Calculate d-Exponent to Predict Pore Pressure Trends

This Excel spreadsheet calculates the d-exponent, a parameter used by drilling engineers to investigate ppore pressure trends when drilling into over-pressurized zones.

Normally, formation density increases with the drilling depth. But if the formation contains sand below the surface, then the drilling rate may increases with drilling depth. The d-exponent is used in several calculations to investigate these effects.

Jorden and Shirley (1966) suggested the d-exponent method, basing it on the Bingham equation. A later adjustment to the equation by Rehm and Mcledon (1971) included the effect of mud weight

The modified equation to calculate the d-exponent is

where

• c is the shale compactibility coefficient
• ρ_n is the mud weight equivalent (lb gal^-1)
• ρ_m is the mud weight used (lb gal^-1)
• D is drill bit diameter (in)
• W is the weight on the bit (x 1000 lb)
• R is the penetration rate (rpm)
• N is the rotary speed.

The d-exponent is often used in Eaton's equation

where

• P is the formation pore pressure (psi)
• P_ob is the overburden pressure (ft)
• Z is the vertical depth (ft)
• d is the d exponent
• d_n is the normal compaction trend of the d exponent
• P_p is the formation pore pressure (psi)
• P_p/Z is the normal pore pressure gradient (psi ft^-1)

Download Excel Spreadsheet to Calculate D Exponent

Inflow Performance Relationship of Vertical & Slanted Solution Gas-Drive Wells

This Excel spreadsheet calculates the Inflow Performance Relationship, or IPR, for vertical and slanted solution-gas drive wells.

The IPR of a well determines the relationship between its flowing bottom pressure, and the well production rate (or deliverability). IPR also helps engineers investigate the economics of a well, and is critical in optimizing the well, artificial lift design and determining the nature of the surface equipment.

For single-phase fluids, the IPR relationship is linear. However, when two-phase liquid and gas below its bubble-point pressure are produced, the relationship is non-linear.

Several researchers have studied this process, most notably Vogal (1968) and Cheng (1990). Cheng's semi-empirical correlation is applied to slanted wells, while Vogal's work applies to vertical wells.

Vogel and Cheng's equations are

where

• q₀ is the flow rate in bbl/day
• q_0,max is the oil flow rate at a flowing bottom hole pressure of 0 in bbl/day
• p_wf is the flowing bottom hole pressure in psi
• p_r is the reservoir pressure in psi
• a₀, a₁ and a₂ are empirical parameters that vary with the slant angle. In the spreadsheet these parameters are listed again several values of the slant angle. Intermediate values are linearly interpolated.

Download Excel Spreadsheet to Calculate Inflow Performance Relationship for Solution-Drive Gas Well

Fetkovich Decline Curve Analysis

This Excel spreadsheet plots Fetkovich decline curves for gas wells. Decline curve analysis is an empirical procedure that predicts the decline in production rates of gas and oil wells. 

Fetkovich (1968) improved on earlier work by Arps in predicting the declining production rate of oil and gas wells. He suggested that experimental production rate data could be overlaid on a graph and matched to a series of type curves. The production rate is then extrapolated into the future with the assistance of the curves.

The Excel spreadsheet reproduces the plot given in Figure 8 of the following reference.

Fetkovich, M.J., "Decline Curve Analysis Using Type Curves", Journal of Petroleum Technology (June 1980) 1065-77.

The decline curve rate-time equations are given below.

where

• n is a factor that governs the shape of the back pressure curve
• q_Dd is the decline curve dimensionless production rate
• t_Dd is the decline curve dimensionless time

Download Excel Spreadsheet to Plot Fetkovich Decline Curves for Gas Reservoirs

Water Breakthrough Time in a Vertical Oil Well

Consider an oil reservoir with an underlying water zone. An oil well that is producing from this reservoir will experience the phenomenon of water breakthrough if the well produces above its critical rate. Since economic considerations often demand high flowrates, this can be a real risk.

This Excel spreadsheet uses the Sobocinski-Cornelius method to calculate the water breakthrough time.  This method was published in 1965, and was derivied from laboratory tests. It uses these equations.

where

• B_o is the oil formation volume factor
• μ_o is the oil viscosity (cp)
• μ_w is the water viscosity (cp)
• φ is the porosity
• h is the oil column thickness (ft)
• h_p is the perforated interval (ft)
• Q_o is the oil production rate (STB day^-1)
• α is 0.5 if M <=1, or 0.6 otherwise
• M is the water-oil mobility ratio
• t_BT is the time to breakthrough
• t_D is the dimensionless time (Sobocinski-Cornelius method)
• Z is the dimensionless cone height
• ρ_w is the water viscosity (lb ft^-3)
• ρ_o is the oil density (lb ft^-3)

Download Excel Spreadsheet to Calculate Water Breakthrough Time with Sobocinski-Cornelius method