Gas Well Performance Evaluation
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Questions and Answers

What is the range of the exponent 'n' in the gas flow rate equation Qg = C[pr − p2wf]n [3.1.20]?

  • 1.0 ≤ n ≤ 1.5
  • 1.5 ≤ n ≤ 2.0
  • 0.0 < n ≤ 0.5
  • 0.5 ≤ n ≤ 1.0 (correct)

    • What is the method of calculating gas flow rate by Equation 3.1.11 called?

    pressure-squared approximation method

    The pressure-squared approximatio______ form of the gas flow rate equatio______ is: Qg = C[pr − p2wf]_ [3.1.20]

    n

    What is the equation for the productivity index (J) for a gas well?

    <p>J = Qg / (ψr - ψwf)</p> Signup and view all the answers

    How can the absolute open flow potential (AOF) be calculated?

    <p>AOF = Qg max = J ψr</p> Signup and view all the answers

    What shape factor is typically used for a circular drainage area in the gas well performance evaluation?

    <p>31.62</p> Signup and view all the answers

    The productivity index J can be introduced into the gas flow rate equation for pressures below 3000 psi.

    <p>False</p> Signup and view all the answers

    What does the pressure quadratic form equation represent?

    <p>Gas flow rate</p> Signup and view all the answers

    Which coefficients are determined from the linear plot of Equation 3.1.32?

    <p>a1 and b1</p> Signup and view all the answers

    In the pseudopressure equation ψ r − ψwf = __ Qg + __ Qg2, fill in the blanks with the correct terms.

    Signup and view all the answers

    What is the back-pressure equation for this system?

    <p>log(Qg) = log(C) + n log(pr - p2wf)</p> Signup and view all the answers

    In the equation Qg = 0.0169 (3,810,000 - p2wf)0.87, what does Qg stand for?

    <p>Gas flow rate</p> Signup and view all the answers

    What does the exponent 'n' represent in the equation involving the logarithms of Qg and pressure?

    <p>Performance coefficient</p> Signup and view all the answers

    True or False: The IPR data can be generated by assuming various values of pwf.

    <p>True</p> Signup and view all the answers

    Match the following methods with their respective equations:

    <p>Pressure-squared method = pr - p2wf = aQg + bQg^2 Pressure method = (1952 - pwf) = 0.06Qg + 1.111 × 10^-5 Qg^2 Pseudopressure method = (316 × 10^6 - ψwf) = 22.28 × 10^3 Qg + 1.727 Qg^2</p> Signup and view all the answers

    What is the purpose of the performance coefficient C in Equation 3.1.20?

    <p>To account for reservoir rock properties, fluid properties, and reservoir flow geometry.</p> Signup and view all the answers

    What is the assumption underlying Equation 3.1.20?

    <p>The gas flow obeys the pseudosteady-state or the steady-state flowing condition.</p> Signup and view all the answers

    In Equation 3.1.21, a plot of Qg vs. pr − p2wf on a log-log scale results in a straight line with a slope of n.

    <p>True</p> Signup and view all the answers

    Equation 3.1.22 is used to determine the deliverability exponent __ from two points on a straight line.

    <p>n</p> Signup and view all the answers

    Match the types of deliverability tests with their descriptions:

    <p>Conventional deliverability (back-pressure) test = Flowing wells at multiple rates and measuring bottom-hole pressure over time. Isochronal test = A specific test method used to determine gas well flow potential. Modified isochronal test = Another variation of a test used to characterize gas well flow potential.</p> Signup and view all the answers

    What is the gas flow rate when pwf is 1800 and ψ is 270 × 10^6?

    <p>1794 Mscf/day</p> Signup and view all the answers

    Which method resulted in the most accurate IPR data with an absolute average error of 5.4%?

    <p>Pressure-squared equation</p> Signup and view all the answers

    Adjust the coefficients a and b of the back-pressure equation when the reservoir pressure changes from pr1 to pr2 by applying the expression: a2 = a1 and b2 = ___

    <p>b1</p> Signup and view all the answers

    Match the method with the correct adjustment expression for adjusting the coefficients of the deliverability equation:

    <p>Back-pressure equation = a2 = a1 and b2 = b1 Pressure-squared equation = a2 = a1 and b2 = b1 Pseudopressure approach = a2 = a1 and b2 = b1</p> Signup and view all the answers

    What is one of the fundamental tools of reservoir engineering according to the text?

    <p>Material balance</p> Signup and view all the answers

    How can gas reserves be calculated if enough production-pressure history is available?

    <p>Without knowing the areal extent of the reservoir or the drainage area of the well</p> Signup and view all the answers

    What does np stand for in the material balance equation?

    <p>Moles of gas produced</p> Signup and view all the answers

    Equation 3.3.7 is commonly expressed in two forms: one in terms of p/Z, and another in terms of _____.

    <p>Bg</p> Signup and view all the answers

    What is the effective wellbore radius (rw) calculated to be?

    <p>477.54 ft</p> Signup and view all the answers

    What is the flow rate calculated using the pressure-squared approximation approach?

    <p>9594 Mscf/day</p> Signup and view all the answers

    What is the flow rate calculated using the ψ approach?

    <p>9396 Mscf/day</p> Signup and view all the answers

    Calculate the cumulative gas production at 1000 psi.

    <p>30.95 MMMscf</p> Signup and view all the answers

    Calculate the recovery factor at 400 psi.

    <p>86.3%</p> Signup and view all the answers

    What is the formula to adjust coefficient C in the back-pressure equation?

    <p>C2 = C1 * (µg1 * Z1) / (µg2 * Z2)</p> Signup and view all the answers

    What is the formula for the future gas flow rate?

    <p>Qg = 0.01727 * (17002 - pwf) / L</p> Signup and view all the answers

    What is the equation for combining the Cullender and Smith equation with the back-pressure equation?

    <p>((p2wf - eS * p2t) / L) = C * (p2r - p2wf)^2n * (Fr * T * Z)^2 * (eS - 1) / H</p> Signup and view all the answers

    What is the formula for gas flow rate from a horizontal well in a pseudosteady-state flow?

    <p>Qg = (kh * (pr - p2wf)) / (1422 * T * µg * Z_avg * ln(reh / rw) - 0.75 + s)</p> Signup and view all the answers

    What is the formula for gas formation volume factor Bg?

    <p>Bg = (psc * ZT) / (5.616 * Tsc * p)</p> Signup and view all the answers

    What does the term 'a1 Qg' represent in Equation 3.1.29?

    <p>The pressure drop due to laminar flow</p> Signup and view all the answers

    What does the term 'b1 Qg2' account for in Equation 3.1.29?

    <p>The additional pressure drop due to turbulent flow condition</p> Signup and view all the answers

    What can be determined from the linear plot of Equation 3.1.32?

    <p>Gas flow rate</p> Signup and view all the answers

    In the pseudopressure equation ψ r − ψwf = a2 Qg + b2 Qg2, the term a2 Qg represents the pseudopressure drop due to __________ flow.

    <p>laminar</p> Signup and view all the answers

    Match the gas flow equations with their respective forms:

    <p>Pressure-squared equation = pr − p2wf = aQg + bQg2 Pressure equation = = a1 + b1 Qg Pseudopressure equation = ψ r − ψwf = a2 Qg + b2 Qg2</p> Signup and view all the answers

    Study Notes

    Evaluating Reservoir Behavior and Gas Well Performance

    • The objective of this chapter is to document methods for evaluating and predicting vertical and horizontal gas well performance and conventional and non-conventional gas field performance.
    • The flow capacity of a gas well is determined by the relationship between the inflow gas rate and the sand face pressure or flowing bottom-hole pressure.

    Gas Flow under Laminar (Viscous) Flowing Conditions

    • The gas flow rate (Qg) can be calculated using Equation 3.1.1, which is a function of permeability (k), thickness (h), average reservoir real-gas pseudo-pressure (ψr), bottom-hole flowing pressure (ψwf), and temperature (T).
    • The productivity index (J) is defined as the production rate per unit pressure drop.
    • The absolute open flow potential (AOF) is the maximum gas flow rate (Qg)max, which can be calculated by setting ψwf = 0.

    Pressure Approximation Method

    • The pressure approximation method is used when both pwf and pr are higher than 3000 psi.
    • The pressure function (2p/µZ) is nearly constant in this region, and the pressure term (1/µgBg) can be treated as a constant and removed outside the integral.
    • The gas flow rate (Qg) can be calculated using Equation 3.1.9, which is a function of permeability (k), average reservoir pressure (pr), and bottom-hole flowing pressure (pwf).

    Intermediate-Pressure Region

    • The intermediate-pressure region is between 2000 and 3000 psi, where the pressure function shows distinct curvature.
    • The pseudopressure gas pressure approach (Equation 3.1.1) should be used to calculate the gas flow rate in this region.

    Low-Pressure Region

    • The low-pressure region is below 2000 psi, where the pressure functions (2p/µZ) and (1/µgBg) exhibit a linear relationship with pressure.
    • The gas flow rate (Qg) can be calculated using Equation 3.1.11, which is a function of permeability (k), average reservoir pressure (pr), and bottom-hole flowing pressure (pwf).

    Pressure-Squared Approximation Method

    • The pressure-squared approximation method is used when both pr and pwf are lower than 2000 psi.
    • The gas flow rate (Qg) can be calculated using Equation 3.1.12, which is a function of permeability (k), average reservoir pressure (pr), and bottom-hole flowing pressure (pwf).

    Example Calculations

    • Example 3.1 demonstrates the calculation of gas flow rate (Qg) using the pressure approximation method and the pseudopressure approach.
    • The results show that the pressure approximation method can be used to estimate the gas flow rate with an absolute percentage error of 2.25%.### Gas Flow Equations
    • Three forms of pseudosteady-state equations:
      • Pressure-squared approximation form: Qg = kh (pr^2 - pwf^2) / (1422T µg Z avg ln re /rw - 0.75 + s + DQg)
      • Pressure approximation form: Qg = 7.08 x 10^(-6) kh (pr - pwf) / (µg Bg avg T ln re /rw - 0.75 + s + DQg)
      • Real-gas pseudopressure form: Qg = kh (ψr - ψwf) / (1422T ln re /rw - 0.75 + s + DQg)

    Simplified Treatment Approach

    • Postulated by Rawlins and Schellhard (1936)
    • Relationship between gas flow rate and pressure can be expressed in the pressure-squared form
    • Essentially, a quadratic relationship in Qg and (pr - pwf)

    Laminar-Inertial-Turbulent (LIT) Approach

    • Total pressure drop is the sum of pressure drops due to Darcy's (laminar) flow and turbulent flow
    • Three forms of the semisteady-state equation can be rearranged in quadratic forms for the purpose of separating the "laminar" and "inertial-turbulent" terms

    Pressure-Squared Quadratic Form

    • pr - pwf = aQg + bQg^2
    • a and b are laminar and inertial-turbulent flow coefficients, respectively
    • Can be used to determine the gas flow rate at any pwf

    Pressure Quadratic Form

    • pr - pwf = a1 Qg + b1 Qg^2
    • a1 and b1 are laminar and inertial-turbulent flow coefficients, respectively
    • Can be used to determine the gas flow rate at any pwf

    Real-Gas Pseudopressure Form

    • ψr - ψwf = a2 Qg + b2 Qg^2
    • a2 and b2 are laminar and inertial-turbulent flow coefficients, respectively
    • Can be used to determine the gas flow rate at any pwf

    Back-Pressure Test

    • A method used to determine the flow potential and establish the inflow performance relationships of a gas well
    • Three types of deliverability tests: conventional deliverability (back-pressure) test, isochronal test, and modified isochronal test
    • Data from deliverability tests can be used to construct the linear relationship between pr - pwf and Qg### Testing Gas Wells
    • The conventional deliverability test, also known as the back-pressure test, is used to test gas wells.
    • The test involves gauging the well's ability to flow against particular pipeline back-pressures greater than atmospheric pressure.

    Steps for Conducting the Back-Pressure Test

    • Step 1: Shut in the gas well for a sufficient time to allow the formation pressure to equalize at the volumetric average pressure pr.
    • Step 2: Place the well on production at a constant flow rate Qg1 for a sufficient time to allow the bottom-hole flowing pressure to stabilize at pwf1.
    • Step 3: Repeat step 2 for several rates and record the stabilized bottom-hole flow pressure at each corresponding flow rate.

    Pseudopressure Equation

    • The pseudopressure equation is given by: ψr - ψwf = a2Qg + b2Qg2
    • The equation can be written in a more simplified form as: ψr - ψwf = a2Qg + b2Qg2
    • The term a2Qg represents the pseudopressure drop due to laminar flow, while the term b2Qg2 accounts for the pseudopressure drop due to inertial-turbulent flow effects.

    Calculating the Stabilization Time

    • The stabilization time (pseudosteady-state time) is the time when the rate of change of pressure with respect to time is constant through the reservoir at a constant flow rate.
    • The stabilization time can be estimated using the equation: tpss = 15.8φµgi cti A / k

    Application of the Back-Pressure Test Data

    • The back-pressure test data can be used to determine the coefficients of any of the empirical flow equations.
    • The recorded data can be analyzed in several graphical forms to determine the coefficients of the selected flow equation.

    Flow Equations

    • Back-pressure equation: log(Qg) = log(C) + nlog(pr - p2wf)
    • Pressure-squared equation: pr - p2wf = aQg + bQg2
    • Pressure equation: pr - pwf = a1Qg + b1Qg2
    • Pseudopressure equation: ψr - ψwf = a2Qg + b2Qg2

    Example of Applying the Back-Pressure Test Data

    • A gas well was tested using a three-point conventional deliverability test with an initial average reservoir pressure of 1952 psi.
    • The recorded data was used to generate the IPR (inflow performance relationship) data using the back-pressure equation, pressure-squared equation, pressure equation, and pseudopressure equation.
    • The results were compared to determine the best method for calculating the gas flow rates.

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    Description

    This chapter covers the methods used to evaluate and predict gas well performance, including vertical and horizontal gas wells, and conventional and non-conventional gas fields.

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