Well Test Analysis

Schematic of well-test:

The basis of well-test analysis is understanding of single-phase-flow in porous media concepts.

Basic Concept

The pressure-transient response is divided into 3 regions:

• Early-time region (ETR): the wellbore-storage period (determined from Horner plot of shut-in well test, see Chapter 7.5)
• Middle-time region (MTR): where well behaves infinite-acting (determined from semilog plot, see Chapter 7.2)
• Late-time region (LTR): where well behaves finite-acting, reservoir boundary effects dominate (see Chapter 7.2)

The purposes of well-test analysis are to determine the following by analyzing the pressure-transient response.

• Permeability k or permeability-thickness factor kh
• Skin factor s. Skin factor is the measure of how damaged the well is.
• Pressure drop delta_ps due to skin damage.
• Reservoir size re and reservoir pore volume vp (from constant-rate drawdown test and multirate buildup test).
• Reservoir initial pressure pi (from shut-in well test)

Types of Well-Test

• Constant-Rate Drawdown Test: pressure declines as rate is constant
• Multirate Drawdown Test: pressure declines as rate changes
• Constant-Pressure Flow Test: rate changes
• Constant-Rate Buildup Test (Infinite-acting analysis): flow is shut-in at time t, q=0, pressure builds up (opposite of Constant-Rate Drawdown Test), flow in infinite-acting condition
• Multirate Buildup Test: shut-in is preceded by multirate flow
• Constant-Rate Buildup Test (Finite-acting analysis): flow is shut-in at time t, q=0, pressure builds up (opposite of Constant-Rate Drawdown Test), flow in finite-acting condition

Analysis

• Constant-Rate Drawdown Test: Semilog drawdown plot of pressure vs time to find slope m and intercept c of MTR region and Normal drawdown plot of pressure vs time to find slope m*. Slope m is used to calculate k, intercept c to calculate s, and slope m* to calculate reservoir size

• Multirate Drawdown Test: Normal drawdown plot of (pi-pwf)/qn vs Fp to find slope m and intercept c. m is used to calculate k and c to calculate s.

• Constant-Pressure Flow Test: Normal plot of 1/q vs log(time) to find m and c. m is used to calculate k and c to calculate s.

• Constant-Rate Buildup Test (Infinite-acting analysis): Horner plot of shut-in pressure pws vs log((tp+delta_t)/delta_t) to identify wellbore-storage period or the ETR, find m and c. m is used to calculate k and c to calculate s. c also equals to reservoir initial pressure pi.

• Multirate Buildup Test: Normal plot of pws vs sigma(log((t - t_j-1)/(t - t_j) to find m and c. m is used to calculate k and c to calculate s. c also equals to reservoir initial pressure pi.

• Constant-Rate Buildup Test (Finite-acting analysis): Two methods (1) Nonlinear regression to fit with equation: pws = c + m * log(t) + m_star * t, find m, m_star, and c simultaneously, (2) Slider's plot of pws - m_star * delta_t vs log(delta_t) if m_star is known. m_star is the pressure decline rate. m is used to calculate k and m_star to calculate reservoir pore volume and reservoir size. s cannot be determined.

Notes

• It is important to check again the units must be in oilfield units. Convert to oilfield unit if units in SI.
• Learn the equations of k and s for different well-test types. Equations can be different from one type to another. See functions perm_welltest (see: welltest.py) and skinfactor.py.
• Check the data 1: sometimes data is in rate-Bo qB, not in rate q. In this case, you should check the inputs for function perm_welltest.
• Check the data 2: sometimes pressure data in pi-pwf, not in pwf.
• Check the data 3: in the case if reservoir thickness h is not known, calculate kh not k.

Useful reference