Program solves for gas well inflow performance

Roy Engineer
AERA Energy LLC
Bakersfield, Calif.

Gary Grillette
Bechtel Petroleum Operations Inc.
Tupman, Calif.

Equations For Caculation Gas Well IPR [172,501 bytes]

A Windows-based program, "GasIPR," can solve for the gas well inflow performance relationship (IPR).

The program calculates gas producing rates at various pressures and is applicable for both turbulent and non-turbulent flow. It also has the following capabilities:

Computes PVT properties Yg, P_c', T_c', heating value, Z, µ_g, B_g, and P_g from input gas composition data.
Calculates the Reynolds number (N_Re) and shows the gas flow rates at the sandface at which the turbulence effect must be considered.
Helps the user to optimize the net perforation interval (h_p) so that the turbulence effect can be minimized.
Helps the user to evaluate the sensitivity of formation permeability on gas flow rate for a new play.

IPR is a critical component in forecasting gas well deliverability. IPRs are used for sizing optimum tubing configurations and compressors, designing gravel packs, and solving gas well loading problems. IPR is the key reference for nodal analysis.

A program by the authors on calculating oil well IPR appeared in OGJ, June 23, 1997, pp. 60-63.

Program concept

Gas well IPRs relate bottom hole flowing pressure, P_wf, with gas production rate, q_g.

The program uses the Jones, et al.,¹ derived flow equation to calculate the gas rate at constant flowing pressure, including skin effect and turbulent flow consideration. This equation is expressed as Equation 1 (see equation box). In the equation, a is the turbulent flow term and b is the Darcy flow term. The a and b terms are defined by Equations 2 and 3, where:

P_r = Reservoir static pressure, psia
P_wf = Sandface flowing pressure, psia
q = Gas flow rate at standard conditions, Mscfd
T = Reservoir temperature, °R.
Y_g = Gas gravity
µ_g = Gas viscosity, cp
Z = Gas deviation factor
k = Gas permeability of the formation, md
h = Net pay thickness of the gas zone, ft
h_p = Net pay thickness in the perforated interval, ft
r_e = Drainage radius, ft
r_w = Well bore radius, ft
S = Skin effect, dimension less
ß = Turbulence coefficient, 1/ft, as determined in Equation 4.

Once the a and b terms are calculated, the gas flow rate at a sandface pressure of P_wf is calculated from Equations 5 and 6.

When the turbulence is neglected at Reynolds number less than 1, the program uses the radial flow equation, Equation 7. A brief description of the key parameters are:

Z and µ_g- The program has two input options. Option 1 allows the user to input the Z and µ_g data at the specified pressures, and Option 2 allows the user to input the gas composition including the mole fraction of each constituent at the reservoir temperature. The gas deviation factor, Z, is then calculated using Yarborough, et al.,² correlations. The gas viscosity uses the correlation presented by Lee.³ Both of the above parameters are calculated at an average pressure, P_w, where P_w is the root mean square pressure defined by Equation 8.
B_g and gas density- The gas formation volume factor (B_g) at a pressure, P, is computed with Equation 9. In Equation 9, B_g is cu ft/scf and the gas density at any pressure, P, is calculated from Equation 10. In Equation 10, gas density is in lb_m/cu ft and R equals 10.73.
Reynolds number-The program computes the Reynolds number using Equation 11, where gas velocity at the sandface is defined by Equation 12, and d is the grain size diameter in feet.

The grain size diameter default is 2.208E-04 ft, but it also can be input by the user. The Reynolds number is used to check whether the estimated flow rate is Darcy flow or is in a turbulent flow regime as follows: N_Re< 1 for darcy flow, 1 < N_Re< 10 for transition zone flow, and N_Re 10 for turbulent flow.

If the flow is in the transition zone, non-Darcy flow should be considered. The program prints the Reynolds number for each flow rate in the IPR calculations.

Program use

Most flow equations in GasIPR can be found in Reference 4. Table 1 [35,272 bytes] shows an example of the program input for a hypothetical well. The input includes gas composition and other reservoir parameters.

The objective is to determine the pressure-volume-temperature (PVT) properties and the flow rates for varying flowing pressures, including and excluding the turbulence term when all of net pay is perforated. It is also desired to check the impact of the perforated interval (hp) on the flow rates when only 50% of the net pay is perforated.

Table 2 [41,905 bytes] and Table 3 [48,361 bytes] show the computed gas PVT properties and the IPR output for the well. The IPR plot for the well with an hp/h = 1 is shown in Fig. 1 [40,715 bytes].

It can be noted from Fig. 1 that at a Pwf of 1,500 psia, the flow rate excluding the turbulance term is 110 MMcfd. This compares to 81.4 MMcfd with the turbulence term.

Fig. 2 [41,110 bytes] shows the IPR curve for the well with turbulent flow when only 50% of the net pay is perforated. Here, it can be noted that the gas flow rate is further reduced to 56 MMcfd at 1,500 psia.

Considerations

GasIPR is a powerful program for analyzing gas well flow capacity and determine PVT properties from the gas composition data. In addition, the program can evaluate the effect of the following reservoir parameters on the flow rate:

Partial perforated interval (h_p)-The value of turbulent flow term increases with decreasing values of the perforated interval, thus decreasing the gas flow rate. Therefore, a user can optimize the hp for a new completion. For low-permeability reservoirs, the effect of this variant can normally be neglected.⁴
The effect of reservoir permeability-The effect of the turbulent flow term increases with increasing permeability.⁴

Therefore, a user can evaluate the effect of this variable on the forecasted initial rate (IP) for risking the economics of a new play.

Acknowledgment

The authors thank Stan Roy and Phil Bremner of Pinnacle Software for their support in the development of this software.

Editor's note: To obtain a copy of the GasIPR program subscribers can send a blank 31/2 diskette formatted to MS DOS and a self-addressed, postage paid or stamped return diskette mailer to: Production Editor, Oil & Gas Journal, 3050 Post Oak Blvd., Suite 200, Houston, TX 77056, USA.
Subscribers outside the U.S. should send the diskette and return mailer without return postage to the same address. This mail offer will expire Jan. 31, 1998.

References

Jones, L.G., Blount, E.M., Glaze, O.H., "Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence," Paper No. SPE 6133, 1976.
Yarborough, L., and Hall, K.R., "How to Solve Equation of State for Z Factors," OGJ, Feb. 18, 1974.
Lee, A.L., Gonzales, M.H., and Akin, B.E., "The Viscosity of Natural Gases," Transactions AIME, Vol. 237, 1966, p. 997.
Brown, K.E., "The Technology of Artificial Lift Methods," PennWell Books, Vol. 4, 1984.

The Authors

Roy Engineer is a staff reservoir engineer with AERA Energy LLC, Bakersfield, Calif. He has over 20 years of oil field experience and has worked for Bechtel Petroleum Operations Inc., Occidental Petroleum Corp., Champlin Petroleum Inc., Mobil Oil Corp., and Core Laboratories Inc. Engineer has a BS and MS in petroleum engineering and is a registered Professional Engineer.

Gary Grillette is a senior production engineer for Bechtel Petroleum Operations Inc. He has 15 years of oil field experience. Grillette holds a BS in petroleum and natural gas engineering from Penn State University.