Changes

The relationship between the production flow rate measured at the stock tank, ''q''_o, and the bottomhole flowing pressure, ''p''_wf, is called the ''inflow performance relationship (1PR)''. The IPR of a well can be determined directly by ''production test'' data, or it can be predicted from reservoir data. Whether presented graphically or expressed by a formula, the IPR is a statement of the production capacity and is widely used to design and analyze the production performance of wells

The relationship between the production flow rate measured at the stock tank, ''q''_o, and the bottomhole flowing pressure, ''p''_wf, is called the ''inflow performance relationship (1PR)''. The IPR of a well can be determined directly by ''production test'' data, or it can be predicted from reservoir data. Whether presented graphically or expressed by a formula, the IPR is a statement of the production capacity and is widely used to design and analyze the production performance of wells

Good general references on flow in reservoirs and wells include Golan and Whitson,<ref name=pt10r12>Golan, M., Whitson, G. H., 1991, Well Performance, 2nd. ed.: Englewood Cliffs, NJ, Prentice Hall.</ref> Bradley,<ref name=pt10r3>Bradley, H. B., ed., 1987, Petroleum Engineering Handbook: Richardson, TX, Society of Petroleum Engineers.</ref> and Craft et al.<ref name=pt10r7>Craft, B. C., Hawkins, M., Terry, R. E., 1991, Applied Petroleum Reservoir Engineering, 2nd. ed.: Englewood Cliffs, NJ, Prentice Hall, p. 210–263.</ref>

Good general references on flow in reservoirs and wells include Golan and Whitson,<ref name=pt10r12>Golan, M., and G. H. Whitson, 1991, Well Performance, 2nd. ed.: Englewood Cliffs, NJ, Prentice Hall.</ref> Bradley,<ref name=pt10r3>Bradley, H. B., ed., 1987, Petroleum Engineering Handbook: Richardson, TX, Society of Petroleum Engineers.</ref> and Craft et al.<ref name=pt10r7>Craft, B. C., M. Hawkins, and R. E. Terry, 1991, Applied Petroleum Reservoir Engineering, 2nd. ed.: Englewood Cliffs, NJ, Prentice Hall, p. 210–263.</ref>

==Empirical IPR equations==

==Empirical IPR equations==

[[file:fundamentals-of-fluid-flow_fig2.png|thumb|300px|{{figure number|2}}Plots of multi-rate production data.]]

[[file:fundamentals-of-fluid-flow_fig2.png|thumb|300px|{{figure number|2}}Plots of multi-rate production data.]]

Several IPR formulas have been developed to represent the inflow behavior of various types of wells. Matching a formula to multi-rate production data ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2]]) allows determination of the value of the characteristic constants in the equations, which in turn characterize the productivity of the well. The empirical formulas are the primary tools to quantify well productivity and to perform production calculations.

Several IPR formulas have been developed to represent the inflow behavior of various [[types of wells]]. Matching a formula to multi-rate production data ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2]]) allows determination of the value of the characteristic constants in the equations, which in turn characterize the productivity of the well. The empirical formulas are the primary tools to quantify well productivity and to perform production calculations.

===Productivity index equation for undersaturated oil===

===Productivity index equation for undersaturated oil===

The characteristic constants ''A'' and ''B'' are the corresponding slope and the intercept of the straight line obtained from a Cartesian plot of the multiple rate test data ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2c]]) in the following form:

The characteristic constants ''A'' and ''B'' are the corresponding slope and the intercept of the straight line obtained from a Cartesian plot of the multiple rate test data ([[:file:fundamentals-of-fluid-flow_fig2.png|Figure 2c]]) in the following form:

:<math>(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})/q\quad \mbox{versus}\quad (A + Bq)</math>

:<math>\frac{(p_{\rm R}{}^{2} - p_{\rm wf}{}^{2})}{q}\quad \mbox{versus}\quad (A + Bq)</math>

===Extended range undersaturated oil IPR===

===Extended range undersaturated oil IPR===

==Extension of Darcy's law==

==Extension of Darcy's law==

Darcy's law (see [[Laboratory methods]]), which was originally developed for water flow, has been extended to describe flow of hydrocarbon reservoir fluids (compressible and multiple phases).

Darcy's law, which was originally developed for water flow, has been extended to describe flow of [[hydrocarbon reservoir]] fluids (compressible and multiple phases).

For single-phase oil flow, the proportional constant that relates flow rates to pressure differences in the original Darcy's law is broken down into two independent factors: rock [[permeability]], ''k'', and fluid viscosity, μ For a linear flow system, this gives

For single-phase oil flow, the proportional constant that relates flow rates to pressure differences in the original Darcy's law is broken down into two independent factors: rock [[permeability]], ''k'', and fluid [[viscosity]], μ For a linear flow system, this gives

:<math>q = (A/L)(k/\mu)\Delta p</math>

:<math>q = (A/L)(k/\mu)\Delta p</math>

===Units of Darcy's law formulas===

===Units of Darcy's law formulas===

The ''practical field system'' is widely used for practical petroleum engineering calculations. It is a hybrid system that consists of various metric, English, and oil field units. It uses the millidarcy (md) for permeability. Other dimensions and units in this system are as follows:

The ''practical field system'' is widely used for practical [[petroleum]] engineering calculations. It is a hybrid system that consists of various metric, English, and oil field units. It uses the millidarcy (md) for permeability. Other dimensions and units in this system are as follows:

* ''q''_o = stock tank oil rate (STB/day, or stock tank barrels per day)

* ''q''_o = stock tank oil rate (STB/day, or stock tank barrels per day)

[[Category:Reservoir engineering methods]]

[[Category:Reservoir engineering methods]]