Title:

Modelling Wellbore Observed Fracture-Borne Fluid Heat Advection – Application to EGS Stimulation in Basement Rock

Authors:

Peter LEARY, Peter MALIN and Rami NIEMI

Key Words:

fractures, advection, Peclet number, wellbore stimulation,

Conference:

Stanford Geothermal Workshop

Year:

2017

Session:

Enhanced Geothermal Systems

Language:

English

Paper Number:

Leary

File Size:

1293 KB

View File:

Abstract:

Wellbore logs of neutron porosity φ and thermal gradient Tz recorded in a western Colorado tight gas sandstone reservoir formation are observed to be 65% correlated over a 500-meter interval containing conspicuous fracturing. The strong φ-Tz spatial correlation can be understood in terms of a regional groundwater heat transport system locally transected by a series of fracture intervals with elevated porosity and associated increased permeability leading to extensive anomalous temperature distributions associated with fracture-connectivity fluid conduits activated by the wellbore. We compute the observed temperature phenomenology for advective fluid flow in fractures embedded in an otherwise stochastically uniform crust, and apply the heat transport model to fracture-connectivity flow to an EGS wellbore-to-wellbore flow stimulation scenario at depth in Finnish basement rock. Fluid flow in crustal rock and hosted fracture sequences is characterised by a trio of empirical rules attested across a wide range geological settings. For crustal fluid flow systems of either conventional and unconventional oil/gas, geothermal/aquifer waters, or fossilized-flow mineral deposits, the spectral power of well-log spatial fluctuations, most particularly that of porosity φ, is observed to scale inversely with spatial frequency, S(k) ~ 1/kβ, where β ~ 1 over 5 decades of scale length 1/cm less than k less than 1/km. Over the same range of geological settings, well-production of crustal fluids is observed to be lognormally distributed as described by well-scale permeability distribution κ ~ κ0 exp(αφ) for porosity 0 less than φ less than 1 and scale parameter 20 less than α less than 50; the magnitude of parameter α guarantees a lognormal distribution of flow system permeability for normally distributed porosity. Plentiful spatial fluctuation sequences of hydrocarbon well-core porosity δφ and the logarithm of well-core permeability δlogκ are observed to be highly correlated, ~70% less than Γ(δφ, δlogκ) less than ~ 85%. Some tens of well-core poroperm sequence data from both geothermal systems and crystalline basement are statistically strongly consistent with δφ-δlogκ spatial correlation. The trio of generic crustal flow system characteristics are attested for the tight gas sand formations in which the φ-Tz spatial correlation was recorded. The neutron porosity well-log fluctuation power-spectrum scales inversely with spatial frequency, S(k) ~ 1/k1.17. Well-core porosity and permeability sequences are ~ 80% spatially correlated. Western Colorado regional gas-field well-productivities are lognormally distributed. For reasonable assumptions of regional crustal structure and properties, the spatial correlation between wellbore temperature gradient fluctuations δTz and neutron porosity fluctuations δφ can be expressed as δTz ~ Pe(T – T0)/h δφ, for Peclet number Pe ≡ C*rho^2*g*kappa*h/Kμ. With Pe ~ 5, wellbore interval temperature T – T0 ~50oC, regional groundwater flow system head h ~ 0.850km, and wellbore neutron porosity log spatial fluctuations δφ ~ 30%, the spatial temperature gradient fluctuations associated with fracture intervals are of order δTz ~ 100oC/km ≡ 10oC/100m in accord with observation. Using the crustal fluid-rock interaction empirics, the observed advective fluid flow and associated temperature distribution are computed for a wellbore transecting a fracture sequence in a 2D crustal section. With local permeability controlled by local porosity, κ ~ κ0 exp(αφ), conservation of mass 𝛻⋅(κ𝛻P) = 0 fixes the model pressure P(x,z) for Darcy flow v(x,z)= κ(x,z)/μ 𝛻P(x,z). Fluid flow in the model section is divided between low permeability flow in the ambient crust and high permeability flow in the fracture intervals. Conservation of thermal energy 𝛻⋅(𝛻T – ρC/K Tv) = 0 fixes the temperature field for advective fluid velocity v(x,z). A non-linear finite-element solver for 𝛻^2T = 1/D (𝛻T⋅v + T𝛻⋅v), D ~ 0.7 10-6 m^2/s = rock/water system thermal diffusivity, reproduces the observed φ-Tz and Tz –T magnitudes and spatial relationships for fluid flow velocity of order 10^-6 m/s in the fractures. The generic empirics of crustal fracture-borne fluid flow allow the observed wellbore φ-Tz spatial correlation to serve as a template for wellbore-to-wellbore fluid flow in an EGS crustal heat-exchange volume. Based on well-log spectral scaling, S(k) ~ 1/k, well-core poroperm δφ-δlogκ spatial correlation, and lognormal groundwater well-production distributions for Finnish basement rock, fluid flow and advective heat transport analogues can be computed for input/outtake well pairs in a EGS stimulation volume. High wellbore pressurization can plausibly activate effective Peclet number Pe ~5 wellbore-to-wellbore flow in basement rock of well-core porosity φ ~ 1% and κ0 ~ 1μD base permeability. Wellbore pressurization may also reactivate relic permeability pathways attested by high degrees of neutron scattering from the hydrated mineral content of basement rock.


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