Stress-dependent permeability in unconsolidated sand reservoirs
Avoiding collapsing reservoir rocks
Porosity versus initial permeability (300 psi) between the different rock types from conventional cores of deepwater, turbidite reservoirs offshore Gulf of Mexico.
During the production life cycle of a reservoir, absolute permeability at any given location may change in response to localized changes in stress within the rock pore system, due to de-pressurization during production. De-pressurization can increase the net effective reservoir stress (overburden pressure minus pore pressure), resulting in a significant reduction of the in-situ permeability.
The rate of permeability decline with increasing values of reservoir stress is highly variable. As a result, reservoir characteristics related to permeability, such as productivity, reserves, and abandonment pressure can vary widely even, within a single field or formation. When deliverability is predicted in these stress-sensitive reservoirs, it is necessary to take into account permeability as a dynamic variable.
Permeability loss as a function of dropping pressure from 1800 psi to 300 psi. The rock types respond very differently to production pressure drops.
Data for this study is derived from measurements made in conventional cores of deepwater, turbidite reservoirs from the offshore Gulf of Mexico, California, and offshore West Africa. The database is restricted to unconsolidated reservoir sands with porosity >/=25% and shale volume <10%. The porosity-permeability data reveal that little or no relationship exists between porosity and permeability in unconsolidated sand reservoirs when porosity exceeds 25%.
Permeability varies over several orders of magnitude for a given value of porosity. In addition, unconsolidated sands with the highest values of initial permeability do not necessarily have the highest values of porosity. Thus, in unconsolidated sand reservoirs, porosity may not be a reliable predictor of permeability (and reservoir quality).
Permeability, rock types
Unconsolidated sandstones lose significant amounts of both porosity and permeability when the net effective reservoir stress is increased from 300 psi to 1800 psi (average permeability loss is 55%). The actual rate of reduction of permeability with stress for any sample is highly variable. Some samples lose <10% and others lose >65% of initial permeability. The cumulative distribution curve has been used to identify three rock types:
- Rock type A - permeability reduction: >65%
- Rock type B - permeability reduction: 40% to 65%
- Rock type C - permeability reduction: <10%
This distinction between rock types is entirely statistical. It is important to determine if this statistical classification of rock types has any basis in reality. Does it relate to actual differences in the physical characteristics of the pore system of the reservoir rocks?
The pore structure of these samples has been determined using data from nuclear magnetic resonance (NMR) analysis and petrographic image analysis (PIA) of core samples. Each curve presented is an arithmetic mean curve for several different samples of each rock type.
This data reveals that each rock type is characterized by a distinctly different T2 relaxation time, indicating a difference in pore structure. Unfortunately, NMR does not measure absolute pore size. PIA analysis allows for direct measurement of pore size. Pore sizes were measured for the same plug samples from the unconsolidated sands used in NMR analysis. This analysis reveals that the mean pore size (diameter) and range of pore sizes is significantly different for each rock type.
Permeability is a function of both rock type and porosity. Permeability prediction requires knowledge of both porosity and rock type. Equations that define a least squares relationship between porosity and permeability for each rock type are used to predict permeability at any given value of porosity (for any value of net effective reservoir stress).
It is important to note that the highest quality sands (Rock type A) will lose the greatest amount of permeability as the reservoir pressure is reduced (as net effective reservoir stress is increased during production). Thus wells dominated by Rock type A (the "best" wells) may produce over time at a significantly lower rate than wells in which the lower quality rock types are dominant.
Wireline log identification
Relaxation time for the three rock types showing the response of their different pore structures.
Rock types are identified statistically, using a combination of log responses to define specific "cut-off" values and using the comparison of the core-based determination of rock type. The specific log responses depend on the characteristics of the formation in question, and include a combination of several of the following:
- Gamma ray
- Resistivity (when sands are at irreducible water saturation)
- Two porosity tools (combination of either density and neutron, sonic and density, or neutron and sonic).
In this manner, the rock types are identified, and permeability is predicted for any value of net effective stress, foot-by-foot, in all wells with a sufficient logging suite. This results in a rock-based log model that is used for net pay determination and field-wide mapping of rock type distributions.
The results of this study indicate that in any reservoir characterized by stress-dependent permeability, the so-called static reservoir model is not static. It is dynamic. Reservoir permeability (and to a lesser extent porosity) can change significantly through the production life cycle. This has important practical implications.
- Reservoir evaluation: It is necessary to identify the rock types within the reservoir interval and to determine the precise rate of permeability decline with increasing stress for each rock type. Permeability should be predicted on a foot-by-foot basis for different values of net effective reservoir stress. This allows for prediction of permeability at different stages of reservoir development. The existence of stress dependent permeability in a reservoir obviously impacts the interpretation of bottomhole pressure tests. BHP and pressure transient analyses are significantly confounded when permeability is a dynamic variable.
- Reservoir productivity: Reservoir productivity is a function of permeability and pressure which, in turn, is a function of producing conditions, well design, and completion strategies. High production rates can result in a significant reduction of near well bore permeability. The relationship between production rate and well bore pressure can be predicted if the stress dependence of permeability and pressure drawdown are known.
- Reservoir management: Operations (producing conditions) in one wellbore can influence pressures in inter-well areas. Thus, stress-permeability data for each well bore must be integrated into a field-wide reservoir model. Permeability is an essential parameter in reservoir simulation. Flow unit maps should be made of the field-wide distribution of rock types, permeability and overburden stress.
These maps are then incorporated into the geologic models used for reservoir simulation in a simulator that includes stress, or pressure dependent permeability. The reservoir simulation then provides important information regarding the delicate balance that must be achieved in stress dependent reservoirs between economics and reservoir management philosophy, particularly in regards to rate of production (number and design of wells), reserves and return on capital employed. Recommendations are to:
- Identify rock types using conventional cores and/or percussion sidewall cores
- Determine permeability at different values of stress for each rock type
- Develop a rock-based log model that allows for the foot-by-foot determination of porosity, rock type and permeability. Determine relative proportions of each rock type in the reservoir
- Map the field-wide distribution of rock types and the stress regimes for each reservoir layer (flow unit). These maps should be based on detailed knowledge of the trends of depositional environments, diagenesis and structure (faults, folds) as determined from integrated sedimentological and geophysical analysis.
- Use relative proportions of rock types and values of permeability at stress in reservoir simulation.
Rock-based model log resulting from identifying rock types and predicting permeability for any value of net effective stress. This can be used for net pay determination and field-wide mapping of rock type distributions.
Pore geometry is a fundamental control on stress-dependent permeability in unconsolidated, offshore sand reservoirs. In these reservoirs, the most significant loss of permeability with increasing stress occurs in sands with the highest initial reservoir quality (sands with the largest pores).
The existence of stress dependent permeability has a significant effect on the performance of an individual well and the reservoir. Estimates of reserves and flow rates are significantly impacted when stress dependency is included in the simulation. Successful economic evaluation of offshore reservoirs requires an evaluation of the stress dependency of permeability. Optimally, this should be (and can be) done early in the history of field development.
This paper is taken, in part, from SPE Paper 56813, published at the SPE National Convention and Exhibition, Houston, October 10-13, 1999.
John P. Davies is a Reservoir Engineer with the Mid-Continent Division of Chevron USA.
David K. Davies is President of David K. Davies and Associates, Inc. in Houston, Texas.