K.U. Weyer Ph.D., P.Geol., P.HG.
WDA Consultants Inc., 4827 Vienna Drive NW, Calgary, Alberta, Canada

© 2010 K. U. Weyer


Introduction

An invitation by the Brazilian petroleum company PetroBras to their September 2008 CO₂ Seminar in Salvador, Brazil, caused me to integrate Hubbert’s Force Potential (Hubbert, 1940) and the Theory of Gravitational Groundwater Flow Systems (Tóth, 1962) to the geological storage of CO₂. Both theories are physically consistent and have been tested in many practical cases throughout the world by the oil industry and hydrogeologists for more than 40 years. Both geophysicists by training, Hubbert worked in the exploration end of Shell, while Tóth was at the time employed by the Alberta Research Council.

Building on the misdirecting influence of Muskat (1937), reservoir engineering applies the methods of continuum mechanics (energy related to volume) to fluid flow within oil fields. At the time, Hubbert realized that Muskat’s (1937) approach was physically inconsistent and lacked physical causality (Hubbert, 1969; see Introduction) and, in response, put together the 1940 treatise presenting physically-consistent derivations for subsurface fluid flow. Hubbert’s Force Potential relates energy to mass. Hubbert (1953) subsequently applied force potential treatment of all subsurface fluid flow to the exploration for petroleum. The basic equations of Hubbert’s Force Potential are shown in the introduction to chapter 5 (Poster 4).

The subsequent development of the Theory of Groundwater Flow Systems was based on Hubbert’s force potential and on practical oilfield data, namely on the strange behaviour of water level data (head levels) in boreholes drilled by cable tools without mud circulation in the Turner Valley oil field southwest of Calgary [poster 1; chapter 3]. These water level data were then evaluated with respect to the topography of the groundwater table and to the depth and permeability of geologic layers encountered. It turned out that, due to thermodynamic reasons of minimizing the total energy consumption, regional groundwater flow systems penetrate aquitards (caprocks in oil field terminology) on their way from recharge areas to discharge areas and may reach great depths in doing so. These conclusions were also based on the results of 2D vertical mathematical models applying Hubbert’s force potential [poster 2; chapter 3]. Hubbert (1953) showed that the force field of fresh groundwater determines the natural flow directions of liquid and gaseous hydrocarbons at depth. Fresh groundwater force fields exert the same effect on injected CO₂. Weyer (1978) deduced under which hydrodynamic and geological conditions the so-called ‘buoyancy forces’ will be directed downwards. Under these conditions fluids lighter than water (including gaseous fluids) will move downwards faster than both water and fluids denser than water [poster 3; chapter 4]. Weyer (1978) named the effect of these conditions Buoyancy Reversal [short: BR]

Under hydrostatic conditions the value of the mechanical hydraulic gradient (grad F) is zero. Therefore no gravity-driven flow takes place. Such conditions exist at StatoilHydro’s off-shore CO₂ injection site Sleipner. At Encana’s on-shore CO₂ injection site, Weyburn, and other onshore sites grad F is unequal to zero and gravity-driven flow and hydrodynamic conditions exist.

Hence naturally occurring Buoyancy Reversal only occurs on-shore. In both environments, onshore and off-shore, Buoyancy Reversal can perceivably be created by hydrocarbon production and other persistent pumping from deep wells.

Poster 4 [chapter 5] deals with the trapping of CO₂ by means of subsurface water flow through the mechanism of Buoyancy Reversal. This new trapping mechanism establishes the whole thickness of an aquitard (caprock) as a barrier to upward movement of CO₂ and not just the thin boundary layer exerting capillary forces. Moreover any breakthrough of CO₂ near the injection site due to increased pressure potentials under the caprock can be prevented by increasing the pressure potential above the top of the aquitard (caprock). In doing so one could use hydrous fluids from the lower part of the injection layer and thus increase, as a beneficial effect, the injection layer’s storage capacity for injected CO₂. As the pressure potential will dissipate from the injection site towards the surroundings, the pressure at the injection site will be reduced upon cessation of injection and thereby allow eventual discontinuation of water injection above the caprock.

The posters collected here explain, in condensed form and with straightforward terminology, the physical concepts of Hubbert’s Force Potential, of gravitational groundwater flow systems, of Buoyancy Reversal and its application to an improved geological storage of CO₂. Posters 1 and 2 [chapter 3 and 4] were written as introduction into the Theory of Gravitational Groundwater Flow Systems, which forms one of the pillars for the subsequent posters 3 and 4. Poster 3 was first presented and discussed at SEG 2009 Summer Research Workshop: CO₂ Sequestration Geophysics, Banff, Alberta, Canada, 23-27 August, 2009. Posters 4 was first presented and discussed at the ESF Conference ‘CO₂ Geological Storage - Latest Progress’ in Obergurgl, Austria, 22-27 November 2009 together with Poster 3. In addition, Posters 3 and 4 have also been presentated and discussed at the GCEP/USGS participatory workshop ‘Caprocks and Seals for Geologic Carbon Sequestration’ in Monterey, CA, USA, January 12-15th, 2010.

Chapter 6 determines the magnitude of the hydraulic gradient (grad F), which, under conditions of vertically downward directed flow, forms the threshold between conditions with pressure potential increasing with depth and the conditions of pressure potential decreasing with depth (Buoyancy Reversal). It also presents a basic diagram relating the occurrence of Buoyancy Reversal to the amount of downward flux and permeability. Both the above threshold value and the basic diagram were first shown during discussions at the Obergurgl conference. The numbers and diagrams have been derived and calculated in a physically consistent manner by applying Hubbert’s Force Potential and summarizing tables of Weyer, 1978, and Weyer, 1996. Field data from Hitchon et al., 1989a, Hitchon et al.,1989b, and Bachu et al., 1989, establish the natural occurrence of Buoyancy Reversal in regionally extended downward flow sections under large regional groundwater recharge areas in Alberta. The extent of areas with downward flow at depth (under uplands) is often much larger than areas with upward flow (under valleys and lowlands). This is shown by Fig. 8 and 10 (Ch. 4) and 4 and 6 (Ch. 5). All of the Swan Hills are an extended upland area with strong downward flow penetrating the Clearwater-Willrich Aquitard (the layer with naturally occurring Buoyancy Reversal) while, under pre-petroleum production conditions, the deep-seated upward flow through the same aquitard occurred only in a limited area under the valley of the Athabasca River.

Chapter 7 elaborates on the presence of hydrostatic conditions at off-shore sites like Sleipner in the North Sea and the presence of hydrodynamic conditions at on-shore sites like Weyburn, Saskatchewan, and Zama Lake and Wabamun, both located in Alberta, Canada. Hence the flow behaviour of the CO₂ at the Sleipner site cannot be taken as a precedent for the Weyburn site or other on-shore sites. The chapter also presents a road map for future investigations applying physically-consistent methods to CO₂ storage.

Chapter 8 provides a roadmap for integrating and applying Hubbert’s force potential and Buoyancy Reversal to the geological storage of CO₂.

Appendix 1 presents the summary of a 16 page review of the above chapters 1 to 7 (version December 21, 2009) by two eminent hydrogeological modellers, Emil Frind of the University of Waterloo, Ontario, and John Molson of Laval University, Quebec (Frind & Molson, 2010). The full review with the detailed coments is available from the website www.wda-consultants.com. In response to the review I have corrected the use of the term "principle" (Dec.21, 2009 version: p.11, last line) to read "principal flow patterns" and changed "removal" (Dec.21, 2009 version: p. 29, line 3) to "reversal". In Figure 1 (chapter 6) the labelling error discovered in the review has been corrected.

I appreciate Emil’s and John’s unsolicited review efforts immensely, in particular as their mathematical models confirmed the occurrence of Buoyancy Reversals which I had first derived from theoretical considerations (Weyer, 1978) and later confirmed by field data (taken from Hitchon et al., 1989a, Hitchon et al., 1989b, and Bachu et al., 1989).

With respect to my use of the term Buoyancy Reversal and the proposal by Frind and Molson (2010) to use the term "pressure gradient reversal" instead, I find my term to be more suited to express the physical meaning that the so-called "buoyancy forces" are directly dependant on the pressure potential forces and therefore, in a hydrodynamic environment, follow the nonvertical directions of the pressure potential force vector. The opinion that so-called vertically upwards directed buoyancy forces would be an omnipresent force for lighter parcels within fluids is erroneous.

The term Buoyancy Reversal relates closely to the physics of force fields involved. The so-called "buoyancy forces" are created by pressure potential forces (see chapters 5 and 6) which in the hydrostatic case happen to be directed upwards. Under general hydrodynamic conditions the same pressure potential forces may be directed in any direction in the subsurface including downwards. Downwards directed pressure potential forces may then lead to Buoyancy Reversal.

The concept applied assumed strong vertically downwards-directed flow through a three layer system with an low permeable aquitard sandwiched between two aquifers (chapter 4: Figure 7). In both aquifers the pressure potential force (the buoyancy force) is directed upwards, while the pressure potential force within the aquitard is directed downwards. Ergo what is commonly considered to be the "buoyancy force" has been reversed. Under these conditions lighter parcels would move downwards faster than heavier parcels, in contrast to common experience in hydrostatic conditions. One always should keep in mind that Hubbert’s force potential mainly consists of two physical fields: the gravitational energy field and the pressure potential energy field (which in the subsurface is derived from the gravitational field).

Frind and Molson (2010) followed my opinion and make the point that all simulations need to be based on head values and gradients not on pressure gradients. They (ibid) agree that simulators which take caprocks as top model boundaries are unsuitable for modelling CO₂ sequestration.


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