Gravity may be measured in different ways – as absolute gravity, relative gravity or by gravity gradiometry.

In terms of absolute gravity measurement, a gravity meter is designed to measure the local gravitational acceleration (g) of the earth, whose normal or background value is ~9.81 m/s². Since the variations in g are caused by local mass distribution variations, adequate gravity measurements may help in the localization of large bodies with densities different from their surroundings, e.g., regions of fluid saturation changes in oil or gas reservoir.

The change of g in a well is strongly influenced by the mass density of the formation layers surrounding the wells and by the density in the reservoir between wells. A gravity measurement of g produced by these density variations in a wellbore can be derived directly from Newton’s Inverse Square Law of Gravitation Attraction.

There are two primary means of utilizing borehole gravity measurements – Apparent density and Time-lapse

The first is the calculation of apparent density, which can represent the formation bulk density. Figure 1 shows the physical principle of the borehole gravity measurement and its use in this manner. The measured difference ∆g of vertical gravity is sensitive to the strata away from the borehole and to the separation, ∆Z, between the two measurements. From these measurements, we can compute an apparent density (ρa, kg/m³) of the layer of rock within the interval ∆Z by the following formula:

where F is the free-air gravity gradient correction term and G is Newton’s Universal Gravitational Constant (6.674 × 10^-11 m³/kg/s²). In the absence of major 3D density variations, ρa can be treated as an approximate value of the formation density ρb.

By increasing ∆Z in the measurement, more rock is affecting ∆g; therefore, greater density effects may be detected that are further away from the wellbore. The ∆g can be a result of stratigraphic, structural or diagenetic effects (matrix or porosity effects). Further useful summaries of principles can be read at Marsala (2014), Ander (1997), Schultz (1989), and LaFehr (1983).

The second means of using measured borehole gravity is in the time-lapse sense, in which repeated borehole gravity measurements are taken at the same locations in the wells over a period of time. The difference of the measured gravity over time produces the time-lapse borehole gravity data. In a reservoir scenario, ∆g over time are predominantly produced by the migration and of different reservoir fluids such as oil, gas, and/or water.

At any time, the density in a formation or reservoir is given by the general formula in equation 2 that describes the total bulk density for a formation that has three fluids in its pore space:

ρ_b= (1- φ) ρ_matrix + φ (ρ_wS_w+ ρ_oS_o + ρ_gS_g)

where φ is porosity in fraction, S is the saturation of water (w), oil (o) or gas (g) in fraction, and ρ are the density of fluids and matrix (kg/m3). As fluid saturations change over time, the changes in bulk densities leads a time-lapse density change ∆p which is detected by the time-lapse gravity measurements.

The relationship between time-lapse gravity measurements and the time-lapse density change is again given by the Newton’s law of gravitational attraction. Well established modeling and inversion techniques can then be employed to image and characterize the 3D time-lapse density. The imaged 3D density change is then used to characterize the fluid movements in the formation or reservoir.

Vector gravity is the measurement of the three components of the gravity anomaly produced by anomalous density in the subsurface. In a truly vertical wellbore, the vertical component is in the earth background gravity field direction (g_z), and the two horizontal components (g_x, g_y) are perpendicular.

It is important to state the three-axis capability is general but practical applications in applied geophysics are only concerned with the anomalous field and its three components.

The primary application of our technology, in comparison to previous single axis measurements is the measurement of gravity anomaly in 3 axes.

Our sensor is triaxial and it yields a three-component gravity anomaly gx, gy, gz

We place three single-axis sensors close together and orient them to be orthogonal to each other. Although the three sensors are not strictly co-located, their offset distance is below 50 cm so for geophysical applications they are effectively collocated and the sensor package is effectively tri-axial.

SMG talk of sensitivity in terms of the noise floor at which a true signal ceases to be distinguishable and therefore it is a detection threshold. Currently the detection threshold for bench tests of our current wireline sensor module are of the order of <8 µGal.

Microgravity measurements are subject to environmental noise often exceeding the desired signal in size and which are removed by reference to their sources, such as cyclical earth-tides, influence of large nearby masses, precision location measurements, air pressure effects, temperature, vibration, tilt and electronic noise. Depth positioning is critical for borehole surveys.

In addition to these direct factors in the borehole, there are several general environmental factors that affect the measurements:

1. ground water change
2. atmospheric pressure change that produces direct gravity effect up to 20 micro-Gal in coastal regions
3. subsidence/surface topography

Sensing density differences between a gas and water, which are of the order of 0.2 - 0.3 gm/cc, place demands on the sensitivity of the instrument, and the depth to which the difference can be observed. There is no simple answer since a gravimeter does not measure density changes directly. Instead, we process and invert the gravity data to back-out the density changes. Case studies have shown that water-oil substitution with a density change on the order of 0.01 g/cc can be detected depending on the reservoir thickness and other factors.

Our modelling shows that <5 µGal is required to distinguish between all most common fluid substitution end members, gas, oil, water; and <10 µGal between gas/water for a typical clastic reservoir sand. Clearly, this is dependent on saturation and reservoir properties. Each survey candidate will be modelled to determine its suitability for detection and imaging prior to the survey.

SMG like to reframe the question of depth of investigation within a borehole or reservoir environment usually asked by petrophysicists/well log analysts who are more used to wireline logging tools sensing properties close to the borehole. While this tool is deployed as ‘wireline’ sensor, our modelling shows, as explained in the first FAQ, the measurement will be sensitive to changes in density further away (often 10s or 100s of meters) common reservoir scenarios and closer to seismic scale.

There is not a reliable body of work that allows this clear definition, LaFehr (1983) discusses implicit detection thresholds in the vertical sense of gravity measurements.

One can consider two depths of investigation, depending on how data are used or interpreted.

1. A quick and effective way is to calculate apparent densities along the borehole and use them to approximate the formation bulk densities. Then the sensing depth away from the borehole is proportional to the distance between adjacent measurements used in calculating the apparent density. . It has already been noted above that by increasing ∆Z in the measurement, more rock is affecting ∆g; therefore, the further away from the wellbore, greater reservoir effects can be detected. The ∆g can be a result of stratigraphic, structural or diagenetic effects (matrix or porosity effects). The more substantial ∆g effects are predominantly due to the existence of different reservoir fluids, i.e., oil, water and/or gas. The rule of thumb developed in LaFehr (1983) is excellent for this purpose. Because the BHGM bulk density measurement samples such a large formation volume, BHGM logs can be obtained from both cased and uncased wells. In fact, it is the only borehole method that can reliably obtain bulk density through casing! The bulk density is directly related to the formation density.
2. Modern borehole gravity has advanced much beyond the simple calculation of apparent density and its use in interpretation. With gravity measurements in multiple boreholes, on can holistically interpret the gravity by constructing a 3D density model using a 3D inversion algorithm. More details can be found in, for example, Li and Oldenburg (1998). Krahenbuhl and Li (2006, 2012), and Rim and Li (2015). With such an approach, the depth of investigation depends on the total lengths of boreholes in which the data are taken, and a data set can sense deep within reservoir, up to kilometers.

Similar to depth of investigation, reframing to seismic scale is a worthy backdrop to understand a sense of vertical resolution. However, it is worth noting that small intervals contributing a large density contrast will have a significant effect on gravity measurements (and has analogy to sub-seismic fault detection on seismic). Pre-well forward, and post well inversion modelling will help predict most likely scenario (by altering beds and combinations of, for closest fit) causing that contrast.

Gravity measurements are not interpreted in isolation and it is the more complete conditioned data set that will ultimately reduce most uncertainties. Our modelling uses a number of data points from the reservoir model including modelled bed surfaces.

There could be two aspects to the concept of vertical resolution: (1) when used as a logging tool, the vertical resolution pertains to the formation density changes along the borehole that can be resolved by borehole gravity; or (2) the features within the reservoir far away from any boreholes that can be detected by time-lapse gravity.

1. This is directly dependent upon the stations spacing of borehole measurements. If two sensors are used to make simultaneous measurements, then the density can be resolved on the scale same as the sensor separation, as in the basic principles of borehole microgravity above.
2. For the size of features detectable through 3D inversion, the answer is more involved. One cannot make a simple statement. For example, the work by Davis et al (2008) showed that one can resolve the distribution of water in a 30-m thick rubble zone at 330-m depth using surface data, which also applies to borehole scenarios.

Yes, following the basic principles of borehole microgravity above, we can calculate apparent densities, which can serve as an approximation to bulk density when pairs of adjacent borehole gravity measurements are separated by a small distance such as a 1 to 10 meters.

The advantage of the gravity-derived density is that it is deep looking, i.e., it senses the density at a greater distance from the wellbore than the few inches by typical density logging tools.

Pre-well forward models and survey feasibility, as well as post acquisition inversion processing of gravity data sets are performed for our customers. Interpretation ready data will be provided in common formats to be incorporated into available industry platforms.

Our feasibility study based on forward modelling assumes the reservoir simulation / geological data (porosity, matrix and fluid densities geometry, bed boundary up/down, so we know the confines of the space the density will change). If you can image the density change, it will enable tracking of the fluid movement because density is linearly proportional to the saturation change.

Density inversion can then be performed for 3D reservoir volume for example, using a BINARY inversion that assumes porosity and the maximum fluid substitution as end members. Other inversion methods are being explored, such as the COUPLED INVERSION that considers time-lapse gravity data with injection and production data together.

No subsurface interpretation is ever unique. As with any subsurface interpretation, the more constraints that are available (quality-controlled data, and enough geometrical and porosity information), a tighter assumption will allow forward and inversion models to be refined and those non-unique scenarios distinguished. We therefore incorporate borehole gravity with all the available information to improve the imaging of subsurface and its integration reduces general non-uniqueness of subsurface interpretation.

Any common environment for wireline logging will be suitable to a gravity survey, given that there is a measurable density contrast due to fluid substitutions which will be determined with pre-well feasibility study. A station measurement is generally required to obtain a stabilised measurement.

Cased and open hole conditions and deviations can be handled. Arguably, it is almost unique wireline logging tool that can obtain bulk density through well casing and the only deep-reading tools that can directly sense the density change in the reservoir.

Gravity measurements can be made per routine wireline logging operations which can be both open and shut-in.

The sensor and its low power requirement and small potential size lends it to be well situated in a permanent installation.

Possibly, if a severe contrast in fluid density of those produced fluids is present, although likely to be negligible in most cases.

Yes, this has been studied and presented by Rim and Li (2015) and by Krahenbuhl et al. (2011), Lofts et al. (2019) . Over time-lapse periods, the changes in the three components of gravity anomaly are different. There are significant directional (azimuthal) and also TVD (vertical depth) advantages that indicate fluid body movements. We observe the vertical component starts to flatten at a level that indicates the passing of a water flood front. In contrast, the horizontal components show significantly more sensitivity after the water front has passed. Furthermore, the vertical component does not sense the azimuthal change of water front, whereas the horizontal components are highly sensitive to azimuthal distribution of fluids around the borehole.

When rigorously applied and interpreted, 4D seismic can provide a valuable spatial image of the reservoir structure and its fluid distributions. However, the use of 4D seismic entails considerable time gaps between repeat surveys and is costly, both during acquisition and its subsequent interpretation. Moreover, not all geological conditions are favourable for use of 4D seismic. As such, to overcome the limitations of existing monitoring techniques, we are exploring the application to compliment 4D seismic surveys with gravity surveys added to a workflow. Borehole microgravity can provide and time-lapse measurements relevant to the dynamic advance of fluid/gas fronts within a reservoir.

Yes. It is the direct relationship of gravity to density changes due to fluid substitution (changes in gas/oil/water in a pore space) that allow a measurement of saturation. In fact gravity based saturation measurements will be independent of near well bore phenomenon that affect pulsed neutron cased hole measurements.

Gravity based measurements exhibit a number of advantages:

• Insensitive to water salinity: sensitivity to water salinity causes uncertainties in traditional MDPN (pulsed neutron) interpretation.
• Able to identify true matrix gas movement. The measurement is unaffected by other sources of gas such as secondary gas
  cap coning or secondary gas cap channeling through fractures which can affect near wellbore measurements.
• Saturation measurements independent of near well bore phenomenon that affect MDPN
• Identification of gas coning or fracture channeling that could be remediated by patching or straddling
• Insight into nearby well behavior
• Monitoring of secondary gas cap local to the well
• Monitoring for any downwards OWC movement (For down-dip well production opportunities)
• Love et al SPWLA VVVV, 2018 explain a surveillance plan involving the above.

Yes and No. The current sensor is not yet suitable for such applications. However, future configuration may enable us to directly measure gravity differences and quantify the formation density on the scales approaching that of current density logging tools.