Pore Pressure and Methods of Analysis Section 4 PPFG Modeling Process Parts 1 and 2

Section 4.???????The Pore Pressure and Fracture Gradient Modeling Process

?Part 1.???Compaction Model Characteristics

???????????????Resistivity and sonic travel time models detect changes in the trend of porosity of impermeable formation members to calculate changes to the pore pressure gradient. Where available, the data through the normally pressured section of the well is used to establish the normal compaction trend. When the normally pressured section of the well is not logged, the normal compaction trend is established by assessment of a calculated pore pressure with the data collected and observations made while the well was drilled.

The d-Exponent model is not a compaction model because it does not detect changes in the porosity trend, whereas compaction models do. The d-Exponent model uses the relationship between the hardness of the rock and the difference between annulus pressure and pore pressure to calculate a parameter used to calculate a pore pressure gradient.

???????????????After determining the model reference height for calculations there are seven basic steps to constructing a PPFG model:

Calculate OBG

Select shale intervals

Define normal compaction trend

Calculate pore pressure gradient

Calculate effective stress ratio

Calculate fracture gradient

Calculate permeable formation hydraulic heads

Part 2.???Calculating the Overburden Gradient

???????????????Because equivalent depth models base all calculations on a relationship with the overburden gradient, the Overburden Gradient is the core element of the pore pressure model. If the overburden gradient is not representative of the actual vertical stress, all calculations of pore pressure and fracture gradient will be erroneous. Thus, a representative overburden gradient is critical to the applicability and confidence of the pore pressure model.

The calculated overburden stress at any depth is a function of the combined effect of the force of gravity on the total mass above and tectonic stresses. In the Oil and Gas Industry, the overburden stress has never been measured. The stress has been measured in other industries such as mining. They utilize strain gauges to measure the actual stress in the formation. Placing a strain gauge in an open borehole has not been practical, thus the overburden stress has never been measured in a well.

In pore pressure modelling, the overburden stress at any depth is assumed to consist of the combined effect of the force of gravity on the total mass above that depth without including the effect of tectonic stresses.

The calculated overburden stress at any depth is the sum of the force applied by the total mass above that particular depth. As depth increases, the density of the formation is not constant. The overburden stress is calculated by dividing the strata into a continuous series of discrete elements from the surface or mud line to a specified depth, then adding incrementally the force due to gravity of each element, beginning at the model reference height. At any specified depth, the calculated overburden stress will be the force due to gravity applied by the total mass above that depth.

The calculated overburden gradient is equal to the equivalent density of a fluid of a column height equal to the distance from the specified depth to the reference height (such as a drill floor or mean sea level) necessary to generate a force equal to the calculated overburden stress.

The densities used to calculate the overburden stress are from density logs, density transforms using sonic travel time and interval velocity, and an assumed shallow density profile. Very seldom is there density log measurements for the shallowest portion of the subsurface. The shallow density profile begins at the surface for onshore locations, and at the mud line for offshore locations. Determining the shallow density for a surface location is relatively easy. Go to the location, collect a sample of the surface strata, and measure the density. For offshore locations the mud line density is almost always not a data element collected when surface coring is conducted, and is not known.

Most often, a mud line density and shallow density profile for the offshore location must be assumed.

Part 2a.???Shallow Density Profile Assumption

The most commonly applied method for assuming shallow density is the Miller method. The Miller method assumes a non-linear increase of density from the surface or mud line to a depth where normal compaction begins and a more or less linear increase of density with depth as compaction increases.

The default Miller options are near sediment source, and distant from sediment source. The near sediment source assumes larger average grain size sandier deposition, and distant from sediment source assumes a smaller average grain size clay fraction being deposited. The sediment source may be the mouth of a river, or the termination of a submarine canyon, or any other location where the sediment being deposited is transported from immediately prior to deposition.

The Miller shallow density algorithm assumes the density of the clay at the mud line for distant from sediment source is 1.435 g/cc, and for near the sediment source is 1.516 g/cc.

Figure 24.???????????Example Miller Shallow Density Profiles and Calculated Overburden Gradients

? The choice of shallow density options affects the shallowest portion of the overburden gradient. The effect diminishes with increased depth. Also, this example is at a water depth of approximately 6,700 feet. In shallower water, the difference in calculated overburden gradients would be greater.

At the two-dimensional boundary of the water and seafloor the density of clay is relatively constant over a large area. Immediately below this two-dimensional surface a location will have a characteristic clay density called the “mud line density”. The mud line density of clay varies with rate of deposition. The more rapid the deposition, the less time the clay is compacted for a specific depth. High rates of deposition will have lower densities in the shallowest sections below the mud line than lower rates of deposition.

???????????????Local rate of deposition is affected by shallow geologic structures. Time, in addition to the overburden stress, is a factor influencing the degree of compaction. At the apex of a structure, the depositional sequence being deposited today will be thinner than away from the crest of the structure. For a given depth, the deposits at the crest of the structure will have been subjected to compaction for a longer period of time than away from the crest of the structure. Therefore, mud line density of clay is greater at the apex of the structure than away from the crest of the structure.

Figure 25.???????????Variation of Mud Line Density Related to Shallow Geologic Structure

???????????????The mud line density of the Miller shallow density profile is adjusted to conform to the rate of deposition inferred by the shallow geologic structure. Mud line density usually varies between 1.62 and 1.87 g/cc, depending on the depositional environment of the location and the position on the local geologic structure. However, where deposition is most rapid and consists of only clay fraction particle size, mud line density can be as low as 1.44 g/cc. The pore pressure analyst must determine the depositional environment of the location and the most likely mud line density.

???????????????The choice of mud line density has a more significant effect on the calculated overburden gradient in shallower water than deeper water. In the examples below, the mud line density was varied from 1.51 to 1.87 g/cc. With a water depth of 6,743 feet, the difference between overburden gradient calculations at 2,500 feet below the mud line was 0.139 ppg. When the water depth was changed to 4,132 feet, the difference between overburden gradient calculations was 0.202 ppg.

???????????????In deep water exploration, the surface casing shoe is normally set at approximately 2,500 feet below the mud line. A difference of overburden gradient of 0.139 is not significant in the practical drilling environment. However, when the difference becomes 0.2 ppg, it becomes significant when analyzing problems encountered during drilling or running casing.

???????????????Most commonly, a mud line density measurement is not available. The analyst must use his best judgment, considering the complete geologic system, when choosing a shallow density option.

Figure 26.???????????Water Depth 6,743 feet: Mud Line Density Variations Effect on Overburden Gradient Calculation

Figure 27.???????????Water Depth 4,132 feet: Mud Line Density Variations Effect on Overburden Gradient Calculation

Part 2b.???Deriving Density Below the Shallow Density Profile

???????????????Below the shallow un-compacted zone the densities are taken from offset well density logs, or calculated using sonic log data or interval velocity with a Gardner transform. If a partial density log is available from an offset well, the Gardner transform must be calibrated to match the measured density.

???????????????The formula for the Gardner Δt density conversion is:

RHOB = c (106/?t)e

???????????????????????where:

????????????????????????t = sonic transit time, μsec/ft, μsec/m

???????????????c = empirical constant (default 0.23 when ?t is expressed in μs/ft)

???????????????e = empirical constant (default 0.25 when ?t is expressed in μs/ft)

???????????????The Gardner calculated density must agree with accepted industry shallow density and deeper measured density. If there are no measured density data to calibrate with, the uncertainty of the overburden calculation becomes significant.

Figure 28.???????????Gardner Density Transform Calibration

???????????????The composite density data set used to calculate the overburden consists of the Miller shallow density estimate, the Gardner calculated density from sonic data, and the measured wireline density.

Figure 29.???????????Overburden Gradient Calculated Using Composite Density Data Set

Part 2c.???Effect of Water Depth on Calculated Overburden Gradient

???????????????The overburden gradient is calculated using the total mass above the depth of the calculation. For different water depths, the percentage of density attributed to water varies at a specific total depth will be different for each different water depth. Water has a density of 1.0 to 1.05 g/cc, and rock densities normally range from 2.2 to 2.5 g/cc below the depth of shallow density. Given the same rock density below the mud line, the total overburden stress at 30,000 feet and a water depth of 3,000 feet will be greater than the total overburden stress at 30,000 feet true vertical depth and a water depth of 9,000 feet.

???????????????It is not appropriate to generate a general overburden gradient and apply it to an area of varying water depths. The resulting pore pressure models will not be representative of the environment.

???????????????The graph in Figure 30 shows the different overburden gradient calculations below the mud line using the same density profile with different water depths.

Figure 30.???????????Effect of Various Water Depths on the Calculated Overburden Gradient