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Cross-well EM devices are an extension of the resistivity logging tools. These tools measure the conductivity of the formation, where its reciprocals give the resistivity. The measurements are presented by a resistivity log, which is a plot of resistivity versus depth. The resistivity log reflects the nature of hydrocarbon presence in the penetrated formation. The basis behind the measurements is the conductivity and insulation concepts. Conductive materials pass electrical current easily compared to insulators. In the formation, water is an electrolyte. An electrolyte is an electrically conducting solution that contains dissolved cations and anions. These ions help pass electrical currents through the formation. In contrast, completely dry rocks are insulators, which give incredibly large resistivity.

Cross-well EM devices are an extension of the resistivity logging tools. These tools measure the conductivity of the formation, where its reciprocals give the resistivity. The measurements are presented by a resistivity log, which is a plot of resistivity versus depth. The resistivity log reflects the nature of hydrocarbon presence in the penetrated formation. The basis behind the measurements is the conductivity and insulation concepts. Conductive materials pass electrical current easily compared to insulators. In the formation, water is an electrolyte. An electrolyte is an electrically conducting solution that contains dissolved cations and anions. These ions help pass electrical currents through the formation. In contrast, completely dry rocks are insulators, which give incredibly large resistivity.

[[file:AlsaudKatterbauerFigure2.jpg|thumb|300px|{{figure number|2}}Cross-well EM current direction between the wells and to the targeted zone.<ref name=Schlumberger_2021>S. O. Glossary, "Crosswell electromagnetic tomography," Schlumberger, 2021. [Online]. Available: https://glossary.oilfield.slb.com/en/Terms/c/crosswell_electromagnetic_tomography.aspx. Accessed 2021.</ref>]]  

[[file:AlsaudKatterbauerFigure2.jpg|thumb|300px|{{figure number|2}}Cross-well EM current direction between the wells and to the targeted zone.<ref name=Schlumberger_2021>S. O. Glossary, 2021, [https://glossary.oilfield.slb.com/en/Terms/c/crosswell_electromagnetic_tomography.aspx Crosswell electromagnetic tomography]</ref>]]  

Resistivity devices are divided into two primary types, electrode (galvanic) devices, and induction devices. Electrode devices measure the electrical potential (voltage) of the passing electrical current. For the measurement to take place, the electrodes should be within a water-based mud, specifically salty water. The induction devices use an alternating current to generate an alternating primary magnetic field that induces a current into the formation. Then, the induced current generates a secondary magnetic field that is measured by the coils. The induction device's advantage over the electrode devices is that it is used in an oil-based mud or a relatively low conductive mud, like freshwater-based mud.<ref name=Schon_2015>J. Schön, Basic Well Logging and Formation Evaluation, 1st ed., London: Bookboon, p. 51 and 56.</ref>   

Resistivity devices are divided into two primary types, electrode (galvanic) devices, and induction devices. Electrode devices measure the electrical potential (voltage) of the passing electrical current. For the measurement to take place, the electrodes should be within a water-based mud, specifically salty water. The induction devices use an alternating current to generate an alternating primary magnetic field that induces a current into the formation. Then, the induced current generates a secondary magnetic field that is measured by the coils. The induction device's advantage over the electrode devices is that it is used in an oil-based mud or a relatively low conductive mud, like freshwater-based mud.<ref name=Schon_2015>J. Schön, Basic Well Logging and Formation Evaluation, 1st ed., London: Bookboon, p. 51 and 56.</ref>   

Waves propagation into the formation depends on the amount of frequency used, since the reservoir is further away from the borehole, a high wave frequency, in the MHz, can only give information near the borehole. Therefore, a lower frequency system is used due to its high wavelength, which ultimately results in a higher depth of investigation. The wave propagation concept is applied together with the diffusion equation to design the EM system.

Waves propagation into the formation depends on the amount of frequency used, since the reservoir is further away from the borehole, a high wave frequency, in the MHz, can only give information near the borehole. Therefore, a lower frequency system is used due to its high wavelength, which ultimately results in a higher depth of investigation. The wave propagation concept is applied together with the diffusion equation to design the EM system.

   

   

The EM regions between the source and receiver shaped like a quasi-ellipse. The primary EM fields are considered to be uniformed and are donated as the background conductivity of the medium (σ_b). The source receiver sensitivity between the wells are measured by perturbing a small volume or a point in the quasi ellipse region. This perturbation results in having a non-uniform secondary EM field. As a result, the disturbed secondary field is calculated by using the Fréchet derivative.<ref name=Spiesandhabashy_1995>B. R. Spies and T. M. Habashy, "Sensitivity analysis of crosswell electromagnetics," Geophysics, vol. 60, no. 3, pp. 629-929.</ref> <ref name=Wiltetal_1995>M. Wilt, D. L. Alumbaugh, H. F. Morrison, A. Becker, K. H. Lee and M. Deszcz-Pan, "Crosswell electromagnetic tomography: System design considerations and field results," Geophysics, vol. 60, no. 3, pp. 629-929.</ref> The result of the Fréchet derivative is displayed in equation (1), which represent the magnetic field sensitivity.

The EM regions between the source and receiver shaped like a quasi-ellipse. The primary EM fields are considered to be uniformed and are donated as the background conductivity of the medium (σ_b). The source receiver sensitivity between the wells are measured by perturbing a small volume or a point in the quasi ellipse region. This perturbation results in having a non-uniform secondary EM field. As a result, the disturbed secondary field is calculated by using the Fréchet derivative.<ref name=Spiesandhabashy_1995>B. R. Spies and T. M. Habashy, "Sensitivity analysis of crosswell electromagnetics," Geophysics, vol. 60, no. 3, pp. 629-929.</ref> <ref>M. Wilt, D. L. Alumbaugh, H. F. Morrison, A. Becker, K. H. Lee and M. Deszcz-Pan, "Crosswell electromagnetic tomography: System design considerations and field results," Geophysics, vol. 60, no. 3, pp. 629-929.</ref> The result of the Fréchet derivative is displayed in equation (1), which represent the magnetic field sensitivity.

    

    

Equation (1) K_Hz = σ_b G^hz E_ϕb  

Equation (1) K_Hz = σ_b G^hz E_ϕb  

In the early 1970s, the Lawrence Livermore National Laboratory (LLNL) developed the first-ever high-frequency cross-well electromagnetic system using electric dipole sensors. These sensors were intended primarily for hard rock, either igneous or metamorphic rocks, and tunnel detection. Due to the initial EM system high frequency and high conductivity regions in the reservoirs, the signals can only propagate a few inches into the formation (small depth of investigation). Thus, to measure the resistivity of the formation by using this technology, a low-frequency EM system is needed. However, the emitting signals are highly diffusive so, it is difficult to map the data. Based on this situation, the LLNL, together with the University of California-Berkley (UC-Berkley), extended the work on the induction logging tools to create the cross-well EM tomography.<ref name=Wiltetal_1995 />  

In the early 1970s, the Lawrence Livermore National Laboratory (LLNL) developed the first-ever high-frequency cross-well electromagnetic system using electric dipole sensors. These sensors were intended primarily for hard rock, either igneous or metamorphic rocks, and tunnel detection. Due to the initial EM system high frequency and high conductivity regions in the reservoirs, the signals can only propagate a few inches into the formation (small depth of investigation). Thus, to measure the resistivity of the formation by using this technology, a low-frequency EM system is needed. However, the emitting signals are highly diffusive so, it is difficult to map the data. Based on this situation, the LLNL, together with the University of California-Berkley (UC-Berkley), extended the work on the induction logging tools to create the cross-well EM tomography.<ref name=Wiltetal_1995 />  

The LLNL and UC-Berkley team tested this technology by using very simplistic tools (see [[:file:AlsaudKatterbauerFigure3.jpg|Figure 3]]). The system worked by sending a high alternating current from the source on the surface down the logging cable to the transmitter. The transmitter is made of a magnetic core wrapped with a wire, and it is tuned with a capacitor. To achieve the optimum single operating frequency suitable for the borehole condition, the coil is tuned by either replacing the capacitor or/and increasing/decreasing the number of turns around the magnetic core. The research team tested different frequencies to reach the optimum resolution and range. The antenna detects the emitted signal from the transmitter in the receiver located in the other borehole. The signal is then sent uphole through the logging cable to the lock-in detector to decode the signal. The received signal is coupled with the source signal with an isolated wireline for configuration. The transmitter and receiver are two isolated structures, where each one has its generator. The only way to connect these coils is by a surface isolated cable. This kind of separation is vital for generating high-quality data and minimizing the earth loops' noise. In the borehole, the logged information is between an interval of depths, so to log the data, multiple receivers stay at a separated interval while the transmitter travels upward at a constant velocity. Following this technique, a complete cross-well tomography is generated.<ref name=WiltAlumbaughetal_1995>M. Wilt, D. L. Alumbaugh, H. F. Morrison, A. Becker, K. H. Lee and M. Deszcz-Pan, "Crosswell electromagnetic tomography: System design considerations and field results," Geophysics, vol. 60, no. 3, pp. 629-929.</ref> <ref name=Wiltetal_1995 />  

The LLNL and UC-Berkley team tested this technology by using very simplistic tools (see [[:file:AlsaudKatterbauerFigure3.jpg|Figure 3]]). The system worked by sending a high alternating current from the source on the surface down the logging cable to the transmitter. The transmitter is made of a magnetic core wrapped with a wire, and it is tuned with a capacitor. To achieve the optimum single operating frequency suitable for the borehole condition, the coil is tuned by either replacing the capacitor or/and increasing/decreasing the number of turns around the magnetic core. The research team tested different frequencies to reach the optimum resolution and range. The antenna detects the emitted signal from the transmitter in the receiver located in the other borehole. The signal is then sent uphole through the logging cable to the lock-in detector to decode the signal. The received signal is coupled with the source signal with an isolated wireline for configuration. The transmitter and receiver are two isolated structures, where each one has its generator. The only way to connect these coils is by a surface isolated cable. This kind of separation is vital for generating high-quality data and minimizing the earth loops' noise. In the borehole, the logged information is between an interval of depths, so to log the data, multiple receivers stay at a separated interval while the transmitter travels upward at a constant velocity. Following this technique, a complete cross-well tomography is generated.<ref name=WiltAlumbaughetal_1995>M. Wilt, D. L. Alumbaugh, H. F. Morrison, A. Becker, K. H. Lee and M. Deszcz-Pan, "Crosswell electromagnetic tomography: System design considerations and field results," Geophysics, vol. 60, no. 3, pp. 629-929.</ref><ref name=Wiltetal_1995 />  

The team did two field trials in Richmond, California, where the distance between the two wells is 50 m, the other in Devine, Texas, where the wells are 100 m apart. The Richmond test targeted a shallower depth compared to the Devine trial, and the EM system was used to monitor the injected saltwater.<ref name=WiltAlumbaughetal_1995 /> <ref name=Wiltetal_1995 />  

The team did two field trials in Richmond, California, where the distance between the two wells is 50 m, the other in Devine, Texas, where the wells are 100 m apart. The Richmond test targeted a shallower depth compared to the Devine trial, and the EM system was used to monitor the injected saltwater.<ref name=WiltAlumbaughetal_1995 /> <ref name=Wiltetal_1995 />