Update bl_parameters.jl

darcy/pluto/bl_parameters.jl

@@ -39,8 +39,15 @@ Set up BL scenario
 
 # ╔═╡ 963b3405-b02c-4190-8078-2edf15a0a03e
 md"""
-##### LaTeX
-We solve the Buckley-Levrett problem with $\lambda_o = S^N/\mu$ and $\lambda_w = S^N$
+##### Buckley-Leverett problem
+Conservation of mass:
+
+$$\frac{\partial \rho_\alpha S_\alpha \phi}{\partial t} + \nabla \cdot v_\alpha = q_\alpha, \alpha \in \{w, o\}$$
+
+Fluxes are given by Darcy's law:
+$$v_t = -K (\lambda_w + \lambda_o) \nabla p, \quad v_\alpha = \frac{\lambda_\alpha}{\lambda_w + \lambda_o} v_t$$
+
+We solve the Buckley-Levrett problem with $\lambda_o = S^N/\mu$ and $\lambda_w = S^N$. The displacement can be stable or unstable depending on the viscosity ratio.
 """
 
 # ╔═╡ d6a3bac0-b5dd-4fcf-bf36-afbd57bc7be7
@@ -69,16 +76,19 @@ begin
 	P = setup_well(g, K, [(nx, 1, 1)], name = :Producer)
 	I = setup_well(g, K, [(1, 1, 1)], name = :Injector)
 	sys = ImmiscibleSystem((AqueousPhase(), LiquidPhase()))
-	model, parameters = setup_reservoir_model(g, sys, wells = [I, P], block_backend = false)
+	model, parameters = setup_reservoir_model(g, sys, wells = [I, P],
+		                                              block_backend = false)
 	kr = BrooksCoreyRelPerm(2, nkr)
 	μ = ConstantVariables([1, mu].*1e-3)
-	replace_variables!(model, RelativePermeabilities = kr, PhaseViscosities = μ)
-
+	model = replace_variables!(model, RelativePermeabilities = kr,
+									  PhaseViscosities = μ)
+	nothing
 end
 
 # ╔═╡ 17d3061a-bd02-4379-b198-ebc9ac040496
 begin
-	state0 = setup_reservoir_state(model, Pressure = 150*1e5, Saturations = [0.0, 1.0])
+	state0 = setup_reservoir_state(model, Pressure = 150*1e5, 
+		                                  Saturations = [0.0, 1.0])
 	day = 3600*24.0
 	T = 1000*day
 	nt = 50
@@ -105,32 +115,40 @@ end
 
 # ╔═╡ 7f3d7a62-65e9-4d64-add7-f0fb81669327
 begin
-		sim, config = setup_reservoir_simulator(model, state0, parameters, info_level = -1)
-		states, reports = simulate(sim, dt, forces = forces, config = config);
+		sim, config = setup_reservoir_simulator(model, state0, parameters,
+			                                    info_level = -1)
+		states, reports = simulate(sim, dt, forces = forces,
+			                                config = config);
 		s_w = hcat(map(x -> x[:Reservoir][:Saturations][1, :], states)...);
 end;
 
 # ╔═╡ 265591ef-549c-4c69-a585-690ab0965203
-plot_title = "$nx cells, Corey exp $nkr, viscosity ratio $mu"
+plot_title = "$nx cells, Corey exp $nkr, viscosity ratio $mu, pvi $pvi"
 
-# ╔═╡ 21b7dd5c-ef28-4729-bbdf-62fc67a9b91c
-plot(s_w, color = :black, title = plot_title, label = nothing)
+# ╔═╡ d667ebe9-7b1e-4066-bc5c-8f92b570a5b4
+md"""
+plot type: $(@bind plot_type Select(["lines", "contour"]))
+"""
 
-# ╔═╡ 940cfa2a-868c-42da-9039-b0ceef35ed73
-contourf(s_w, title = plot_title)
+# ╔═╡ 21b7dd5c-ef28-4729-bbdf-62fc67a9b91c
+if plot_type == "lines"
+	plot(s_w, color = :black, title = plot_title, label = nothing, ylim=(0,1))
+else
+	contourf(s_w, title = plot_title)
+end
 
 # ╔═╡ Cell order:
-# ╠═e25f84e0-b7e4-11ec-215a-15d61473a706
-# ╠═6ac645bd-fcff-4923-ae5d-a51ef19e8817
-# ╠═5f179657-8ec1-43f0-8f16-2f08d87f7ad2
-# ╟─b53d1c1f-9217-4658-8915-b9e2235e8870
-# ╟─3d207ba8-23fa-4c65-8da0-c17756018143
+# ╟─e25f84e0-b7e4-11ec-215a-15d61473a706
+# ╟─6ac645bd-fcff-4923-ae5d-a51ef19e8817
+# ╟─5f179657-8ec1-43f0-8f16-2f08d87f7ad2
+# ╠═b53d1c1f-9217-4658-8915-b9e2235e8870
+# ╠═3d207ba8-23fa-4c65-8da0-c17756018143
 # ╟─931359ca-7d00-4d4e-b9f1-fce440c3d3b9
-# ╟─17d3061a-bd02-4379-b198-ebc9ac040496
-# ╟─7f3d7a62-65e9-4d64-add7-f0fb81669327
+# ╠═17d3061a-bd02-4379-b198-ebc9ac040496
+# ╠═7f3d7a62-65e9-4d64-add7-f0fb81669327
 # ╠═265591ef-549c-4c69-a585-690ab0965203
 # ╟─963b3405-b02c-4190-8078-2edf15a0a03e
 # ╟─d6a3bac0-b5dd-4fcf-bf36-afbd57bc7be7
 # ╟─7ce78aae-5ba4-41f0-be79-6eef9ef7da58
-# ╠═21b7dd5c-ef28-4729-bbdf-62fc67a9b91c
-# ╠═940cfa2a-868c-42da-9039-b0ceef35ed73
+# ╟─d667ebe9-7b1e-4066-bc5c-8f92b570a5b4
+# ╟─21b7dd5c-ef28-4729-bbdf-62fc67a9b91c