Feasibility of 4D Gravity Monitoring in Deep-Water Turbidites Reservoirs

Abstract

We present a seafloor 4D gravity feasibility analysis for monitoring deep-water hydrocarbon reservoirs. To perform the study, we have simulated the gravity effect due to different density and pore pressure distributions derived from a realistic model of a turbiditic oil field in Campos Basin, offshore Brazil. These reservoirs are analogs of several other passive-margin turbiditic systems located around the world. We considered four reservoir scenarios including and not including seafloor subsidence. Our results indicate that the gravity responses are higher than the feasible value of 3 μGal 12 years following the base survey. The area of maximum gravity anomaly corresponds to where we suppose hydrocarbon extraction occurs. A maximum seafloor subsidence of 0.6 cm was estimated, resulting in no detectable gravity effects. Our results endorse the 4D seafloor gravity acquisition as a beneficial tool for monitoring deep-water passive-margin turbiditic reservoirs.

1. Introduction

Currently, the oil industry is seeking ultra-deep marine exploratory opportunities that can reach water depths of over 2000 m with sedimentary overloads of a few kilometers. In these scenarios, using geophysical methods as an imaging tool is challenging because the distance between sources and the sensor can be substantial and impacts data quality. In these cases, an effective way to reduce the signal amplitude loss is to place the geophysical sensors on the seafloor closer to the desired targets. Concerning gravity measurements, high-resolution instruments set on the seafloor can allow for hydrocarbon production monitoring through 4D (time-lapse) acquisitions [1,2,3].

Gravity acquisitions can be conducted in almost every type of environment. Regarding aquatic environments, gravimetric surveys have been performed since the 1940s. First in lakes and later in marine regions with shallow depths [4]; then, going to deeper and more complicated sites over the years. Land 4D gravity acquisitions have been performed for some decades with various purposes, from geothermal field studies to volcano monitoring, aquifer water storage, mine subsidence, tectonic and post-glacial isostatic movements, and hydrocarbon exploration and production [3,5,6]. Since the end of the 1990s, seafloor 4D gravity acquisitions have been performed in the shallow waters of the North Sea to monitor the fluid dynamics in hydrocarbon fields [3,7,8] and seafloor subsidence due to hydrocarbon production.

Once the gravimetric method is sensitive to mass variations, seafloor 4D gravity measurements can improve our understanding of fluid movements inside a reservoir. Moreover, it directly impacts hydrocarbon recovery and reduction of geological uncertainties such as mass variation estimation, reservoir water influx characterization, gas/oil or oil/water contact estimation, and $C{O}_2$ injection and storage. It can also contribute to a better and optimized drilling plan by diminishing the number of wells, substantially reducing the costs of a hydrocarbon field development project [3,9,10,11,12,13,14,15]. Furthermore, if pressure gauges are settled with gravimeters on the seafloor, one can obtain information about seafloor movement due to oil production [3,8,11,16,17,18]. The measure of seafloor deformation is crucial to reduce the risks of human exposure and production facilities. At last, seafloor 4D gravity is a relatively fast, cost-effective, and environmentally friendly geophysical method that can be used complementary to 4D seismic surveys [3,5,8,9,15,18,19].

Several studies performed all over the world in the last two decades show the efficiency of the seafloor 4D gravity technique. These include feasibility studies, survey improvements, time-lapse gravity processing, application of inversion methods, use of borehole and gravity gradiometry information, and real data interpretation [7,10,11,12,16,17,19,20,21,22,23,24,25,26,27].

In deep and ultra-deep waters, as in the case of the largest Brazilian hydrocarbon fields, the seafloor 4D gravity survey is a technological challenge. In this scenario, it is necessary to evaluate the technical feasibility of using the seafloor 4D gravity surveys for hydrocarbon-field monitoring. Thus, this study focuses on the feasibility of the seafloor 4D gravity acquisition for monitoring hydrocarbon reservoirs and seafloor movement. By improving the work developed by [28], we have performed 4D forward gravity modeling of a typical passive-margin turbiditic reservoir at Campos Basin, offshore Brazil. We tested three scenarios with seafloor movement and another without this phenomenon. Using the feasible (threshold) limit of 3 μGal, which can be considered as a conservative value concerning recent seafloor 4D gravity acquisitions [15,18], results exhibit gravity responses higher than the feasible limit, which validate the seafloor 4D gravity survey for similar situations.

2. Materials and Methods

2.1. Gravity Anomalies and Seafloor Changes

Consider a marine sedimentary basin where the seafloor is the interface separating the water column from the basin sediments (Figure 1). We assume that the water column and the sediments are homogeneous, with constant densities ${\rho }_w$ and ${\rho }_s$, respectively. Inside the sediment layer stands a hydrocarbon-producing reservoir, with known dimensions and time-variable bulk density ${\rho }_b\left(t\right)$ due to its function.

Let us simulate a seafloor 4D gravity survey over the model described in Figure 1. In this case, three phenomena can generate time-variable gravity anomalies: (1) water layer variation due to tides and waves; (2) reservoir mass variation due to hydrocarbon production; and (3) seafloor relief movement due to hydrocarbon production. The role of gravity modeling is to facilitate the study of the gravity response by isolating the gravity effects caused by these phenomena. This work focuses on the 4D gravity effect yielded by the reservoir’s mass variation and the seafloor movement due to hydrocarbon production. Thus, the 4D gravity effect of the ocean water movement has not been taken into account.

The gravity effect of a 3D density distribution can be calculated by dividing the study region in a sequence of vertical prisms adjacent in the three spatial directions with the $x-$axis to the north, $y-$axis rising to the east, and $z-$axis falling downward. From now on, this mesh of 3D vertical, juxtaposed prisms in the horizontal and vertical directions is called the interpretation model. The gravitational acceleration in the vertical direction $g_z(P_i,t_k)$ evaluated in a point $P_i=(x_i,y_i,z_i\left(t_k\right))$ representing the seafloor in a time $t_k$ can be calculated according to Blakely [29]:

$$g_z(P_i,t_k)=\gamma \sum _{j=1}^N\Delta {\rho }_j\left(t_k\right)f_{ij}(P_i,x_j,y_j,z_j\left(t_k\right)),$$

(1)

with

$$f_{ij}(P_i,x_j,y_j,z_j\left(t_k\right))={\int }_{z_{1j}\left(t_k\right)}^{z_{2j}\left(t_k\right)}{\int }_{y_{1j}}^{y_{2j}}{\int }_{x_{1j}}^{x_{2j}}\frac{z_j\left(t_k\right)-z_i\left(t_k\right)}{d_{ij}^3}d{x}_{j}d{y}_{j}d{z}_j,$$

(2)

where $\gamma$ is the gravitational constant, $\Delta {\rho }_j\left(t_k\right)$ is the time-variable density contrast between the jth prism and its surroundings. N is the number of prisms in the interpretation model. The variable $d_{ij}$ is the distance between the ith measurement point and the jth integration point within the jth prism $(x_j,y_j,z_j\left(t_k\right))$:

$$d_{ij}={[{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i\left(t_k\right)-z_j\left(t_k\right))}^2]}^{1/2}.$$

(3)

Note that in Equations (1)–(3), the vertical coordinates $z_i\left(t_k\right)$ and $z_j\left(t_k\right)$ are also dependant on time because they can vary in the case of seafloor movement. In Equation (2), the integration is conducted in the variables $x_j$, $y_j$, and $z_j$ denoting the x-, y-, and z-coordinates of an arbitrary point belonging to the interior of the jth prism. The integrals limits (Equation (2)) correspond to the jth prism borders in the following way: $x_{1j}$ and $x_{2j}$ are their south and north borders; $y_{1j}$ and $y_{2j}$ are their west and east borders; and $z_{1j}$ and $z_{2j}$ are their depths to the top and bottom. The analytical solution for Equation (1), for a mesh of rectangular prisms, was taken from Nagy et al. [30].

2.2. Reservoir Fluid Substitution and Seafloor Movement Effects

In a hydrocarbon-producing field (gas, oil, or both), the reservoir bulk density is time-variable because of the hydrocarbon removal or its substitution by water or other fluids inside the reservoir. As they have different densities, a time-variable gravity effect is generated. To calculate this effect in a specific position $P_i$ and moment $t_k$, defined here as $g_z^r(P_i,t_k)$, we represent the reservoir as a mesh of vertical prisms (Figure 2) and use Equation (1). In this case, the density contrast is between the reservoir density at that time (${\rho }_j\left(t_k\right)$) and the background sediment density (${\rho }_s$).

Another important phenomenon is the seafloor movement caused by hydrocarbon exploitation. If the reservoir pore pressure decreases, it generates reservoir compaction, resulting in the seafloor sinking [16,31,32,33]. When it occurs, the region of subsidence, initially composed of seafloor sediments in time $t_0$ (Figure 3a), is replaced by water in time $t_1$ (Figure 3b) just after the subsidence. We assume that there is only vertical displacement on the seafloor. It means that the ith measurement point on the seafloor in $t_0$, $P_i=(x_i,y_i,z_i\left(t_0\right))$, changes to $P_i^{\prime }=(x_i,y_i,z_i^{\prime }\left(t_1\right))$ in $t_1$ (Figure 3). The opposite occurs when the pore pressure increases.

The change of the seafloor’s vertical coordinates also causes an additional gravity effect that must be taken into account in the modeling calculations once the observation points are on the seafloor. The gravity variation $\Delta g_z^s$ due to the change of the vertical position in the measurement points (Figure 3) is defined by:

$$\Delta g_z^s=0.3086\Delta z_i=0.3086(z_i^{\prime }\left(t_1\right)-z_i\left(t_0\right)),$$

(4)

where $z_i\left(t_0\right)$ is the original vertical coordinate of the observation point $P_i$ (Figure 3a), and $z_i^{\prime }\left(t_1\right)$ is the vertical coordinate of the observation point after the bathymetric change at the point $P_i^{\prime }$ (Figure 3b). Equation (4) is the free-air gradient used to correct the gravity effect of the vertical distance between the measurement point and the difference in station elevation [29].

The total gravity effect due to seafloor movement, defined here as $g_z^s(P_i^{\prime },t_1)$, is the sum of the gravity effect due to the substitution of sediments by water and the free-air gradient (Equation (4)). To calculate the first part, we discretize the new bathymetry region (i.e., the sinking volume after the seafloor movement) into a mesh of vertical prisms (blue prisms in Figure 3b). Then, the gravity effect due to this substitution can be calculated using Equation (1), where the density contrast is between the seafloor sediments (${\rho }_s$) and the ocean water (${\rho }_w$). If there is a subsidence movement, the density contrast is negative because the ocean water (less dense) substitutes the sediments (more dense). Moreover, if there is an uplift movement, the density contrast is positive.

2.3. Seafloor Movement Estimation

To simulate the seafloor subsidence due to the reservoir compaction in a semi-infinite elastic medium, we selected the strain nucleus concept originally applied in thermodynamics theory [34,35,36,37]. The seafloor subsidence $\Delta z_i$ shown in Figure 3b can be calculated considering the subsurface as a set of strain nuclei that are elements of infinitesimal volume. Once we assume there is no compaction/expansion outside the reservoir, the total subsidence is due to the movement inside the reservoir. Moreover, we consider that there is no change in the reservoir volume, so the compaction is only due to the variation in the reservoir pore pressure. Then, total movement on the seafloor at $P_i$ (Figure 3) is the summation of the movement occurring in the $N_r$ strain nuclei in the reservoir, i.e.,

$$\Delta z(x_i,y_i,z_i\left(t_0\right))=\sum _{j=1}^{N_r}\left[\int \int {\int }_{V_{1j}}{w}_{1ij}d{V}_j^{\prime }+\int \int {\int }_{V_{2j}}{w}_{2ij}d{V}_j^{\prime }\right]$$

(5)

where $w_{1j}$ represents the infinitesimal vertical displacement in the jth strain nucleus in an infinite medium and $w_{2j}$ is the correction of the vertical displacement considering a semi-space. The second integration in Equation (5) is called the “image nucleus solution” (Figure 4). The infinitesimal vertical displacement in the jth prism and its correction due to jth image nucleus are, respectively, given by:

$$w_{1ij}=\frac{A(1+\nu )}{E}\frac{\partial }{\partial z}\frac{1}{r_{1ij}}\Delta p_j,$$

(6)

and

$$w_{2ij}=\frac{A(1+\nu )}{E}\left[2z_i\left(t_0\right)\frac{{\partial }^2}{\partial z^2}\frac{1}{r_{2ij}}-(3-4\nu )\frac{\partial }{\partial z}\frac{1}{r_{2ij}}\right]\Delta p_j,$$

(7)

with

$$A=-\frac{c_{m}E}{4\pi (1+\nu )},$$

(8)

where $c_m$ is the uni-axial compaction coefficient given by:

$$c_m=\frac{(1+\nu )(1-2\nu )}{E(1-\nu )}.$$

(9)

E is the Young modulus, $\nu$ is the Poisson ratio, and $\Delta p_j$ is the difference of pore pressure in the jth nucleus between the moments $t_0$ and $t_1$. $r_{1ij}$ and $r_{2ij}$ are the distances from the i-th point $(x_i,y_i,z_i)$ to the j-th strain nucleus $(x_j^{\prime },y_j^{\prime },z_j^{\prime })$ and the j-th image nucleus $(x_j^{\prime },y_j^{\prime },z_j^{\prime })$, respectively (see Figure 4).

One can note the similarity between the integral functions that describe the gravity anomaly (Equation (1) and the vertical displacement in a semi-infinite elastic medium (Equation (5)). We solved these equations by using the approach proposed by [37] that have taken advantage of this similarity and used the closed expressions of the gravitational potential and its derivatives produced by the 3D right rectangular prism derived by [30,38] for calculating the displacement field on the seafloor.

Upon calculating the vertical displacement of the seafloor (Equation (5)), we obtain the new bathymetry, that is, the vertical coordinates $z_i^{\prime }\left(t_1\right)$. Then, we use these coordinates in Equation (1) to obtain the gravity anomaly due to the vertical displacement of the seafloor.

2.4. Four-Dimensional Gravity Anomaly

If there is no movement of the seafloor, the 4D gravity anomaly is the difference of the gravity effect at the station point $P_i$ due to the reservoir production at different times ($t_0$ and $t_1$), i.e.,

$$\Delta g_z^{4D}(P_i,t_0,t_1)=g_z^r(P_i,t_1)-g_z^r(P_i,t_0),$$

(10)

where the function $g_z^r$ represents the gravity effect of the reservoir region.

Moreover, if we have seafloor subsidence or uplifting (Figure 3b), it is necessary to consider the gravity effect due to these changes on the seafloor. Thus, the 4D gravity anomaly at the measurement point $P_i^{\prime }$ can be written as:

$$\Delta g_z^{4D}(P_i,P_i^{\prime },t_0,t_1)=g_z^s(P_i^{\prime },t_1)+g_z^r(P_i^{\prime },t_1)-g_z^r(P_i,t_0),$$

(11)

where the functions $g_z^s$ and $g_z^r$, respectively, represent the gravity effects due to seafloor movement and reservoir fluid substitution.

We stress that before the production starts, there is no seafloor movement; hence, the gravity effect in time $t_o$ is only calculated at the original seafloor (point $P_i$). Equations (10) and (11) are the main point of this work. For all tested models, we adopted 3 μGal (equivalent to $3.{10}^{-8}m{s}^{-2}$ in SI) as a feasible value to detect the gravity anomalies. This is a conservative value comparing the precision achieved in the present surveys of this type [15,18].

2.5. Campos Basin Geological Setting

Several turbiditic oilfields are situated in the northeastern portion of the offshore Campos Basin, Brazil. The passive margin Campos Basin is one of the predominant Brazilian offshore oil provinces. Its tectonic-sedimentary evolution is associated with the breakup of the Gondwana supercontinent and the opening of the South Atlantic Ocean [39]. It comprises three main tectonic stages: rift, transitional, and drift (Figure 5).

The rift sedimentary sequence includes the Barremian lacustrine deposits of the Lagoa Feia Formation overlaying the Hauterivian (120–130 Ma) Cabiunas basalts. These volcanic rocks characterize the economic basement of the basin. The Lagoa Feia sediments are understood as the principal non-marine source rocks in the Campos Basin [40].

The transitional sequence encloses the Aptian sedimentation, from bottom to top: conglomerates, carbonates, and predominantly the evaporitic rocks deposited during a period of tectonic quiescence. This transitional stage defines the marine drift phase’s antecedent, where the sediments are associated with the first seawater invasion via the Walvis Ridge [41].

The drift sequence starts with the Albian/Cenomanian shallow-water calcarenites and calcilutites of the Macaé Formation. They were followed by the Carapebus Formation, a marine Upper Cretaceous to Paleogene deep-water clastic section formed by shale, marls, and sandstone turbidite lenses. These sediments were deposited during general tectonic inactivity and thermal subsidence. The turbidite reservoir systems are sedimented in deep-water settings associated with slope and continental rise deposits [42] and form the most valuable post-salt petroleum reservoirs in the Campos Basin [40]. These turbidites are potential targets for several multi-physics appraisal and monitoring studies [43,44,45].

Figure 5. Simplified stratigraphic chart of Campos Basin, modified from [46].

Figure 5. Simplified stratigraphic chart of Campos Basin, modified from [46].

The reservoir model comprises a typical turbiditic reservoir of the Campos Basin. The reservoir facies are thick, up to 300 m, formed by clean, massive, turbidite sandstones interbedded with shales and marls. The trap is of the structural/stratigraphic type. These reservoirs usually have high porosity values in the 26%–32% range [47,48].

2.6. Reservoir Model

The entire interpretation model comprises the extent of 14,050 m in the north axis, 13,250 m in the east axis, and 625 m in the vertical direction. The top and bottom depths are 2712 m and 3337 m deep, respectively. The data relating to the reservoir model (e.g., pore pressure, density, and Poisson’s ratio) make up 1,950,312 measurements for each property, with a grid spacing of 50 m along the north and east directions and 25 m in the vertical direction. The data came from reservoir fluid flow simulations for the following years: 2002, 2013, 2014, 2015, and 2018. It is worth noting that the field produces only oil, not gas. The observation points consist of a regular grid of 57 × 54 points in the north and east directions, respectively, with a grid spacing of 250 m in both directions, totaling 3078 observations. The depth of the observation grid is 1338 m deep, the average bathymetry in the oil field region. Over the years, the variation in density has gone from 2.08 to 2.64 ${\mathrm{g}/\mathrm{cm}}^3$, and pore pressure data range from 33.2 to 34.2 MPa. The model background has a density of 2.64 ${\mathrm{g}/\mathrm{cm}}^3$ and a pore pressure of 0 Mpa, representing the region outside the reservoir. Poisson’s ratio data values vary from 0.3237 to 0.3723. Figure 6, Figure 7 and Figure 8 show, respectively, the 3D distributions of density, pore pressure, and Poisson’s ratio in 2002. In order to obtain a better visualization, only the values different from the background are shown.

3. Results

The results were divided into two groups regarding seafloor movement. The first group shows just one scenario with no seafloor movement, while the second group includes three scenarios where seafloor movement is considered.

3.1. Scenario without Seafloor Movement

In a scenario without seafloor movement, only density changes inside the reservoir are assumed to generate gravity anomalies. Thus, the data used in this scenario are the density differences over the years (Figure 9). Although we do not have information provided by boreholes, we can see an increase in density in the central-northeast region of the area (red arrows in Figure 9), which probably indicates where the production was occurring. This increase is due to the oil replaced with a denser fluid in the reservoir, probably formation water. Only values that are different from zero are shown in Figure 9, which means the colored cells represent where density has changed over the years.

Using Equation (1), we calculate the gravity anomaly in each year produced by a set of $N_r$ = 1,861,625 prisms simulating the reservoir model (lower volume in Figure 6) at the grid of observations located on the seafloor (upper surface in Figure 6). Since the reservoir is less dense than its surroundings, gravity anomalies are negative in all years, reaching a maximum amplitude of more than 1000 μGal. The resulting gravity anomalies in each year are not shown because the anomalies are very similar.

Since 2002 is the first year for which we have data, the differences over the years (2013 to 2018) due to density changes within the reservoir (Figure 9) were related to it, producing 4D gravity anomalies (Equation (10)). Figure 10 shows the 4D gravity anomalies over the production years, where we can see that the feasible limit of 3 μGal (dashed red line) is surpassed in 2014 and reaches the amplitude of about 7 μGal in 2018. Thus, according to this scenario, the 4D gravity effect due to oil production (Equation (10)) could be detected after 12 years from the base year.

3.2. Scenarios with Seafloor Movement

We also modeled scenarios with seafloor movement calculated using Equation (5), which demands pore pressure and Poisson’s ratio data from the reservoir flow simulator. In the case of Poisson’s ratio, we choose three possible values according to the original data: 0.33, 0.35, and 0.37. Each value generates different scenarios. We defined Young’s modulus as the constant value of 5 GPa related to reservoir sandstone rocks.

The differences over the years in pore pressure distribution (Figure 11) have a more complex pattern than the density differences (Figure 9). For ease of visualization, we split the pore pressure differences (Figure 11) into two parts: negative (left panels) and positive (right panels) parts. Equivalent to Figure 9, Figure 11 shows only cells with values that are different from zero. Note that between 2002 and 2013, the pore pressure differences are only negative and more intense in the same region where the density differences increase (red arrow in Figure 9). From 2013 to 2018, the pore pressure decreased in this region (red arrows in the left panels in Figure 11), but with less intensity and in smaller volume (i.e., a smaller number of model cells). However, pore pressure increased in the southwest region of the model (blue arrows in the right panels in Figure 11) between 2013 and 2018. We believe that this rise in pore pressure is related to fluid injection in the reservoir as a strategy to avoid severe depletion during the production life of the oil field.

The modeled seafloor movement in 2013 using three different Poisson ratios can be seen in Figure 12. When Poisson’s ratio rises by 0.02, the amplitude of the seafloor displacement (subsidence or uplift) decreases by about 5 %. Figure 12 also shows small changes in the seafloor relief in the order of a few millimeters. Figure 13 shows that even the lowest value of Poisson’s ratio ($\nu =0.33$) does not produce seafloor movement greater than 0.6 cm. Between 2013 and 2015, the subsidence (positive values in Figure 13) grows in the central-northeast area while it diminishes in the southwest area. However, between 2015 and 2018, the subsidence in the central-northeast and the southwest regions decreases. As expected, these results are linked to the pore pressure dynamics over the years (Figure 11).

Upon estimating the seafloor movement we calculated for each year, the gravity effect due to this phenomenon, which is the sum of the gravity effects from the replacement of sediments by water on the seafloor (Equation (1)) and the free-air correction (Equation (4)). Because 2002 is the base year, we do not have subsidence effect for this year. Figure 14 exemplifies the changes in gravity effect in 2013 due to seafloor movement with $\nu =0.33$. The shapes of the gravity anomalies concerning the rock/water substitution effect (Figure 14a) and of the vertical correction effect (Figure 14b) have a high correlation with the geometry of the seafloor movement (Figure 13). The rock/water substitution effect (Figure 14a) is one order of magnitude lower than the vertical correction effect (Figure 14b). In isolation, these two gravity effects (Figure 14a,b) are below the feasible limit of 3 μGal, but the second one is in the same order of magnitude as this limit. The same procedure was repeated for years 2014, 2015, and 2018 with similar results, so they are not shown.

Using the modified bathymetry, we updated the reservoir gravity effect over the years (with $\nu =0.33$) to compare with the seafloor change gravity effects. These effects for 2013 are shown in Figure 15, where the total gravity is the sum of the reservoir and seafloor effects. The reservoir effect (Figure 15a) dominates the total gravity effect (Figure 15c) because it is three orders of magnitude greater than the gravity effect due to the seafloor changes (Figure 14c and Figure 15b). The same is valid for other scenarios in different years and with different Poisson ratios.

At last, we calculated the 4D gravity anomaly over the years (using Equation (11) and $\nu =0.33$) for the scenarios with seafloor changes. Figure 16 shows that the resulting 4D gravity anomaly is very similar in shape to that of the no-subsidence scenario (Figure 10). However, there is an increase in the maximum anomaly amplitude of about 14 %, which also occurs with the other two Poisson ratios (0.35 and 0.37), although with less intensity. In addition, the 4D gravity anomaly exceeds the feasible limit in 2013 when considering the vertical movement one year earlier than the case with no vertical movement (Figure 10). This result shows that even changes in the seafloor of a few millimeters cannot be neglected. In the Supplementary Material, we conducted tests on synthetic noise-corrupted data to investigate the sensitivity of our method to deal with distinct noise levels (Figures S1–S6).

4. Discussion

Density, pore pressure, and Poisson’s ratio from a reservoir flow simulator based on a Brazilian hydrocarbon field were the cornerstone information from which we modeled gravity anomalies and seafloor movement between 2002 and 2018. Negative pore pressure and positive density differences in the central-northeast area of the reservoir model suggest the occurrence of oil production there. Moreover, the increase in pore pressure in the southwest area since 2013 could be explained by the beginning of reservoir re-injection as a strategy for oil production. Once there is no density difference in the southwest between 2013 and 2018, the fluid used in this supposed injection could be the formation water or other fluid with the same density.

In this realistic reservoir model, between 2002 and 2018, the 4D gravity anomalies surpass the feasible limit of 3 μGal in the four tested scenarios: one without seafloor movement and three scenarios with subsidence and uplift, varying the Poisson ratios. These modeling results validate the use of 4D gravity measures for monitoring oil production and seafloor movement in considerable depths. In addition, The area of maximum gravity anomaly corresponds to where we suppose hydrocarbon extraction occurs. They also showed that seafloor subsidence leads to a 14 % increase in the 4D gravity anomaly amplitude. According to the methodology, gravity anomalies related to seafloor movement do not reach the detectability limit (3 μGal) but are in its order of magnitude (between −0.2 and 1.6 μGal, Figure 16). The order of magnitude of the time-lapse gravity anomalies calculated in all scenarios of some μGal agrees with the 4D anomalies obtained in real measurements in the North Sea [8,16,19]. We draw the readers’ attention to the fact that several parameter combinations related to the reservoir in production could result in detectable anomalies due to seafloor changes. Some examples could be the variations in the Young modulus or the arrangement of density and pore pressure distributions with reservoir volume and depth.

5. Conclusions

Following various and diversified tests using a realistic geophysical model that includes 3D density, pore pressure, and Poisson’s ratio distributions, we conclude that the seafloor 4D gravity survey should be beneficial for monitoring the reservoirs of the Brazilian turbiditic fields in deep waters, with or without seafloor movement due to production. There are many active fields already in the Brazilian offshore post-salt that could benefit from this technique. The extension of this work to analyze the feasibility of using 4D gravity acquisitions in the monitoring of reservoirs in Brazilian pre-salt fields has no methodological obstacles.