Changes

|+ {{table number|1}}Summary of methods used to derive hydrocarbon reserves

|+ {{table number|1}}Summary of methods used to derive hydrocarbon reserves

|-

|-

! Method

! Method || Application || Accuracy

! Application

! Accuracy

|-

|-

| Volumetric

| Volumetric || OOIP, OGIP, recoverable reserves. Use early in life of field. || Dependent on quality of reservoir description. Reserves estimates often high because this method does not consider problems of reservoir heterogeneity.

| OOIP, OGIP, recoverable reserves. Use early in life of field.

| Dependent on quality of reservoir description. Reserves estimates often high because this method does not consider problems of reservoir heterogeneity.

|-

|-

| Material balance

| Material balance || OOIP, OGIP (assumes adequate production history available), recoverable reserves (assumes OOIP and OGIP known). Use in a mature field with abundant geological, petrophysical, and engineering data. || Highly dependent on quality of reservoir description and amount of production data available. Reserve estimates variable.

| OOIP, OGIP (assumes adequate production history available), recoverable reserves (assumes OOIP and OGIP known). Use in a mature field with abundant geological, petrophysical, and engineering data.

| Highly dependent on quality of reservoir description and amount of production data available. Reserve estimates variable.

|-

|-

| Production history

| Production history || Recoverable reserves. Use after a moderate amount of production data is available. || Dependent on amount of production history available. Reserve estimates tend to be realistic.

| Recoverable reserves. Use after a moderate amount of production data is available.

| Dependent on amount of production history available. Reserve estimates tend to be realistic.

|-

|-

| Analogy

| Analogy || OOIP, OGIP, recoverable reserves. Use early in exploration and initial field development. || Highly dependent on similarity of reservoir characteristics. Reserve estimates are often very general.

| OOIP, OGIP, recoverable reserves. Use early in exploration and initial field development.

| Highly dependent on similarity of reservoir characteristics. Reserve estimates are often very general.

|}

|}

* 7758 = conversion factor from acre-ft to bbl

* 7758 = conversion factor from acre-ft to bbl

* ''A'' = area of reservoir (acres) from map data

* ''A'' = area of reservoir (acres) from map data

* ''h'' = height or thickness of pay zone (ft) from log and/or core data

* ''h'' = height or thickness of pay zone (ft) from log and/or [[Overview of routine core analysis|core data]]

* ø = [[porosity]] (decimal) from log and/or core data

* ø = [[porosity]] (decimal) from log and/or core data

* ''S''_w = connate water saturation (decimal) from log and/or core data

* ''S''_w = connate water saturation (decimal) from log and/or core data

* B_oi = formation volume factor for oil at initial conditions (reservoir bbl/STB) from lab data; a quick estimate is ''B''_oi = 1.05 + (''N'' × 0.05), where ''N'' is the number of hundreds of ft³ of gas produced per bbl of oil [for example, in a well with a GOR of 1000, ''B''_oi = 1.05 + (10 × 0.05)]

* B_oi = formation volume factor for oil at initial conditions (reservoir bbl/STB) from lab data; a quick estimate is <math>B_{oi} = 1.05 + (N \times 0.05)</math>, where ''N'' is the number of hundreds of ft³ of gas produced per bbl of oil [for example, in a well with a GOR of 1000, ''B''_oi = 1.05 + (10 × 0.05)]

Another basic volumetric equation is

Another basic volumetric equation is

|+ {{table number|2}}Estimation of primary recovery factor

|+ {{table number|2}}Estimation of primary recovery factor

|-

|-

!

! Drive Mechanidm || Primary Recovery Factor Drive Mechanism (%)

! Primary Recovery Factor Drive Mechanism (%)

|-

|-

| Depletion

| colspan = 2 | Depletion

|-

|-

|     Solution gas

|     Solution gas || 18–25

| 18–25

|-

|-

|     Expansion

|     Expansion || 2–5

| 2–5

|-

|-

| Gas cap drive

| Gas cap drive || 20–40

| 20–40

|-

|-

| Water drive

| colspan = 2 | Water drive

 

|-

|-

|     Bottom

|     Bottom || 20–40

| 20–40

|-

|-

|     Edge

|     Edge || 35–60

| 35–60

|-

|-

| Gravity

| [[Gravity]] || 50–70

| 50–70

|}

|}

* ''E''_V = vertical sweep efficiency

* ''E''_V = vertical sweep efficiency

These efficiency terms are influenced by such factors as residual oil saturation, [[relative [[permeability]]]], reservoir heterogeneity, and operational limitations that govern reservoir production and management. Thus, it is difficult to calculate the recovery factor directly using these terms, and other methods, such as decline curves, are often applied.

These efficiency terms are influenced by such factors as residual oil saturation, relative [[permeability]], reservoir heterogeneity, and operational limitations that govern reservoir production and management. Thus, it is difficult to calculate the recovery factor directly using these terms, and other methods, such as decline curves, are often applied.

The basic equation to calculate recoverable gas reserves is

The basic equation to calculate recoverable gas reserves is

One general equation is

One general equation is

:Change in pore volume = Change in oil volume + change in free gas volume + change in water volume

:<math>\text{Change in pore volume} = \text{ Change in oil volume } + \text{ change in free gas volume } + \text{ change in water volume}</math>

where

where

* Change in pore volume = ''NB''_oi/(1 – ''S''_wi)''c''_f''P''

* <math>\text{Change in pore volume} = \frac{NB_{oi}}{(1 - S_{wi})}c_fP</math>

* Change in oil volume = ''NB''_oi –(''N'' – ''N''_p)''B''_oi

* <math>\text{Change in oil volume} = NB_{oi} - (N - N_p)B_{oi}</math>

* Change in gas volume = (''GB''_gi – ''GB''_g) + [''N''_p''R''_p ''(N'' – ''N''_p) – NR_si]''B''_g due to gas produced, evolved, and encroached from a gas cap

* <math>\text{Change in gas volume} = (GB_{gi} - GB_g) + [N_p R_p (N - N_p) - NR_{si}] B_g</math> due to gas produced, evolved, and encroached from a gas cap

* Change in water volume = –''NB''_oi''S''_wi/(1 – S_wi)''c''_w''P'' – ''W''_e + ''W''_p''B''_w, due to connate water volume change, encroached water, and produced water

* <math>\text{Change in water volume} = \frac{-NB_{oi}S_{wi}}{(1 - S_{wi})}c_wP - W_e + W_pB_w</math>, due to connate water volume change, encroached water, and produced water

where

where

The material balance technique for calculating gas reserves, like material balance for oil, attempts to mathematically equilibrate changes in reservoir volume as a result of production. The basic equation is

The material balance technique for calculating gas reserves, like material balance for oil, attempts to mathematically equilibrate changes in reservoir volume as a result of production. The basic equation is

:Weight (or SCF) of gas produced = weight (or SCF) of gas initially in the reservoir – weight (or SCF) of gas remaining in the reservoir

:<math>\text{Weight (or SCF) of gas produced} = \text{ weight (or SCF) of gas initially in the reservoir } - \text{ weight (or SCF) of gas remaining in the reservoir}</math>

The equations used to calculate OGIP are

The equations used to calculate OGIP are

===Reservoir simulation===

===Reservoir simulation===

The material balance method is actually a subset of the mathematical techniques that are available to modern petroleum engineers. Reservoir simulators use material balance as well as fluid flow equations to model the reservoir as a group of interconnected tanks. The advent of powerful computers has made the use of numerical simulation quite common for estimating reserves and recovery as well as initial volume in place. Since reservoir simulation can account for performance history through history matching, this method incorporates facets of all the techniques discussed. With sufficient data and prudent use of simulators, this method provides the best recovery estimates for complex reservoirs.

The material balance method is actually a subset of the mathematical techniques that are available to modern [[petroleum]] engineers. Reservoir simulators use material balance as well as fluid flow equations to model the reservoir as a group of interconnected tanks. The advent of powerful computers has made the use of numerical simulation quite common for estimating reserves and recovery as well as initial volume in place. Since reservoir simulation can account for performance history through history matching, this method incorporates facets of all the techniques discussed. With sufficient data and prudent use of simulators, this method provides the best recovery estimates for complex reservoirs.

==Production history analysis==

==Production history analysis==

<gallery>

<gallery mode=packed heights=200px widths=200px>

file:reserves-estimation_fig1.png|{{figure number|1}}Production history curves.<ref name=pt10r16>IHRDC, 1982, Production rate decline curves: PE107, Boston, MA, IHRDC.</ref>

file:reserves-estimation_fig1.png|{{figure number|1}}Production history curves.<ref name=pt10r16>IHRDC, 1982, Production rate decline curves: PE107, Boston, MA, IHRDC.</ref>

file:reserves-estimation_fig2.png|{{figure number|2}}Semi-log plot of rate of production versus time.<ref name=pt10r16 />

file:reserves-estimation_fig2.png|{{figure number|2}}Semi-log plot of rate of production versus time.<ref name=pt10r16 />

</gallery>

</gallery>

Production history analysis is used to estimate economic ultimate recovery (or recoverable reserves) and the expected economic life of a reservoir. The rate of production and cumulative production at any point in time can also be estimated. This method relies on historical production data to extrapolate future production performance. A variety of curves can be used (Figure 1), the most common being a semilog plot of rate of production versus time (Figure 2). These data are easily obtained through operator records or state regulatory agencies.

Production history analysis is used to estimate economic ultimate recovery (or recoverable reserves) and the expected economic life of a reservoir. The rate of production and cumulative production at any point in time can also be estimated. This method relies on historical production data to extrapolate future production performance. A variety of curves can be used ([[:file:reserves-estimation_fig1.png|Figure 1]]), the most common being a semilog plot of rate of production versus time ([[:file:reserves-estimation_fig1.png|Figure 2]]). These data are easily obtained through operator records or state regulatory agencies.

Three mathematical models can be used to describe decline curve (usually rate versus time) behavior. They are

Three mathematical models can be used to describe decline curve (usually rate versus time) behavior. They are

Exponential and hyperbolic decline are commonly used to describe reservoirs. Harmonic decline is an infrequently applied special case of hyperbolic decline.

Exponential and hyperbolic decline are commonly used to describe reservoirs. Harmonic decline is an infrequently applied special case of hyperbolic decline.

The different types of decline behavior are not necessarily mutually exclusive. Often different decline curve characteristics are related to different stages of reservoir development, and the overall trends can be significantly affected by [[workovers]] or [[stimulation]], infill drilling, a change in lift mechanics, or secondary or tertiary flood initiation (Figure 3).

The different types of decline behavior are not necessarily mutually exclusive. Often different decline curve characteristics are related to different stages of reservoir development, and the overall trends can be significantly affected by [[workovers]] or [[stimulation]], infill drilling, a change in lift mechanics, or secondary or tertiary flood initiation ([[:file:reserves-estimation_fig1.png|Figure 3]]).

Formulas used to calculate the rate of production, cumulative production, and economic life of a reservoir are given in Table 3.

Formulas used to calculate the rate of production, cumulative production, and economic life of a reservoir are given in Table 3.

|+ {{table number|3}}Decline equations

|+ {{table number|3}}Decline equations

|-

|-

! Solving for

! Solving for || Exponential || Hyperbolic

! Exponential

! Hyperbolic

|-

|-

| Rate of production

| Rate of production || <math>q_t = q_{\text{i}}e^{-Dt}</math> || <math> q_{t} = q_{\rm i}(1 + nD_{\rm i}t)^{-1/n}</math>

| ''q''_t = ''q''_i ''e''^{– ''Dt''}

| ''q''_t = ''q''_i (1 + ''nD''_i ''t'' )^{–1/ ''n''}

|-

|-

| Cumulative production

| Cumulative production || <math>N_p = \frac{(q_{\text{i}} - q_t)}{D}</math> || <math> N_{\rm p} = \frac{q_{\rm i}^{n}}{[(1 - n)D_{\rm i}]}(q_{\rm i}^{1 - n} - q_{\rm t}^{1-n})</math>

| ''N_p'' = ( ''q''_i – ''q_t'' )/ ''D''

| <math> q_{t} = q_{\rm i}(1 + nD_{\rm i}t)^{-1/n}</math><br />

<math> N_{\rm p} = q_{\rm i}^{n}/[(1 - n)D_{\rm i}](q_{\rm i}^{1 - n} - q_{\rm t}^{1-n})</math><br />

<math>t = [(q_{\rm i}/q_{\rm ec})^{n} - 1/nD_{\rm i}</math>

|-

|-

| Life of reservoir

| Life of reservoir || <math>t = \left( \frac{1}{D} \right) \ln \left( \frac{q_{\text{i}}}{q_{ec}} \right)</math> || <math>t = \left( \frac{q_{\rm i}}{q_{\rm ec}} \right)^n -\frac{1}{nD_{\rm i}}</math>

| ''t'' = (1/ ''D'' )ln( ''q''_i / ''q''_ec )

| ''t'' = [( ''q''_i ''/q''_ec ) ''ⁿ'' – 1/ ''nD''_i

|}

|}

==Analogy method==

==Analogy method==

* [[Reservoir modeling for simulation purposes]]

* [[Reservoir modeling for simulation purposes]]

* [[Waterflooding]]

* [[Waterflooding]]

* [[Fundamentals of fluid flow]]

* [[Fluid flow fundamentals]]

* [[Conducting a reservoir simulation study: An overview]]

* [[Conducting a reservoir simulation study: an overview]]

* [[Introduction to reservoir engineering methods]]

* [[Introduction to reservoir engineering methods]]

* [[Petroleum reservoir fluid properties]]

* [[Petroleum reservoir fluid properties]]

* [http://archives.datapages.com/data/alt-browse/aapg-special-volumes/me10.htm Original content in Datapages]

* [http://archives.datapages.com/data/alt-browse/aapg-special-volumes/me10.htm Original content in Datapages]

* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]

* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]

[[Category:Reservoir engineering methods]] [[Category:Pages with bad references]]

[[Category:Reservoir engineering methods]]

[[Category:Methods in Exploration 10]]