Statistical data correlations in tight gas reservoirs

Tight gas reservoirs generate many difficult problems for geologists, engineers, and managers. Cumulative gas recovery (thus income) per well is limited because of low gas flow rates and low recovery efficiencies when compared to most high permeability wells. To make a marginal well into a commercial well, the engineer must increase the recovery efficiency by using optimal completion techniques and decrease the costs required to drill, complete, stimulate, and operate a tight gas well.

To minimize the costs of drilling and completion, many managers want to reduce the amount of money spent to log wells and totally eliminate money spent on extras such as well testing. However, in these low-permeability layered systems, the engineers and geologists often need more data than is required to analyze high permeability reservoirs. To balance the need for more data with the need to minimize costs, the logical solution is to spend money gathering accurate data on a few wells, then use correlations developed from that data to evaluate the wells that will be drilled and completed thereafter. Once acceptable correlations are developed for specific reservoirs in specific geographic areas, the correlations can be applied to all wells in the area. By using these "calibrated" correlations, accurate datasets can be developed for new wells at a minimal cost.

For example, if one spends $100,000 to cut cores, analyze the cores, and generate core-log correlations, and these correlations can be used to plan and conduct an infill drilling plan for 100 wells, the cost per well to generate accurate datasets is only $1,000. Normally, the most critical data items are formation permeability and in-situ stress. If accurate correlations, in which logs can be used to estimate permeability and in-situ stress, can be developed, the well completion and stimulation plans can be optimized.

Correlating core and log data

All cores from tight gas reservoirs must be properly handled and tested to obtain the accurate data required for developing useful correlations between log and core data. Information concerning how to cut and test core plug samples was discussed earlier in the chapter. Also, information concerning how to develop correlations for determining permeability from logs has been previously discussed. One can use Eqs. 1 through 7 (Same as Eqs. 1 though 7 in Permeability estimation in tight gas reservoirs) to generate accurate correlations between log data and formation permeability derived from core or well tests. These correlations can then be used to determine values of formation permeability using log data from wells that have not been cored or well tested.

....................(1)

....................(2)

....................(3)

....................(4)

....................(5)

....................(6)

where

e1	=	5.87–6.89,
e2	=	0.2–0.3,
e3	=	1.18–2.54,
e4	=	1.08–1.65,
and
U	=	correlation factor.

....................(7)

To generate valid correlations in most layered, tight gas reservoirs, the core and log data normally must be subdivided by lithology, rock type or flow units prior to finalizing the correlations. If one tries to correlate the core and log data for the entire reservoir, the correlation coefficient is usually not very high. For example, consider the dataset in Fig. 1 that contains 1,078 data points from a large Travis Peak dataset. The correlation coefficient between core permeability at net overburden pressure is only 0.692. However, if the cores containing visible natural or coring induced fractures are removed and only cores from clean, fluvial-deltaic channel sands are correlated, the correlation coefficient between permeability and porosity increases to 0.865, as illustrated in Fig. 2.

• 

  Fig. 1—Relation of Klinkenberg corrected gas permeability measured at NOB pressure to porosity at NOB pressure, all data.

• 

  Fig. 2—Relation of Klinkenberg corrected gas permeability measured at NOB pressure to porosity at NOB Pressure, fluvial/deltaic channel sands only, invalid data excluded. (Same as Fig. 3 in Core analyses in tight gas reservoirs)

Some have used flow units to segregate core and log data to develop better correlations. Amaefule et al. used the same Travis Peak data set as illustrated in Fig. 1 and analyzed the data using a flow unit concept. In their paper, Amaefule et al. defined a rock quality index (RQI) and a flow zone indicator (FZI). Using these two parameter groups, they developed a scheme to correlate formation permeability with effective porosity as a function of the FZI.

Original gas-in-place (OGIP) distribution

As suggested by the Resource Triangle, Fig. 3, the distribution of any natural resource is skewed in nature. For natural gas, the distribution is log-normal. As the value of reservoir permeability decreases, the value of OGIP increases exponentially. There is obviously a difference between OGIP and reserves. The OGIP represents all the gas in the rocks that comprise the reservoir layers. Reserves represent the amount of gas that can be produced economically. The value of reserves is a function of gas prices, costs, and the level of technology used to develop the resource.

• 

  Fig. 3—Resource triangle for gas. (Same as Fig. 1 in Tight gas reservoirs)

Often the amount of OGIP is computed by using porosity, water saturation, and shale volume cutoffs. In high permeability reservoirs, using such cutoffs may be appropriate, especially if the reservoir produces water above a certain water saturation cutoff and the OGIP estimates are not very sensitive to the cutoff values chosen. However, in most tight gas reservoirs, only dry gas and small volumes of water that condense in the wellbore are produced. Very seldom are large volumes of water produced in tight gas reservoirs.

A good rule of thumb for selecting cutoffs to determine net pay to determine gas-in-place for tight gas reservoirs is to use 3% gas porosity. The first step is to compute the value of porosity after making clay correlations with Eqs. 8 through 10 (Same as Eqs. 5 through 7 in Log analyses in tight gas reservoirs). The porosity can then be used to compute the water saturation, normally using the dual-water saturation model. One can compute gas porosity and include all zones with gas porosity values of 3% or greater in the net pay count. In the tight gas sands research project sponsored by the Gas Research Inst., special core analyses on numerous core samples indicated that gas could flow at 3% gas saturation in typical tight gas cores.

....................(8)

....................(9)

....................(10)

Permeability distribution

Permeability within a gas reservoir, field, or basin is distributed log-normally. To illustrate this concept, four data sets obtained from public records are presented for discussion. The data in Fig. 4 are from the Travis Peak Formation in east Texas, the Cotton Valley Formation in east Texas, the Wilcox Lobo Formation in south Texas, and the Cleveland Formation in northwest Texas. These reservoirs are in different basins but, remarkably, have very similar log-normal permeability distributions. More information concerning the permeability distribution for these four data sets is presented in Table 1. The median permeability for all four formations ranges from 0.028 to 0.085 md, while the arithmetic mean values of permeability range from 0.179 to 7.378 md.

• 

  Fig. 4—Comparison of permeability distribution from four tight gas formations in Texas.

• 

  Table 1—Arithmetic Means and Medians for Field Cases

When the permeability is distributed log-normally, the median value rather than the arithmetic mean should be used to determine the average value of permeability for the formation. Statistical distributions of porosity, permeability and net pay can be used to determine the expected gas recovery from a tight gas reservoir. The statistical distribution of permeability, porosity and net gas pay for the Travis Peak formation from one study are illustrated in Figs. 5, 6, and 7, respectively.

• 

  Fig. 5—Permeability distribution in the Travis Peak formation.

• 

  Fig. 6—Porosity distribution in the Travis Peak formation.

• 

  Fig. 7—Net pay distribution in the Travis Peak formation.

In Fig. 5, the permeability distribution is clearly log-normal. There is a positive correlation between porosity and permeability, as illustrated in Fig. 6. As porosity increases, the permeability increases. There is a negative correlation between net gas pay and permeability, as illustrated in Fig. 7. As the value of permeability increases, the net thickness of the layer decreases. This correlation leads to a log-normal distribution of OGIP. The layers of rock that are the most permeable are thin, compared to the layers of rock that have low permeability. If one uses the data in Figs. 5 through 7 in a reservoir simulator, along with other appropriate data for the Travis Peak formation (see Table 2), one can determine the gas recovery for the average well in the Travis Peak formation. The results from the calculations are shown in Table 3.

• 

  Table 2—Travis Peak Reservoir Data

• 

  Table 3—Computation of Average Gas Recovery

• 

  Table 4—Distribution of Net Pay and Porosity for Travis Peak Formation

First, one must recognize that the gas recovery from a well completed in a tight gas reservoir is a function of the average drainage area and the hydraulic fracture length, as well as the values of permeability, porosity, net gas pay, reservoir pressure, and other reservoir parameters. In Table 4, the column labeled "Actual Average Recovery" was computed for each case using simulation runs representing 1,000 wells drilled for each well space and fracture length using the data in Tables 2 and 4. The results show that the average recovery varies from 1.97 Bcf for an unfractured well draining 160 acres to 7.95 Bcf for a well containing a 500-foot-long fracture half-length draining 640 acres. The column labeled "Recovery for Median" illustrates the values of gas recovery that one computes using the median values of all parameters, including permeability, porosity, and net gas pay. The column labeled "Recovery for Arithmetic Mean" illustrates the gas recovery one computes using the arithmetic mean values for permeability, porosity, and net gas pay. The data clearly show that the median values best represent are "average" values when the parameters are log-normally distributed.

Reserves distribution

Even though the permeability distribution and the OGIP distribution are log-normally distributed, the distribution of reserves may or may not be log normally-distributed because of the changing recovery efficiency vs. permeability and the number of wells drilled in each permeability range. Reserves represent the volume of gas that can be produced economically using existing technology. Reserves are a function of the:

• Permeability
• Net gas pay
• Porosity
• Drainage area
• Initial reservoir pressure
• Flowing bottomhole pressure
• Gas prices
• Operating costs
• Effective fracture half-length
• Effective fracture conductivity
• Other economic factors such as taxation rates and overhead charges

The data in Figs. 8, 9, and 10 illustrate how the abandonment pressure and recovery efficiency varies as functions of permeability, net gas pay, and fracture half-length for a specific set of Vicksburg data. At the time the graphs were generated, an economic limit of 250 Mcf/D was being used in the Vicksburg because of low gas prices. If these same cases were computed with a lower value of economic limit, the abandonment pressure would decrease, and the recovery efficiency would increase. These examples illustrate how one should use reservoir engineering to evaluate the effects of drainage area, hydraulic fracture properties, and economic parameters to determine values of recovery efficiency and, thus, the distribution of reserves.

• 

  Fig. 8—Tight reservoir performance.

• 

  Fig. 9—Tight reservoir efficiency.

• 

  Fig. 10—Influence of fracture.

Fig. 8 shows that as the permeability increases and the net gas pay increases, the abandonment pressure in the reservoir, when the economic limit is reached, decreases. The data in Fig. 9 illustrate the recovery efficiencies for the same cases as shown in Fig. 8. For thick, high permeability reservoirs, the recovery efficiency can be 80% or more of the OGIP. However, as the value of permeability decreases below a value of 0.1 md, the recovery efficiency decreases substantially. For the case in which the net gas pay was only 25 ft and the permeability was between 0.02 and 0.1 md, the recovery efficiency varied from 0 to 45% of the OGIP. The data in Figs. 8 and 9 are for semisteady-state radial flow. Fig. 10 illustrates the effect of a hydraulic fracture on the recovery efficiency for the 25 feet of net gas pay case. It is clear that a hydraulic fracture that extends out to 40% of the drainage area substantially increases the recovery of gas in a tight gas reservoir.

In-situ stress correlations

It is important to generate correlations between logs, cores, and measured values of in-situ stress. The values of in-situ stress are very important to the engineer planning the well completion and stimulation treatment. The engineer can usually correlate values of in-situ stress measured from pump-in tests with data measured using logs and cores. A common equation used to correlate lithology (using Poisson’s ratio) with the in-situ stress is given in Eq. 11.

....................(11)

where

σmin	=	the minimum horizontal stress (in-situ stress),
ν	=	Poisson’ s ratio,
σ1	=	overburden stress,
α	=	Biot’ s constant,
σp	=	reservoir fluid pressure (pore pressure),
and
σext	=	tectonic stress.

To use Eq. 11, one must determine the values of Poisson’s ratio using log data. Poisson’s ratio can be correlated with sonic log data or estimated using the lithology of a formation layer. Table 5 illustrates typical ranges for Poisson’s ratio as a function of the lithology. Thus, it is possible to estimate values of Poisson’s ratio from correlations with log data, then use those estimates to compute estimates of in-situ stress.

• 

  Table 5—Typical Ranges of Poisson’s Ratio for Various Types of Rocks

Another correlation that usually works for tight gas sands is one between the GR log and values of in-situ stress. Gongora used data from the Travis Peak formation collected during the GRI tight-gas-sands research program. Data from two wells, SFE No. 1 and SFE No. 2, are shown in Figs. 7.24 and 7.25. SFE No. 1 was an infill well drilled into the Travis Peak formation. There were several zones that were partially depleted and many other zones that were at original pressure. Thus in Fig. 11, the zones were correlated using both the GR log reading and the reservoir pressure. SFE No. 2 was drilled in a location where little drainage had occurred. As such, the correlation between in-situ stress and the GR log was accomplished using a single correlation, as illustrated in Fig. 12.

• 

  Fig. 11—Correlation of in-situ stress value with average GR reading for two different reservoir pressures for SFE No. 1.

• 

  Fig. 12— Correlation of in-situ stress value with average GR reading for two different reservoir pressures for SFE No. 2.

The correlations included in this chapter were generated using log, core, and well-test data for the Travis Peak formation; hence, one cannot use these correlations for other formations in other basins around the world. These correlations are included in this chapter to illustrate how values of permeability and in-situ stress can be correlated with log and core data. The methods explained in this chapter can be used to generate other correlations in other formations in other basins.

Once specific correlations have been developed and verified, they can be used to evaluate layered, tight gas reservoirs to make basic decisions, such as whether the casing should be set. Once the casing is set, the correlations can be used to generate the data required to design the completion and the stimulation treatment for the reservoir layers that are determined to be commercially viable.

Nomenclature

A	=	surface area
D	=	diameter (for grain size) or constant for computing s′
h	=	net pay, ft
I	=	index
k	=	permeability, md
q	=	flow rate, Mcf/D
r	=	radius, ft
R	=	resistivity, ohm-m
s	=	skin
s′	=	effective skin factor
ρ	=	density, g/mL
Δt	=	travel time, μsec/ft
t	=	time, hours or days
T	=	temperature, °F
U	=	correlation factor
V	=	volume, fraction
φ	=	porosity, fraction
μ	=	gas viscosity, cp
ψ	=	pseudopressure

Subscripts

b	=	bulk
d	=	drainage
e	=	at the extremity of the reservoir
f	=	fluid or fracture
g	=	grain or gas (for flow rate)
i	=	investigation (for radius)
ild	=	induction log deep
ma	=	matrix
N	=	neutron log
NC	=	neutron corrected for shale
rh	=	relative to hydrocarbon flow
sfl	=	spherically focused log
SC	=	sonic corrected
SH	=	shale
t	=	true (for conductivity); total (for compressibility)
w	=	wellbore (for radius); water (for saturation)
wf	=	well flowing; free water (for conductivity)
wir	=	irreducible water

Superscripts

e

=

exponent

Noteworthy papers in OnePetro

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See also

Tight gas reservoirs

Modeling tight gas reservoirs

Permeability estimation in tight gas reservoirs

Log analyses in tight gas reservoirs

Core analyses in tight gas reservoirs

Reserves estimation in tight gas reservoirs

Hydraulic fracturing in tight gas reservoirs

Tight gas drilling and completion

PEH:Tight_Gas_Reservoirs