. time plot, 40, 41

• multiplot analysis, 40

• original gas in place calculation, 39

• performance history, 28–29, 40, 41

• producing and reservoir properties, 42

• quadratic solution, 40, 42

• in rate vs. time plot, 39

• reservoir properties and OGIP, 39

• semilog rate vs. time, 40, 41

• straight line approximation, 40

boundary-dominated flow segment (BDF), 38

Buckley–Leverett plot, 126–127

C

carbon/hydrogen (C/H) ratio, 69

character production curve, 2

D

Darcy equation, 49, 64, 65

decline curves

• advanced decline curve analysis, 2

• applications, 2

• Arps equations (see Arps equations)

• assumptions, 4

• boundary-dominated flow, 3–4

• character production curve, 2

• drainage volume, 2

• of dually completed well, 16–17

• expanding drainage radius, 3

• of Hollands No. 3A well, 14–15

• of north Texas gas condensate well, 17–18

• oil and gas production rates decline, 2

• production rates, 2

• reservoir drainage limits, 3

• shapes of production decline curves, 4, 5

• transient and boundary-dominated flow periods, 2

• transient boundary-dominated conditions

  • Glenn Pool Field, depletion history, 12–14

  • log rate vs. log time plot, 12

  • North Sea field, depletion history, 12

• unforeseen water production, performance analysis, 17

• very-low-permeability gas case, 4

• of Wafford No. 1 well, rate vs. time history, 14

depletion model

• b-exponent, 73–74

• conventional plotting methods, 74

• drainage area aspect ratio, 71

• flow system, 72

• fracture stages, 71

• normalizing curves, 74

• pressure-transient solution, 72

• pseudo-linear flow behavior, 72

• reciprocal flow rate vs. square root of time, 72

• reciprocal rate-transient solution, 72

• stimulated reservoir volume, 71, 72

• system characteristic length, 72

diffusivity equation

• application, 48

• constant pressure solution, 51

• constant rate solution, 50–51

• definition, 49

• van Everdingen and Hurst solutions, 49–50

Dirichlet inner boundary condition, 86

drainage area aspect ratio (AR), 71

dual-porosity Austin Chalk well, production history, 20, 21

E

effects of field conditions

• Bollycotton Gas Field, performance history, 28–29

• different-scale performance plots, 19

• dual-porosity Austin Chalk well, production history, 20, 21

• Ellenberger gas well, performance history, 20, 28

• Gulf of Mexico field, performance history, 26–27

• informational plots

  • API gravity, 26

  • Salt Creek Field, production history, 24, 25

  • well records, 25

• multiplot analysis, 26

• production segments

  • L95 well, production history, 23

  • production history, matching curves, 22

  • waterflooded Canadian reservoir, 21–22

• production system schematic diagram, 19, 20

• water influx effect, 20, 21

• well downtime, 23, 24

• west Texas hydraulically fractured oil well, performance history, 27

Ellenberger gas well, 20

Ershagi plot, 136, 140

estimated ultimate recovery (EUR), 7, 10, 15, 37, 74, 134, 141

F

Fetkovich method

• Arps (1945) late-time production decline model behavior, 89–91

• boundary-dominated flow stems, 87

• cumulative production, 88

• decline analysis time, 88

• decline curve model, 89

• dimensionless decline flow rate, 87, 88

• dimensionless decline flow time, 87, 88

• dimensionless drainage radius, 88, 89

• flow rate variables, 88, 89

• Golden Zuma well, productive character, 109–112

• graphical scaling parameters, 85

• infinite-acting transient, 87

• logarithmic rate vs. time curve, 108, 109

• logarithmic transformations, 88

• rate-transient dimensionless time, 89

• semilog rate vs. time plot, 108, 109

• transient and bounded flow production history, 85

• transient decline curve

  • analysis procedure, 93

  • apparent wellbore radius and skin, 92, 96

  • boundary-dominated example, 93–94

  • bulk volume of reservoir, 96

  • computer-generated type curve match, 95, 96

  • drainage area, 92

  • drainage volume, 96

  • formation conductivity, 92

  • infinite-acting transient flow behavior, 95

  • log rate vs. log time plot, 94, 95

  • matching of production data, 91

  • M–4X well production history, 94, 95

  • permeability calculation, 95

  • rate and time solutions, 91–92

  • rate-transient performance, 91

  • reservoir drainage area, 97

  • reservoir information, 92

  • reservoir pore volume, 92

  • skin factor, 96

  • total compressibility calculation, 96

  • total system compressibility, 92

  • transient flow studies, 89

  • transient side analysis, 97

  • unique decline curve analysis, 88

flowing bottomhole pressures (FBHP), 74

fractured horizontal wells

• depletion model

  • b-exponent, 73–74

  • conventional plotting methods, 74

  • drainage area aspect ratio, 71

  • flow system, 72

  • fracture stages, 71

  • normalizing curves, 74

  • pressure-transient solution, 72

  • pseudo-linear flow behavior, 72

  • reciprocal flow rate vs. square root of time, 72

  • reciprocal rate-transient solution, 72

  • stimulated reservoir volume, 71, 72

  • system characteristic length, 72

• early time behavior, 82–84

• geological setting

  • capillary effects, 67

  • carbonate sediments, 68

  • clay- and silt-sized sediments, 68

  • current-velocity and grain-size effects, 68

  • hydrocarbon generation, 69–70

  • maturation and generation of hydrogen, 70–71

  • oil- and gas-saturated shales, 67

  • potential problems, 68

  • productive shales, 67

• regional analysis example

  • interpretation, 79, 81

  • log production rate vs. log time analysis, 79, 80

  • plotting methods, 78

  • reciprocal flow rate vs. square root of time analysis, 79, 80

  • south Texas Eagle Ford Shale lease, horizontal well completions, 79

  • time ratio plot, 79, 80

  • well production data, 79

• shale well examples

  • Fetkovich type curve, 75, 78

  • Hixon oil well production history, 75

  • linear flow parameter, 77

  • matrix/fracture interface area, 77

  • normalized flow rate and square root of pseudo production time smoothed data, 75, 77

  • pressure drop normalized flow rate vs. pseudo production time plot, 75, 76

  • pressure drop normalized production flow rate vs. time plot, 75, 76

  • 1/q vs. √t plot, 78

  • reciprocal flow rate vs. square root of time, 75, 77

  • t_mb/t ratio, 75, 76

fractured vertical wellbore case

• b-exponent, 58–59

• dimensionless fracture conductivity, 55–57

• finite conductivity, 55

• formation damage, 61, 62

• fracture conductivity, 55

• geometrical relationship, 55

• infinite-conductivity-vertical-fracture response, 55

• log flow rate vs. log time plot, 59

• performance history, 57, 58

• principal transient flow regimes, 57

• production performance, 55

• reciprocal flow rate vs. square root of time plot, 60

• straight-line extrapolation, 61, 62

frontal advance theory, 128–130

G

Glenn Pool Field

• depletion history, 12, 13

• initial production decline curve, 13

• performance histories, 13, 14

• production history, 12, 13

• reserves to production ratio, 14

Golden Zuma well, productive character, 109–112

Gulf of Mexico (GOM) field, performance history, 26–27

H

Hixon oil well production history, 75

horizontal-unfractured-well case, 51–52

hydrogen/carbon (H/C) ratio, 69

K

Kentucky well, 113–114

M

ME 232 well, production history, 149, 151–153

multiple performance plots, two phase flow

• Cartesian rate vs. time plot, 136, 138

• Cartesian scale WOR vs. time plot, 136, 139

• composite performance history, 136, 137

• decline rate, 141

• Ershagi plot, 136, 140

• fractional flow and WOR results, 141

• oil and water production histories, 136, 139

• oil rate vs. cumulative recovery plot, 136, 138

• relating cumulative production to producing time plot, 136

• semi-log rate vs. time plot, 136, 138

• total well liquid flow rate, 136, 139

• watercut plot, 136, 140

• well history, 136

• 1/WOR + WOR plot, 136, 140

N

Neumann inner boundary condition, 86

normal decline curve analysis, 115

North Sea field, depletion history, 12

O

oil/water contact (OWC), 116

oxygen/carbon (O/C) index ratio, 69

P

Poe and Poston method

• advantages, 104

• completion models

  • composite decline curves, 107

  • finite conductivity vertically fractured well, 106

  • horizontal wellbore case, 107–108

  • unfractured vertical well, 105

  • vertical fracture decline curves, 107

• composite decline curves, 103

• computer-aided analysis, 102

• dimensionless cumulative production, 103

• dimensionless decline cumulative production, 104

• dimensionless decline flow rate, 103

• dimensionless pseudo production time, 103

• graphical analysis technique, 85

• imaging factor, 103

• iterative computations, 104

• pressure drop normalized cumulative production, 104

• rate equations, 104

• reservoir parameters, 103

• vertical well decline curve match and analysis, 103

Provost Field, performance history

• Arps curve fits, 122, 123

• GOR and water-cut performance history, 121, 122

• oil, total liquid producing rate, and water injection history, 121, 122

• segments of, 122, 123

• water handling costs, 123, 124

• well history water handling costs, 121, 122

pseudo production time

• characteristic length, 32

• definition, 31

• dimensionless material balance time, 32

• equivalent material balance time, 31, 32

• superposition dimensionless time

  • fractured vertical well, 32–33

  • horizontal wellbore length, 33–34

  • material balance, 32

  • unfractured well, 32, 33

R

regional analysis example

• interpretation, 79, 81

• log production rate vs. log time analysis, 79, 80

• plotting methods, 78

• reciprocal flow rate vs. square root of time analysis, 79, 80

• south Texas Eagle Ford Shale lease, horizontal well completions, 79

• time ratio plot, 79, 80

• well production data, 79

S

Salt Creek Field, production history, 24, 25

shale well examples

• Fetkovich type curve, 75, 78

• Hixon oil well production history, 75

• linear flow parameter, 77

• matrix/fracture interface area, 77

• normalized flow rate and square root of pseudo production time smoothed data, 75, 77

• pressure drop normalized flow rate vs. pseudo production time plot, 75, 76

• pressure drop normalized production flow rate vs. time plot, 75, 76

• 1/q vs. √t plot, 78

• reciprocal flow rate vs. square root of time, 75, 77

• t_mb/t ratio, 75, 76

smoothing variable production

• assumptions and limitations, 37

• Bollycotton Gas Field

  • Cartesian rate vs. cumulative production, 40, 42

  • G_a and OGIP plot, 40

  • initial condition (p/z) relationship, 39

  • logarithmic rate vs. time plot, 40, 41

  • multiplot analysis, 40

  • original gas in place calculation, 39

  • performance history, 40, 41

  • producing and reservoir properties, 42

  • quadratic solution, 40, 42

  • in rate vs. time plot, 39

  • reservoir properties and OGIP, 39

  • semilog rate vs. time, 40, 41

  • straight line approximation, 40

• boundary-dominated flow segment, 38

• computer programs, 31

• exponential and quadratic curves, 36, 37

• flowing pressure history, 37

• initial pressure, 37

• initial producing rate, 37

• normalizing production, 34–35

• pseudo production time

  • characteristic length, 32

  • definition, 31

  • dimensionless material balance time, 32

  • equivalent material balance time, 31, 32

  • superposition dimensionless time, 32–34

• quadratic equation, 31, 37, 38

• quadratic model, 35–36

• West Virginia Well A analysis problem

  • Cartesian rate vs. cumulative production, 42, 43

  • flow rate cumulative production plot, 45

  • logarithmic rate-logarithmic time plot, 44

  • logarithmic rate vs. log time, 42, 43

  • log flow rate vs. time plot, 45

  • log rate vs. time, 42, 43

  • quadratic equation, 42, 44

  • quadratic plot, 45

  • summary analysis, 44

• z-factor, 37

stimulated reservoir volume (SRV), 71, 72

T

two phase flow

• geological influences, 116

• ME 232 well, production history, 149, 151–153

• multiple performance plots

  • Cartesian rate vs. time plot, 136, 138

  • Cartesian scale WOR vs. time plot, 136, 139

  • composite performance history, 136, 137

  • decline rate, 141

  • Ershagi plot, 136, 140

  • fractional flow and WOR results, 141

  • oil and water production histories, 136, 139

  • oil rate vs. cumulative recovery plot, 136, 138

  • relating cumulative production to producing time plot, 136

  • semi-log rate vs. time plot, 136, 138

  • total well liquid flow rate, 136, 139

  • watercut plot, 136, 140

  • well history, 136

  • 1/WOR + WOR plot, 136, 140

• performance history, Provost Field

  • Arps curve fits, 122, 123

  • GOR and water-cut performance history, 121, 122

  • oil, total liquid producing rate, and water injection history, 121, 122

  • segments of, 122, 123

  • water handling costs, 123, 124

  • well history water handling costs, 121, 122

• relative permeability

  • Buckley–Leverett plot, 131, 133

  • definition, 127

  • field parameters, 131

  • fractional flow curves, 134

  • frontal advance theory, 128–130

  • GOR and drilling history, 131, 132

  • historical time and cumulative production, 131, 133

  • interpretation of field history, 132

  • interpretive concepts, 134–136

  • k_w/k_o ratio curve, 127

  • oil and water relative permeability curves, 127, 128

  • oil production rate and WOR, 131, 132

  • primary and subordinate stages, 133–134

  • pseudorelative permeability, 130–131

  • segment parameters, 132, 133

  • straight-line approximation, 131

• reserves and predicting performance

  • analysis procedure, 124–126

  • Arps’s equations, 123

  • assumptions, 124

  • Buckley–Leverett plot, 126–127

  • cumulative production, 124

  • hyperbolic equations, 124

  • oil flow rate and WOR predictions, 126, 127

  • rate equation, 124

  • solution procedure, 124

• waterflooding

  • capillary force, 118

  • capillary/viscous number, 118

  • constant vigilance, 115

  • degree of crossflow, 117

  • depletion stages, 120

  • efficiency, 115

  • flood-front pattern, 117

  • gravity force, 118

  • incremental production, 115

  • linearization technique, 120

  • material balance techniques, 117

  • permeability distribution, 117

  • phase flow relationships, 115

  • pseudorelative permeability curves, 119

  • two-step process, 117

  • viscous force, 118

  • viscous/gravity number, 118

  • water- to oil-mobility ratio, 117

  • WOR vs. N_p plot, 119

• well diagnostics plots

  • Cartesian rate vs. time, 146, 147

  • derivative plots, 143–144

  • Evans Well 11, 146, 147

  • GOR and derivative history, 144, 145

  • log rate vs. time, 146, 148

  • near-wellbore channeling, 142

  • oil and water producing rates, 146, 148

  • performance history, 142

  • producing history, 144, 145

  • rate vs. cumulative production, 146, 148

  • total system flow rate, 146, 149

  • water cones, 142

  • Well MR-321, 144–146, 149–151

  • WOR vs. time plot, 142

• Well PP4, production history, 147, 149

type curves

• apparent wellbore radius calculation, 112

• Blasingame et al. method

  • assumptions and characteristics, 97–98

  • composite type curve, 98

  • correlating functions, 98–101

  • decline curve solution, 102

  • empirical scaling term, 102

  • horizontal well decline curves, 102

  • integral and integral-derivative function transformations, 85

  • matching procedure, 101–102

  • normalized rate and pressure changes, 97

  • production rate normalization, 97

  • step- and ramp-rate boundary flux models, 102

  • water influx and waterflood performance, 102

• boundary-dominated flow regime, 86

• definition, 86

• dimensionless and field data match points, 86

• dimensionless time, 87

• dimensionless well flow rate solution, 87

• Dirichlet inner boundary condition, 86

• Fetkovich method

  • Arps (1945) late-time production decline model behavior, 89–91

  • boundary-dominated flow stems, 87

  • cumulative production, 88

  • decline analysis time, 88

  • decline curve model, 89

  • dimensionless decline flow rate, 87, 88

  • dimensionless decline flow time, 87, 88

  • dimensionless drainage radius, 88, 89

  • flow rate variables, 88, 89

  • graphical scaling parameters, 85

  • infinite-acting transient, 87

  • logarithmic transformations, 88

  • rate-transient dimensionless time, 89

  • transient and bounded flow production history, 85

  • transient decline curve, 91–97

  • transient flow studies, 89

  • unique decline curve analysis, 88

• 0 to 1 flow regime, 86

• 1 to 2 flow regime, 86

• 2 to 3 flow regime, 86

• formation permeability calculation, 112

• general production rate decline flow regimes, 86

• inner boundary condition, 86

• Kentucky well, 113–114

• Neumann inner boundary condition, 86

  • Poe and Poston method

  • advantages, 104

  • completion models, 105–108

  • composite decline curves, 103

  • computer-aided analysis, 102

  • dimensionless cumulative production, 103

  • dimensionless decline cumulative production, 104

  • dimensionless decline flow rate, 103

  • dimensionless pseudo production time, 103

  • graphical analysis technique, 85

  • imaging factor, 103

  • iterative computations, 104

  • pressure drop normalized cumulative production, 104

  • rate equations, 104

  • reservoir parameters, 103

  • vertical well decline curve match and analysis, 103

• quadratic equation, 113

• reference type curve solutions, 86

• reservoir drainage pore volume calculation, 113

• skin effect evaluation, 112

• system characteristic length, 87

• terminal pressure inner boundary condition, 86–87

• transition flow period, 86

U

unfractured vertical wellbore models, 48–49

V

van Krevelen plot, 69

W

waterdrive displacement mechanisms, 116

well and reservoir models

• analysis procedure

  • Cartesian flow rate vs. cumulative recovery plot, 61

  • log flow rate vs. log time plot, 61

  • production data, 61

  • 1/q vs. $t$ plot, 61, 63, 64

  • semilog flow rate vs. time plot, 61, 63, 64

  • time ratio plot, 63

• flow equations

  • Darcy equation, 49, 64, 65

  • diffusivity equation, 48–51

• fractured vertical wellbore case

  • b-exponent, 58–59

  • dimensionless fracture conductivity, 55–57

  • finite conductivity, 55

  • formation damage, 61, 62

  • fracture conductivity, 55

  • geometrical relationship, 55

  • infinite-conductivity-vertical-fracture response, 55

  • log flow rate vs. log time plot, 59

  • performance history, 57, 58

  • principal transient flow regimes, 57

  • production performance, 55

  • reciprocal flow rate vs. square root of time plot, 60

  • straight-line extrapolation, 61, 62

• geological considerations, 48

• horizontal-unfractured-well case, 51–52

• horizontal well

  • learning objectives, 52

  • performance history, 53–54

  • transient production performance, 52

  • turbidities, 52

• producing interval transmissibility, 47

• reservoir geologic factors, 47

• unfractured vertical wellbore models, 48–49

• well completion configurations, 47

• well stimulation techniques, 47

well diagnostics plots

• Cartesian rate vs. time, 146, 147

• derivative plots, 143–144

• Evans Well 11, 146, 147

• GOR and derivative history, 144, 145

• log rate vs. time, 146, 148

• near-wellbore channeling, 142

• oil and water producing rates, 146, 148

• performance history, 142

• producing history, 144, 145

• rate vs. cumulative production, 146, 148

• total system flow rate, 146, 149

• water cones, 142

• Well MR-321, 144–146, 149–151

• WOR vs. time plot, 142

Well MR-321

• Cartesian rate vs. time plot, 149, 150

• cumulative production, 149, 150

• derivative plot, 144, 146

• oil and water producing rates, 149, 151

• performance plots, 146

• producing history, 144, 145|

• in rate vs. time plot, 149, 150

• total flow through system, 149, 151

west Texas hydraulically fractured oil well, performance history, 27

west Virginia Well A analysis problem

• Cartesian rate vs. cumulative production, 42, 43

• flow rate cumulative production plot, 45

• logarithmic rate-logarithmic time plot, 44

• logarithmic rate vs. log time, 42, 43

• log flow rate vs. time plot, 45

• log rate vs. time, 42, 43

• quadratic equation, 42, 44

• quadratic plot, 45

• summary analysis, 44