Add some simple profiling to teqp docs

cc8b4294 · Ian Bell · 1bb83908 · cc8b4294
Commit cc8b4294 authored 2 years ago by Ian Bell
--- a/doc/source/models/PCSAFT.ipynb
+++ b/doc/source/models/PCSAFT.ipynb
@@ -57,6 +57,23 @@
    "model = teqp.PCSAFTEOS(coeffs)"
   ]
  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "19ec9bfb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Here are some rudimentary timing results\n",
+    "T = 300.0\n",
+    "rhovec = np.array([3.0, 4.0, 5.0])\n",
+    "rho = rhovec.sum()\n",
+    "x = rhovec/np.sum(rhovec)\n",
+    "%timeit model.get_fugacity_coefficients(T,rhovec)\n",
+    "%timeit (-1.0)*model.get_Ar20(T, rho, x)\n",
+    "%timeit model.get_partial_molar_volumes(T, rhovec)"
+   ]
+  },
  {
   "cell_type": "markdown",
   "id": "578630c8",
@@ -191,7 +208,7 @@
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
-   "version": "3.10.4"
+   "version": "3.10.6"
  }
 },
 "nbformat": 4,

 %% Cell type:markdown id:f406bbb5 tags:

 # PC-SAFT

 The PC-SAFT implementation in teqp is based on the implementation of Gross and Sadowski (https://doi.org/10.1021/ie0003887), with the typo from their paper fixed.  It does NOT include the association contribution, only the dispersive contributions.

 The model in teqp requires the user to specify the values of ``sigma``, ``epsilon/kB``, and ``m`` for each substance.  A very few substances are hardcoded in teqp, for testing purposes.

 %% Cell type:raw id:d9efd027 tags:

 The Python class is here: :py:class:`PCSAFTEOS <teqp.teqp.PCSAFTEOS>`

 %% Cell type:code id:984925ce tags:

 ``` python
 import teqp
 import numpy as np
 teqp.__version__
 ```

 %% Cell type:code id:7bbd7129 tags:

 ``` python
 TeXkey = 'Gross-IECR-2001'
 ms = [1.0, 1.6069, 2.0020]
 eoverk = [150.03, 191.42, 208.11]
 sigmas = [3.7039, 3.5206, 3.6184]

 coeffs = []
 for i in range(len(ms)):
    c = teqp.SAFTCoeffs()
    c.m = ms[i]
    c.epsilon_over_k = eoverk[i]
    c.sigma_Angstrom = sigmas[i]
    coeffs.append(c)

 model = teqp.PCSAFTEOS(coeffs)
 ```

+%% Cell type:code id:19ec9bfb tags:
+
+``` python
+# Here are some rudimentary timing results
+T = 300.0
+rhovec = np.array([3.0, 4.0, 5.0])
+rho = rhovec.sum()
+x = rhovec/np.sum(rhovec)
+%timeit model.get_fugacity_coefficients(T,rhovec)
+%timeit (-1.0)*model.get_Ar20(T, rho, x)
+%timeit model.get_partial_molar_volumes(T, rhovec)
+```
+
 %% Cell type:markdown id:578630c8 tags:

 The model parameters can be queried:

 %% Cell type:code id:d4e47e54 tags:

 ``` python
 model.get_m(), model.get_epsilon_over_k_K(), model.get_sigma_Angstrom()
 ```

 %% Cell type:markdown id:5cbb382d tags:

 ## Adjusting k_ij

 Fine-tuned values of $k_{ij}$ can be provided when instantiating the model.  A complete matrix of all the $k_{ij}$ values must be provided. This allows for asymmetric mixing models in which $k_{ij}\neq k_{ji}$.

 %% Cell type:code id:a32c41b5 tags:

 ``` python
 k_01 = 0.01; k_10 = k_01
 kmat = [[0,k_01,0],[k_10,0,0],[0,0,0]]
 teqp.PCSAFTEOS(coeffs, kmat)
 ```

 %% Cell type:markdown id:ca52e844 tags:

 ## Superancillary

 The superancillary equation for PC-SAFT has been developed, and is much more involved than that of the cubic EOS. As a consequence, the superancillary equation has been provided as a separate package rather than integrating it into to teqp to minimize the binary size of teqp. It can be installed from PYPI with: ``pip install PCSAFTsuperanc``

 The scaling in the superancillaries uses reduced variables:

 $$ \tilde T = T/(\epsilon/k_{\rm B}) $$
 $$ \tilde\rho = \rho_{\rm N}\sigma^3 $$

 where $\rho_{\rm N}$ is the number density, and the other parameters are from the PC-SAFT model

 %% Cell type:code id:f6e3b8d2 tags:

 ``` python
 import PCSAFTsuperanc

 sigma_m = 3e-10 # [meter]
 e_over_k = 150.0 # [K]
 m = 5

 # The saturation temperature
 T = 300

 [Ttilde_crit, Ttilde_min] = PCSAFTsuperanc.get_Ttilde_crit_min(m=m)
 print('Ttilde crit:', Ttilde_crit)

 # Get the scaled densities for liquid and vapor phases
 [tilderhoL, tilderhoV] = PCSAFTsuperanc.PCSAFTsuperanc_rhoLV(Ttilde=T/e_over_k, m=m)
 # Convert back to molar densities
 N_A = PCSAFTsuperanc.N_A # The value of Avogadro's constant used in superancillaries
 rhoL, rhoV = [tilderho/(N_A*sigma_m**3) for tilderho in [tilderhoL, tilderhoV]]

 # As a sanity check, confirm that we got the same pressure in both phases
 c = teqp.SAFTCoeffs()
 c.sigma_Angstrom = sigma_m*1e10
 c.epsilon_over_k = e_over_k
 c.m = m
 model = teqp.PCSAFTEOS([c])
 z = np.array([1.0])
 pL = rhoL*model.get_R(z)*T*(1+model.get_Ar01(T, rhoL, z))
 pV = rhoV*model.get_R(z)*T*(1+model.get_Ar01(T, rhoV, z))
 print('Pressures are:', pL, pV, 'Pa')
 ```

 %% Cell type:markdown id:0bdf568f tags:

 ## Maximum density

 The maximum number density allowed by the EOS is defined based on the packing fraction. To get a molar density, divide by Avogadro's number. The function is conveniently exposed in Python:

 %% Cell type:code id:3c8491a9 tags:

 ``` python
 max_rhoN = teqp.PCSAFTEOS(coeffs).max_rhoN(130.0, np.array([0.3, 0.3, 0.4]))
 display(max_rhoN)
 max_rhoN/6.022e23 # the maximum molar density in mol/m^3
 ```